It appears that ante rem structuralism describes the notion of a structure in a somewhat circular manner. A structure is described as places that stand in relation to each other, but a place cannot be described independently of the structure to which it belongs. Yet this is not necessarily a problem. For the ante rem structuralist, the notion of structure is a primitive concept, which cannot be defined in other more basic terms. At best, we can construct an axiomatic theory of mathematical struc