If you're talking about math, Bayes' theorem is true and that's the end of that. If you're talking about degrees of belief that real people hold - especially if you want to convince your opponent to update in a specific direction because Bayes' theorem says so - I'd advise to use another strategy. Going meta like "you must be persuaded by these arguments because blah blah blah" gives you less bang per buck than upgrading the arguments.
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...
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