Breaking the Tie: Benacerraf's Identification Argument Revisited

Arnon Avron*, Balthasar Grabmayr

*Corresponding author for this work

Research output: Contribution to journalReview articlepeer-review


Most philosophers take Benacerraf's argument in 'What numbers could not be' to rebut successfully the reductionist view that numbers are sets. This philosophical consensus jars with mathematical practice, in which reductionism continues to thrive. In this note, we develop a new challenge to Benacerraf's argument by contesting a central premise which is almost unanimously accepted in the literature. Namely, we argue that - contra orthodoxy - there are metaphysically relevant reasons to prefer von Neumann ordinals over other set-theoretic reductions of arithmetic. In doing so, we provide set-theoretical facts which, we believe, are crucial for informed assessment of reductionism.

Original languageEnglish
Pages (from-to)81-103
Number of pages23
JournalPhilosophia Mathematica
Issue number1
StatePublished - 1 Feb 2023


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