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.)
I'm not really sure what frequentism is, though...Can you spell out what you think the coherent frequentist position is?
I'm not sure either, as I've confessed before, but here's how it seems to me: whereas Bayesians view beliefs as "thermometer readings" that go up and down as new information comes in, frequentists view beliefs as "certificates" that have to be "earned" through specific rituals, and are subject to periodic renewal.
Since (in view of results such as Cox's theorem) one can't really deny that probability the...
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