Suppose that, like me, one is inclined to believe that type-type identity theory is true. This will mean that the mental state type pain will be identical to some brain state. I have argued that we can class the brain into two kinds of state, brain states (synchronous neural firing in the same frequency) and states of the brain(chemical neuro-modular states). According to such a view mental states will be identical to one or the other (or a combination) of these two kinds of states. In my opinion, a mental state like belief will most likely turn out to be some state of (some part) of the brain against which there will be a certain synchronous pattern of firing. I haven’t argued for this, but it fits nicely with my view that the propositional attitudes consist in a qualitative mental attitude held towards some representational content. At any rate, this is neither here nor there. The question at hand is ‘is such a theory reductive?’
In one sense it is and in another sense it is not. So, in the ontological sense it is NOT a reductive theory. It can’t be. What it says is that there is only ONE thing there, the brain and its various states, and you cannot reduce something to itself! There are not two things, mental states and brain states; there is just one thing (if the identity theory is true). Consider some parallel examples. The musical note named ‘B flat’ and the note named ‘A sharp’ are the same note (ignore the problem of temperament, if you know what it is). There are not two notes here, though you may see some scales written with A sharp and others written with B flat they each tell you to play the same note. In telling you that I did not (ontologically) reduce B flat to A sharp or vice verse. It is useful for us to treat these notes as distinct even though we know that they are not. So too, the type-type identity theory is not an ontologically reductive theory.
In another sense, though, it clearly might be a reductive theory. This is the sense in which we reduce one theory to another theory. Traditionally we do this by positing (theoretical) identities that hold between the terms of one theory and the terms of the other theory. This will allow us to, in effect, deduce the reduced theory from the reducing theory (with the help of the identities). The identity theory has certainly been held in the form, but the reduction here is explanatory not ontological. At the end of a reduction like this we are not left with fewer things in the world, we are left with fewer theories about the world. To explanatorily reduce pain to brain states is to link the terms in our folk psychological/psychological theories to terms in our neuroscientific/physical theories of the world. Some identity theoriests have been reductive in this sense, others have not.
Now, the debate between the dualist and the materialist is clearly a debate about ontology. The dualist claims that there is more stuff in the world than the physical stuff. What this means is that the debate between the dualist and the materialist is NOT a debate about reduction in any sense. To assume that it is a debate about ontological reduction is to beg the question against the materialist, for it is to assume that mental phenomena are non physical from the get go. The fact that there can be coherent identity theories that are not explanatorily reductive (Davidson’s is one example of this kind of view) shows that the debate cannot be about explanatory reduction.
So the debate between the dualist and the materialist is in no way a debate about reduction.