Structures and structuralism in contemporary philosophy of mathematics

Erich Reck

University of California Riverside

Michael P. Price

pp. 341-383

in: Synthese 125 (3), 2000.

Abstract

In recent philosophy of mathematics avariety of writers have presented ``structuralist''views and arguments. There are, however, a number ofsubstantive differences in what their proponents take``structuralism'' to be. In this paper we make explicitthese differences, as well as some underlyingsimilarities and common roots. We thus identifysystematically and in detail, several main variants ofstructuralism, including some not often recognized assuch. As a result the relations between thesevariants, and between the respective problems theyface, become manifest. Throughout our focus is onsemantic and metaphysical issues, including what is orcould be meant by ``structure'' in this connection.