Identity, indiscernibility, and ante rem structuralism: the tale of i and -i

Stewart Shapiro

Research output: Contribution to journalArticlepeer-review

73 Citations (Scopus)

Abstract

Some authors have claimed that ante rem structuralism has problems with structures that have indiscernible places. In response, I argue that there is no requirement that mathematical objects be individuated in a non-trivial way. Metaphysical principles and intuitions to the contrary do not stand up to ordinary mathematical practice, which presupposes an identity relation that, in a sense, cannot be defined. In complex analysis, the two square roots of -1 are indiscernible: anything true of one of them is true of the other. I suggest that 'i' functions like a parameter in natural deduction systems.

Original languageEnglish
Pages (from-to)285-309
Number of pages25
JournalPhilosophia Mathematica
Volume16
Issue number3
DOIs
Publication statusPublished - Oct 2008

Keywords

  • MATHEMATICAL STRUCTURALISM
  • UNIVERSALS

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