 Benacerraf argues, in particular, that the natural numbers should not be identified with any set-theoretic objects; in fact, they should not be taken to be objects at all. Instead, numbers should be treated as “positions in structures”, e.g., in “the natural number structure”, “the real number structure”, etc. All that matters about such positions are their structural properties, i.e., those “stem[ming] from the relations they bear to one another in virtue of being arranged in a progression” (1965: 70), as opposed to further set-theoretic properties of the von Neumann ordinals, Dedekind cuts, etc. What we study and try to characterize in modern mathematics, along such lines, are the corresponding “abstract structures”. It is in this sense that Benacerraf suggests a structuralist position concerning mathematics. The details of the position are left open and somewhat vague, however, including how we should think about Benacerraf’s abstract structures in the end, except that they are not to be identified with set-theoretic relational systems (consisting of sets as domains, with set-theoretic relations and functions defined on them). 