What we talk about when we talk about numbers

Richard Pettigrew

doi:10.1016/j.apal.2018.08.009

What we talk about when we talk about numbers

Richard Pettigrew

Department of Philosophy

Research output: Contribution to journal › Article (Academic Journal) › peer-review

2 Citations (Scopus)

127 Downloads (Pure)

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.

Original language	English
Pages (from-to)	1437-1456
Number of pages	20
Journal	Annals of Pure and Applied Logic
Volume	169
Issue number	12
Early online date	8 Aug 2018
DOIs	https://doi.org/10.1016/j.apal.2018.08.009
Publication status	Published - Dec 2018

Structured keywords

Centre for Science and Philosophy

Keywords

Foundations of mathematics
Mathematical structuralism
Nominalism
Philosophy of mathematics
Set-theoretic foundations

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10.1016/j.apal.2018.08.009

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Elsevier at https://doi.org/10.1016/j.apal.2018.08.009 . Please refer to any applicable terms of use of the publisher.
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KW - Foundations of mathematics

KW - Mathematical structuralism

KW - Nominalism

KW - Philosophy of mathematics

KW - Set-theoretic foundations

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ER -

What we talk about when we talk about numbers

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Keywords

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