The problem with the Mav's analysis can be located here:
Obviously, this won't do. Well, why not just say that the soul does not think, that only the compound thinks? One might say that soul and body are each sub-psychological, and that to have a psyche and psychic activity (thinking), soul and body must work together. Soul and body in synergy give rise to thinking which qualifies the whole man. But this makes hash of substance dualism. For one of the reasons for being a substance dualist in the first place is the conceivability of disembodied thinking. (We'll have to look at Kripke's argument one of these days.) Disembodied thinking is obviously inconceivable if it is a soul-body composite that thinks. Second, if it takes a soul and a body working together to produce thinking, then the soul is not a mind or thinking substance -- which again makes hash of substance dualism.
and followed by here:
In the Summa Contra Gentiles, Book II, chapters 49-51, we find a variety of arguments to the conclusion that the intellect is a subsistent form and so not dependent for its existence on matter. This is not the place to examine these arguments, some of which are defensible. Now since the intellect is that in us which thinks, the same ambiguity we found in Cartesian dualism, as between pure dualism and compound dualism, is to be found in Aquinas. Is it the composite that thinks, or a part of the composite?
Bill conflates the Cartesian thinking substance with the Thomistic intellect. But the the Thomistic intellect is not a thinking substance; the Thomistic intellect is the organ of knowledge, albeit an immaterial one. Like any organ, it only functions (except in extraordinary circumstances) in the context of the human being of which it is an integral part. Just as the eye doesn't see nor does the ear hear unless it does so in its organic role in the human body, neither does the intellect know except in its organic role in the human being - except under extraordinary circumstances. These extraordinary circumstances are when the soul, separated by death from the body, nonetheless comes to know through direct infusion of knowledge by God. In death, the subsistent form of human being still remains in existence, but it is "inert", utterly incapable of independent action detached from the material body of which it is a form, and this includes an activity like thinking.
For the Thomist, there is no immaterial "thinking substance" like there is for the Cartesian. The subject of thinking, in the sense of an active process of reasoning is, for the Thomist, the particular human being, a composite of body and soul. Thinking involves the imagination, among other things, and the imagination is a function of bodily organs. There is no thinking as such after death. But there can be knowing, and a subject of knowing, should God grace a subsistent human intellect with infused knowledge.
Contra Bill's statement that one of the reasons for being a substance dualist is the conceivability of disembodied thinking, the Thomist is not a substance dualist because he is worried about disembodied thinking. He is a substance dualist because he recognizes that knowledge of universals cannot be the function of a material organ (which is the substance of the arguments the Mav cites in the Summa Contra Gentiles). St. Thomas is strictly disciplined in his conclusions from this fact: He has only proven that man must have an immaterial organ to know universals, not that man can think in a disembodied state. In a disembodied state he is a potential knower, but has no way to become an active knower absent the grace of God.
So man, the composite of body and form, is the subject of thinking. Within him, his immaterial intellect is the subject of knowing (universals). When he dies, the composite no longer exists, so there is no longer a subject of thinking. But there remains a subject of knowing.