Groundwork for a Fallibilist Account of Mathematics

Philosophical Quarterly 7 (4):823-844 (2021)
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Abstract

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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Silvia De Toffoli
University School of Advanced Studies IUSS Pavia

Citations of this work

Mathematics and Metaphilosophy.Justin Clarke-Doane - 2022 - Cambridge: Cambridge University Press.
Intersubjective Propositional Justification.Silvia De Toffoli - forthcoming - In Luis R. G. Oliveira & Paul Silva Jr (eds.), Propositional and Doxastic Justification. Routledge.
Open texture, rigor, and proof.Benjamin Zayton - 2022 - Synthese 200 (4):1-20.

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