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Torben comments on Open Thread, August 2010 - Less Wrong
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Thank you all. It seems I perhaps haven't phrased my question the way I thought of it.
I don't doubt the validity of the proofs underlying Bayes' theorem, just as I don't doubt the validity of Euclidian geometry. The question is rather if BT/probability theory hinges on assumptions that may turn out not to be necessarily true for all possible worlds, geometries, curvatures, whatever. This turned out to be the case for Euclidian geometry, as it did for Zeno. They assumed features of the world which turned out not to be the case.
It may be that my question doesn't even make sense, but what I was trying to convey was what apriori assumptions does BT rely on which may turn out to be dodgy in the real world?
I'm not as such trying to convince people, rather trying to understand my own side's arguments.
I think Kevin Van Horn's introduction to Cox's theorem (warning: pdf) is exactly what you're looking for.
(If you read the article, please give me feedback on the correctness of my guess that it addresses your concern.)
Bayes' Theorem assumes that it is meaningful to talk about subjective degrees of belief, but beyond that all you really need is basic arithmetic. I can't imagine a universe in which subjective degrees of belief aren't something that can be reasoned about, but that may be my failure and not reality's.