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Randomized arguments are transferable

Jeffrey C. Jackson

Philosophia Mathematica 17 (3):363-368 (2009)

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Why Is Proof the Only Way to Acquire Mathematical Knowledge?Marc Lange - forthcoming - Australasian Journal of Philosophy.details This paper proposes an account of why proof is the only way to acquire knowledge of some mathematical proposition’s truth. Admittedly, non-deductive arguments for mathematical propositions can be strong and play important roles in mathematics. But this paper proposes a necessary condition for knowledge that can be satisfied by putative proofs (and proof sketches), as well as by non-deductive arguments in science, but not by non-deductive arguments from mathematical evidence. The necessary condition concerns whether we can justly expect that if (...) Download Export citation Bookmark 1 citation
Probabilistic Proofs, Lottery Propositions, and Mathematical Knowledge.Yacin Hamami - 2021 - Philosophical Quarterly 72 (1):77-89.details 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. This 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 (...) Download Export citation Bookmark 1 citation
Knowledge of Mathematics without Proof.Alexander Paseau - 2015 - British Journal for the Philosophy of Science 66 (4):775-799.details Mathematicians do not claim to know a proposition unless they think they possess a proof of it. For all their confidence in the truth of a proposition with weighty non-deductive support, they maintain that, strictly speaking, the proposition remains unknown until such time as someone has proved it. This article challenges this conception of knowledge, which is quasi-universal within mathematics. We present four arguments to the effect that non-deductive evidence can yield knowledge of a mathematical proposition. We also show that (...) Download Export citation Bookmark 17 citations
Non-deductive methods in mathematics.Alan Baker - 2010 - Stanford Encyclopedia of Philosophy.details Download Export citation Bookmark 22 citations
Proofs, Reliable Processes, and Justification in Mathematics.Yacin Hamami - 2021 - British Journal for the Philosophy of Science 74 (4):1027-1045.details Although there exist today a variety of non-deductive reliable processes able to determine the truth of certain mathematical propositions, proof remains the only form of justification accepted in mathematical practice. Some philosophers and mathematicians have contested this commonly accepted epistemic superiority of proof on the ground that mathematicians are fallible: when the deductive method is carried out by a fallible agent, then it comes with its own level of reliability, and so might happen to be equally or even less reliable (...) Download Export citation Bookmark 2 citations

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