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Is there a Dutch Book argument saying that the agent (to avoid book) must have credences defined for all the propositions in the event space? All DB proofs I know assume as much, and I am worried you would have to make controversial assumptions about one gambles with no credence?
(Sorry if I am missing something basic, but help a brother out you know? I have a job now so I don't have to pretend I know what I am doing any more!)
Neat. One thing you can say: given a prob triple (X,S,p) and a subfield A of S, every prob measure on A (your partial deg of belief) has a unique extension to S that is a conditional probability. This follows from the theory of conditional expectations.
So: if you're committed to Bayesian conditionalization (maybe due to Dutch Books) then there is a unique strategy for extending your partial beliefs.
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