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The individuation of mathematical objects.

Bahram Assadian1, Robert Fraser2

  • 1School of Philosophy, Religion and History of Science, University of Leeds, Woodhouse Lane, Leeds, LS2 9JT UK.

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|December 26, 2024
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Summary
This summary is machine-generated.

This paper examines the nominalist objection to mathematical platonism, specifically concerning the individuation of mathematical objects. It concludes that the objection lacks merit as platonists can adequately explain object individuation without invoking mysterious metaphysical properties.

Keywords:
GroundingIdentityIndividuationMathematical objectsMathematical platonism

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Area of Science:

  • Philosophy of Mathematics
  • Metaphysics
  • Epistemology

Background:

  • Mathematical platonism posits the existence of abstract mathematical objects.
  • A key objection is that mathematical objects are mysterious and their individuation is unexplained.
  • Nominalism challenges the nature and existence of abstract mathematical entities.

Purpose of the Study:

  • To evaluate the nominalist objection regarding the individuation of mathematical objects.
  • To explore and analyze different modes of mathematical object individuation.
  • To determine if the individuation of mathematical objects poses a genuine problem for mathematical platonism.

Main Methods:

  • Analysis of three proposed modes of individuation for mathematical objects: intrinsic properties, relations, and underlying substance.
  • Metaphysical examination of the implications of each individuation mode for platonism.
  • Argumentative evaluation of the nominalist objection's validity based on the analysis.

Main Results:

  • Individuation by intrinsic properties and relations does not pose significant metaphysical challenges for platonism.
  • Individuation by underlying 'substance' is the only mode that raises metaphysical problems potentially supporting the mystery objection.
  • Platonism is not obligated to adopt the problematic 'substance' individuation, thus retaining explanatory power.

Conclusions:

  • The nominalist objection, as elaborated through the individuation problem, does not undermine mathematical platonism.
  • Platonists can account for the individuation of mathematical objects through non-problematic means.
  • The mystery objection concerning individuation lacks persuasive force against mathematical platonism.