“the exception that proves the rule” seems like a very un-Bayesian thing to say. The implication is that both X and ~X provide evidence for the hypothesis. (Not that I always communicate my actual and complete hypothesis—sometimes that is a distraction from my main point.)
I think the implication is not that both X and ~X provide evidence for the hypothesis, but rather something like, “yes, there are a few exceptions to the rule, but if you look at what the exceptions are they’re so unusual that they just underline the fact that the rule is generally (though not universally) applicable.”
“the exception that proves the rule” seems like a very un-Bayesian thing to say. The implication is that both X and ~X provide evidence for the hypothesis. (Not that I always communicate my actual and complete hypothesis—sometimes that is a distraction from my main point.)
I think the implication is not that both X and ~X provide evidence for the hypothesis, but rather something like, “yes, there are a few exceptions to the rule, but if you look at what the exceptions are they’re so unusual that they just underline the fact that the rule is generally (though not universally) applicable.”