Why Can't There Be Numbers?

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Abstract

Platonists affirm the existence of abstract mathematical objects, and Nominalists deny the existence of abstract mathematical objects. While there are standard arguments in favor of Nominalism, these arguments fail to account for the necessity of Nominalism. Furthermore, these arguments do nothing to explain why Nominalism is true. They only point to certain theoretical vices that might befall the Platonist. The goal of this paper is to formulate and defend a simple, valid argument for the necessity of Nominalism that seeks to precisify the widespread intuition that mathematical objects are somehow 'spooky' or 'mysterious'.

Original languageEnglish (US)
Pages (from-to)65-76
Number of pages12
JournalPhilosophical Quarterly
Volume72
Issue number1
DOIs
StatePublished - Jan 1 2022
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Philosophy

Keywords

  • mathematical objects
  • modality
  • ontology
  • properties
  • structuralism

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