Bayesian Agnosticism and Constructive Empiricism
1. How should the traditional doxastic attitude of agnosticism be represented in a Bayesian framework? In Laws and Symmetry, Bas van Fraassen proposes that agnosticism be represented as having a certain type of vague opinion. A Bayesian with no vague opinions assigns sharp subjective probabilities to all propositions in a domain of discourse. A Bayesian with vague opinions represents his opinions not by a single probability function, but by a set of probability functions. The probability given to a proposition H is an interval [x, y] iff [x, y] is the smallest closed interval containing the probabilities assigned to H by members of that set. Van Fraassen (1989: 194) gives a general analysis of Bayesian agnosticism when he implicitly suggests that a Bayesian is agnostic about a proposition iff her opinion about the proposition is represented by an interval with zero as the lower limit.1