On Mathematical Structuralism. A Theory of Unlabeled Graphs as Ante Rem Structures

Hannes Leitgeb (MCMP/LMU) gives a talk at the Workshop on Mathematics: Objectivity by Representation (11 November, 2014) titled "On Mathematical Structuralism. A Theory of Unlabeled Graphs as Ante Rem Structures". Abstract: There are different versions of structuralism in present-day philosophy of mathematics which all take as their starting point the structural turn that mathematics took in the last two centuries. In this talk, I will make one variant of structuralism—ante rem structuralism—precise in terms of an axiomatic theory of unlabeled graphs as ante rem structures. I will then use that axiomatic theory in order to address some of the standard objections to ante rem structuralism that one can find in the literature. Along the way, I will discuss also other versions of mathematical structuralism, and I will say something on how the emerging theory of ante rem structures relates to modern set theory.