Criteria of Identity and Structuralist Ontology

H Leitgeb, JAC Ladyman

Research output: Contribution to journalArticle (Academic Journal)

49 Citations (Scopus)

Abstract

In discussions about whether the Principle of the Identity of Indiscernibles is compatible with structuralist ontologies of mathematics, it is usually assumed that individual objects are subject to criteria of identity which somehow account for the identity of the individuals. Much of this debate concerns structures that admit of non-trivial automorphisms. We consider cases from graph theory that violate even weak formulations of PII. We argue that (i) the identity or difference of places in a structure is not to be accounted for by anything other than the structure itself and that (ii) mathematical practice provides evidence for this view.
Translated title of the contributionCriteria of Identity and Structuralist Ontology
Original languageEnglish
Pages (from-to)388-396
Number of pages9
JournalPhilosophia Mathematica
Volume16
Issue number3
Early online date2 Nov 2007
DOIs
Publication statusPublished - 2008

Keywords

  • PII
  • identity
  • structuralism
  • ontology of mathematics
  • graph theory
  • structures

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