Groundwork for a Fallibilist Account of Mathematics

Philosophical Quarterly 7 (4):823-844 (2021)
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According to the received view, genuine mathematical justification derives from proofs. In this article, I challenge this view. First, I sketch a notion of proof that cannot be reduced to deduction from the axioms but rather is tailored to human agents. Secondly, I identify a tension between the received view and mathematical practice. In some cases, cognitively diligent, well-functioning mathematicians go wrong. In these cases, it is plausible to think that proof sets the bar for justification too high. I then propose a fallibilist account of mathematical justification. I show that the main function of mathematical justification is to guarantee that the mathematical community can correct the errors that inevitably arise from our fallible practices.

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Author's Profile

Silvia De Toffoli
University School of Advanced Studies IUSS Pavia

References found in this work

Justification and the Truth-Connection.Clayton Littlejohn - 2012 - New York: Cambridge University Press.
A treatise of human nature.David Hume & D. G. C. Macnabb (eds.) - 1977 - New York: Dutton.
The Fate of Knowledge.Helen E. Longino - 2001 - Princeton University Press.
Mathematical truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
The nature of mathematical knowledge.Philip Kitcher - 1983 - Oxford: Oxford University Press.

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