Weatherall, James Owen and Wolfson, Jesse (2024) Correctness, Artificial Intelligence, and the Epistemic Value of Mathematical Proof. [Preprint]

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Abstract

We argue that it is neither necessary nor sufficient for a mathematical proof to have epistemic value that it be “correct”, in the sense of formalizable in a formal proof system. We then present a view on the relationship between mathematics and logic that clarifies the role of formal correctness in mathematics. Finally, we discuss the significance of these arguments for recent discussions about automated theorem provers and applications of AI to mathematics.

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Item Type:	Preprint
Creators:	Creators Email ORCID Weatherall, James Owen weatherj@uci.edu 0000-0003-1461-7821 Wolfson, Jesse wolfson@uci.edu 0000-0002-1498-9185
Keywords:	formal proof, mathematical correctness, artificial intelligence, philosophy of logic
Subjects:	Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Methodology Specific Sciences > Mathematics > Practice Specific Sciences > Mathematics > Proof Specific Sciences > Mathematics > Values Specific Sciences > Mathematics
Depositing User:	James Owen Weatherall
Date Deposited:	01 Dec 2024 21:34
Last Modified:	01 Dec 2024 21:34
Item ID:	24324
Subjects:	Specific Sciences > Mathematics > Epistemology Specific Sciences > Mathematics > Methodology Specific Sciences > Mathematics > Practice Specific Sciences > Mathematics > Proof Specific Sciences > Mathematics > Values Specific Sciences > Mathematics
Date:	2024
URI:	https://philsci-archive.pitt.edu/id/eprint/24324

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