 However, one can develop a counterexample to the above proposal, by considering two concrete objects that are indiscernible with respect to their intrinsic qualitative properties. Cowling (2017) considers the case of a possible world with only two perfectly spherical balls, \(A\) and \(B\), that share the same intrinsic qualitative properties and that are floating at a certain distance from each other. So \(A\) and \(B\) are distinct concrete objects but indiscernible in terms of their intrinsic qualitative properties.[7] But Lewis has pointed out that “if two individuals are indiscernible then so are their unit sets” (1986a, 84). If this is correct, \(\{A\}\) and \(\{B\}\) would be indiscernible, but (at least for some philosophers) distinct abstract objects, contrary to the discernibility criterion.[8] It is possible to counter-argue that we could happily accept impure sets as concrete; after all, it was always a bit unclear how they should be classified. Obviously, this has the problematic consequence of having some sets—pure sets—as abstract and other sets—impure sets—as concrete. But the idea that abstract objects have distinctive intrinsic natures allows one to establish a criterion less strong than that of discernibility; if an entity has a distinctive intrinsic nature, it cannot have a duplicate. So, the next criterion of non-duplication can be put forward: