ksvanhorn

I have a new paper that strengthens the case for strong Bayesianism, a.k.a. One Magisterium Bayes. The paper is entitled "From propositional logic to plausible reasoning: a uniqueness theorem." (The preceding link will be good for a few weeks, after which only the preprint version will be available for free. I couldn't come up with the $2500 that Elsevier makes you pay to make your paper open-access.) Some background: E. T. Jaynes took the position that (Bayesian) probability theory is an extension of propositional logic to handle degrees of certainty -- and appealed to Cox's Theorem to argue that probability theory is the only viable such extension, "the unique consistent rules for conducting inference (i.e. plausible reasoning) of any kind." This position is sometimes called strong Bayesianism. In a nutshell, frequentist statistics is fine for reasoning about frequencies of repeated events, but that's a very narrow class of questions; most of the time when researchers appeal to statistics, they want to know what they can conclude with what degree of certainty, and that is an epistemic question for which Bayesian statistics is the right tool, according to Cox's Theorem. You can find a "guided tour" of Cox's Theorem here (see "Constructing a logic of plausible inference"). Here's a very brief summary. We write A | X for "the reasonable credibility" (plausibility) of proposition A when X is known to be true. Here X represents whatever information we have available. We are not at this point assuming that A | X is any sort of probability. A system of plausible reasoning is a set of rules for evaluating A | X. Cox proposed a handful of intuitively-appealing, qualitative requirements for any system of plausible reasoning, and showed that these requirements imply that any such system is just probability theory in disguise. That is, there necessarily exists an order-preserving isomorphism between plausibilities and probabilities such that A | X, after mapping from plausi