Structuralism, Indispensability, and the Access Problem

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Structuralism, Indispensability, and the Access Problem

The central problem in the philosophy of mathematics concerns access. The access problem arises from the common supposition that the referents of mathematical terms inhabit a realm separate from us. Quine’s approach in the philosophy of mathematics, his indispensability argument, dissolves the access problem, though his solution sometimes goes unrecognized, even by those who are sympathetic to ...

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Structuralism and the Indispensability Argument

I distill the indispensability argument to four general charateristics, which yield six unfortunate consequences, unwelcome characteristics of the objects yielded by the argument. The indispensabilist’s objects are not mathematical, in any traditional sense, but merely empirical posits. Then, I characterize a form of structuralism in the philosophy of mathematics which relies on an indispensabi...

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According to mathematical structuralism, the subject matter of mathematics is not the study of mathematical objects, but of mathematical structures. By moving away from objects, the structuralist claims to be in a position to solve the ‘access’ problem: structuralism explains the possibility of mathematical knowledge without requiring any access to mathematical objects. Fraser MacBride has chal...

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ژورنال

عنوان ژورنال: Facta Philosophica

سال: 2007

ISSN: 1424-0602

DOI: 10.3726/93525_203