Published online by Cambridge University Press: 01 April 2022
There is no set Δ of probability axioms that meets the following three desiderata:
(1) Δ is vindicated by a Dutch book theorem;
(2) Δ does not imply regularity (and thus allows, among other things, updating by conditionalization);
(3) Δ constrains the conditional probability q(·, z) even when the unconditional probability p(z) (= q(z, T)) equals 0.
This has significant consequences for Bayesian epistemology, some of which are discussed.
For their criticism and encouragement, as well as for their patience with half-baked ideas, I wish to thank Richard Bradley, Chris Gauker, Dick Jeffrey, Jim Joyce, Isaac Levi, John Martin, Rob Rynasiewicz, and two anonymous referees.