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Mathematical Gettier Cases and Their Implications

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2025

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https://doi.org/10.1080/00048402.2025.2521736
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Austrian Science Fund (FWF): P 28420

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Australasian Journal of Philosophy. Taylor & Francis. ISSN 0004-8402. eISSN 1471-6828. Verfügbar unter: doi: 10.1080/00048402.2025.2521736

Zusammenfassung

Let mathematical justification be the kind of justification obtained when we prove theorems. Are Gettier cases possible for this kind of justification? At first sight we might think not: The standard for mathematical justification is proof and, since proof is bound at the hip with truth, there is no possibility of having an epistemically lucky justification of a true mathematical proposition. In this paper, I challenge this idea by arguing that there is conception of mathematical justification which is fallibilist (in addition to infallibilist accounts). I argue that for the fallibilist conception, non-trivial Gettier cases are possible (and indeed actual). I indicate some upshots for mathematical practice, in particular, regarding folklore theorems and pluralism.

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100 Philosophie

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ISO 690BARTON, Neil, 2025. Mathematical Gettier Cases and Their Implications. In: Australasian Journal of Philosophy. Taylor & Francis. ISSN 0004-8402. eISSN 1471-6828. Verfügbar unter: doi: 10.1080/00048402.2025.2521736
BibTex
@article{Barton2025Mathe-75967,
  title={Mathematical Gettier Cases and Their Implications},
  year={2025},
  doi={10.1080/00048402.2025.2521736},
  issn={0004-8402},
  journal={Australasian Journal of Philosophy},
  author={Barton, Neil}
}
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