Probabilistic proofs, lottery propositions, and mathematical knowledge

Research output: Contribution to journalArticlepeer-review

20 Downloads (Pure)

Abstract

In mathematics, any form of probabilistic proof obtained through the application of a probabilistic method is not considered as a legitimate way of gaining mathematical knowledge. In a series of papers, Don Fallis has defended the thesis that there are no epistemic reasons justifying mathematicians’ rejection of probabilistic proofs. The present paper identifies such an epistemic reason. More specifically, it is argued here that if one adopts a conception of mathematical knowledge in which an epistemic subject can know a mathematical proposition based solely on a probabilistic proof, one is then forced to admit that such an epistemic subject can know several lottery propositions based solely on probabilistic evidence. Insofar as knowledge of lottery propositions on the basis of probabilistic evidence alone is denied by the vast majority of epistemologists, it is concluded that this constitutes an epistemic reason for rejecting probabilistic proofs as a means of acquiring mathematical knowledge.
Original languageEnglish
Pages (from-to)77-89
Number of pages13
JournalPhilosophical Quarterly
Volume72
Issue number1
DOIs
Publication statusPublished - Jan 2022

Keywords

  • Probabilistic proofs
  • Lottery propositions
  • Mathematical knowledge

Fingerprint

Dive into the research topics of 'Probabilistic proofs, lottery propositions, and mathematical knowledge'. Together they form a unique fingerprint.

Cite this