 It appears that the central point of EPR was to argue that any interpretation of quantum state functions that attributes real physical states to systems faces these alternatives. It also appears that Einstein’s different arguments make use of different notions of completeness. In the first argument completeness is an ordinary notion that amounts to not leaving out any relevant details. In the second, completeness is a technical notion which has been dubbed “bijective completeness“ (Fine 1996 ): no more than one quantum state should correspond to a real state. These notions are connected. If completeness fails in the bijective sense, and more than one quantum state corresponds to some real state, we can argue that the ordinary notion of completeness also fails. For distinct quantum states will differ in the values they assign to certain quantities. (For example, the observable corresponding to the projector on a state takes value 1 in one case but not in the other.) Hence each will omit something that the other affirms, so completeness in the ordinary sense will fail. Put differently, ordinary completeness implies bijective completeness. (The converse is not true. Even if the correspondence of quantum states to real states were one-to-one, the description afforded by a quantum state might still leave out some physically relevant fact about its corresponding real state.) Thus a dilemma between locality and “completeness“ in Einstein’s versions of the argument still implicates ordinary completeness. For if locality holds, then his two-variable argument shows that bijective completeness fails, and then completeness in the ordinary sense fails as well.