I recently had an insight about this while taking a shower or something like that: the opaque circuits can get quite good at identifying the saliencies in a situation. For example, oftentimes the key to a solution just pops into my awareness. Other times, the 3 or so keys or clues I need to arrive at a solution just make themselves known to me through some process opaque to me.

These "saliency identification routines" are so reliable that in domains I am expert in, I can even arrive at a high degree of confidence that I have identified all the important considerations on which a decision turns without my having searched deliberately through even a small fraction of the factors and combinations of factors that impinge on the decision.

The observation I just made takes some of the sting out of Vladimir M's pessimistic observations (most of the brain's being opaque to introspection, the opaque parts' not outputting numerical probabilities) because although a typical decision you or I face is impinged on by millions of factors, it usually turns on only 2 or 3.

Of course, you still have to train the opaque circuits (and ensure feedback from reality during training).