JoshuaZ comments on Outside the Laboratory - Less Wrong
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They need to have inconsistent attitudes about how they calculate probability, or estimate probabilities by inherently irrational means such as assigning likelyhood based on what hypothesis they want to be true the most and acting like that belief is certain. Empirically, I've met individuals who claim that no amount of evidence would alter some of their beliefs so something like this may be going on. It is however possible that trying to model these beliefs as probabilities implies a degree of rationality that they simply lack. The human mind is not generally a good Bayesian.
It may be a matter of language use--- if I assign something a probability of 1, it means that everything I know now points in that direction, but I leave the possibility open that I might come to know more.
I think my underlying premise is "no evidence could ever convince me otherwise" is so ridiculous that it doesn't need to be included in the schema.