In Defense of Benacerraf’s Multiple-Reductions Argument

Philosophia Mathematica 27 (2):276-288 (2019)
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Abstract

I discuss Steinhart’s argument against Benacerraf’s famous multiple-reductions argument to the effect that numbers cannot be sets. Steinhart offers a mathematical argument according to which there is only one series of sets to which the natural numbers can be reduced, and thus attacks Benacerraf’s assumption that there are multiple reductions of numbers to sets. I will argue that Steinhart’s argument is problematic and should not be accepted.

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Michele Ginammi
Scuola Normale Superiore

Citations of this work

On Number-Set Identity: A Study.Sean C. Ebels-Duggan - 2022 - Philosophia Mathematica 30 (2):223-244.

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References found in this work

What numbers could not be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Mathematics as a science of patterns.Michael David Resnik - 1997 - New York ;: Oxford University Press.
Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 1997 - Oxford, England: Oxford University Press USA.
Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 2002 - Philosophy and Phenomenological Research 65 (2):467-475.
Philosophy of mathematics.Paul Benacerraf (ed.) - 1964 - Englewood Cliffs, N.J.,: Prentice-Hall.

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