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.