Bloomfield, P. (2005). “Let’s Be Realistic About Serious Metaphysics.” Synthese 144: 69-90.
He argues that the only sense of possibility relevant to serious metaphysics (i.e., relevant to the metaphysics of the actual world) is how things may be given how the actual world is. (This notion of possibility-given-the-way-the-actual-world-is is supposed to be related to Chalmers’ secondary intensions, or Jackson’s C-intensions).
Bloomfield maintains that there are no zombies at the actual world and that zombies are “actually impossible” (p. 78; this means zombies are impossible given the way the actual world is), but he doesn’t explain why he believes so.
Bloomfield says he is attacking the method or machinery employed by Chalmers and Jackson, not the way they employ it. He attacks the view that primary intensions are primary and secondary intensions are secondary, and argues that it’s the other way around. But without a clear discussion of what being primary or secondary means, and what follows from it, it’s not clear what difference this makes.
Bloomfield accepts the possibility of alleged “synthetic a priori truths” but never discusses how you are supposed to discover what is possible given the way the world is. How do you discover these synthetic a priori truths, if not by the method offered by Chalmers and Jackson?
What Bloomfield really seems to dislike is the zombie conceivability argument. At bottom, his substantive point is the good old point that conceivability does not entail possibility. I agree, but it will take more than this to score points against Chalmers and Jackson’s sophisticated view.
Furthermore, conceivability arguments can be run without the distinction between primary and secondary intensions (as Kripke himself did; notice that Bloomfield occasionally cites Kripke with approval). In other words, the issue of the merits of Chalmers and Jackson’s two-dimensional semantics is largely orthogonal to the issue of the merits of conceivability arguments.