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According to the probabilistic relevance account of confirmation, E confirms H relative to background knowledge K just in case P(H/K&E) > P(H/K). This requires an inequality between the rational degree of belief in H determined relative to two bodies of total knowledge which are such that one (K&E) includes the other (K) as a proper part. In this paper, I argue that it is quite plausible that there are no two possible bodies of total knowledge for ideally rational agents meeting (...) 

Dutch book and accuracy arguments are used to justify certain rationality constraints on credence functions. Underlying these Dutch book and accuracy arguments are associated theorems, and I show that the interpretation of these theorems can vary along a range of dimensions. Given that the theorems can be interpreted in a variety of different ways, what is the status of the associated arguments? I consider three possibilities: we could aggregate the results of the differently interpreted theorems in some way, and motivate (...) 

According to Bayesian orthodoxy, an agent should updateor at least should plan to updateher credences by conditionalization. Some have defended this claim by means of a diachronic Dutch book argument. They say: an agent who does not plan to update her credences by conditionalization is vulnerable (by her own lights) to a diachronic Dutch book, i.e., a sequence of bets which, when accepted, guarantee loss of utility. Here, I show that this argument is in tension with evidence externalism, i.e., the (...) 

This paper makes explicit the way in which many theorists of the epistemology of uncertainty, or formal epistemologists, are committed to a version of noncognitivism—one about thoughts that something is likely. It does so by drawing an analogy with metaethical noncognitivism. I explore the degree to which the motivations for both views are similar and how both views have to grapple with the Frege‐Geach Problem about complex thoughts. The major upshot of recognizing this noncognitivism is that it presents challenges and (...) 

In this paper, I present an argument for a rational norm involving a kind of credal attitude called a quantificational credence – the kind of attitude we can report by saying that Lucy thinks that each record in Schroeder’s collection is 5% likely to be scratched. I prove a result called a Dutch Book Theorem, which constitutes conditional support for the norm. Though Dutch Book Theorems exist for norms on ordinary and conditional credences, there is controversy about the epistemic significance (...) 

According to the traditional Bayesian view of credence, its structure is that of precise probability, its objects are descriptive propositions about the empirical world, and its dynamics are given by conditionalization. Each of the three essays that make up this thesis deals with a different variation on this traditional picture. The first variation replaces precise probability with sets of probabilities. The resulting imprecise Bayesianism is sometimes motivated on the grounds that our beliefs should not be more precise than the evidence (...) 

This paper discusses how to update one’s credences based on evidence that has initial probability 0. I advance a diachronic norm, Kolmogorov Conditionalization, that governs credal reallocation in many such learning scenarios. The norm is based upon Kolmogorov’s theory of conditional probability. I prove a Dutch book theorem and converse Dutch book theorem for Kolmogorov Conditionalization. The two theorems establish Kolmogorov Conditionalization as the unique credal reallocation rule that avoids a sure loss in the relevant learning scenarios. 



This chapter is a philosophical survey of some leading approaches in formal epistemology in the socalled ‘Bayesian’ tradition. According to them, a rational agent’s degrees of belief—credences—at a time are representable with probability functions. We also canvas various further putative ‘synchronic’ rationality norms on credences. We then consider ‘diachronic’ norms that are thought to constrain how credences should respond to evidence. We discuss some of the main lines of recent debate, and conclude with some prospects for future research. 

