Probabilistic Proofs and the Collective Epistemic Goals of Mathematicians
COLLECTIVE EPISTEMOLOGY, pp. 157-175, Hans Bernard Schmid, Marcel Weber, Daniel Sirtes, eds., Ontos, 2011
14 Pages Posted: 28 Mar 2011
Date Written: July 18, 2010
Mathematicians only use deductive proofs to establish that mathematical claims are true. They never use inductive evidence, such as probabilistic proofs, for this task. Don Fallis (1997 and 2002) has argued that mathematicians do not have good epistemic grounds for this complete rejection of probabilistic proofs. But Kenny Easwaran (2009) points out that there is a gap in this argument. Fallis only considered how mathematical proofs serve the epistemic goals of individual mathematicians. Easwaran suggests that deductive proofs might be epistemically superior to probabilistic proofs because they are transferable. That is, one mathematician can give such a proof to another mathematician who can then verify for herself that the mathematical claim in question is true without having to rely at all on the testimony of the first mathematician. In this paper, I argue that collective epistemic goals are critical to understanding the methodological choices of mathematicians. But I argue that the collective epistemic goals promoted by transferability do not explain the complete rejection of probabilistic proofs.
Keywords: mathematical proof, probabilistic proof, deductive proof, collective epistemic goals, transferability
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