Probabilistic proofs and the collective epistemic goals of mathematicians

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3 Scopus citations

Abstract

Mathematicians only use deductive proofs to establish that mathematical claims are true. They never use inductive evidence, such as probabilistic proofs, for this task. I have previously argued (Fallis 1997 and 2002) 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 my argument. In my earlier work, I 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.

Original languageEnglish (US)
Title of host publicationCollective Epistemology
PublisherDe Gruyter Mouton
Pages157-176
Number of pages20
ISBN (Electronic)9783110322583
ISBN (Print)9783110322231
StatePublished - May 2 2013
Externally publishedYes

ASJC Scopus subject areas

  • Arts and Humanities(all)

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  • Cite this

    Fallis, D. (2013). Probabilistic proofs and the collective epistemic goals of mathematicians. In Collective Epistemology (pp. 157-176). De Gruyter Mouton.