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

Authors
Silvia De Toffoli
Princeton University
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.
Keywords mathematical justification  proof  a priori  fallibility  basing relation  reliability
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Reprint years 2021
DOI 10.1093/pq/pqaa076
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References found in this work BETA

The Fate of Knowledge.Helen E. Longino - 2001 - Princeton University Press.
Realism, Mathematics and Modality.Hartry Field - 1988 - Philosophical Topics 16 (1):57-107.
Mathematical Truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.

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Citations of this work BETA

Intersubjective Propositional Justification.Silvia De Toffoli - forthcoming - In Luis R. G. Oliveira & Paul Silva Jr (eds.), Propositional and Doxastic Justification. Routledge.

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