Fitch's Paradox and the Philosophy of Mathematics

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

This chapter considers the impact of the Fitch paradox on particular epistemological views about mathematics. It assumes therefore, for the sake of argument, that the reasoning leading to Fitch's paradox is valid (which is indeed the case given the logical assumptions made). Having this focus provides a specific context to assess the nature and limitation of the paradox, while also showing the paradox's significance for current debates in the philosophy of mathematics. The chapter examines two versions of Platonism (standard and full-blooded Platonism) and two versions of nominalism (mathematical fictionalism and agnostic fictionalism). It argues that, given the specific assumptions about mathematical knowledge that these views make, (FP) brings trouble for some, but not for all, of them. In particular, full-blooded Platonism and - to a certain extent - mathematical fictionalism are in trouble with the paradox, but traditional Platonism and agnostic fictionalism don't seem to be. The chapter concludes with a dilemma that this situation poses for Platonism, and the prospects it offers for nominalism.

Original languageEnglish (US)
Title of host publicationNew Essays on the Knowability Paradox
PublisherOxford University Press
ISBN (Print)9780191713972, 9780199285495
DOIs
StatePublished - Sep 1 2010

Fingerprint

Platonism
Fitch's Paradox
Philosophy of Mathematics
Fictionalism
Paradox
Nominalism
Mathematics
Epistemological
Logic

Keywords

  • Fitch paradox
  • Knowability paradox
  • Mathematics
  • Nominalism
  • Platonsim

ASJC Scopus subject areas

  • Arts and Humanities(all)

Cite this

Bueno, O. (2010). Fitch's Paradox and the Philosophy of Mathematics. In New Essays on the Knowability Paradox Oxford University Press. https://doi.org/10.1093/acprof:oso/9780199285495.003.0017

Fitch's Paradox and the Philosophy of Mathematics. / Bueno, Otavio.

New Essays on the Knowability Paradox. Oxford University Press, 2010.

Research output: Chapter in Book/Report/Conference proceedingChapter

Bueno, O 2010, Fitch's Paradox and the Philosophy of Mathematics. in New Essays on the Knowability Paradox. Oxford University Press. https://doi.org/10.1093/acprof:oso/9780199285495.003.0017
Bueno O. Fitch's Paradox and the Philosophy of Mathematics. In New Essays on the Knowability Paradox. Oxford University Press. 2010 https://doi.org/10.1093/acprof:oso/9780199285495.003.0017
Bueno, Otavio. / Fitch's Paradox and the Philosophy of Mathematics. New Essays on the Knowability Paradox. Oxford University Press, 2010.
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