 Unlike Shapiro, Parsons does not offer a novel, philosophically motivated structure theory as the backing for his position. For him, we should remain closer to mathematical practice (as it developed in the late nineteenth and the twentieth centuries). In fact, structuralism should be seen as growing out of that practice, rather than being imposed on it from outside. For Parsons this means, among others, taking abstract structures to be introduced directly by categorical axiom systems, a practice he spells out further in a “meta-linguistic” way inspired by Quine (see Parsons 2008). It also means that we should refrain from “cross-structural identifications” (as they can be found in Shapiro’s early works), e.g., from identifying the natural number 1 and the real number 1. Such putative identities should be left indeterminate, as is done in mathematical practice.