These paragraphs from Ed Feser lay out the case so clearly that I will quote him at length:
Now, Nagel’s point is not that there is something wrong per se with overthrowing common sense in this way (as Galileo, Descartes, Newton, Locke etc. did). It is rather that whatever value this method has, it cannot coherently be applied to the explanation of conscious experience itself. If the reductive method involves ignoring the appearances of a thing and redefining the thing in terms of something other than the appearances, then since our conscious experience of the world just is the way the world appears to us, to ignore the appearances is in this case just to ignore the very phenomenon to be explained rather than to explain it. Consciousness is for this reason necessarily and uniquely resistant to explanation via the same method scientific reductionism applies to everything else. For the application of the method in this case, writes Nagel, “does not take us nearer to the real nature of the phenomenon: it takes us farther away from it.” To treat the appearances as essentially “subjective” or mind-dependent is precisely to make them incapable of explanation in entirely “objective” or mind-independent terms.
Hence “in a sense,” Nagel continues, “the seeds of this objection to the reducibility of experience are already detectable in successful cases of reduction.” As I have put it myself in several places, the reductive method in question is like the method of getting rid of all the dirt in the house by sweeping it under a certain rug. While this is a very effective way of getting rid of the dirt everywhere else, it is not a strategy that could possibly be used to get rid of the dirt under the rug itself. On the contrary, it only makes the problem of getting rid of that dirt even worse. And that is exactly why the mind-body problem as it is understood today essentially came into existence with Galileo, Descartes, and Co. and has remained unsolved to the present day. What these early modern thinkers wanted (for certain practical and political ends) was a completely quantitative, mathematical description of the world. Irreducibly qualitative features -- secondary qualities, final causes, and the like -- since they would not fit this model, were thus essentially defined away as mere projections, “swept under the rug” of the mind as it were. But that only makes the idea of dealing with the mind itself in the same manner even more hopeless. For these early moderns, the mind just is, you might say, the holding tank for everything that doesn’t fit their quantitative method. Naturally, then, that method cannot coherently be applied to the mind itself.
Now the lesson Nagel drew from this in the 1974 article was not that physicalism is false so much as that “physicalism is a position we cannot understand because we do not at present have any conception of how it might be true.” But the early moderns who inaugurated this conceptual revolution tended to draw the stronger conclusion. Indeed, writers like Cudworth and Malebranche saw that the method in question can be used to argue for a kind of mind-body dualism. For if you maintain that color, sound, heat, cold, odor, taste, etc., as common sense understands these features, do not exist in matter, then they do not exist in the brain or body any more than they exist in the material world external to the brain and body. If they do exist in the mind, though, then the mind must not be material. Dualism can hardly be refuted by the reductive method, then, precisely because dualism follows from that method.
Now that conclusion is actually a bit too strong, though the Cudworth/Malebranche style of argument has had defenders down to the present (e.g. Richard Swinburne in The Evolution of the Soul). For one could argue instead, as Berkeley did, that only the qualities we know of in conscious experience are real and the mathematically-redefined material world is a mere fiction -- idealism rather than dualism. Or one could argue, as Russellians do, that the sensory qualities presented to us in conscious experience are what “flesh out” the abstract structure described by physics -- thereby putting something like color, sound, etc. as common sense understands them back into matter after all, but in a way that is very different from the way common sense supposes them to be there. (As David Chalmers suggests, though, this really amounts to a kind of riff on property dualism.) And of course, we Aristotelian-Thomistic philosophers would reject the assumptions that lead to this tangle in the first place, dismissing Cartesianism and materialism alike as riffs on the same fundamental error of treating what are really just physics’ useful mathematical abstractions from concrete material reality as if they were the whole of concrete material reality.
What you cannot coherently be, consistent with the reductive method described, is any sort of reductive materialist, which has been at least historically the standard form of materialism. And this, I would say, is why materialism was so rare in modern philosophy before the late twentieth century. It takes real historical ignorance seriously to think that the scientific revolution somehow supports reductive materialism and that Descartes, Locke, Berkeley, et al. were non-materialists merely because they didn’t have the courage and/or foresight to follow out the implications of that revolution. In fact, they were the ones who were consistently following out those implications, while materialists like Hobbes were the wishful thinkers. Perhaps the proud ignorance of the history of philosophy that some (though by no means all) of the early analytic philosophers exhibited made it possible for materialism widely to come to seem plausible by the 1960s.