What follows is a guest post by a long-standing card-carrying member of the MavPhil commentariat, William the Nominalist. He is eager to hear any thoughtful and pertinent comments you may have.
The distinction between reductionism and eliminativism is widely recognised in the philosophy of mind and the philosophy of science. It also seems to be very clear. Here it is, as explained by William Ramsey.
Ontologically conservative theory change occurs when the entities and posits of the replaced theory are relocated, often with some degree of revision, in the replacing theory. For example, as our theory of light was gradually replaced by our understanding of electro-magnetic radiation, our conception of light was dramatically transformed as we recognized ways in which our old conception was mistaken or incomplete. Nevertheless, at no point did we come to say that there is really no such thing as light. Rather, light was eventually identified with a form of electro-magnetic radiation.
By contrast, our notion of demons did not come to find a new home in contemporary theories of mental disorder. There is nothing in the theories of schizophrenia, Tourette's Syndrome, neuro-pathology or any of the other modern explanations for bizarre behavior, that we can sensibly identify with malevolent spirits with supernatural powers. The notion of a demon is just too far removed from anything we now posit to explain behavior that was once explained by demonology. Consequently, the transition from demonology to modern accounts of this behavior was ontologically radical. We dropped demons from our current ontology, and came to realize that the notion is empty — it refers to nothing real.
But after a moment's reflection, I find it is not very clear at all. Why?
The problem is that pretty much every change of theory involves denying some entity or other. The ether theory of light, which was held until the late nineteenth century, depended on the existence of an ether, a hypothetical material or medium which carries light. So the electromagnetic theory of light requires the rejection of ether, and so is eliminativist with respect to ether (even though it is reductionist about light). More generally, every scientific theory requires unobservable entities postulated in order to explain certain observable phenomena. Since a change in theory typically involves denying the existence of the unobservables of the old theory, and replacing them with new ones, practically any change of scientific theory involves eliminativism of some kind. And so the distinction is meaningless, or at best arbitrary.
You object: surely the rejection of the ether theory does not involve the rejection of light? Yet modern psychology does involve the rejection of demons. I reply: this is an arbitrary case where we lost a name in common use - 'demons', which we could easily have kept. We could still today be referring to schizophrenia as 'demonic possession', while rejecting the assumption that a demon is an external supernatural entity that causes mental illness. After all, we still do not know the cause of schizophrenia - it is just a label for a set of observable symptoms, phenomena. All we know is that it is almost certainly not caused by supernatural intellegent beings.
Consider the case of 'humours'. We still talk about people being in a good or bad humour, about them being sanguine, or melancholy, or phlegmatic. As every historian of science knows, these terms originate in an ancient theory of mind, still held in the nineteenth century, according to which our mental states are affected by four basic substances: blood causing a sanguine temperament, black bile causing melancholy, and so on. The theory has long been rejected. But we continue using the terms. Why? They are good labels for certain easily recognisable behaviour patterns - phenomena - which we have kept. We simply reject the entities ('humours') postulated by the ancient theory. Or consider atoms. These are entities postulated to explain the observable differences in elements, and other phenomena. The word 'atom' comes from the Greek word for 'indivisible'. But in the late nineteenth century, it was discovered that atoms are in fact divisible. Did we drop the term 'atom'? Did we stop believing in atoms? No. We simply dropped the idea - an apparently essential idea deriving from the very definition of the term - that atoms are indivisible. They are useful for characterising physical phenomena in exactly the way that 'good humour' is a good way of characterising psychological phenomena. In the same way, I suggest, we might have held on to the term 'demonic possession', while rejecting the original explanation of its causes, just as we reject explanation of 'humour' in terms of blood and bile, but keep the term.
Note that Ramsey's remark that 'the notion of a demon is just too far removed from anything we now posit to explain behavior that once explained by demonology' equally applies to atoms. The notion of an 'indivisible particle' at the atomic level is too far removed from anything we now posit to explain physical and chemical change. Yet we continue to use the term 'atom'. And actually we do continue to use the term 'demons'. Someone asked me recently why I bothered to write philosophy. There is no reward, and the process is painful. Why do it? I replied 'demons'. He understood.
In summary, the distinction between 'eliminative' and 'reductive' theory change is arbitrary and unreal. Theory change of both types involves the rejection of some entity or another. The examples given to illustrate the distinction are arbitrary ones distinguishing the case of terms being dropped, from the case of their continued use under changed meaning or application. The distinction is at best one of linguistic practice, and refers to nothing real.