Feelings of absolute certainty and utter conviction are not rational deliberate conclusions; they are involuntary mental sensations generated by the brain. Like other powerful mental states such as love, anger and fear, they are extraordinarily difficult to dislodge through rational arguments. Just as it's nearly impossible to reason with someone who's enraged and combative, refuting or diminishing one's sense of certainty is extraordinarily difficult. Certainty is neither created by nor dispelled by reason.
As in his book, Burton has suggestions for how we can sort out some useful facts from our bundle of impressions, prejudices and preconceptions.