Platonism and Aristotelianism in Mathematics

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

25 Citations (Scopus)


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
Publication statusPublished - Oct 2008

Structured keywords

  • Centre for Science and Philosophy


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