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entirelyuseless comments on The trouble with Bayes (draft) - Less Wrong Discussion
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I'm not sure how this would be failing, except in the sense that we knew from the beginning that it would fail.
Any mathematical formalization is an imperfect expression of real life. And any formalization of anything, mathematical or not, is imperfect, since all words (including mathematical terms) are vague words without a precise meaning. (Either you define a word by other words, which are themselves imprecise; or you define a word by pointing at stuff or by giving examples, which is not a precise way to define things.)
I think there may have been a misunderstanding here. When So8res and I used the word "ideal" we meant "normative ideal", something we should try to approximate in order to be more rational, or at least progress towards figuring out how a more rational version of ourselves would reason, not just a simplified mathematical formalism of something in real life. So Bayesian probability theory might qualify as a reasonable formalization of real world reasoning, but still fail to be a normative ideal if it doesn't represent progress towards figuring out how people ideally ought to reason.
It could represent progress towards figuring out how people ought to reason, in the sense of leaving us better off than we were before, without being able to give a perfect answer that will resolve completely and forever everything about how people ought to reason. And it seems to me that it does do that (leave us better off) in the way So8res was talking about, by at least giving us an analogy to compare our reasoning to.