Against property dualism

What if you accept irreducibility arguments that defend the claim that mental states are ineliminable and irreducible to physical states. Many philosophers buy these arguments without denying an overall philosophical naturalism. What they accept, instead, is dualism of properties but a monism of substances. At least when I was in graduate school, it seemed to me as if the mainstream position amongst secular philosophers was a non-reductive materialism based on the supervenience of mental states on physical states. There were numerous opposing views about what kind of supervenience relationship had to obtain between mental and physical states.
William Hasker, in his response to me in Philosophia Christi, entitled “What about a Sensible Naturalism,” is talking about just this kind of naturalistic position. He describes a sensible naturalism as “a naturalism that makes a serious effort to accommodate, or at least makes sense of, our ordinary convictions about the mind and its operations—the things we think we all “know” about the mind, when we are not doing philosophy.”
The difficulty here is that the mental and the physical are defined in such a way as to exclude one another. So reductionist accounts of the mental have a tendency to be either fully or partly eliminativist. We have to back off from what we thought were out common-sense conceptions of what the mental is in order to accept a reduction to the physical. To accept reductionist accounts of the mental, for Hasker, is not to be a sensible naturalist.
There is, it seems to me, a paradoxical difficulty for naturalistic philosophies of mind. If you can reduce the mental to the physical, then the issue of mental causation, I think, becomes easier for the naturalist. If the naturalist is inclined in a reductionist/eliminativist direction, then the argument from propositional content becomes the main focus. However, many naturalist philosophers do not think reductionism is plausible. But if the naturalist buys a nonreductive materialism, which means that we accept a dualism of properties, then the argument from mental causation becomes the key argument.

Edward Feser presents the case against the non-reductivist view on mental causation as follows:
…Property dualism seems if anything to have a worse problem with epiphenomenalism than does Cartesian dualism. Recall that the Cartesian dualist who opts for epiphenomenalism seems to be committed to the absurd consequence that we cannot so much as talk about out mental states, because if epiphenomenalism is true, those mental states have no effect at all on our bodies, including our larynxes, tongues and lips. But as Daniel Dennett has pointed out, the property dualist seems committed to something even more absurd: the conclusion that we cannot even think about our mental states, or at least about our qualia! For if your beliefs—including your belief that you have qualia—are physical states of your brain, and qualia can have no effects on anything physical, then whether you have qualia has nothing to do with whether you believe that you have them. The experience of pain you have in your back has absolutely no connection to your belief that you have an experience of pain in your back; for, being incapable of having any causal influence on the physical world, it cannot be what caused you to have beliefs about it.

I had originally presented this on DI, so I am linking back to that, since it is already getting comments over there.