 As Benacerraf argued, there is something wrong with identifying “the natural numbers” with a particular set-theoretic system; or at least, it seems wrong to do so in any absolute sense. Benacerraf’s conclusion was that numbers are not sets, nor objects of any kind, but positions in a structure. Now, one can agree with almost everything Benacerraf says and still want to identify “the natural numbers” with some set-theoretic system in a less absolute sense.  In doing so, one can admit that any other model of the Dedekind-Peano axioms “would do as well”, i.e., could have been chosen instead (except perhaps for pragmatic reasons, e.g., the ability to generalize to the transfinite). This means that what we identify as the natural numbers depends on an initial, provisional, and somewhat arbitrary choice. For most mathematical purposes, such a pragmatic identification is sufficient; in fact, this is exactly what one does in standard axiomatic set theory. The resulting position deserves again to be counted as a form of structuralism, as its defenders insist. What makes it structuralist is the “indifference to identify” the natural numbers in any more absolute sense (cf. Burgess 2015). 