Nice! Basically, it looks like you construct a theory by assembling an infinite quantity of what the prior takes as evidence about s, so that either the prior or the posterior has to take the most extreme odds on s. It’s pretty intuitive in that light, and so I’m not dismayed that the “0 and 1 are not probabilities” property can’t hold when conditioned on arbitrary theories.
Important typo: P assigns conditional probability 1 to some statement that cannot be proven.
Nice! Basically, it looks like you construct a theory by assembling an infinite quantity of what the prior takes as evidence about s, so that either the prior or the posterior has to take the most extreme odds on s. It’s pretty intuitive in that light, and so I’m not dismayed that the “0 and 1 are not probabilities” property can’t hold when conditioned on arbitrary theories.
Important typo: P assigns conditional probability 1 to some statement that cannot be proven.