On Number-Set Identity: A Study

Philosophia Mathematica 30 (2):223-244 (2022)
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Abstract

Benacerraf’s 1965 multiple-reductions argument depends on what I call ‘deferential logicism’: his necessary condition for number-set identity is most plausible against a background Quineanism that allows autonomy of the natural number concept. Steinhart’s ‘folkist’ sufficient condition on number-set identity, by contrast, puts that autonomy at the center — but fails for not taking the folk perspective seriously enough. Learning from both sides, we explore new conditions on number-set identity, elaborating a suggestion from Wright.

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Sean Ebels-Duggan
Northwestern University

References found in this work

New work for a theory of universals.David K. Lewis - 1983 - Australasian Journal of Philosophy 61 (4):343-377.
What numbers could not be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Realism in mathematics.Penelope Maddy - 1990 - New York: Oxford University Prress.
Putnam’s paradox.David Lewis - 1984 - Australasian Journal of Philosophy 62 (3):221 – 236.

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