A man with a conviction is a hard man to change.

From When Prophecy Fails -- A Social and Psychological Study of a Modern Group That Predicted the Destruction of the World by Leon Festinger, Henry Riecken, and Stanley Schachter. Festinger's was a ground level investigation of a cult interpreted through a new theory about the psychology of belief and knowledge. These are the opening paragraphs of the book.

A man with a conviction is a hard man to change. Tell him you disagree and he turns away. Show him facts or figures and he questions your sources. Appeal to logic and he fails to see your point.

We have all experienced the futility of trying to change a strong conviction, especially if the convinced person has some investment in his belief. We are familiar with the variety of ingenious defenses with which people protect their convictions, managing to keep them unscathed through the most devastating attacks.

But man's resourcefulness goes beyond simply protecting a belief. Suppose an individual believes something with his whole heart; suppose further that he has a commitment to this belief, that he has taken irrevocable actions because of it; finally, suppose that he is presented with evidence, unequivocal and undeniable evidence, that his belief is wrong: what will happen? The individual will frequently emerge, not only unshaken, but even more convinced of the truth of his beliefs than ever before. Indeed, he may even show a new fervor about convincing and converting other people to his view.

How and why does such a response to contradictory evidence come about? This is the question on which this book focuses. We hope that by the end of the volume, we will have provided an adequate answer to the question, an answer documented by data.

Let us begin by stating the conditions under which we would expect to observe increased fervor following the disconfirmation of a belief. There are five such conditions.

1. A belief must be held with deep conviction and it must have some relevance to action, that is, to what the believer does or how he behaves.
2. The person holding the belief must have committed himself to it; that is, for the sake of his belief, he must have taken some important action that is difficult to undo. In general, the more important such actions are, and the more difficult they are to undo, the greater is the individual's commitment to the belief.
3. The belief must be sufficiently specific and sufficiently concerned with the real world so that events may unequivocally refute the belief.
4. Such undeniable disconfirmatory evidence must occur and must be recognized by the individual holding the belief.
The first two of these conditions specify the circumstances that will make the belief resistant to change. The third and fourth conditions together, on the other hand, point to factors that would exert powerful pressure on a believer to discard his belief. It is, of course, possible that an individual, even though deeply convinced of a belief, may discard it in the face of unequivocal disconfirmation. We must therefore, state a fifth condition specifying the circumstances under which the belief will be discarded and those under which it will be maintained with new fervor.
5. The individual believer must have social support. It is unlikely that one isolated believer could withstand the kind of disconfirming evidence we have specified. If, however, the believer is a member of a group of convinced persons who can support one another, we would expect the belief to be maintained and the believers to attempt to proselyte or to persuade nonmembers that the belief is correct.

These five conditions specify the circumstances under which increased proselyting would be expected to follow disconfirmation.