Platonism and Aristotelianism in Mathematics

Research output: Contribution to journalArticle (Academic Journal)peer-review

15 Citations (Scopus)

Abstract

Philosophers of mathematics agree that the only interpretation of arithmetic that takes that discourse at 'face value' is one on which the expressions 'N', '0', '1', '+', and '×' are treated as proper names. I argue that the interpretation on which these expressions are treated as akin to free variables has an equal claim to be the default interpretation of arithmetic. I show that no purely syntactic test can distinguish proper names from free variables, and I observe that any semantic test that can must beg the question. I draw the same conclusion concerning areas of mathematics beyond arithmetic.
Translated title of the contributionPlatonism and Aristotelianism in Mathematics
Original languageEnglish
Pages (from-to)310 - 332
Number of pages22
JournalPhilosophia Mathematica
Volume16
DOIs
Publication statusPublished - Oct 2008

Structured keywords

  • Centre for Science and Philosophy

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