Groundwork for a Fallibilist Account of Mathematics

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

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.

Author's Profile

Silvia De Toffoli
University School of Advanced Studies IUSS Pavia

Analytics

Added to PP
2020-12-14

Downloads
1,886 (#4,381)

6 months
278 (#6,764)

Historical graph of downloads since first upload
This graph includes both downloads from PhilArchive and clicks on external links on PhilPapers.
How can I increase my downloads?