What do you think about people like Chalmers who obstinately refuse even the idea of neural correlates of conscious is even a thing, preferring to just assert that the hard problem is hard, full stop?
More seriously, my reading of Chalmers is not that neural correlates of consciousness don't exist per se, it's rather that
1. So-called "access consciousness" (i.e. consciousness in the sense of "I am conscious of X") is distinct from phenomenological consciousness (contrary to what Dennett thinks).
2. Further, access consciousness has very little to do with phenomenological consciousness, to the point that calling it "consciousness" is a misnomer.
3. Therefore, neural correlates of access consciousness will never give us insight into phenomenology.
I think my position is that of most people in the field. I'm agnostic. Or more exactly, damned if I know what I think about that. I find it hard to believe -- as Dennett claims -- that once we've explained everything about neural correlates of (access) consciousness, that there will be nothing left to explain. I also find it hard to believe Chalmers' story that neural correlates have nothing to teach us about about phenomenology. But my arguments ultimately appeal to an interpretation of scientific data in the context of my own experience, so it's really a gut feeling of "neither seems quite right".
Given this, my stance is basically "I don't research hard problems; I research easy problems". Access consciousness -- whatever that is -- is interesting and useful to study. I choose that.
(N.B.: most of this should be written in the past tense, as I have now moved to a different field!)
Terminology doesn't change anything, assume everything is about phenomenological consciousness. According to Chalmers brain doesn't differentiate between access consciousness and phenomenological consciousness, because the zombie concludes that he has phenomenological consciousness based on analysis of access consciousness.
It's been a while, but yes, that does ring a bell.
Ok, so you have a "Zombie" that has all the behaviors and physiological processes associated with access, but no qualia.
In principle, we might learn everything there is to know about access and still have no insight into qualia. Have I summarized that correctly?
Assuming so, my position with respect to "why study neural correlates" is:
1. Access (whatever that is), is still interesting and worth studying, if only to find out what it actually is, and even if it's "just" working memory or attention.
2. At the very least, we will have succeeded in distinguishing access from phenomenology. Our common human understanding of (phenomenal) consciousness will have advanced insofar as we will understand it to exclude access and all its second-order effects.
3. It remains to be proven that there is something more to explain than "just" the physiology and intentionality of brain processes with respect to access. If there is, Chalmers might be right. If not, the point goes to Dennett -- and think about the implications!