Note: I am out of my depth, and simply repeating (probably incorrectly) cached thoughts said by people smarter than me.
The interpretation of probability is a philosophical subject, not something that is a straightforward consequence of the math.
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. And if you want to quibble over the axioms of Cox's theorems, that seems to me squarely within the domain of mathematics.
Philosophy is the name given to the search for well-defined questions. The frequentist/Bayesian dilemma seems to me well-defined enough to be considered within the domain of mathematics. Epistemology just barely intersects with it.
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.
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