Philosophia Mathematica 16 (2):244-255 (2008)

Justin Clarke-Doane
Columbia University
Paul Benacerraf's argument from multiple reductions consists of a general argument against realism about the natural numbers (the view that numbers are objects), and a limited argument against reductionism about them (the view that numbers are identical with prima facie distinct entities). There is a widely recognized and severe difficulty with the former argument, but no comparably recognized such difficulty with the latter. Even so, reductionism in mathematics continues to thrive. In this paper I develop a difficulty for Benacerraf's argument against reductionism that is of comparable severity to the now widely recognized difficulty with his general argument against realism. Thanks to Kit Fine, Hartry Field, Jeff Sebo, Ted Sider, Stephen Schiffer, and anonymous referees at Philosophia Mathematica for helpful comments on earlier versions of this paper. Thanks to Aron Edidin for many helpful discussions of the problems that inspired it. CiteULike Connotea What's this?
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DOI 10.1093/philmat/nkm034
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References found in this work BETA

Principia Ethica.George Edward Moore - 1903 - Dover Publications.
Realism, Mathematics and Modality.Hartry Field - 1988 - Philosophical Topics 16 (1):57-107.
Ontological Relativity.W. V. Quine - 1968 - Journal of Philosophy 65 (7):185-212.

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Citations of this work BETA

Objectivity in Ethics and Mathematics.Justin Clarke-Doane - 2015 - Proceedings of the Aristotelian Society: The Virtual Issue 3.
In Defense of Benacerraf’s Multiple-Reductions Argument.Michele Ginammi - 2019 - Philosophia Mathematica 27 (2):276-288.
On Number-Set Identity: A Study.Sean C. Ebels-Duggan - forthcoming - Philosophia Mathematica.
Arbitrary Reference, Numbers, and Propositions.Michele Palmira - 2018 - European Journal of Philosophy 26 (3):1069-1085.

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