Philosophia Mathematica Advance Access originally published online on November 6, 2008
Philosophia Mathematica 2009 17(3):341-362; doi:10.1093/philmat/nkn032
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Probabilistic Proofs and Transferability
* Department of Philosophy, Research School of Social Sciences, Australian National University, Canberra, ACT 0200, Australia. easwaran{at}gmail.com
In a series of papers, Don Fallis points out that although mathematicians are generally unwilling to accept merely probabilistic proofs, they do accept proofs that are incomplete, long and complicated, or partly carried out by computers. He argues that there are no epistemic grounds on which probabilistic proofs can be rejected while these other proofs are accepted. I defend the practice by presenting a property I call ‘transferability’, which probabilistic proofs lack and acceptable proofs have. I also consider what this says about the similarities between mathematics and, on the one hand natural sciences, and on the other hand philosophy.
I would like to thank Branden Fitelson, John MacFarlane, and the audience at the Midwest Philosophy of Mathematics Workshop in 2006 for helpful comments on an earlier version of this paper. I would also like to thank two anonymous referees, and audiences at UNLV, Berkeley, Leeds, UT Austin, USC, UW Madison, NYU, University of Pittsburgh, Stanford, ANU, and Sydney University for helpful discussion on later versions. And I am especially grateful to Don Fallis for very helpful discussion throughout the project.
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