I had to look up Cartesian dualism, but I realize it's pretty close to what I believe, in a sense.
I know that chemical reactions in a test tube have no consciousness, and yet deterministic science would have me believe that consciousness arises gradually from a web of similar reactions. It's all well and good for analyzing creatures from an external point of view, but when we turn the spotlight on ourselves I think it's impossible to explain why there is anything "on the inside." "I reflect, therefore I am" seems to add an imperfect wrinkle to the idea of monism, at least in my opinion. I'm not at all supposing any kind of free will here, nor am I saying that the mental and physical are not interconnected, but I can't see how the idea of one's own mind can be explained by simple monism.
Though Descartes was way off base with that pineal gland business...