### 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 language | English (US) |
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Title of host publication | New Essays on the Knowability Paradox |

Publisher | Oxford University Press |

ISBN (Print) | 9780191713972, 9780199285495 |

DOIs | |

State | Published - Sep 1 2010 |

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### Keywords

- Fitch paradox
- Knowability paradox
- Mathematics
- Nominalism
- Platonsim

### ASJC Scopus subject areas

- Arts and Humanities(all)

### Cite this

*New Essays on the Knowability Paradox*Oxford University Press. https://doi.org/10.1093/acprof:oso/9780199285495.003.0017