 The AGM model and other logical frameworks for belief revision are based on a dichotomous approach to belief: either something is believed or it is not, in either case without any gradations. Beliefs can be be more or less easily given up, and non-beliefs can be more or less easily turned into beliefs, but the very act of believing does not admit of degrees. In contrast, probabilistic models of belief, usually based on some form of subjective Bayesianism, admit all degrees between the strongest belief and the strongest disbelief. Dichotomous and probabilistic models represent different features of belief systems. It has proved to be difficult to construct a reasonably manageable model that covers both the logic-related and the probabilistic properties of belief change. These difficulties are closely connected with the lottery and preface paradoxes (Kyburg 1961; Makinson 1965).