Structuralism and the concept of set

Charles Parsons

pp. 171-194

in: Evandro Agazzi, György Darvas (eds), Philosophy of mathematics today, Berlin, Springer, 1997

Abstract

In mathematics, I claim, we do not have objects with an “internal” composition arranged in structures, we have only structures. The objects of mathematics, that is, the entities which our mathematical constants and quantifiers denote, are structureless points or positions in structures. As positions in structures, they have no identity or features outside of a structure.1