According to the two-dimensional argument against materialism, developed by David Chalmers, the conceivability of zombies entails primary possibility, and the primary possibility of zombies entails further secondary possibility. I argue that the move from the conceivability to primary possibility of zombies is unjustified. Zombies are primarily impossible despite being conceivable if the corresponding phenomenal and microphysical concepts have coinciding primary intensions (refer to the same properties in all possible worlds considered as actual) despite being distinct concepts. But there is no good reason to think that phenomenal and microphysical concepts cannot have coinciding primary intensions despite being distinct concepts. As I argue, this conclusion follows from reflection on special cognitive features of phenomenal concepts.
In the paper, I discuss Robert Kirk’s attempt to refute the zombie argument against materialism by demonstrating, “in a way that is intuitively appealing as well as cogent”, that the idea of phenomenal zombies involves incoherence. Kirk’s argues that if one admits that a world of zombies z is conceivable, one should also admit the conceivability of a certain transformation from such a world to a world z* that satisfies a description D, and it is arguable that D is incoherent. From which, Kirk suggests, it follows that the idea of zombies is incoherent. I argue that Kirk’s argument has several minor deficiencies and two major flaws. First, he takes for granted that cognitive mental states are physical (cognitive physicalism), although a zombist is free to—and would better—reject this view. Second, he confuses elements of different scenarios of transformation, none of which results in the incoherent description D.