LFU:online

We will explore several paradoxes, pivoting on the liar paradox (Tarski’s schema, Lawvere’s Theorem) and its many incarnations (Cantor’s diagonal argument, Russell’s paradox, Gödel’s Theorem, the Halting problem, Gold’s Theorem). We'll try to escape the paradox by building hierarchies (such as Turing categories or Kripke's hierarchies), or by changing the logic (e.g. with paraconsistent logic). We will then consider other paradoxes beyond self-reference and negation, such as Yablo’s and Curry’s. Finally we will explore the implications of the liar paradox for physics (grandfather’s paradox), biology (gene networks) and philosophy (epistemology, the relation between language and thought, and the mind-computer analogy).