Not in my comfort zone here, but surely you have to allow for probabilities of 0 when building any formal mathematical system. P(A|~A) has to be 0 or you can’t do algebra. As an agent viewing the system on a meta level, I can’t assign a personal probability of 0 to any proof, but within the system it needs to be allowable.
Not in my comfort zone here, but surely you have to allow for probabilities of 0 when building any formal mathematical system. P(A|~A) has to be 0 or you can’t do algebra. As an agent viewing the system on a meta level, I can’t assign a personal probability of 0 to any proof, but within the system it needs to be allowable.
Much discussion of this generally and this point in particular.
I don’t know that the results there are necessarily correct, but they are certainly relevant.
Thanks for linking those, they are exactly what I were referring to.
How to deal with deductive uncertainty is an open problem.