Catrin Campbell-Moore (Bristol): “Belief as Probability Constraints”

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Abstract: I propose that we model one’s beliefs by a collection of probability constraints instead of by, say, a probability function. This can very naturally capture judgements: when you think that the probability of Rain is >0.5, we put {p | p(Rain)>0.5} in your belief state. It can capture the usual models of belief of precise probabilities; but also allows for imprecise probabilities when you are not fully opinionated. I propose constraints on rationality that say that your belief state should be closed under supersets and finite intersections, that is, it should have the mathematical structure of a filter. This also interestingly allows that your beliefs are not closed under infinite consequences. This allows that we can capture attitudes that are usually captured by infinitesimal probabilities when you might believe the probability is >0 but also <0.1,<0.01 etc. It also allows that we can capture the full power of models of belief given by sets of desirable gambles, as is commonly used in the imprecise probability literature.

Catrin Campbell-Moore is a Lecturer in Philosophy at the University of Bristol, working on formal epistemology and logic, and on the connection between the two.