Charles D. Parsons

Edgar Pierce Professor of Philosophy

Harvard University

"Structuralism and Metaphysics"

Abstract:

We consider briefly what are the 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. We articulate our own version of such a view, which is noneliminative in the sense that it does not lead to a program for eliminating reference to mathematical objects. We reply to criticisms of noneliminative structuralism advanced in recent papers by Jukka KerŠnen and Geoffrey Hellman. In replying to the former we 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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