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- Title
Breaking the Tie: Benacerraf's Identification Argument Revisited.
- Authors
Avron, Arnon; Grabmayr, Balthasar
- Abstract
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.
- Subjects
VON Neumann, John, 1903-1957; ARGUMENT; REDUCTIONISM; PHILOSOPHERS; ARITHMETIC
- Publication
Philosophia Mathematica, 2023, Vol 31, Issue 1, p81
- ISSN
0031-8019
- Publication type
Article
- DOI
10.1093/philmat/nkac022