 However, there may be reasons to reject the Parity Thesis. If Lewis’s criticisms of ersatzism in On the Plurality of Worlds are right, then each ersatz account of impossible worlds inherits the limits of ersatz theories of possible worlds: each of these theories has to resort to intensional entities taken as primitive (such as propositions or states of affairs) in its explanation of what ersatz worlds are, or to primitive modal notions (most often, to both). Suppose that, instead, one wants to retain the advantages of both worlds (no pun intended), ersatz and genuine, when it comes to impossibilities. Suppose, that is, that (a) one wants to employ a modal framework including both possible and impossible worlds to retain the theoretical benefits provided by the latter; and (b) one wants to stick to Lewis’s project of a reductive account of intensional and modal notions to fully extensional ones (contra ersatzism); but also (c) one wants to avoid the unwelcome consequences of concrete impossible worlds instantiating impossibilities, such as having true contradictions “out there” in reality (contra Yagisawa’s extended modal realism). One could then try the following hybrid solution: (1) go realist about possible worlds, and (2) exploit the set-theoretic machinery of modal realism to represent different impossible worlds as distinct ersatz, abstract constructions.