In the same Discourse on Method, Descartes makes assumptions about how the human body works and these assumptions are completely wrong. Interesting read just to see how someone perfectly logical can be completely wrong at the same time.
Sad thing is that much of the literature in philosophy of mind will discard dualism solely on the fact that past attempts to explain dualism have failed. And more over, some have just failed to convince the opposite side, which is open for subjectivity.