What Are Structural Properties?

Abstract:

Informally, structural properties are usually characterized in one of two ways: either as the properties expressible purely in terms of the primitive relations of mathematical theories, or as the properties that hold of all structurally similar mathematical objects. In this talk I present two formal explications of structural properties-both formulated originally by Rudolf Carnap-that correspond to these two informal characterizations. I wish to reach two goals: First, to get clear on how the two accounts capture the intuition that structural properties are “grounded in structure”. Second, to understand the relation between the two explications of mathematical properties. As I will show, the two characterizations do not determine the same class of properties. From this observation I draw some philosophical conclusions about the possibility “correct” analysis of structural properties. (This talk is based on joint work with Johannes Korbmacher (MCMP Munich))

Attendance is free and everybody is welcome!