 It is widely acknowledged that it would be too weak to formulate physicalism as the claim that as a matter of mere nomological necessity, everything globally supervenes on the physical. Dualists can accept that thesis, because dualists can maintain that there are fundamental psychophysical laws (McLaughlin 1992, Chalmers 1996). While dualists think that zombies are metaphysically possible, they need not hold that zombies are nomologically possible (recall  Section 3.1).  Physicalists, of course, do not think that zombies are possible at all. Capturing physicalism therefore requires a supervenience thesis that holds with full-blown metaphysical necessity.