On the significance of conditional probabilities

The orthodoxy that conditional probabilities reflect what are for a subject evidential bearings is seconded. This significance suggests that there should be principles equating rationally revised probabilities on new information with probabilities reached by conditionalizing on this information. Several principles, two of which are endorsed, are considered. A ‘book’ is made against a violator of these, and it is argued that there must be something wrong with a person against whom such books can be made. Appendices comment on Popper-functions, elaborate on bets and odds, and relate dutch books and strategies to conditions of inconsistency (Ramsey's idea) and imperfection.

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