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Anatoly_Vorobey comments on Logical Uncertainty as Probability - Less Wrong
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In your scheme you have P=1/2 for anything nontrivial and its negation that's not already in X. It just so happens that this looks reasonable in case of the oddity of a digit of pi, but that's merely a coincidence (e.g. take A="a millionth digit of pi is 3" rather than "...odd").
No, a statement and its negation are distinguishable, unless indeed you maliciously hide them under quantifiers and throw away the intermediate proof steps.