A zombie world is a world physically just like our world but in which there is no consciousness. Must a type-A materialist deny the conceivability of zombie worlds? No, not quite.
Compare the rather uncontroversial hypothesis that "the HI virus" denotes the (type of) virus responsible for most AIDS infections. Is it conceivable that a world could be biologically just like ours but not contain the HI virus? Yes, for it might turn out that scientists have been wrong all the time and no virus is involved in most AIDS infections. If it turned out this way, our own world would be a world biologically just like ours but not containing the HI virus.
Similarly, a type-A materialist can concede the conceivability of a zombie world. What a type-A materialist must not concede is the conceivability of "there is a zombie world and our world is not a zombie world".
Oddly, this gives the type-A materialist a reason to reject the step from conceivability to possibility in the zombie argument:
- It is conceivable that there is a zombie world.
- It is possible that there is a zombie world.
- Our world is not a zombie world.
- Therefore, materialism is false.
Again, compare the HIV case: It is conceivable that a world is biologically just like ours but does not contain the HI virus. (Because it is conceivable that there actually is no HI virus.) But from this it doesn't follow that there really is such a world. After all, if our world does contain the HI virus, then surely the HI virus is biological, and hence contained in any biological duplicate of our world. So only if our world does not contain the HI virus (which is conceivable) is a world biologically like ours but not containing the HI virus possible (and indeed actual).
So where is the fault in the two-dimensionalist argument from conceivability to possibility? It's in the assumption that the A-intension of "zombie world" coincides with its C-intension. Even if A- and C-intension coincide for all phenomenal and physical terms, it doesn't follow that they coincide for "zombie world". They don't if "zombie world" is defined, as usual, by means of the indexical "a world physically like ours but not containing consciousness": Let w be some world physically unlike ours and not containing consciousness. w is in the A-intension of "zombie-world": if our world turns out to be w, it turns out to be a zombie world. But it is not in the C-intension of "zombie-world", since necessarily, every zombie world is physically like ours, whereas by assumption w is not.
Yes, this is why one should really run the conceivability argument with the conceivability of P&~Q (for the specific P that specifies the actual physical truths) as a premise, rather than the conceivability of "there are zombies". That's the way I always do it when formalizing the argument.