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
SN - 0031-8094
VL - 72
SP - 77
EP - 89
JO - Philosophical Quarterly
JF - Philosophical Quarterly
IS - 1
ER -