Two of my favorite bloggers, Richard Chapell and Eliezer Yudkowsky, recently duked it out over reductionism and zombies. (The zombie issue in a nutshell: supposedly, it's just obvious that we could have people physically identical to us but not conscious, so dualism is true). Richard started out with Arguing with Eliezer, part I and Arguing with Eliezer, part II, then Zombie Rationality. Eliezer carried his part of the discussion in Hands vs. Fingers, Zombies! Zombies?, Zombie Responses, and The Generalized Anti-Zombie Principle. The discussion mostly took place at Eliezer's, and Richard complained his opponents there had nothing but "mere ridicule and sloganeering."
In spite of agreeing with Richard about reductionism, in the narrow disputes that got raised, I'm with Eliezer. For one, the idea of conceivability Richard appealed to is weird--it's a sense which entails possibility, but if you take that use of the term, we have no defense against the worry that we often think we're conceiving of something when we are not, in fact, doing so. Yes, I realize an awful lot of philosophers have used "conceivability" in Richard's way, but just because philosophers do it doesn't mean its a good idea.
Richard's other line was to ask for a proof that zombies are impossible. But this is silly. A useful parallel case is that of "vital-force zombies," imaginary people physically identical to us only not alive. In the 19th century such an idea might have seemed possible, but the inability to provide some conceptual disproof didn't make vitalism right. Really, 'nuff said.
If you want to argue for dualism, appeals to esoteric possibilities don't do much good. The way that makes sense, I think, is to appeal to our direct acquaintance with consciousness, and point out that we have there something just not covered in our current theories of physics.