David Christensen and others argue that Dutch Strategies are more like peer disagreements than Dutch Books, and should not count against agents‘ conformity to ideal rationality. I review these arguments, then show that Dutch Books, Dutch Strategies, and peer disagreements are only possible in the case of what computer scientists call Byzantine Failures—uncorrected Byzantine Faults which update arbitrary values. Yet such Byzantine Failures make agents equally vulnerable to all three kinds of epistemic inconsistencies, so there is no principled basis for (...) claiming that only avoidance of true Dutch Books characterizes ideally rational agents. Agents without Byzantine Failures can be ideally rational in a very strong sense, but are not normative for humans. (shrink)

– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

In the Sleeping Beauty problem, Beauty is uncertain whether the outcome of a certain coin toss was heads or tails. One argument suggests that her degree of belief in heads should be 1/3, while a second suggests that it should be 1/2. Prima facie, the argument for 1/2 appears to be stronger. I offer a diachronic Dutch Book argument in favor of 1/3. Even for those who are not routinely persuaded by diachronic Dutch Book arguments, this one has some important (...) morals. (shrink)

Ideal epistemologists investigate the nature of pure epistemic rationality, abstracting away from human cognitive limitations. Non-ideal epistemologists investigate epistemic norms that are satisfiable by most humans, most of the time. Ideal epistemology faces a number of challenges, aimed at both its substantive commitments and its philosophical worth. This paper explains the relation between ideal and non-ideal epistemology, with the aim of justifying ideal epistemology. Its approach is meta-epistemological, focusing on the meaning and purpose of epistemic evaluations. I provide an account (...) on which the fundamental difference between ideal and non-ideal epistemic evaluations is that only the non-ideal epistemic ‘ought’ implies any substantive ‘can’. I argue that only ideal epistemic evaluations are ‘normatively robust’: they are neither conventional nor seriously context-sensitive. Non-ideal epistemic evaluations are normatively non-robust, exhibiting both conventionality and serious context-sensitivity from an interesting variety of distinct sources. For this reason, non-ideal epistemic evaluations won’t characterize the fundamental nature of epistemic rationality. Non-ideal epistemic rationality depends, not merely on what’s epistemically valuable, but also on modally contingent epistemic conventions and contextually contingent constraints on epistemic options. If we want a normatively robust theory of epistemic rationality, ideal epistemology is the only game in town. (shrink)

‘Bayesian epistemology’ became an epistemological movement in the 20th century, though its two main features can be traced back to the eponymous Reverend Thomas Bayes (c. 1701-61). Those two features are: (1) the introduction of a formal apparatus for inductive logic; (2) the introduction of a pragmatic self-defeat test (as illustrated by Dutch Book Arguments) for epistemic rationality as a way of extending the justification of the laws of deductive logic to include a justification for the laws of inductive logic. (...) The formal apparatus itself has two main elements: the use of the laws of probability as coherence constraints on rational degrees of belief (or degrees of confidence) and the introduction of a rule of probabilistic inference, a rule or principle of conditionalization. (shrink)