Conceivably possible zombies
Does the conceivability of zombies threaten type-A materialism, the claim that all mental truths are a priori entailed by the physical truths?
We can imagine beings exactly like us in all physical respects, but lacking consciousness. But this doesn't threaten type-A materialism (as I mentioned here). After all, it isn't a priori that materialism is true. It could have turned out that ectoplasmic states, rather than brain states, occupy the causal roles that, by analytic necessity, belong to mental states. Suppose it turned out that way. Then duplicating only our physical constitution would result in a being that is physically just like us, but lacking consciousness. So by type-A materialist lights, it is conceivable that things are such that there are beings physically just like us without consciousness.
The same holds for the conceivability of a consciousness-free world that is a complete physical duplicate of the actual world: type-A materialism can accept that.
Next, let P be the conjunction of all physical truths, and Q a mental truth, say, "there are conscious beings". Type-A materialism claims that "if P then Q" is a priori. But can't we imagine a world where P is true and Q false (no matter what exactly P says)? Again, type-A materialism can allow for that: even though P is true, it certainly isn't a priori. It could have turned out to be false. It could have turned out that the consciousness role is played by ectoplasmic property E. Then if "consciousness" is a rigid designator of whatever plays the consciousness role, a world where P is true but there's no E will be a world where P is true but Q false. So it is conceivable that things are such that there is a world where P is true and Q false.
(Compare the conceivability of a world where the watery stuff is H2O and yet there is no water: it is conceivable that water turns out to be XYZ, and in this case a counterfactual world where the watery stuff is H2O will be a world without water, just as, if water is H2O, a counterfactual world where the watery stuff is XYZ is a world without water. It is inconceivable, but conceivably possible that the watery stuff is H2O and yet there is no water.)
What the type-A materialist must reject, and what Dave Chalmers uses as premise in his zombie argument, is the conceivability of P and not-Q itself, not merely the conceivability of a world with P and not-Q, nor the conceivability of a world physically like ours but without consciousness.
So can we imagine that P is actually true while Q is false, in the way we can imagine that water is actually XYZ? To me at least, that's far from obvious. The "not-Q" bit alone is quite hard: could it turn out that nobody is, or ever was, conscious, including myself? Not sure. I guess there's no possible discovery or experience that could convince me of that.
Now Dave has an argument to back up his premise: P only gives us causal/structural information about the world, but any amount of that is a priori compatible with the absence of consciousness. In other words, the physical truths do not a priori entail the mental truths. In other words, type-A materialism is false. That's ok as far as it goes, but if one expected an argument against type-A materialism based on some facts about imaginability or conceivability, one obviously doesn't get one from here.