TITLE: "Modus moron" rule of inference?
QUESTION [52 upvotes]: This is an exercise I got from the book "First Order Mathematical Logic" by Angelo Margaris (1967). I have never heard of this rule before, the question is whether what Margaris calls the modus moron rule of inference is correct or not and to explain why I think so.
$$\frac{P\Rightarrow Q, Q}{\therefore P}\qquad \text{(modus moron)}$$
It seems correct to me, my reasoning is that if $P\Rightarrow Q$ and $Q$ it does not matter whether $P$ or $\neg P$ since a false antecedent makes a true conditional, which I would show by the rows of the truth table of $(P\Rightarrow Q)$ where $Q$ is true. 
Is this a valid argument?

REPLY [2 votes]: I strongly disagree with demeaning this rule of inference.  It is a very common problem solving technique to use the inference:
$$\begin{array} {rl}
& P \to Q \\
& Q \\
& Q \text{ is really rare} \\ \hline
\therefore & P \text{ is almost true}
\end{array}$$
For example, your task might be to prove $P$ as "the maximum of $f$ occurs at $x$ (for the sake of discussion ignoring endpoints)".  And you know that at the maximum of the function, $f' = 0$, which is the $Q$.  So $P \to Q$.  But you also know that $f' = 0$ is an infrequent occurrence on an arbitrary graph.  So now you have the 3 ingredients you need to almost establish $P$, all that is left is finding that little bit of missing information, $f'' = 0$ and all other (finite number of usually) maximal points are lesser.
If this inference were useless we wouldn't even have a definition for the concept of stationary points.  I've also used this technique used in algorithm design, "what do we know about the best possible result" and use that to find the algorithm, then use further investigation to prove what is found is optimal.
So rather than "modus moron", I would suggest calling it "modus hopeful".