Does the Conceivability of Zombies Entail Their Possibility?

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.