'Regularity' conditions provide bridges between possibility and probability. They have the form: If X is possible, then the probability of X is positive
(or equivalents). Especially interesting are the conditions we get when we understand 'possible' doxastically, and 'probability' subjectively. I characterize these senses of 'regularity' in terms of a certain internal harmony of an agent's probability space (omega, F, P). I distinguish I review several arguments for regularity as a rationality norm. An agent could violate this norm in two ways: by assigning probability zero to some doxastic possibility, and by failing to assign probability altogether to some doxastic possibility. I argue for the rationality of each kind of violation. Both kinds of violations of regularity have serious consequences for traditional Bayesian epistemology. I consider their ramifications for: - conditional probability - conditionalization - probabilistic independence - decision theory |