Structuralism, Indispensability, and the Access Problem

Facta Philosophica 9 (1):203-211 (2007)

Russell Marcus
Hamilton College
The access problem for mathematics arises from the supposition that the referents of mathematical terms inhabit a realm separate from us. Quine’s approach in the philosophy of mathematics dissolves the access problem, though his solution sometimes goes unrecognized, even by those who rely on his framework. This paper highlights both Quine’s position and its neglect. I argue that Michael Resnik’s structuralist, for example, has no access problem for the so-called mathematical objects he posits, despite recent criticism, since he relies on an indispensability argument. Still, Resnik’s structuralist does not provide an account of our access to traditional mathematical objects, and this may be seen as a problem.
Keywords philosophy of mathematics  structuralism  indispensability
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DOI 10.3726/93525_203
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References found in this work BETA

Two Dogmas of Empiricism.Willard V. O. Quine - 1951 - Philosophical Review 60 (1):20–43.
Realism, Mathematics and Modality.Hartry Field - 1988 - Philosophical Topics 16 (1):57-107.
Mathematics as a Science of Patterns.Michael D. Resnik - 1997 - New York ;Oxford University Press.
Realism in Mathematics.Penelope MADDY - 1990 - Oxford University Prress.

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Citations of this work BETA

The Eleatic and the Indispensabilist.Russell Marcus - 2015 - Theoria : An International Journal for Theory, History and Fundations of Science 30 (3):415-429.

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