Structuralism and Conceptual Change in Mathematics

PSA Proceedings of the Biennial Meeting of the Philosophy of Science Association 1990 (2):397-401 (1990)
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Abstract

Professor Grosholz packs a lot into her interesting and suggestive paper “Formal Unities and Real Individuals” (Grosholz 1990b). In the limited space available I can comment briefly on its several parts, or direct more substantive comments at a single issue. I will opt for the latter; specifically, I want to address her critique of mathematical structuralism, as found especially in the writings of Michael Resnik.I begin with a brief, hence necessarily caricatured, summary of Resnik’s influential view. According to structuralism, the subject matter of a mathematical theory is a given pattern, or structure, and the objects of the theory are intrinsically unstructured points, or positions, within that pattern. Mathematical objects thus have no identity, and no intrinsic features, outside of the patterns in which they occur. Hence, they cannot be given in isolation but only in their role within an antecedently given pattern, and are distinguishable from one another only in virtue of the relations they bear to one another in the pattern (see, e.g., Resnik (1981)).

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Christopher Menzel
Texas A&M University

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References found in this work

Cartesian method and the problem of reduction.Emily R. Grosholz - 1994 - Revue Philosophique de la France Et de l'Etranger 184 (1):119-121.
Two episodes in the unification of logic and topology.E. R. Grosholz - 1985 - British Journal for the Philosophy of Science 36 (2):147-157.

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