# What we talk about when we talk about numbers

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

**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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2018

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Archival date: 2017-11-28

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References found in this work BETA

On What There Is.Quine, W. V. O.

How to Defeat Opposition to Moore.Sosa, Ernest

Realism, Mathematics and Modality.Field, Hartry

What is the Benacerraf Problem?Clarke-Doane, Justin

Science Without Numbers.Field, Hartry

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2017-11-28

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