I'm not an expert in the philosophy of mind, but I did just finish a class that spent a lot of time talking about the Churchlands. I figured I'd give my two cents in case someone might be curious as to weaknesses in their arguments.
The way the Churchlands' approach the mind is through reductive materialism. Basically they argue that the mind is identical to the brain given that brain process A causes mental/internal process B. With that reduction we should either eliminate language for mental experience or root it entirely in the corresponding physical process.
This sort of reduction is more or less a scientific reduction in that it serves an explanatory purpose. However, some philosophers reject the idea that scientific reduction is sufficient for a philosophical reduction which is something along the lines of brain process A completely explaining mental experience B. The problem that a philosophical reduction poses is that of internal experience.
Non-reductionists would argue that no amount of physical data could explain subjective experience. Brain scans can show what happens physiologically when you are happy, but not the 'what it's like to be happy'. Whether or not that's convincing to you is a matter of personal preference.
The bottom line seems to be that there is a major physical aspect to the mind, but also that we feel like we are more than chemical reactions. It is not clear that we can practically get rid of either dualism or materialism.
If you are curious, look at Thomas Nagel, and 'the hard problem of consciousness' by Chalmers.