I did a long, long post on eliminative materialism once, and now it will never be found again. A search was unsuccessful.

I'll try to recreate it, but I may miss points I made before.
Basically, eliminative materialism is a theoretical stance put forth as an alternative to so-called "common-sense", "ordinary", or "folk psychology" ways of understanding the mind and mental states. (There may very well be eliminativist methods which can be used in order to discuss or understand specific concepts-- in other words, essentially denying the existence of whatever is being discussed or understood-- but that's not what we're talking about here; this is the original theory.) Earlier forms of eliminative materialism were really impossible to tell apart from reductive materialism in most ways, because they posited that mental states were basically reducible to brain states. In the 1970's and 1980's, however, as developed by people like Paul and Patricia Churchland, eliminative materialism became a radically different theoretical outlook. Under this theory, mental states are
not reducible to neurological states, even though they do take place only in the brain (in contrast to what someone like Dennett is actually arguing, so I do have to give him that much.) And no matter how elaborately this is explained, it never really does seem to go beyond this bizarre combination of reductionism and dualism. A number of objections to so-called "common-sense" psychology are certainly brought up, but when examined, they all boil down to the same thing: the theoretical framework which poses our behavior and mental states as being controlled by our beliefs is somehow faulty. "Folk psychology" is classified with "folk physics, folk biology, and folk epidemiology", none of which turned out to accurately represent the natural world. Analogies are repeatedly and regularly drawn between "folk psychology" and beliefs in demons, angels, apparitions of God, etc., complete with clear statements that the psychological and psychiatric community will soon discard all theoretical models related to "folk psychology" just as surely as this outmoded medieval silliness was discarded.