Imprecise Probability Models of Rational Belief

Formal areas of philosophy, which deal with the probabilistic representation of mental states, have been amongst the most progressive in the past decade, and Europe remains a centre of excellence for formal philosophy. The work produced by this project will lay the philosophical foundations for a model of rational belief used in active research in fields as diverse as statistics, economics, finance, psychology, engineering and computer science, and of increasing interest in various subfields in philosophy. The rational response to uncertainty is a topic that is extremely important to policy makers and decision making bodies; the appropriate representation of rational belief under uncertainty is a core element of successful policy. Thus, this project will contribute to better decision making at all levels of policy. Such questions set the agenda for the introduction of formal models of degrees of belief.

The standard philosophical model of rational degrees of belief is the Bayesian or probabilistic theory. An agent’s rational degree of belief is represented by a probability function. This theory – or cluster of related theories – has been remarkably successful and widely applied. Despite this success, the Bayesian theory has a number of problems, which will be outlined in the Research methodology section.

The core insight of IP models is that agents continue to be thought of as having levels of confidence in propositions as in the Bayesian model, but those levels are now not appropriately represented by single numerical degrees. Rather, degrees of belief are taken to be imprecise. An agent’s belief state is modelled by a set of probability functions, rather than a single such function, and thus an agent’s degree of belief in a proposition is assigned a range of values.

It is the hypothesis of this project that progress in the formal study of rational belief is to be found in IP models. They provide the basis for a new theory of rationality: a substantial improvement on Bayesian orthodoxy. But though the formal study of IP models has advanced apace, and it is increasingly widely applied, it has not yet been adequately worked out as a philosophical theory of rational belief. The philosophical foundations of these formal models have not been adequately developed. The aim of this project is to provide a careful, thorough and wide-ranging theory of epistemic rationality based on Imprecise Probabilities. The use of IP models will allow us to overcome some limitations of existing theories of rationality. The sustained and systematic study of this topic will allow us to develop a version of an IP theory of rationality that is immune to several current objections to such theories.

Bayesianism naturally extends to a theory of inference and learning, as well as to a theory of decision making. A truly adequate IP epistemology should be able to replicate these successes in providing good theories of inference and decision. Again, work on these topics is in its infancy. This project will move these issues forward signficantly.

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 79229.

Seamus Bradley
Marie Curie Individual Fellow

I’m a philosopher at the University of Leeds.


There is currently much discussion about how decision making should proceed when an agent’s degrees of belief are imprecise; …