Mathematical structuralism and the Identity of Indiscernibles
Ladyman (James)
Source: Analysis 65.3, July 2005, pp. 218-221(4)
Paper - Abstract

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Author’s Abstract

  1. The article focuses on mathematical structuralism. Mathematical structuralism comes in various varieties and faces many problems.
  2. The article offers a solution to a particular problem that has been raised for non-eliminative structuralism about mathematical objects of the kind that has been defended by Stewart Shapiro. He calls his view ante rem structuralism and argues that mathematical objects exist, and are positions in structures, where the latter are universals1.
  3. According to Shapiro, mathematical knowledge fails to describe any intrinsic properties of mathematical objects, but it is nonetheless complete knowledge of its domain because the only properties mathematical objects possess are their structural or relational properties.

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