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Panel on belief change

The principle of categorial matching that has been invoked to mandate that transformations of theories by contraction removing some proposition h from a belief state K should include a specification of the entrenchment of the new belief state K − h as well as the entrenchment of the initial state K masks a substantial assumption that ought to be subject to critical scrutiny and which personally would reject. The assumption is that a belief state K and its entrenchment should be treated as a single unit for purposes of studying change in epistemic state. To bring out the point, I took note of a similar issue that arises in the context of studying changes in state B of credal probability judgment relative to K due to expansion of K by adding datum E (consistent with K in conformity with the requirement that the change go by conditionalization via Bayes’s theorem. In this latter setting, the principle of categorial matching requires that the new state of credal probability judgment carry with it the specification of the rule of Bayesian updating. This rule would call for a specification of the conditional probability function PE(x/y) relative to K+E defined for all y consistent with K + E where the conditional probability is understood to specify the new credal probability function were y added to K + E. This conditional probability is characterized differently than the conditional probability conditional on y