A geometric principle of indifference

That one's degrees of belief at any one time obey the axioms of probability theory is widely regarded as a necessary condition for static rationality. Many theorists hold that it is also a sufficient condition, but according to critics this yields too subjective an account of static rationality. However, there are currently no good proposals as to how to obtain a tenable stronger probabilistic theory of static rationality. In particular, the idea that one might achieve the desired strengthening by adding some symmetry principle to the probability axioms has appeared hard to maintain. Starting from an idea of Carnap and drawing on relatively recent work in cognitive science, this paper argues that conceptual spaces provide the tools to devise an objective probabilistic account of static rationality. Specifically, we propose a principle that derives prior degrees of belief from the geometrical structure of concepts.