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Document comments on Confidence levels inside and outside an argument - Less Wrong
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What should we take for P(X|X) then?
And then what can I put you down for the probability that Bayes' Theorem is actually false? (I mean the theorem itself, not any particular deployment of it in an argument.)
Althoug I'm not sure exactly what to say about it, there's some kind of connection here to Created Already in Motion and The Bedrock of Fairness - in each case you have an infinite regress of asking for a logical axiom justifying the acceptance of a logical axiom justifying the acceptance of a logical axiom, asking for fair treatment of people's ideas of fair treatment of people's ideas of fair treatment, or asking for the probability that a probability of a ratio of probabilities being correct is correct.