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Coscott comments on An Attempt at Logical Uncertainty - Less Wrong Discussion
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I do not think it is a measure. If A B and C are all unprovable, undisprovable, but provably disjoint sentences, then your system cannot assign probability of A or B or C equal to P(A)+P(B)+P(C) because that must be 3/2.
I think that the thing that makes logical uncertainty hard is the fact that you cant just talk about probability measures (on models) because by definition a probability measure on models must assign probability 1 to all provable sentences.
That's a good point, and I concede that you are right. At the moment, it's more of a "probability assignment", as you said, rather than a probability measure. More work needs to be done on the subject, and hopefully we will progress along these lines at the MIRIx workshop.