What we talk about when we talk about numbers

Annals of Pure and Applied Logic 169 (12):1437-1456 (2018)
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Abstract

In this paper, I describe and motivate a new species of mathematical structuralism, which I call Instrumental Nominalism about Set-Theoretic Structuralism. As the name suggests, this approach takes standard Set-Theoretic Structuralism of the sort championed by Bourbaki and removes its ontological commitments by taking an instrumental nominalist approach to that ontology of the sort described by Joseph Melia and Gideon Rosen. I argue that this avoids all of the problems that plague other versions of structuralism.

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Author's Profile

Richard Pettigrew
University of Bristol

Citations of this work

Why Can’t There Be Numbers?David Builes - forthcoming - The Philosophical Quarterly.
The insubstantiality of mathematical objects as positions in structures.Bahram Assadian - 2022 - Inquiry: An Interdisciplinary Journal of Philosophy 20.

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References found in this work

Mathematical truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
How to defeat opposition to Moore.Ernest Sosa - 1999 - Philosophical Perspectives 13:137-49.
On what there is.W. V. Quine - 1953 - In Willard Van Orman Quine (ed.), From a Logical Point of View. Cambridge: Harvard University Press. pp. 1-19.
How to Defeat Opposition to Moore.Ernest Sosa - 1999 - Noûs 33 (s13):141-153.

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