I was under the impression that there are sound decision theoretic and axiomatic justifications for the notion of subjective probability. Also, the sequences themselves provide pretty good justification.
I agree that there are good arguments for Bayesianism. I disagree that most of the premises of those arguments are mathematical premises rather than epistemological (philosophical) premises.
I agree that there are epistemological problems in the foundations, but they seem to me mild enough to refute frequentism. I'm not really sure what frequentism is, though (other than the position that one should not speak of the probability of a hypothesis). Can you spell out what you think the coherent frequentist position is? I won't hold it against you or frequentism if you say no.
(If one just speaks of beliefs, maybe there is a coherent frequentist position that evades Cox's theorem, but frequentists hold that we make decisions [ETA: a metaphysical but not epistemological assumption]; and this should be enough to force probabilistic beliefs.)
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