 Concerning the antisymmetry postulate (18), the picture is even more complex. For one thing, some authors maintain that the relationship between an object and the stuff it is made of provides a perfectly ordinary counterexample of the antisymmetry of parthood: according to Thomson (1998), for example, a statue and the clay that constitutes it are part of each other, yet distinct. This is not a popular view: as already mentioned, most contemporary authors would either deny that material constitution is a relation of parthood or else treat it as improper parthood, i.e., identity, which is trivially antisymmetric (and symmetric). Moreover, those who regard constitution as a genuine case of proper parthood tend to follow Aristotle's hylomorphic conception and deny that the relation also holds in the opposite direction: the clay is part of the statue but not vice versa (see e.g. Haslanger 1994, Koslicki 2008). Still, insofar as Thomson's view is a legitimate option, it represents a challenge to the putative generality of (18). Second, one may wonder about the possibility of unordinary cases of symmetric parthood relationships. Sanford (1993: 222) refers to Borges's Aleph as a case in point: “I saw the earth in the Aleph and in the earth the Aleph once more and the earth in the Aleph …”. In this case, a plausible reply is simply that fiction delivers no guidance to conceptual investigations: conceivability may well be a guide to possibility, but literary fantasy is by itself no evidence of conceivability (van Inwagen 1993: 229). Perhaps the same could be said of Fazang's Jeweled Net of Indra, in which each jewel has every other jewel as part (Jones 2012). However, other cases seem harder to dismiss. Surely the Scholastics were not merely engaging in literary fiction when arguing that each person of the Trinity is a proper part of God, and yet also identical with God (see e.g. Abelard, Theologia christiana, bk. III). And arguably time travel is at least conceivable, in which case again (18) could fail: if time-traveling wall W ends up being one of the bricks that compose (say) its own bottom half, H, then we have a conceivable scenario in which W is part of H and H is part of W while W ≠ H (Kleinschmidt 2011). Third, it may be argued that antisymmetry is also at odds with theories that have been found acceptable on quite independent grounds. Consider again the theory of structured propositions. If A is the proposition that the universe exists—where the universe is something of which everything is part—and if A is true, then on such a theory the universe would be a proper part of A; and since A would in turn be a proper part of U, antisymmetry would be forfeit (Tillman and Fowler 2012). Likewise, if A is the proposition that B is true, and B the proposition that A is contingent, then again A and B would be part of each other even though A ≠ B (Cotnoir 2013b). Finally, and more generally, it may be observed that the possibility of mereological loops is to be taken seriously for the same sort of reasons that led to the development of non-well-founded set theory, i.e., set theory tolerating cases of self-membership and, more generally, of membership circularities (Aczel 1988; Barwise and Moss 1996). This is especially significant in view of the possibility of reformulating set theory itself in mereological terms—a possibility that is extensively worked out in the works of Bunt (1985) and especially Lewis (1991, 1993b) (see also Burgess 2015 and Hamkins and Kikuchi forthcoming). For all these reasons, the antisymmetry postulate (18) can hardly be regarded as constitutive of the basic meaning of ‘part’, and some authors have begun to engage in the systematic study of “non-well-founded mereologies” in which (18) may fail (Cotnoir 2010; Cotnoir and Bacon 2012; Obojska 2013). 