Formal epistemology

Belief Models: a very general theory of aggregation

This paper has two goals. The first goal is to say some thing about how one might combine different agents' imprecise probabilities to generate an aggregate imprecise probability. The second goal is to champion the very general theory of "belief …

Nonclassical probability and convex hulls

It is well known that the convex hull of the classical truth value functions contains all and only the probability functions. Work by Paris and Williams has shown that this also holds for various kinds of nonclassical logics too. This note summarises …

Imprecise Probabilities

It has been argued that imprecise probabilities are a natural and intuitive way of overcoming some of the issues with orthodox precise probabilities. Models of this type have a long pedigree, and interest in such models has been growing in recent …

Can free evidence be bad?: Value of information for the imprecise probabilist

This paper considers a puzzling conflict between two positions that are each compelling: (A) it is irrational for an agent to pay to avoid 'free' evidence before making a decision, and (B) rational agents may have *imprecise* beliefs and/or desires. …

How to choose among choice functions

If one models an agent's degrees of belief by a set of probabilities, how should that agent's choices be constrained? In other words, what choice function should the agent use? This paper summarises some suggestions, and outlines a collection of …

Uncertainty, learning, and the 'problem' of dilation

Imprecise probabilism, which holds that rational belief/credence is permissibly represented by a set of probability functions, apparently suffers from a problem known as *dilation*. We explore whether this problem can be avoided or mitigated by one …

Should subjective probabilities be sharp?

There has been much recent interest in *imprecise probabilities*, models of belief that allow unsharp or fuzzy credence. There have also been some influential criticisms of this position. Here we argue, chiefly against Elga (2010), that subjective …

Sure Loss and Logical Ignorance

Here’s something I’ve been thinking about. The basic idea is to wonder what consequences follow from relaxing the standard assumption that Bayesian agents are logically omniscient. Bayesian epistemology and decision theory typically assume that the ideal agents are logically omniscient. Borrowing a practice from I.J. Good, I refer to my putative ideal agent as “you”. That is, they assume that if $\phi$ and $\psi$ are logically equivalent, then you should believe them to the same degree.