In this paper, I examine the relationship between physicalism and property dualism in the light of the dialectic between anti-physicalist arguments and physicalist responses. Upon rehearsing the moves of each side, it is hard not to notice that there is a puzzling symmetry between dualist attacks on physicalism and physicalist replies. Each position can be developed in a way to defend itself from attacks from the other position, and it seems that there are neither a priori nor a posteriori grounds to choose between the two. I suggest that the reason for the intractability of the disagreement, perhaps surprisingly, is they are both true: physicalism and dualism are formulated in terms of different conceptual schemes, each involving basic met...