Structuralism, Indispensability, and the Access Problem

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

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.

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Russell Marcus
Hamilton College

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References found in this work

Ontological relativity and other essays.Willard Van Orman Quine (ed.) - 1969 - New York: Columbia University Press.
Two Dogmas of Empiricism.W. Quine - 1951 - [Longmans, Green].
From a Logical Point of View.Willard Van Orman Quine - 1953 - Cambridge: Harvard University Press.
Two Dogmas of Empiricism.Willard V. O. Quine - 1951 - Philosophical Review 60 (1):20–43.
Realism, Mathematics & Modality.Hartry H. Field - 1989 - New York, NY, USA: Blackwell.

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