Non-deductive Justification in Mathematics

A. C. Paseau ()
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A. C. Paseau: Oxford University

A chapter in Handbook of the History and Philosophy of Mathematical Practice, 2024, pp 2401-2416 from Springer

Abstract: Abstract In mathematics, the deductive method reigns. Without proof, a claim remains unsolved, a mere conjecture, not something that can be simply assumed; when a proof is found, the problem is solved, it turns into a “result,” something that can be relied on. So mathematicians think. But is there more to mathematical justification than proof? The answer is an emphatic yes, as I explain in this chapter. I argue that non-deductive justification is in fact pervasive in mathematics, and that it is in good epistemic standing.

Keywords: Proof; Justification; Mathematical knowledge; Mathematical justification; Non-deductive evidence; Empiricism; Non-deductive knowledge; Deductive knowledge; Induction; Foundationalism; Euclidean program (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-40846-5_116

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DOI: 10.1007/978-3-031-40846-5_116

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