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  1. Modus Ponens and Modus Tollens for Conditional Probabilities, and Updating on Uncertain Evidence.Jordan Howard Sobel - 2009 - Theory and Decision 66 (2):103 - 148.
    There are narrowest bounds for P(h) when P(e) = y and P(h/e) = x, which bounds collapse to x as y goes to 1. A theorem for these bounds -- bounds for probable modus ponens -- entails a principle for updating on possibly uncertain evidence subject to these bounds that is a generalization of the principle for updating by conditioning on certain evidence. This way of updating on possibly uncertain evidence is appropriate when updating by ’probability kinematics’ or ’Jeffrey-conditioning’ is, (...)
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  • Cyclical preferences and world bayesianism.Jordan Howard Sobel - 1997 - Philosophy of Science 64 (1):42-73.
    An example shows that 'pairwise preferences' (certain hypothetical choices) can cycle even when rational. General considerations entail that preferences tout court (certain relations of actual valuations) cannot cycle. A world-bayesian theory is explained that accommodates these two kinds of preference, and a theory for rational actions that would have them maximize and be objects of ratifiable choices. It is observed that choices can be unratifiable either because of troublesome credences or because of troublesome preferences. An appendix comments on a third (...)
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