Why Be a Structuralist? Several Unsuccessful Structuralist Strategies for the Philosophy of Mathematics.

Abstract

Structuralism is a relatively new program that has emerged within Philosophy of Mathematics. Stewart Shapiro presents a Structural Realist position. Geoffrey Hellman presents a Nominalist Structuralist position. Both believe structuralist nuances to existing views will make them more successful. I demonstrate that these structuralist additions do little to nothing to improve the realist and nominalist positions. Structuralism must find its own independent method of approaching philosophy of mathematics.