 To elaborate this advantage further, number systems of basic arithmetic can be characterized in such categorical frameworks as “natural number objects”, as was first shown by Lawvere. In contrast to their ZFC-based representation, such objects are not just isomorphic but share “exactly the same properties”, namely those expressible in the language of the category of sets. In other words, any two natural number objects are “provably indiscernible”, in the sense that they “provably have the same properties” (McLarty 1993). Moreover, all of these properties are structural in the above sense. As a consequence, Benacerraf’s dilemma of isomorphic numbers systems with different set-theoretic properties does not arise in the context of categorical set theory. The conclusion is that numbers can, after all, be identified with sets, but with structural ones as defined in ETCS.