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alex_zag_al comments on A Limited But Better Than Nothing Way To Assign Probabilities to Statements of Logic, Arithmetic, etc. - Less Wrong Discussion
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Comments (16)
Yeah, this makes sense.
Does this apply to Boolean logic to, in addition to deductions using the axioms of the system?
The archetype I've got in my head is Jaynes's derivation of P(A or B) = P(A) + P(B) - P(A and B).
The first step is that P(A or B) = P(~(~A and ~B)). So if we're updating on computations rather than facts, what we really have is only P(A or B|C) = P(A|C) + P(B|C) - P(A and B|C), where C is the computation that (A or B) is the same as ~(~A and ~B)).
Does that make sense, or is that a different kind of thing?