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buybuydandavis comments on The Logic of the Hypothesis Test: A Steel Man - Less Wrong Discussion
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Yes, you can say it in that framework. And you should. That's part of the steelmanning exercise - putting in the things that are missing. If you steelman enough, you get to be a good bayesian.
P0 = "X <= 0" and {All My other assumptions}
NOT(P0) = NOT("X <= 0") or NOT({All My other assumptions})