In the video of Quine I posted yesterday he says that it is only a terminological difference whether the physicalist says that they are identifying the mental with the physical or that they are eliminating the physical (“disavowing the mental”). This has never seemed right to me but it is hard to say what is wrong with It seems to me that in one obvious sense of the word ‘reduction’ the identity theory cannot be reductive. The identity theorist holds that there is not the mind and the brain but that there is just the brain. This sounds like it is getting rid of the mind (“there is just the brain”) but it is not. One does not get rid of A# when one finds out that it is just Bb. One does not eliminate water when one discovers that it is H2O. Identity theorists have always been resentful of the talk of ‘reduction’, ‘elimination’, and ‘correlation’. Smart puts it well in his classic paper; “you can not correlate something with itself.” Water is not correlated with H2O it just is H2O. Only if one is already assuming that ‘physical’ and ‘mental’ have different referents will one see the identity as eliminative. Surely there is all the difference in the world between saying that the true nature of the mental is that it does not exist and saying that the true nature of the mental is that it is neural! I mean, right?
On the other hand, Quine is right that at the semantic level the identification of mental and physical would allow us to “disavow” the mental terms in our ultimate theory since wherever we saw one we could replace it with the thing it was identical to (compare: we could eliminate the word “bachelor” from our language if we wanted to since it is really identical to “unmarried male”). In that sense eliminating the mental predicates from our completed theory wouldn’t affect any truth values of statements in the physical theory. This is surely right but the elimination/identification that is going on here is at the level of semantics (or concepts if one likes) not ontology. Now if one adds to this the Quinian thesis that one is ontologically committed to what one’s variables range over one will not be committed to mental entities at the level of particle physics. But this is not an embarrassment for the physicalist! The physicalist denies that the completed micro-physics will have to appeal to mental properties as basic constituents of reality and that is all that Quine has said here. It may still be the case that one is ontologically committed to mental items at a different theoretical level.
Now this way of talking is at odds with John Searle and Ned Block. According to Searle we cannot get an ontological reduction because consciousness essentially has a first-person ontology whereas brains have a third-person ontology but even so we can get what he calls a causal reduction. Now this sounds a lot like property dualism but Searle denies that it is. Block on the other hand argues that we can have a scientific reduction of consciousness (that is, we can find out that its essential property is being physical) but we cannot have an explanatory reduction of consciousness (that is an a priori conceptual reduction of consciousness). For Block identities are at bottom unexplainable which translates into the claim that they cannot be deduced from a completed micro-physics. They have to be postulated on the basis of additional explanatory power.
Glossing over some obvious differences Quine, Searle, Block, and even Chalmers seem to think that if we have an explanatory reduction of consciousness then we have really eliminated consciousness and so they think that (at best) we can give a causal/scientific reduction but that we cannot deduce the qualitative properties from the physical properties. But if we combine the Lewisian-Armstrong style of argument with 2-d semantics we can see how it would be possible to give this kind of explanatory reduction. We start with the correlations between qualitative states and physical states. As Dave noted there are several options at this point one of which is postulating an identity between the qualitative properties and the physical properties but instead of postulating this identity we should be able to deduce that it is true. Real identities are earned not postulated. I think we can do this, or at least see that it is in principle possible.
So the upshot is that on this view there is a difference between reduction and elimination that is more than terminological. When we reduce something we discover what the primary intension picks out in the actual world whereas when we eliminate something we discover that the primary intension doesn’t pick anything out in the actual world. Hence we reduce water to H2O and eliminate phlogiston. The physicalist can be reductive (claiming the the primary intensions pick out brain states at the actual world) but not eliminative (by denying that the primary intensions fail to pick anything out at the actual world) in this sense. But even so this is not reductive in the first sense: everything that was there before we started theorizing is still there after the explanatory reduction.