### 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 language | English (US) |
---|---|

Title of host publication | Collective Epistemology |

Publisher | De Gruyter Mouton |

Pages | 157-176 |

Number of pages | 20 |

ISBN (Electronic) | 9783110322583 |

ISBN (Print) | 9783110322231 |

State | Published - May 2 2013 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Arts and Humanities(all)

### Cite this

*Collective Epistemology*(pp. 157-176). De Gruyter Mouton.

**Probabilistic proofs and the collective epistemic goals of mathematicians.** / Fallis, Don T.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Collective Epistemology.*De Gruyter Mouton, pp. 157-176.

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TY - CHAP

T1 - Probabilistic proofs and the collective epistemic goals of mathematicians

AU - Fallis, Don T

PY - 2013/5/2

Y1 - 2013/5/2

N2 - 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.

AB - 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.

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SN - 9783110322231

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EP - 176

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