Kevin M. Clermont (Cornell Law School) has posted Justifying the Oft-Maligned Principle of Conjunctive Closure—and Thereby the Law’s Proof Process on SSRN. Here is the abstract:
The principle of conjunctive closure says that if you believe each of two or more facts, you believe them together. Despite its commonsensical appeal, many (but not all) philosophers have attacked it over the years because of probabilistic unease triggered by the famed lottery and preface paradoxes.
These philosophers have, however, overlooked the differences between traditional probabilities and most beliefs. Most prominently, the former framework assumes the additivity axiom, but the latter does not; additive probabilities apply the product rule for odds, but nonadditive beliefs do not. Once these differences are recognized, those paradoxes vaporize and, with slight refinement, the principle of conjunctive closure delivers complete accuracy.
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