First, I must admit I'm having trouble formulating this question because I'm somewhat confused about the relationship between these two items (cognition and qualia). Please let me know if I can improve it or if it should be multiple questions.
I was recently reading a textbook (Cognitive Science: An Introduction to the Study of Mind by Jay Friedenberg and Gordon Silverman) on cognitive science. Unsurprisingly, it advocated functionalism. More surprisingly, it flat-out admitted that there isn't a good functionalist account of qualia. (I've heard this objection from John Searle and others but was surprised to hear an advocate of functionalism admit so bluntly that that was a problem).
This strikes me as a rather fatal flaw: is cognition without qualia actually really consciousness? Can you actually separate the two?
On the one hand, you have an experience and awareness of thinking. Who or what, exactly, is having the awareness?
Cognition appears to be able to change and cause qualia; Albert Ellis et al (along with advocates of the Schachter-Singer theory of emotions) have argued (successfully, in my opinion) that your feelings about (and, therefore, your experience of) a particular situation is heavily cognitively mitigated. How can experience be both cognitively mediated and there be an awareness of cognition?
You can also have "subconscious" cognition of sorts, which seems to be a problem for those who say that you can't separate the two.
Is it possible to have consciousness that consists only of cognition (but not qualia)? Does it even make sense to talk about one but not the other?