The epistemological status of computer-assisted proofs

Philosophia Mathematica 16 (3):374-387 (2008)
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Abstract

Several high-profile mathematical problems have been solved in recent decades by computer-assisted proofs. Some philosophers have argued that such proofs are a posteriori on the grounds that some such proofs are unsurveyable; that our warrant for accepting these proofs involves empirical claims about the reliability of computers; that there might be errors in the computer or program executing the proof; and that appeal to computer introduces into a proof an experimental element. I argue that none of these arguments withstands scrutiny, and so there is no reason to believe that computer-assisted proofs are not a priori. Thanks are due to Michael Levin, David Corfield, and an anonymous referee for Philosophia Mathematica for their helpful comments. Earlier versions of this paper were presented at the Hofstra University Department of Mathematics colloquium series, and at the 2005 New Jersey Regional Philosophical Association; I am grateful to both audiences for their comments. CiteULike    Connotea    Del.icio.us    What's this?

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Mark McEvoy
Hofstra University

References found in this work

Content Preservation.Tyler Burge - 1993 - Philosophical Review 102 (4):457-488.
The Nature of Mathematical Knowledge.Philip Kitcher - 1983 - Oxford, England: Oxford University Press.
Mathematics as a Science of Patterns.Michael David Resnik - 1997 - Oxford, England: New York ;Oxford University Press.
Towards a Philosophy of Real Mathematics.David Corfield - 2003 - Cambridge University Press.
Naming and Necessity.S. A. Kripke - 1972 - Tijdschrift Voor Filosofie 45 (4):665-666.

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