Topics in Logic: Strict Finitism, Feasible Mathematics, and the Limits of AI

Harvard FAS

This seminar will explore the question: What does it mean to say that something is "feasible"? We will start by laying out the metamathematical prerequisites. This will involve (a) the connection between very weak systems of arithmetic and the theory of computational complexity, and (b) even more concrete matters (like the celebrated Meyer-Stockmeyer result) involving circuit complexity. We will then turn to such questions as: How can one best articulate the standpoint of the strict finitist?…