Two types of abstraction for structuralism

Richard G Pettigrew, Øystein Linnebo

Research output: Contribution to journalArticle (Academic Journal)peer-review

26 Citations (Scopus)


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
JournalPhilosophical Quarterly
Issue number255
Early online date7 Feb 2014
Publication statusPublished - Apr 2014

Structured keywords

  • Centre for Science and Philosophy


  • structuralism
  • abstraction
  • Dedekind
  • Frege


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