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fsopho comments on two puzzles on rationality of defeat - Less Wrong Discussion
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Well, puzzle 2 is a puzzle with a case of knowledge: I know (T). Changing to probabilities does not solve the problem, only changes it!
But that's the thing: you don't "know" (T). You have a certain degree of belief, which is represented by a real number between 1 and 0, that (T) is true. You can then update this degree of belief based on (RM) and (TM).