Bayesians often appeal to “merging of opinions” to rebut charges of excessive subjectivity. But what happens in the short run is often of greater interest than what happens in the limit. Seidenfeld and coauthors use this observation as motivation for investigating the counterintuitive short run phenomenon of dilation, since, they allege, dilation is “the opposite” of asymptotic merging of opinions. The measure of uncertainty relevant for dilation, however, is not the one relevant for merging of opinions. We explicitly investigate the (...) short run behavior of the metric relevant for merging, and show that dilation is independent of the opposite of merging. (shrink)

Elga (2010) argues that no plausible decision rule governs action with imprecise credences. I follow Moss (2015a) in claiming that the solution to Elga’s challenge is found in the philosophy of mind, not in devising a special new decision rule. Moss suggests that in decision situations that involve imprecise credences, we must identify with a precise credence, but she says little about identification. By reflecting on the common conception of identification and on what is necessary for Moss’s solution to succeed, (...) I argue that identifying with a precise credence is fundamentally accepting (in the sense of Bratman 1992; Cohen 1989) a proposition about probabilities. The norm on action with imprecise credences is then a special case of the general norm on action and acceptance. I delineate a number of attractive features of this position. (shrink)

An indifference principle says that your credences should be distributed uniformly over each of the possibilities you recognise. A chance deference principle says that your credences should be aligned with the chances. My thesis is that, if we are anti-Humeans about chance, then these two principles are incompatible. Anti-Humeans think that it is possible for the actual frequencies to depart from the chances. So long as you recognise possibilities like this, you cannot both spread your credences evenly and defer to (...) the chances. I discuss some weaker forms of indifference which will allow anti-Humeans to defer to the chances. (shrink)

This paper is about a tension between two theses. The first is Value of Evidence: roughly, the thesis that it is always rational for an agent to gather and use cost‐free evidence for making decisions. The second is Rationality of Imprecision: the thesis that an agent can be rationally required to adopt doxastic states that are imprecise, i.e., not representable by a single credence function. While others have noticed this tension, I offer a new diagnosis of it. I show that (...) it arises when an agent with an imprecise doxastic state engages in an unreflective inquiry, an inquiry where they revise their beliefs using an updating rule that doesn't satisfy a weak reflection principle. In such an unreflective inquiry, certain synchronic norms of instrumental rationality can make it instrumentally irrational for an agent to gather and use cost‐free evidence. I then go on to propose a diachronic norm of instrumental rationality that preserves Value of Evidence in unreflective inquiries. This, I suggest, may help us reconcile this thesis with Rationality of Imprecision. (shrink)

Imprecise probabilities are an increasingly popular way of reasoning about rational credence. However they are subject to an apparent failure to display convincing inductive learning. This paper demonstrates that a small modification to the update rule for IP allows us to overcome this problem, albeit at the cost of satisfying only a weaker concept of coherence.

Rational credence should be coherent in the sense that your attitudes should not leave you open to a sure loss. Rational credence should be such that you can learn when confronted with relevant evidence. Rational credence should not be sensitive to irrelevant differences in the presentation of the epistemic situation. We explore the extent to which orthodox probabilistic approaches to rational credence can satisfy these three desiderata and find them wanting. We demonstrate that an imprecise probability approach does better. Along (...) the way we shall demonstrate that the problem of “belief inertia” is not an issue for a large class of IP credences, and provide a solution to van Fraassen’s box factory puzzle. (shrink)