TY - JOUR

T1 - Probabilistic proofs, lottery propositions, and mathematical knowledge

AU - Hamami, Yacin

PY - 2022/1

Y1 - 2022/1

N2 - 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.

AB - 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.

KW - Probabilistic proofs

KW - Lottery propositions

KW - Mathematical knowledge

UR - http://www.scopus.com/inward/record.url?scp=85127373166&partnerID=8YFLogxK

U2 - 10.1093/pq/pqab007

DO - 10.1093/pq/pqab007

M3 - Article

VL - 72

SP - 77

EP - 89

JO - Philosophical Quarterly

JF - Philosophical Quarterly

SN - 0031-8094

IS - 1

ER -