Finally, the conclusion of the discussion I began so long ago! Feser begins chapter 6 by mocking the Churchlands. It is obvious from recent psychological research that there are mistakes and confusions in people's common understanding of notions like "belief" and "desire." For that matter, this has long been obvious to those who have tried to understand those notions; many philosophers (Spinoza, Hume, and Nietzsche come to mind) anticipated some of the discoveries of the recent psychological research. So the serious question is whether "belief" is more like "phlogiston" or "aether" or more like "heat" or "metal." Thinking we know exactly what it refers to and that something exactly like that exists is absurd. The Churchlands, of course, think belief theory is more like phlogiston theory.
Feser makes heavy weather of how hard it is to state their theory. Since I don't myself reject beliefs, I can of course simply talk about what they believe, but as Feser notes, it seems that they shouldn't. I do actually think it's a problem for them that they speak of these successor concepts without providing them; nobody did, or should have, rejected phlogiston chemistry before the rival oxygen theory was proposed. But equally, nobody should have said phlogiston theory couldn't be replaced, and nobody should say that about folk psychological notions either. Patricia Churchland makes a pretty convincing case for the thesis that folk psychology is deeply defective. That doesn't make it clear how much should be revised and how much replaced, much less exactly what revisions and replacements should be made (Paul seems to make more radical claims about those things than Patricia, and to be less careful about citing evidence), but Feser seems to think everything is fine, and that's just absurd.
Perhaps the Churchlands should be taken as speaking about beliefs and desires analogically when they talk about what people think or want. I complained when Feser said that God is "analogically" a person, because that seems to mean that God is a person when Feser needs God to have human-like features and not when those features seem to be problematic, but obviously the notion that something could be analogically like something else is not inherently defective. I can't see how there would be any fatal confusion were Patricia Churchland to claim to analogically know her own mind better than Feser analogically knows it.
Certainly Feser doesn't provide anything like a decisive argument. He is tacky enough to make jokes about the Churchlands' pillow talk; I will not speculate on what it sounds like when Thomists talk to their lovers in private, but thinking of my own case, I certainly hope that it is not a strike against any philosopher that what they say to their lovers in private seems rather silly.
Feser also makes much of what he takes to be the a priori character of his own theories about mind and intentionality, suggesting that we should take the Churchlands no more seriously than we should take someone who says we should expect a new form of addition to be discovered according to which 2+2=23. As usual, I think the mathematics analogies are misguided on many levels, but even if intentionality were the same kind of a priori matter as addition, what would Aristotle or Aquinas have thought of the claim that there's a number n such that n is greater than 1 and n+n=n? No doubt that whatever any future oddballs who proposed such a thing would be doing would not be arithmetic. And yet I doubt that's Feser's own opinion of Cantor (it would be odd that he expresses such admiration for Frege if he rejects modern mathematical ideas like cardinal numbers).
Of course, most modern materialists are not eliminativists, as Feser grants. Before talking about his specific arguments, I do want to mention one general issue which seems to me to be at work in some of his complaints. It is logically impossible to theorize about everything, because the theorizer is part of everything, and including the theorizer among the objects of the theory generates self-reference paradoxes that should be familiar to anyone who knows anything about modern philosophy from Frege onward. Having a total theory of everything requires being outside of everything; it requires the impossible "view from nowhere" in Nagel's memorable phrase. This fact may generate theological problems (it may make divine omniscience incoherent), but it is no problem for materialism. There is no principled obstacle to generating a complete material theory of anyone except myself, or to them generating a complete material theory of me (it's puzzling that I couldn't use their complete material theory of me as a complete material theory of myself, but a little reflection on the nature of the problem will show that puzzling or not, that's just how it must work). A number of the problems Feser tries to raise for materialism seem to involve this required distinction between the thinker and the object of thought, but as indicated these are not actually problems (just facts), and if they were problems, Feser's view wouldn't solve them; the problem isn't that the thinker must be distinct from any material facts thought about, but that the thinker must be distinct from any facts at all that are thought about. Souls and final causes don't make any difference to that issue.
It seems to me that this is part of the confusion involved when Feser makes heavy weather of the fact that a symbol must be interpreted by a thinker as representing in order to represent. He's right to insist that how I as a thinker manage to do that interpreting itself involves me representing things, and isn't something that I can fully account for in terms outside of my thoughts. But he fails to recognize that the reason is that it's something I can't fully account for at all (and it is something someone else could fully account for materialistically).
Still, Feser is right about another point; teleology is necessary to understanding thought. And he briefly mentions the most popular way to explain teleology materialistically; use evolutionary accounts, as Millikan does in Language, Thought and Other Biological Categories. Feser is not impressed. He cites Fodor as saying we can make a shrewd guess as to the functions of many biological features without knowing their evolutionary history. It is hard to see how anyone could take that seriously as an objection to the theory; it is as if someone objected to the theory that gold is the element with atomic number 79 on the basis that one can make a shrewd guess as to whether some substance is gold without counting the protons in any of the atoms the substance is composed of.
Feser also claims that on Millikan's story the first instance of some trait, or the traits of swampman, will not have functions. For the first instance of a trait, there seems no reason not to say that it has a function based on how selection will operate on it in the future. As for swampman, I think in that case it is less clear that swampman's organs do have functions (does Feser also think swampman has beliefs and desires? If so, I wish he'd indicated that he holds that highly controversial view!) But if we must say they do have functions, that still isn't really a problem. It would hardly constitutes abandonment of Millikan's principles to say the functions are determined by counterfactuals about how selection would operate on the traits of those organs in some suitable range of circumstances.
Still, Feser says the deeper problem is that the teleology in Millikan's theory isn't real teleology. I think the confusion I mentioned above is at work here; part of the reason he's suspicious of it is that it doesn't provide the view from nowhere, but his view doesn't do that either. At least, I can't see anything else that final causes are needed for that Millikan's "Normal functions" can't do perfectly well. And it's clear that Dennett is talking about what Millikan is talking about. The only sense I can make of Feser's complaints against Dennett in this section is that he thinks Dennett needs some "real" teleology which goes beyond that. And the only sense in which that seems remotely true is the sense in which Dennett as thinker must be outside the kinds of things he's thinking about even when he's thinking about thought. But that doesn't mean that some special kind of teleology other than Millikan's must be going on in Dennett; any different senses of teleology wouldn't have anything to do with the real sense in which a thinker must be distinct from the objects of thought.
Feser concludes with a discussion of the "new essentialists" and various advocates of non-Humean understandings of causation and scientific theories generally. He oversimplifies the Humean view, as usual, and I actually think that if it isn't oversimplified the Humean approach is superior to the alternatives, but as he says this "new essentialism" is extremely popular, so he would have a lot of allies if it were as closely allied to his position as he believes. But it isn't, for reasons I've already discussed from various angles. Feser completely blurs the line between the minimal thesis that things have properties which determine their behaviors in some way (a thesis even Humeans accept) and the very substantial thesis that pretty much the essences Aristotle believed in are present in things and produce their behavior in pretty much the way Aristotle described them as doing. It helps him blur this distinction that Aristotle was often extremely vague in his descriptions, but the details of Feser's philosophy depend on his getting very specific about them at times (as I've discussed extensively for the specific case of the form or essence of humanity).
The new essentialists are somewhere between the minimal thesis and the very substantial thesis, but they reject the very substantial thesis for the same reason the Humeans do; it's obviously false. And so perhaps there are powers in the world of the kind Armstrong and Cartwright and others believe in; there's no evidence against that thesis, at least. Or perhaps there are powers of kinds nobody has thought of; certainly there is no evidence conclusively showing there couldn't be unimagined powers. But the potentials Aristotle described? Unless we strip out all the details (in which case Feser can't make his claims about morality, God, etc.), there is plenty of evidence against those.