Mathematical Contingentism
Miller (Kristie)
Source: Erkenntnis (1975-), Vol. 77, No. 3 (November 2012), pp. 335-359
Paper - Abstract

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Author’s Abstract

  1. Platonists and nominalists disagree about whether mathematical objects exist. But they almost uniformly agree about one thing: whatever the status of the existence of mathematical objects, that status is modally1 necessary.
  2. Two notable dissenters from this orthodoxy are Hartry Field, who defends contingent nominalism, and Mark Colyvan, who defends contingent Platonism. The source of their dissent is their view that the indispensability argument provides our justification for believing in the existence, or not, of mathematical objects.
  3. This paper considers whether commitment to the indispensability argument gives one grounds to be a contingentist about mathematical objects.

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