Fictionalism in the Philosophy of Mathematics

by

Mark Balaguer

• LAST REVIEWED: 19 September 2022
• LAST MODIFIED: 28 August 2018
• DOI: 10.1093/obo/9780195396577-0080

Introduction

Fictionalism (about mathematics) is best thought of as a reaction to platonism (about mathematics). Platonism is the view that (a) there exist abstract mathematical objects (i.e., nonspatiotemporal mathematical objects), and (b) our mathematical sentences and theories provide true descriptions of such objects. Thus, on this view, sentences such as “4 is even” provide straightforward descriptions of certain objects; for example, “4 is even” tells us something about the number 4. Moreover, according to platonists, numbers are abstract objects; that is, they are wholly nonphysical, nonmental, nonspatial, nontemporal, and noncausal. Thus, on this view, the number 4 exists independently of us and our thinking, but it does not exist in space or time, it is not a physical or mental object, and it does not enter into causal relations with other objects. Fictionalism, on the other hand, which was originally formulated in Field 1980 (cited in the Hard-Road Response to the Indispensability Argument), is the view that (a) our mathematical sentences and theories do purport to be about abstract mathematical objects, as platonists suggest, but (b) there are no such things as abstract objects, and so (c) our mathematical theories are not true. Thus, the idea is that sentences such as “4 is even” are false, or untrue, for the same reason that, say, “Santa Claus lives at the North Pole” is false or untrue—because just as there is no such person as Santa Claus, so too there is no such thing as the number 4.

General Overviews

General discussions of fictionalism can be found in two online encyclopedia articles, Balaguer 2008 and Leng 2010.

• Balaguer, Mark. “Fictionalism in the Philosophy of Mathematics.” In The Stanford Encyclopedia of Philosophy. Edited by Edward N. Zalta. 2008.

  Provides an overview of fictionalism in the philosophy of mathematics.

• Leng, Mary. “Fictionalism in the Philosophy of Mathematics.” In the Internet Encyclopedia of Philosophy. Edited by James Fieser and Bradley Dowden. 2010.

  Provides an overview of fictionalism in the philosophy of mathematics.