TITLE: What is the manner of inconsistency of Girard's paradox in Martin Lof type theory
QUESTION [25 upvotes]: I am aware that assigning the type of Type to be Type (rather than stratifying to a hierarchy of types) leads to an inconsistency.  But does this inconsistency allow the construction of a well-typed term with no normal form, or does it actually allow a proof of False?  Are these two questions equivalent?

REPLY [6 votes]: It leads to a well-typed term, having no normal form, which is assigned the type False.  You can find the term given explicitly in A simplification of Girard's paradox