TY - JOUR
T1 - Breaking the Tie
T2 - Benacerraf's Identification Argument Revisited
AU - Avron, Arnon
AU - Grabmayr, Balthasar
N1 - Publisher Copyright:
© 2022 The Authors [2022].
PY - 2023/2/1
Y1 - 2023/2/1
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85160243204&partnerID=8YFLogxK
U2 - 10.1093/philmat/nkac022
DO - 10.1093/philmat/nkac022
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AN - SCOPUS:85160243204
SN - 0031-8019
VL - 31
SP - 81
EP - 103
JO - Philosophia Mathematica
JF - Philosophia Mathematica
IS - 1
ER -