Two types of abstraction for structuralism

Oystein Linnebo*, Richard Pettigrew

*Corresponding author for this work

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

If numbers were identified with any of their standard set-theoretic realizations, then they would have various non-arithmetical properties that mathematicians are reluctant to ascribe to them. Dedekind and later structuralists conclude that we should refrain from ascribing to numbers such 'foreign' properties. We first rehearse why it is hard to provide an acceptable formulation of this conclusion. Then we investigate some forms of abstraction meant to purge mathematical objects of all 'foreign' properties. One form is inspired by Frege; the other by Dedekind. We argue that both face problems.

Original languageEnglish
Pages (from-to)267-283
Number of pages17
JournalThe Philosophical Quarterly
Volume64
Issue number255
Early online date7 Feb 2014
DOIs
Publication statusPublished - Apr 2014

Keywords

  • structuralism
  • abstraction
  • Dedekind
  • Frege
  • mathematics

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