If we say that (1) I am a thinking being and (2) that thinking beings and souls are the same, then we should also say (3) that I am a soul; and therefore (if we take 'have' in its ordinary sense) we should say (4) that I do not have a soul. ("On the Simplicity of the Soul," Philosophical Perspectives 5, 1991, p. 178)
If this is right, then hylomorphic dualism is untenable as well as any substance-dualist position according to which I am a composite of two substances. If I have a soul, speaking loosely, then I don't have it, speaking strictly, but am identical to it. But why suppose that one either has or is a soul? Why can't one be a brain-body composite? For essentially the same reasons that I gave last time for my not being a soul-body composite.
First an argument to the conclusion that I am not identical to a brain-body composite, then an argument that I am not identical to my brain.
Suppose for reductio 1) that I am a brain-body composite and 2) that the brain is that in me which thinks. (Surely, if a physical part of me thinks, it is not the liver or heart but the brain.) Then 3) I think in virtue of my brain thinking. But 4) my brain is a proper part of me, whence it follows 5) that I think in virtue of the thinking of a proper part of me. Now 6) that which is a proper part of me is numerically distinct from me. Therefore, 7) I think in virtue of the thinking of something numerically distinct from me. But 8) this is absurd. Why? For the reasons given, mutatis mutandis, in the earlier post. Therefore, 9) if the brain is that in me which thinks, then I am identical to my brain.
But could I be identical to my brain? If I am not identical to my brain plus the rest of my body, then I am not identical to my whole brain either, since not every part of my brain is involved in thinking. But the real problem is that it makes little or no sense to suppose that the brain or any part of it is thinking when I am thinking. My brain is no more thinking when I am thinking than my eyes are seeing when I am seeing. (And my eyes are no more seeing when I am seeing than my glasses are.) I see with or by means of my eyes just as I hear with or by means of my ears; but when I see something it is not my eyes that see it. I see it. As Chisholm puts it, "Those physical organs do not do my seeing and hearing for me." (171) The same goes for the brain. If I hope you find this post interesting, then it is I who hope this, not my brain.
I am not denying that the brain is causally necessary for thinking to occur. The point is rather that the brain cannot be the subject of thinking, that in me which thinks. I, the subject of thinking, cannot be identical to my brain. This can be argued Kripke-style:
a. If x = y, then necessarily x = y. (Principle of the Necessity of Identity)
b. If I = my brain, then necessarily I = my brain. (From (a))
c. I can conceive myself existing without my brain existing.
d. What is conceivable is possible.
e. Possibly, I exist but my brain does not. (From (c) and (d))
f. Possibly, I am not identical to my brain. (From (e))
g. I am not identical to my brain. (From (b) and (f) by Modus Tollens)