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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| 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
A Treatise of Human Nature: Being an Attempt to Introduce the Experimental Method of Reasoning Into Moral Subjects.David Hume & D. G. C. Macnabb (eds.) - 1738 - Collins.
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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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