Dutch Book Arguments (DBAs) have been invoked to support various requirements of rationality. Some are plausible: probabilism and conditionalization. Others are less so: credal transparency and reflection. Anna Mahtani has argued for a new understanding of DBAs which, she claims, allow us to keep the DBAs for probabilism (and perhaps conditionalization) and reject the DBAs for credal transparency and reflection. I argue that Mahtani’s new account fails as (a) it does not support highly plausible requirements of rational coherence and (b) (...) it does not, even setting aside the first objection, succeed in undermining the DBAs for credal transparency or reflection. (shrink)

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.

Conditionalization governs how to reallocate credence in light of new evidence. One prominent argument in favor of Conditionalization holds that an agent who violates it is vulnerable to a diachronic Dutch book: a series of acceptable bets offered at multiple times that inflict a sure loss. van Fraassen argues that an agent who violates the Principle of Reflection is likewise vulnerable to a diachronic Dutch book. He concludes that agents should conform to both Conditionalization and Reflection. Some authors reply that (...) Reflection is implausible and hence that there must be something wrong with diachronic Dutch book arguments. Other authors try to isolate a principled difference between the Dutch book argument for Conditionalization and the Dutch book argument for Reflection, such that the former argument may succeed even though the latter fails. I pursue a version of this strategy. I contend that, once we properly elucidate the notion of sure loss, non‐reflectors are not vulnerable to a sure loss. An agent who violates Reflection is not thereby subject to a diachronic Dutch book. Appearances to the contrary result from an unmotivated focus upon an overly narrow set of gambling scenarios. (shrink)

This paper is about the standard Reflection Principle :235–256, 1984) and the Group Reflection Principle :478–502, 2007; Bovens and Rabinowicz in Episteme 8:281–300, 2011; Titelbaum in Quitting certainties: a Bayesian framework modeling degrees of belief, OUP, Oxford, 2012; Hedden in Mind 124:449–491, 2015). I argue that these principles are incomplete as they stand. The key point is that deference is an intensional relation, and so whether you are rationally required to defer to a person at a time can depend on (...) how that person and that time are designated. In this paper I suggest a way of completing the Reflection Principle and Group Reflection Principle, and I argue that so completed these principles are plausible. In particular, they do not fall foul of the Sleeping Beauty case :143–147, 2000), the Cable Guy Paradox :112–119, 2005), Arntzenius’ prisoner cases :356–370, 2003), or the Puzzle of the Hats :281–300, 2011). (shrink)

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 (...) rationality constraints based on this aggregation; we could be permissive, and accept the conclusions of the Dutch book and accuracy arguments under all interpretations of the associated theorems; or we could select one uniquely correct interpretation of the Dutch book or accuracy theorem, and use that to justify certain rationality constraints. I show that each possibility faces problems, and conclude that Dutch book and accuracy theorems cannot be used to justify any principle of rationality. (shrink)

This chapter is a philosophical survey of some leading approaches in formal epistemology in the so-called ‘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.

Reflecting on our engagement with fiction has compelled some theorists to expand the domain of the mental. They have posited a novel conative state, so-called “i-desire”. The central thesis of this approach is that i-desire relates to imagination in the same way as desire relates to belief. We formulate principles which are plausible consequences of this thesis. We then put pressure on these principles by focusing on desire concepts such as hoping, and show that the imaginative analogues of these concepts—if (...) such there be—do not satisfy the principles. We conclude by considering what our result suggests about the relationship between i-desire and propositional attitude psychology. (shrink)

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 (...) opportunities not only in the philosophy of mind and language but also in epistemology itself. I present some examples where attention to the implicit noncognitivism in formal epistemology has affected or should affect epistemological theory. And I suggest that it is likely that further examples of this sort will arise. (shrink)

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 (...) calls for. One known problem for this evidentially motivated imprecise view is that in certain cases, our imprecise credence in a particular proposition will remain the same no matter how much evidence we receive. In the first essay I argue that the problem is much more general than has been appreciated so far, and that it’s difficult to avoid without compromising the initial evidentialist motivation. The second variation replaces descriptive claims with moral claims as the objects of credence. I consider three standard arguments for probabilism with respect to descriptive uncertainty—representation theorem arguments, Dutch book arguments, and accuracy arguments—in order to examine whether such arguments can also be used to establish probabilism with respect to moral uncertainty. In the second essay, I argue that by and large they can, with some caveats. First, I don’t examine whether these arguments can be given sound non-cognitivist readings, and any conclusions therefore only hold conditional on cognitivism. Second, decision-theoretic representation theorems are found to be less convincing in the moral case, because there they implausibly commit us to thinking that intertheoretic comparisons of value are always possible. Third and finally, certain considerations may lead one to think that imprecise probabilism provides a more plausible model of moral epistemology. The third variation considers whether, in addition to conditionalization, agents may also change their minds by becoming aware of propositions they had not previously entertained, and therefore not previously assigned any probability. More specifically, I argue that if we wish to make room for reflective equilibrium in a probabilistic moral epistemology, we must allow for awareness growth. In the third essay, I sketch the outline of such a Bayesian account of reflective equilibrium. Given that this account gives a central place to awareness growth, and that the rationality constraints on belief change by awareness growth are much weaker than those on belief change by conditionalization, it follows that the rationality constraints on the credences of agents who are seeking reflective equilibrium are correspondingly weaker. (shrink)

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 (...) of these results. So, my conclusion is that if Dutch Book Theorems do, in general, support norms on credal states, then we have support for the suggested norm on quantificational credences. Providing conditional support for this norm gives us a fuller picture of the normative landscape of credal states. (shrink)

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 (...) this requirement. Hence, the positive relevance account may have to be rejected. (shrink)

Our decision-theoretic states are not luminous. We are imperfectly reliable at identifying our own credences, utilities and available acts, and thus can never be more than imperfectly reliable at identifying the prescriptions of decision theory. The lack of luminosity affords decision theory a remarkable opportunity — to issue guidance on the basis of epistemically inaccessible facts. We show how a decision theory can guarantee action in accordance with contingent truths about which an agent is arbitrarily uncertain. It may seem that (...) such advantages would require dubiously adverting to externalist facts that go beyond the internalism of traditional decision theory, but this is not so. Using only the standard repertoire of decision-theoretic tools, we show how to modify existing decision theories to take advantage of this opportunity. These improved decision theories require agents to maximize conditional expected utility — expected utility conditional upon an agent’s actual decision situation. We call such modified decision theories ‘self-confident’. These self-confident decision theories have a distinct advantage over standard decision theories: their prescriptions are better. (shrink)