Abstract
This paper offers a qualified defense of Terry Horgan’s view of brute, inexplicable supervenience theses as physically unacceptable—as having no place in physicalist metaphysics—and his corresponding emphasis on the importance of “superdupervenience”, metaphysical supervenience that can be explained in a “materialistically acceptable” way. I argue, in response to Tom Polger, that it may be possible to ground the physical unacceptability of brute supervenience in its relation physically unacceptable properties supervening on physical properties; moreover, I argue that Horgan’s emphasis on the need for superdupervenience cannot be rejected as unreasonably demanding for the reasons that Polger offers. I furthermore respond to Jessica Wilson’s reasons for thinking that superdupervenience is neither necessary nor sufficient for physical acceptability. Reflection on these topics helps to bring out several issues about the role of supervenience in physicalist metaphysics and ultimately a problem that any supervenience-based approach to physicalism may face.