In Hans Bernhard Schmid, Daniel Sirtes & Marcel Weber (eds.),
Collective Epistemology. Heusenstamm, Germany: Ontos. pp. 157-175 (
2011)
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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. 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.