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Jayson_Virissimo comments on Which parts of philosophy are worth studying from a pragmatic perspective? - Less Wrong Discussion
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I'm not a Frequentist (so I won't bother writing up a justification for the position), but non-Bayesians like R. A. Fisher, Jerzy Neyman, and Egon Pearson didn't just dogmatically refuse to accept the conclusion of a valid mathematical argument. They denied the truth of Bayesianism's epistemological premises (note: I disagree with their judgment in this case). Not one of them denied that Baye's Rule could be derived from the very definition of conditional probability (which is a straightforward consequence of the mathematics).
My comment was intended to point out that it takes more than standard probability theory and deduction to get you to Bayesianism. Additional premises (from outside of mathematics) must be present (at least implicitly).
That's a reasonable response to Will's first two comments, but [ETA: not] as a response to his third comment, mentioning Cox's theorem, or my comment, mentioning decision theory. I don't blame you for not knowing whether they had a coherent system of beliefs, but I do blame you for this non sequitur.
ETA: maybe that would be reasonable if you just substituted Cox for Bayes, but only if these frequentists explicitly rejected their contemporary Cox, rather than just ignored him.