ksvanhorn comments on 0 And 1 Are Not Probabilities - Less Wrong
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For any state of information X, we have P(A or not A | X) = 1 and P(A and not A | X) = 0. We have to have 0 and 1 as probabilities for probability theory even to work. I think you're taking a reasonable idea -- that P(A | X) should be neither 0 nor 1 when A is a statement about the concrete physical world -- and trying to apply it beyond its applicable domain.