Here's the crux of Vallicella's case:
Vallicella appears to me to be offering one, maybe two, arguments here against (token-)identity theory, my unsatisfying default position out of a boatload of unsatisfying alternatives. I'm far from thinking that I can make a great case for identity theory, but I don't think either of Vallicella's arguments make a good case against it, either. Naturally, my assessment depends, in part, on whether I have understood him correctly in the first place, so here's my reconstruction of the arguments I think he makes:Now here is the problem: if the pain sensation is identical to a brain event, then there is no place for the felt painfulness. For the brain event has a third person mode of existence and among the properties of this brain event you will not find anything that has a first person mode of existence. A brain event is purely physical and has only physical properties.
But even if you insist that the phenomenal property of painfulness—the sensory quale—is a property of the brain state, this phenomenal property surely plays no causal role in bringing about the aversive behavior. For it is only the physical aspects of the brain state that play a causal role in bringing about the the other physical states that comprise aversive behavior.
The materialist seems to be no better off than the substance dualist. Both face the problem of interaction since common sense strongly suggests that mind acts on body, and body acts on mind. (Parallelists and occasionalists deny this, but they move quite a distance from common sense.) The problem for the dualist is the problem of bridging the gap between two disjoint ontological categories, while the problem for the materialist is explaining the causal relevance of a pain sensation, say, to other physical events when the very painfulness which accounts for the aversive behavior cannot play any causal role if the pain sensation is identical to a brain state.
Although the materialist avoids the dualists' gap problem, he faces a different problem which is just as bad: the problem of explaining how a brain state can bring about aversive behavior when the property of this brain state that ought to be causally relevant, namely, the phenomenal painfulness of it, cannot be causally relevant.
(MPI) Pain sensations cause aversive behavior.
(MN) If identity theory is true, then pain sensations do not exist.
∴ (AI) Identity theory cannot explain MPI.
Argument 2 (which I'm less sure he makes—more on this anon):
(CI) Pain sensations cause aversive behavior.
(MS) Identity theory renders pain sensations causally superfluous.
∴ (AI) Identity theory cannot explain MPI.
(For reference, my premise labels stand for: MPI = mental-physical interaction, MN = mental nonexistence, MS = mental superfluity, AI = anti-identity.)
First, let's be clear that MN and MS cannot simply be read off of identity theorists' beliefs; that is, they are not propositions which an identity theorist would accept. As Vallicella points out earlier in his post, (token-)identity theory identifies physical and mental tokens with one another. That is not eliminationism—identity theorists accept the existence of both the physical and the mental, as one [but, see update below]. So, identity theorists would reject MN. Identity theorists also believe that physical tokens are causally efficacious. Eo ipso, identity theorists believe that mental tokens are causally efficacious. So, identity theorists would reject MS.
All this means that Vallicella must offer further argument to show that the identity theorist is wrong about MN and MS; and this he does, at least for MN, by using the familiar first-person vs. third-person argument (I forget what it's called in the technical literature):
(FPP) Pain sensations have a first-person mode of existence.
(ETPB) Brain events have only a third-person mode of existence.
∴ (NI) Pain sensations are not identical with brain events.*
(FPP = first-person nature of pain sensations, ETPB = exclusively third-person nature of brain events, NI = non-identity between pain sensations and brain events).
I'm not going to try to assess this argument in it's own right; ETPB certainly doesn't seem obvious to me, but suffice it to say that there's a huge literature on the topic, and I am content remain agnostic for the present. All that I would like to point out with respect to Vallicella is that reliance on this line of argument renders his causal interaction argument superfluous. NI is inconsistent with identity theory, so, if the first-person vs. third-person argument works, it demonstrates that identity theory is false. No further work is done by arguing, effectively, that because a theory is false, it cannot explain certain kinds of causal interactions.
How about MS? I see no further argument for it, so I presume that, if Vallicella accepts it at all, he must offer the same NI argument for it, which would make it equally superfluous. However, I'm not sure Vallicella accepts MS; I can read him as having already dismissed identity theory by the time he gets to the second quoted paragraph, and instead turning his attention to a form of property dualism, in which physical objects possess nonphysical properties which are not identical to physical properties. If that is Vallicella's target at that point, then I quite agree with his conclusion; I think the causal closure of physics is sufficient to justify our dismissing such metaphysical danglers. All I would emphasize for the reader is that the argument really would have no bearing on identity theory: identity theory is not property dualism (indeed, the latter is not even materialistic). In identity theory, mental properties are not nonphysical at all—they are physical. They are identical to, and therefore must have exactly the same causal power as, particular physical properties. Is such a contention plausible? Well, it gets us right back to arguments about things such as ETPB, where the literature is crushing and the answers not obvious to me. (Not that Vallicella is oblivious to the literature—check out his archived posts on mind. By the time I get through all of them, I may be a dualist.)
To sum, it would have been very interesting to show that identity theory, like dualism, has a causal interaction problem even if true—that's why I got excited when I saw the title of Vallicella's post—but that's not what Vallicella has shown. All he has shown is that identity theory has a causal interaction problem if it is false, which we already knew. Interaction truly is a fundamental (though not fatal) problem for dualism; it is not a fundamental problem for identity theory, whatever other problems the theory might suffer from.
* * *
OK, but one more thing: identity theory does have a causal interaction problem. At its root, all causal interaction is mysterious. I'm with Hume: I don't understand why things in the same ontological category can interact with one another. It's not that I think they shouldn't be able to, but search me if I can explain why they should. It's just one of those things that feels natural, because it's what we see.
At the level at which philosophy of mind is pursued (the level at which it is, for instance, appropriate to use Occam's razor), this argument is of no interest, but it goes to show you (or at least me) that when one pushes deep enough—when one refuses to bracket certain questions and work on an as-if level—then everything becomes deeply, deeply mysterious.
* You may notice that NI is not the same thing as MN, and a non-truth-functional form of MN (I take it to be expressing a subjunctive) would not necessarily follow from NI. That's another way of making my point, and perhaps more rigorous, but I think my way will be easier for most readers to follow.
Update (17:29): Poking around in some of Vallicella's older posts, I see that he does believe that "token-token-identity theory in the philosophy of mind collapses into eliminativism about mental items" (scroll to the last paragraph of the immediately linked post). I'm sure he has an argument for that claim in one of his older posts; I'll link to it when I find it, or when he lets me know where it is. Suffice it to say, again, that if he has a good argument for that claim, it would render further argument about causal interaction superfluous, since no identity theorist (correct me if I'm wrong) would endorse eliminitavism.