Duede, Eamon and Davey, Kevin (2024) Apriori Knowledge in an Era of Computational Opacity: The Role of AI in Mathematical Discovery. In: UNSPECIFIED.

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Abstract

Can we acquire apriori knowledge of mathematical facts from the outputs of computer programs? People like Burge have argued (correctly in our opinion) that, for example, Appel and Haken acquired apriori knowledge of the Four Color Theorem from their computer program insofar as their program simply automated human forms of mathematical reasoning. However, unlike such programs, we argue that the opacity of modern LLMs and DNNs creates obstacles in obtaining apriori mathematical knowledge from them in similar ways. We claim though that if a proof-checker automating human forms of proof-checking is attached to such machines, then we can obtain apriori mathematical knowledge from them after all, even though the original machines are entirely opaque to us and the proofs they output may not, themselves, be human-surveyable.

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Item Type:	Conference or Workshop Item (UNSPECIFIED)
Creators:	Creators Email ORCID Duede, Eamon eduede@purdue.edu 0000-0002-3592-0478 Davey, Kevin kjdavey@uchicago.edu
Keywords:	Philosophy of Science, Philosophy of Artificial Intelligence, Philosophy of Mathematics
Subjects:	Specific Sciences > Mathematics > Proof Specific Sciences > Artificial Intelligence Specific Sciences > Mathematics
Depositing User:	Dr. Eamon Duede
Date Deposited:	17 Dec 2024 17:54
Last Modified:	17 Dec 2024 17:54
Item ID:	24406
Subjects:	Specific Sciences > Mathematics > Proof Specific Sciences > Artificial Intelligence Specific Sciences > Mathematics
Date:	2024
URI:	https://philsci-archive.pitt.edu/id/eprint/24406

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