### Weakening Cycles So That Turing Can Halt

It is notable how often paradoxes arose in the historical journey that led to the Rise of Type Theory. Resolving Russell’s paradox led to his theory of types. Gödel’s Incompleteness theorems rested its proof around a variation of the Liar Paradox. Church and Turing recapitulated this result using their distinctive formalisms. Intuitionistic type theory was deliberately designed to avoid these paradoxes. And so it goes.
As an undergraduate, I had the pleasure of studying Gödel’s ingenious proof as part of a course on Predicate Logic.