Fictionalism in the philosophy of mathematics

In Edward Craig (ed.), Routledge Encyclopedia of Philosophy: Genealogy to Iqbal. New York: Routledge (1996)
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Abstract

Fictionalism in the philosophy of mathematics is the view that mathematical statements, such as ‘8+5=13’ and ‘π is irrational’, are to be interpreted at face value and, thus interpreted, are false. Fictionalists are typically driven to reject the truth of such mathematical statements because these statements imply the existence of mathematical entities, and according to fictionalists there are no such entities. Fictionalism is a nominalist (or anti-realist) account of mathematics in that it denies the existence of a realm of abstract mathematical entities. It should be contrasted with mathematical realism (or Platonism) where mathematical statements are taken to be true, and, moreover, are taken to be truths about mathematical entities. Fictionalism should also be contrasted with other nominalist philosophical accounts of mathematics that propose a reinterpretation of mathematical statements, according to which the statements in question are true but no longer about mathematical entities. Fictionalism is thus an error theory of mathematical discourse: at face value mathematical discourse commits us to mathematical entities and although we normally take many of the statements of this discourse to be true, in doing so we are in error (cf. error theories in ethics).

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Mark Colyvan
University of Sydney

Citations of this work

A Conventionalist Account of Distinctively Mathematical Explanation.Mark Povich - 2023 - Philosophical Problems in Science 74:171–223.

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References found in this work

Mathematical truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
The myth of the seven.Stephen Yablo - 2005 - In Mark Eli Kalderon (ed.), Fictionalism in Metaphysics. New York: Oxford University Press UK. pp. 88--115.
Fictionalism.Matti Eklund - 2010 - Stanford Encyclopedia of Philosophy.

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