Non-uniqueness as a non-problem

Philosophia Mathematica 6 (1):63-84 (1998)
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Abstract

A response is given here to Benacerraf's (1965) non-uniqueness (or multiple-reductions) objection to mathematical platonism. It is argued that non-uniqueness is simply not a problem for platonism; more specifically, it is argued that platonists can simply embrace non-uniqueness—i.e., that one can endorse the thesis that our mathematical theories truly describe collections of abstract mathematical objects while rejecting the thesis that such theories truly describe unique collections of such objects. I also argue that part of the motivation for this stance is that it dovetails with the correct response to Benacerraf's other objection to platonism, i.e., his (1973) epistemological objection.

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Mark Balaguer
California State University, Los Angeles

References found in this work

Mathematical truth.Paul Benacerraf - 1973 - Journal of Philosophy 70 (19):661-679.
What numbers could not be.Paul Benacerraf - 1965 - Philosophical Review 74 (1):47-73.
Philosophy of mathematics: structure and ontology.Stewart Shapiro - 1997 - New York: Oxford University Press.
Models and reality.Hilary Putnam - 1980 - Journal of Symbolic Logic 45 (3):464-482.
Philosophy of Mathematics: Structure and Ontology.Stewart Shapiro - 2002 - Philosophy and Phenomenological Research 65 (2):467-475.

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