Epistemology Probabilized

Abstract

Here is a framework for judgment in terms of a continuum of “subjective” probabilities, a framework in which probabilistic judgments need not stand on a foundation of certainties. In place of propositional data bases, this radical probabilism (“probabilities all the way down to the roots”) envisages full or partial probability assignments to probability spaces, together with protocols for revising those assignments and their interconnections in the light of fresh empirical or logico-mathematical input. This input need not be of the limiting 0-or-1 sort. Updating by ordinary conditioning is generalized (sec. 2.2) to probability kinematics, where an observation on a random variable X need not single out one value, but may prompt a new probability distribution Q over all values of X.The effect of an observation itself, apart from the influence of prior probabilities (sec. 3), is given by the (“Bayes”) factors \(\frac{{new\;odds}}{{old\;odds}}\) by which the observer’s odds between hypotheses are updated. We are not generally interested in adopting an observer’s new odds as our own, for those are influenced by the observer’s old odds, not ours. It is rather the observer’s Bayes’s factors that we need in order to use that observation in our own judgments. An account of collaborative updating is presented in these terms.Jon Dorling’s bayesian solution of the Duhem-Quine “holism” problem is sketched in sec. 4.We finish with a brief look at the historical setting of radical probabilism (sec. 5), and an indication of how “real” probabilities can be accomodated in subjectivistic terms (sec. 6).KeywordsSubjective ProbabilityRadical ProbabilismProbabilistic JudgmentGreen BallAuxiliary HypothesisThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.