The message at the heart of this book is that the feelings of knowing, correctness, conviction, and certainty aren't deliberate conclusions and conscious chohices. They are mental sensations that happen to us.
Burton's model of conscious thought reminds me of an arcade game in which there are 10 toy horses lined up to race. Each human contestant has a squirt gun and and a target to shoot at. When a bell rings, you try to squirt your target. The closer to the center of the target you hit, the faster your horse goes. The best shooter will win the race.
For Burton, a thought or belief is like one of the horses in the game. The squirt gun is the various emotions and sensations that move that thought into consciousness.
The thoughts that win the horse race in an individual's head depend in part on how the individual's squirt-guns are configured. If certain squirt guns are stronger than others, that affects the likelihood that a particular belief will be held by that person.
One point is that the statement "I am certain of X" is nothing more than the statement "I believe X" with an emotional kicker. He suggests that we try to drop the emotional kicker.
My guess is that the book is somewhat of a catch-22. The lower the likelihood that one reads it, the greater would be its value to that person.