Topics in Logic: Strict Finitism, Feasible Mathematics, and the Limits of AI
PHIL 244F
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Description
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? Are there natural instances of independence with respect to very weak systems of arithmetic? Is there a prospect of results in this area that bear on the question of whether the mind can be feasibly mechanized -- e.g. in the sense of whether LLMs can, or cannot, supplant the activity of the working (human) mathematician?
Available for Harvard Cross Registration
