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hairyfigment comments on Applications of logical uncertainty - Less Wrong
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If you automatically assign the axioms an actually unobtainable certainty, you don't get the rational degree of belief in every proposition, as the set of "propositions" includes those not conditioned on the axioms.
Hmm? If these are physically or empirically meaningful axioms, we can apply regular probability to them. Now, the laws of logic and probability themselves might pose more of a problem. I may worry about that once I can conceive of them being false.