 A fourth basic challenge for structuralism, mostly again in its non-eliminative form, is how we can have “access” to structures seen as abstract objects (cf. Hale 1996, among others). To some degree, this revives an older, more general debate about such objects. An initial response, by Resnik, Shapiro, and Parsons (all following Quine here), is to talk about the “positing” of structures, which promises to undercut the access problem.  But under what conditions is such positing legitimate (given the threat of paradox familiar from naïve set theory)? A plausible answer points to the “coherence” of the relevant theories (which, after Gödel’s incompleteness results, is seen as taking the place of provable consistency). Yet what exactly does such coherence amount to? An interesting outcome of the debate about this issue is that Shapiro and Hellman, coming from very different directions, have arrived at views that are very close to each other (see Hellman 2005). Thus, in terms of some basic commitments—ultimate conditions for existence in Shapiro’s case and for possibility in Hellman’s case—their approaches converge in surprising ways. (This may be seen as providing support for both sides, but also as undermining the realism/nominalism dichotomy.)