It is useful to keep in mind the difference between public knowledge and personal knowledge.
Public knowledge is that which can at least in principle be reliably shared by all open-minded people. The best filter our species has yet devised for obtaining reliable, consensus knowledge of the world is science: mathematical reasoning, quantitative experiment, double-blind tests, peer review, Ockham's razor, and all the other apparatus of the scientific method. The result isn't Truth with a capital T, but the very existence of modern, technological civilization attests to the effectiveness of the method.
Personal knowledge can be just as firmly held to be true. For example, I know with certainty how I feel about my wife, but I wouldn't expect another person to credit my feelings with the same assumption of veracity as he would give to nuclear fusion at the center of the sun. I might give expression to my feelings for my wife through poetry, music or art, but the truth I thereby share becomes a public part of the work itself, separate from what I feel in my heart.
Public knowledge makes common discourse possible. If I say the Earth is four billion years old and another person says the Earth is four thousand years old we can refer our disagreement to the filter which is the global scientific community. (Whether we are willing to accept arbitration by the scientific community is another matter.)
Personal knowledge belongs to me alone, and I have no right to assume that others must share it. Much of the world's mischief derives from the belief that others should embrace what I personally hold to be true. It is a striking feature of the scientific method that a global consensus has been achieved without resorting to violent persuasion. If physicists everywhere believe in quarks, it is not because anyone has resorted to thumbscrews.
In a civilized society we rely on secure public knowledge to provide cohesiveness and stability. Within that commonwealth of shared belief we live out our lives in a life-enhancing (or life-depressing) milieu of personal knowledge.
(Tomorrow: Finding the balance.)