 So, supervenience relations can hold with either metaphysical or nomological necessity, and perhaps even with some other kind of necessity. The fact that supervenience comes in different modal strengths is important. Sometimes there is widespread agreement that a certain supervenience relation holds, but dispute over what its modal force is. One important example is the supervenience of the mental on the physical. Just about everyone, even a Cartesian dualist, believes some version of this supervenience claim. But there is vigorous disagreement about whether the supervenience relation holds with metaphysical or merely nomological necessity. Ask yourself—could there be an individual that has no conscious experience at all, despite being physically indiscernible from an individual that is conscious (Kirk 1994; Chalmers 1996)? That is, could there be what philosophers call a ‘zombie’? Because it is widely agreed that the mental nomologically supervenes on the physical, it is widely agreed that zombies are nomologically impossible—that their existence would violate psychophysical laws. But some philosophers (e.g., Chalmers 1996) think that zombies are metaphysically possible. This remains a matter of lively dispute, and resolving it requires addressing some hard questions about the relationship between conceivability and metaphysical possibility. Suffice it to note that the dispute is precisely over the modal force of the ‘cannot’ in “there cannot be a mental difference without a physical difference.” (For discussions of the relationship between conceivability and metaphysical possibility see, e.g., the essays in Gendler and Hawthorne 2002. For a discussion of physicalism, see  Section 5.4  and the separate entry on  physicalism.)