Full textBlue print
De Toffoli, Silvia. Groundwork for a Fallibilist Account of Mathematics
2021, The Philosophical Quarterly, 71(4).
Added by: Fenner Stanley Tanswell
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.

Comment (from this Blueprint): De Toffoli makes a strong case for the importance of mathematical practice in addressing important issues about mathematics. In this paper, she looks at proof and justification, with an emphasis on the fact that mathematicians are fallible. With this in mind, she argues that there are circumstances under which we can have mathematical justification, despite a possibility of being wrong. This paper touches on many cases and questions that will reappear later across the Blueprint, such as collaboration, testimony, computer proofs, and diagrams.

Export citation in BibTeX format

Export text citation

View this text on PhilPapers

Export citation in Reference Manager format

Export citation in EndNote format

Export citation in Zotero format


Share on Facebook
Share on LinkedIn
Share by Email

Leave a Reply

Your email address will not be published.