Believing Probabilistic Contents: On the Expressive Power and Coherence of Sets of Sets of Probabilities

Abstract

Moss argues that rational agents are best thought of not as having degrees of belief in various propositions. Instead, they are best thought of as having beliefs in probabilistic contents. Probabilistic contents are sets of probability functions. Probabilistic belief states, in turn, can then be modelled by sets of probabilistic contents, or sets of sets of probability functions. We argue that this Mossean framework is of considerable interest quite independently of its role in Moss’s account of probabilistic knowledge or her semantics for epistemic modals and probability operators. It is an extremely general model of uncertainty. Indeed, it is at least as general and expressively powerful as every other current imprecise probability framework, including lower probabilities, lower previsions, sets of probabilities, sets of desirable gambles and choice functions. In addition, we partially answer an important question that Moss leaves open, viz., why should rational agents have consistent probabilistic beliefs? We will show that a large range of failures of consistency will lead you to be Dutch bookable.