What we talk about when we talk about numbers

Research output: Contribution to journalArticle (Academic Journal)

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 languageEnglish
Pages (from-to)1437-1456
Number of pages20
JournalAnnals of Pure and Applied Logic
Volume169
Issue number12
Early online date8 Aug 2018
DOIs
Publication statusPublished - Dec 2018

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Structured keywords

  • Centre for Science and Philosophy

Keywords

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

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