Are you agreeing, then, that X=mind and Y=brain chunks? That's surprising to me. I would have thought that X was all of the relevant behaviors -- walking, talking, breathing, playing games, writing on internet forums, ... I didn't think you would want an identity thesis between Mind and Some Class of Behaviors. Maybe I'm thinking about this wrong, but I thought for soul-ish theories, the mind just was the soul. And then you get a causal picture (for interactionists, anyway) that looks like Soul --> Brain --> Intelligent Behaviors.
No plot spoilers here, just wanted to flag a bit of poor reasoning that shows up in Chapter 39:
This is a surprisingly common fallacy. Just because X depends on Y, it doesn't follow that X depends on nothing but Y. A phenomenon may involve more than just its most obvious failure point.
To illustrate: Suppose I'm trapped in a box, and my only way to communicate with the outside world is via radio communication. Someone on the other end argues that I don't really exist -- "There's no person beyond the radio receiver, for if there was then there wouldn't be any such thing as damaged radios!" Pretty silly, huh? But people say this kind of thing in defense of physicalism all the time.
(N.B. This is not to defend the existence of souls. It's just to point out that this particular argument against them is invalid.)