 One way to understand Benacerraf’s discussion in his 1965 article is that he proposes to treat the natural number structure as a new kind of abstract entity, different from set-theoretic objects and systems of objects. All depends then on what exactly that amounts to, including whether one should treat such structures as objects themselves, thus reifying them in some substantive and still to be worked out way, or not. Benacerraf himself was reluctant to do the latter, in line with his overall hesitancy to talk about mathematical objects. 