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gwern comments on XKCD - Frequentist vs. Bayesians - Less Wrong Discussion
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Since probabilistic reasoning is a superset of deductive logic (pace our Saint Jaynes, RIP), it's not a surprise if some formulations of some problems turn out that way.
Ah, you mean like in chapter 1 of his book? :P
Anyhow, I think this should be surprising. Deductive logic is all well and good, but merely exercising it, with no mention of probabilities, is not the characteristic behavior of something called an "interpretation of probability." If I run a vaccine trial and none of the participants get infected, my deductive conclusion is "either the vaccine worked, or it didn't and something else made none of the participants get infected - QED." And then I would submit this to The Lancet, and the reviewers would write me polite letters saying "could you do some statistical analyses?"
And you might say 'well, I don't know what 'something else' is, I can't define it as a limit of any frequency!' At least, not with more info than is presented in a 3 panel comic. ('I am pretty darn sure about that disjunction, though.')