Structuralism and metaphysics

Philosophical Quarterly 54 (214):56--77 (2004)
Abstract
I consider different versions of a structuralist view of mathematical objects, according to which characteristic mathematical objects have no more of a 'nature' than is given by the basic relations of a structure in which they reside. My own version of such a view is non-eliminative in the sense that it does not lead to a programme for eliminating reference to mathematical objects. I reply to criticisms of non-eliminative structuralism recently advanced by Keränen and Hellman. In replying to the former, I rely on a distinction between 'basic' and 'constructed' structures. A conclusion is that ideas from the metaphysical tradition can be misleading when applied to the objects of modern mathematics
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References found in this work BETA
Paul Benacerraf (1965). What Numbers Could Not Be. Philosophical Review 74 (1):47-73.
John Hawthorne & Karson Kovakovich (2006). Disjunctivism. Aristotelian Society Supplementary Volume 80 (1):145-83.

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