The following is from William G. Lycan, A PARTICULARLY COMPELLING REFUTATION OF ELIMINATIVE MATERIALISM:
[. . .] I contend that the Eliminativist is refuted by Moore's technique, in just the same way as was the temporal idealist. The argument will now be quite straightforward: Numerous common-sense mental ascriptions, such as that Granny wants a beer and believes there is one under the sofa, are individually more plausible, and always will be more plausible, than are the purely philosophical premises of any argument designed to convince us to the contrary. As Moore saw, purely philosophical assumptions have very weak epistemic credentials and cannot by themselves outweigh simple common-sense facts.
The Eliminativist may protest that her/his case is not purely philosophical, but rests on scientific considerations of cognitive psychology, neuroscience, connectionist modelling, and the like. Indeed, that flaunted feature is what often makes Eliminativism sound so hip. But this is to misunderstand the Moorean argument a third time. Moore would not deny that arguments for Eliminativism contain premises that are endorsed, perhaps simply established, by science. The point is that each argument also contains at least one purely philosophical premise. Make no mistake: In order to reach the staggering conclusion that there has never been a belief, a desire, or any other propositional attitude, any argument for Eliminativism will have to rest on one or more a priori principles connecting scientific truths to negative ontology. And it is terminally unlikely that any such principle could be more credible for me than that Granny wants beer. Come to think of it, I want beer.8. Notice that my Moorean argument is immune to the customary Churchland-Churchland counterblow, a comparison to alchemy, witchcraft, and other folk but false theories. However beloved such theories were to their proponents, they do not qualify as Moorean common sense. To count as Moorean-commonsensical, a belief must be the sort of belief that every normal human being holds every day of her/his life, such as "Here is one hand and here is another" or "I had breakfast before I had lunch" or "The sun is shining." Thus, to address the Conference topic directly: Whatever science can show about the mind, it cannot show that there is none.
Lycan thinks that Moorean arguments refute Bradley and McTaggart and that there is no essential difference between the characteristic claims of the British Idealists and the claims of eliminativists in the philosophy of mind. I believe he is very wrong about that, but that's a different story. The above Moorean argument, however, does in my opinion decisively refute eliminativism in the philosophy of mind. For those of you who protest that no refutation can be so quick and easy, I will ask, Why not? The more preposterous the thesis, the quicker and easier the refutation! Lunacy can and ought to be dispatched laconically. Indeed, the simplicity of Lycan's argument makes it all the stronger. It is a case of simplex sigillum veri. He who maintains what is plainly false ought to be prepared for an unceremoniously facile reply. And please don't call such a reply 'puerile' or 'sophomoric' since the very fact that any boy or sophomore can make it is precisely what makes the objection so powerful.