Suppose, for the sake of argument, that non-actual possible worlds necessarily exist. Then the second premises, B2 and C2, are both true on the modal entailment account. Moreover, on the modal entailment account, both of these arguments are necessarily truth preserving. It seems to follow that the conclusion that non-actual possible worlds exist can be supported either by arguing for B1, that modal realism is true, or by arguing for C1, that materialism is true. But, surely, an argument for mate