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Revisiting “The New 4CT Problem”

In: Handbook of the History and Philosophy of Mathematical Practice

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  • Mark McEvoy

    (Hofstra University)

Abstract

According to what one might label the traditional view of proof in mathematics, proofs have the following characteristics. They are knowable a priori, the knowledge they provide is certain, rather than merely probable, they are surveyable, and, because of these other features, a mathematical proof is convincing to one who understands it. Opponents of this view typically drew their motivation not from the study of mathematics, but rather from a more general antipathy to apriority in epistemology and necessity in metaphysics (Mill, Putnam and Quine all spring to mind here). Tymoczko (1979) provides a different sort of challenge, taking as its cue a development within mathematics itself, rather than being based on philosophical scruples over apriority or necessity.

Suggested Citation

  • Mark McEvoy, 2024. "Revisiting “The New 4CT Problem”," Springer Books, in: Bharath Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice, pages 2459-2479, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-40846-5_38
    DOI: 10.1007/978-3-031-40846-5_38
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