Metodo

International Studies in Phenomenology and Philosophy

Series | Book | Chapter

192029

A non-error theory approach to mathematical fictionalism

Phil Bériault

pp. 181-189

Abstract

Mary Leng has published many spirited, insightful defences of mathematical fictionalism, the view that the claims of mathematics are not literally true. I offer as an alternative an anti-realist approach to mathematics that preserves many of Leng's valuable insights while ridding fictionalism of its most unpalatable feature, the claim that substantive mathematical claims are "in error". In making my argument, I first present the virtues of Leng's fictionalism by considering how she defends it against influential objections due to John Burgess. Leng's view is roughly that indispensability in science is necessary but not sufficient for believing in the reality of something, and that philosophical analysis can make clear why some things, including mathematics, are necessary for science but not real. I suggest we can accept this without adopting error theory. Marrying features of Leng's view with constructivism, a quite different sort of anti-realism about mathematics, allows us to: maintain that mathematical assertions are (at least often) literally true, but that it is a mistake to understand them as referring to abstract entities; to be anti-realists about mathematics; and to make use of the fictionalist toolkit Leng supplies for explaining why mathematics is indispensable, even if not real.

Publication details

Published in:

Zack Maria, Schlimm Dirk (2018) Research in history and philosophy of mathematics: the CSHPM 2017 annual meeting in Toronto, Ontario. Basel, Birkhäuser.

Pages: 181-189

DOI: 10.1007/978-3-319-90983-7_12

Full citation:

Bériault Phil (2018) „A non-error theory approach to mathematical fictionalism“, In: M. Zack & D. Schlimm (eds.), Research in history and philosophy of mathematics, Basel, Birkhäuser, 181–189.