Are there degrees of belief?

John Maynard Keynes claimed that not all probabilities were comparable. Frank Ramsey argued that they were, and that Keynes's views to the contrary rested on a confusion of degree of entailment and degree of belief. We will argue that Keynes and Ramsey largely talked past each other, and yet that there are issues of great significance underlying their dispute. In particular, the simple principle of maximizing expected utility may be seen in a new light as one step of a rich and complex process.     

When Vague Sentences Inform: A Model Of Assertability

A speaker often decides whether or not to saysomething based on his assessment of the impact itwould have on his hearer's beliefs. If he thinks itwould bring them more in line with the truth, he saysit; otherwise he does not. In this paper, I developa model of these judgments, focusing specifically onthose of vague sentences. Under the simplifyingassumption that an utterance only conveys a speaker'sapplicability judgments, I present a Bayesian model ofan utterance's impact on a hearer's beliefs. Fromthis model I derive a model of a speaker's judgment ofwhether or not an utterance would be informative. Iillustrate it with several examples of judgments ofvague and non-vague sentences. For instance, I showthat it models the common judgment that assertingeither ``George is tall' or ``George is not tall' wouldbe misleading if George were borderline tall, butasserting ``George is tall and he isn't tall' would notbe.     

Conditionals and consequences

We examine the notion of conditionals and the role of conditionals in inductive logics and arguments. We identify three mistakes commonly made in the study of, or motivation for, non-classical logics. A nonmonotonic consequence relation based on evidential probability is formulated. With respect to this acceptance relation some rules of inference of System P are unsound, and we propose refinements that hold in our framework.     

Getting fancy with probability

There are a number of reasons for being interested in uncertainty, and there are also a number of uncertainty formalisms. These formalisms are not unrelated. It is argued that they can all be reflected as special cases of the approach of taking probabilities to be determined by sets of probability functions defined on an algebra of statements. Thus, interval probabilities should be construed as maximum and minimum probabilities within a set of distributions, Glenn Shafer's belief functions should be construed as lower probabilities, etc. Updating probabilities introduces new considerations, and it is shown that the representation of belief as a set of probabilities conflicts in this regard with the updating procedures advocated by Shafer. The attempt to make subjectivistic probability plausible as a doctrine of rational belief by making it more flowery — i.e., by adding new dimensions — does not succeed. But, if one is going to represent beliefs by sets of distributions, those sets of distributions might as well be based in statistical knowledge, as they are in epistemological or evidential probability.