David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
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Philosophia Mathematica 16 (3):374-387 (2008)
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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References found in this work BETA
Tyler Burge (1993). Content Preservation. Philosophical Review 102 (4):457-488.
Margarita R. Levin (1981). On Tymoczko's Argument for Mathematical Empiricism. Philosophical Studies 39 (1):79 - 86.
Mark McEvoy (2007). Kitcher, Mathematical Intuition, and Experience. Philosophia Mathematica 15 (2):227-237.
Thomas Tymoczko (1979). The Four-Color Problem and its Philosophical Significance. Journal of Philosophy 76 (2):57-83.
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David Casacuberta & Jordi Vallverdú (2013). E-Science and the Data Deluge. Philosophical Psychology 27 (1):1-15.
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