Goodman describes the criterion as demanding that “sameness of content” entails identity. Systems that have only mereological means of “generating” composite objects (see section  3.2 Mereology below)  count as nominalistic according to this criterion. Parthood is transitive, so from atoms a and b only one further object can be “generated”, the mereological sum of a and b. A set-forming operation, however, will distinguish, for instance, between {a, b} (the set of a and b) and {{a, b}} (the set containing the set of a and b) and {{a}, {b}} (the set containing the singleton set of a and the singleton set of b). None of the these three are pairwise identical. Membership is not transitive. The first and third contain two members, but not the same members (both a and b are members of the first set, but not of the third), while the second set has only one member (namely the first set). All three (and infinitely many others) are generated from the same atoms, however, or as Goodman might put it, they have the same content: a and b. A system featuring a set-theoretic generating relation thus does not count as nominalistic.