How ante-rem structuralism solves Benacerraf’s identification problem against mathematical platonism? Does it resolve it?
Through the position that numbers are objects occupying positions in a structural universal, ante-rem structuralism attempts to resolve Benacerraf’s identification problem against mathematical Platonism, which states that we cannot identify objects by their structural properties. This attempt fails because it is subject to the indiscernibility problem, according to which some structures include structurally indiscernible objects. While ante-rem structuralists seek to resolve this problem by appealing to a particular interpretation of mathematical practice, namely, that we do not need to identify structurally indiscernible objects, this appeal is ad hoc, as it is this interpretation that raised the problem in the first place.
