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Jon Williamson's Objective Bayesian Epistemology relies upon a calibration norm to constrain credal probability by both quantitative and qualitative evidence. One role of the calibration norm is to ensure that evidence works to constrain a convex set of probability functions. This essay brings into focus a problem for Williamson's theory when qualitative evidence specifies non-convex constraints.

Bayesian decision theory is here construed as explicating a particular concept of rational choice and Bayesian probability is taken to be the concept of probability used in that theory. Bayesian probability is usually identified with the agent’s degrees of belief but that interpretation makes Bayesian decision theory a poor explication of the relevant concept of rational choice. A satisfactory conception of Bayesian decision theory is obtained by taking Bayesian probability to be an explicatum for inductive probability given the agent’s evidence.

Bayesian epistemology postulates a probabilistic analysis of many sorts of ordinary and scientific reasoning. Huber ([2005]) has provided a novel criticism of Bayesianism, whose core argument involves a challenging issue: confirmation by uncertain evidence. In this paper, we argue that under a properly defined Bayesian account of confirmation by uncertain evidence, Huber's criticism fails. By contrast, our discussion will highlight what we take as some new and appealing features of Bayesian confirmation theory. Introduction Uncertain Evidence and Bayesian Confirmation Bayesian Confirmation by Uncertain Evidence: Test Cases and Basic Principles CiteULike Connotea Del.icio.us What's this?

There is a lot of philosophically interesting work being done in the borderlands between traditional and formal epistemology. It is easy to think that this would all be one-way traffic. When we try to formalise a traditional theory, we see that its hidden assumptions are inconsistent or otherwise untenable. Or we see that the proponents of the theory had been conflating two concepts that careful formal work lets us distinguish. Either way, the formalist teaches the traditionalist a lesson about what the live epistemological options are. I want to argue, more or less by example, that the traffic here should be twoway. By thinking carefully about considerations that move traditional epistemologists, we can find grounds for questioning some presuppositions that many formal epistemologists make. To make this more concrete, I’m going to be looking at a Bayesian objection to a certain kind of dogmatism about justification. Several writers have urged that the incompatibility of dogmatism with a kind of Bayesianism is a reason to reject dogmatism.1 I rather think that it is reason to question the Bayesianism. To put the point slightly more carefully, there is a simple proof that dogmatism (of the kind I envisage) can’t be modelled using standard Bayesian modelling tools. Rather than conclude that dogmatism is therefore flawed, I conclude that we need better modelling tools. I’ll spend a fair bit of this paper on outlining a kind of model that (a) allows us to model dogmatic reasoning, (b) is motivated by the epistemological considerations that motivate dogmatism, and (c) helps with some familiar problems besetting the Bayesian. I’m going to work up to that problem somewhat indirectly. I’ll start with looking at the kind of sceptical argument that motivates dogmatism. I’ll then briefly rehearse the argument that shows dogmatism and Bayesianism are incompatible. Then in the bulk of the paper I’ll suggest a way of making Bayesian models more flexible so they are no longer incompatible with dogmatism..

Recently in epistemology a number of authors have mounted Bayesian objections to dogmatism. These objections depend on a Bayesian principle of evidential confirmation: Evidence E confirms hypothesis H just in case Pr(H|E) > Pr(H). I argue using Keynes’ and Knight’s distinction between risk and uncertainty that the Bayesian principle fails to accommodate the intuitive notion of having no reason to believe. Consider as an example an unfamiliar card game: at first, since you’re unfamiliar with the game, you assign credences based on the indifference principle. Later you learn how the game works and discover that the odds dictate you assign the very same credences. Examples like this show that if you initially have no reason to believe H, then intuitively E can give you reason to believe H even though Pr(H|E) ≤ Pr(H). I show that without the principle, the objections to dogmatism fail.

In this chapter we draw connections between two seemingly opposing approaches to probability and statistics: evidential probability on the one hand and objective Bayesian epistemology on the other.

This paper develops connections between objective Bayesian epistemology—which holds that the strengths of an agent’s beliefs should be representable by probabilities, should be calibrated with evidence of empirical probability, and should otherwise be equivocal—and probabilistic logic. After introducing objective Bayesian epistemology over propositional languages, the formalism is extended to handle predicate languages. A rather general probabilistic logic is formulated and then given a natural semantics in terms of objective Bayesian epistemology. The machinery of objective Bayesian nets and objective credal nets is introduced and this machinery is applied to provide a calculus for probabilistic logic that meshes with the objective Bayesian semantics.

Bayesianism is our leading theory of uncertainty. Epistemology is defined as the theory of knowledge. So “Bayesian Epistemology” may sound like an oxymoron. Bayesianism, after all, studies the properties and dynamics of degrees of belief, understood to be probabilities. Traditional epistemology, on the other hand, places the singularly non-probabilistic notion of knowledge at centre stage, and to the extent that it traffics in belief, that notion does not come in degrees. So how can there be a Bayesian epistemology?

In Thinking and Acting John Pollock offers some criticisms of Bayesian epistemology, and he defends an alternative understanding of the role of probability in epistemology. Here, I defend the Bayesian against some of Pollock's criticisms, and I discuss a potential problem for Pollock's alternative account.

Bayesian epistemology addresses epistemological problems with the help of the mathematical theory of probability. It turns out that the probability calculus is especially suited to represent degrees of belief (credences) and to deal with questions of belief change, confirmation, evidence, justification, and coherence. Compared to the informal discussions in traditional epistemology, Bayesian epis- temology allows for a more precise and fine-grained analysis which takes the gradual aspects of these central epistemological notions into account. Bayesian epistemology therefore complements traditional epistemology; it does not re- place it or aim at replacing it.