James Joyce's article “A Nonpragmatic Vindication of Probabilism” introduced an approach to arguing for credal norms by appealing to the epistemic value of accuracy. The central thought was that credences ought to accurately represent the world, a guiding thought that has gone on to generate an entire research paradigm on the rationality of credences. Recently, a number of epistemologists have begun to apply this same thought to full beliefs, attempting to explain and argue for norms of belief in terms of (...) epistemic value. This paper examines these recent attempts, showing how they interact with work on the accuracy of credences. It then examines how differing judgments about epistemic value give rise to distinct rational requirements for belief, concluding by considering some of the fundamental questions and issues yet to be fully explored. (shrink)

The aim of this paper is to apply the accuracy based approach to epistemology to the case of higher order evidence: evidence that bears on the rationality of one's beliefs. I proceed in two stages. First, I show that the accuracy based framework that is standardly used to motivate rational requirements supports steadfastness—a position according to which higher order evidence should have no impact on one's doxastic attitudes towards first order propositions. The argument for this will require a generalization of (...) an important result by Greaves and Wallace for the claim that conditionalization maximizes expected accuracy. The generalization I provide will, among other things, allow us to apply the result to cases of self-locating evidence. In the second stage, I develop an alternative framework. Very roughly, what distinguishes the traditional approach from the alternative one is that, on the traditional picture, we're interested in evaluating the expected accuracy of conforming to an update procedure. On the alternative picture that I develop, instead of considering how good an update procedure is as a plan to conform to, we consider how good it is as a plan to make. I show how, given the use of strictly proper scoring rules, the alternative picture vindicates calibrationism: a view according to which higher order evidence should have a significant impact on our beliefs. I conclude with some thoughts about why higher order evidence poses a serious challenge for standard ways of thinking about rationality. (shrink)

Suppose you’d like to believe that p, whether or not it’s true. What can you do to help? A natural initial thought is that you could engage in Intentionally Biased Inquiry : you could look into whether p, but do so in a way that you expect to predominantly yield evidence in favour of p. This paper hopes to do two things. The first is to argue that this initial thought is mistaken: intentionally biased inquiry is impossible. The second is (...) to show that reflections on intentionally biased inquiry strongly support a controversial ‘access’ principle which states that, for all p, if p is part of our evidence, then that p is part of our evidence is itself part of our evidence. (shrink)

Epistemologists have recently noted a tension between (i) denying access internalism, and (ii) maintaining that rational agents cannot be epistemically akratic, believing claims akin to ‘p, but I shouldn’t believe p’. I bring out the tension, and develop a new way to resolve it. The basic strategy is to say that access internalism is false, but that counterexamples to it are ‘elusive’ in a way that prevents rational agents from suspecting that they themselves are counterexamples to the internalist principles. I (...) argue that this allows us to do justice to the motivations behind both (i) and (ii). And I explain in some detail what a view of evidence that implements this strategy, and makes it independently plausible, might look like. (shrink)

Conditionalization is a norm that governs the rational reallocation of credence. I distinguish between factive and non-factive formulations of Conditionalization. Factive formulations assume that the conditioning proposition is true. Non-factive formulations allow that the conditioning proposition may be false. I argue that non-factive formulations provide a better foundation for philosophical and scientific applications of Bayesian decision theory. I furthermore argue that previous formulations of Conditionalization, factive and non-factive alike, have almost universally ignored, downplayed, or mishandled a crucial causal aspect of (...) Conditionalization. To formulate Conditionalization adequately, one must explicitly address the causal structure of the transition from old credences to new credences. I offer a formulation of Conditionalization that takes these considerations into account, and I compare my preferred formulation with some prominent formulations found in the literature. (shrink)

Lewis proved a Dutch book theorem for Conditionalization. The theorem shows that an agent who follows any credal update rule other than Conditionalization is vulnerable to bets that inflict a sure loss. Lewis’s theorem is tailored to factive formulations of Conditionalization, i.e. formulations on which the conditioning proposition is true. Yet many scientific and philosophical applications of Bayesian decision theory require a non-factive formulation, i.e. a formulation on which the conditioning proposition may be false. I prove a Dutch book theorem (...) tailored to non-factive Conditionalization. I also discuss the theorem’s significance. (shrink)

Conditionalization is one of the central norms of Bayesian epistemology. But there are a number of competing formulations, and a number of arguments that purport to establish it. In this paper, I explore which formulations of the norm are supported by which arguments. In their standard formulations, each of the arguments I consider here depends on the same assumption, which I call Deterministic Updating. I will investigate whether it is possible to amend these arguments so that they no longer depend (...) on it. As I show, whether this is possible depends on the formulation of the norm under consideration. (shrink)

Epistemic decision theory produces arguments with both normative and mathematical premises. I begin by arguing that philosophers should care about whether the mathematical premises (1) are true, (2) are strong, and (3) admit simple proofs. I then discuss a theorem that Briggs and Pettigrew (2020) use as a premise in a novel accuracy-dominance argument for conditionalization. I argue that the theorem and its proof can be improved in a number of ways. First, I present a counterexample that shows that one (...) of the theorem’s claims is false. As a result of this, Briggs and Pettigrew’s argument for conditionalization is unsound. I go on to explore how a sound accuracy-dominance argument for conditionalization might be recovered. In the course of doing this, I prove two new theorems that correct and strengthen the result reported by Briggs and Pettigrew. I show how my results can be combined with various normative premises to produce sound arguments for conditionalization. I also show that my results can be used to support normative conclusions that are stronger than the one that Briggs and Pettigrew’s argument supports. Finally, I show that Briggs and Pettigrew’s proofs can be simplified considerably. (shrink)

Conditionalization is a widely endorsed rule for updating one’s beliefs. But a sea of complaints have been raised about it, including worries regarding how the rule handles error correction, changing desiderata of theory choice, evidence loss, self-locating beliefs, learning about new theories, and confirmation. In light of such worries, a number of authors have suggested replacing Conditionalization with a different rule — one that appeals to what I’ll call “ur-priors”. But different authors have understood the rule in different ways, and (...) these different understandings solve different problems. In this paper, I aim to map out the terrain regarding these issues. I survey the different problems that might motivate the adoption of such a rule, flesh out the different understandings of the rule that have been proposed, and assess their pros and cons. I conclude by suggesting that one particular batch of proposals, proposals that appeal to what I’ll call “loaded evidential standards”, are especially promising. (shrink)

Wordly internalists claim that while internal duplicates always share the same evidence, our evidence includes non-trivial propositions about our environment. It follows that some evidence is false. Worldly internalism is thought to provide a more satisfying answer to scepticism than classical internalist views that deny that these propositions about our environment might belong to our evidence and to provide a generally more attractive account of rationality and reasons for belief. We argue that worldly internalism faces serious difficulties and that its (...) apparent advantages are illusory. First, it cannot adequately handle some not terribly strange cases of perceptual error. Second, it cannot explain why one should plan to use their evidence to update their beliefs. The second issue allows us to explain why cases of misplaced certainty do not require us to introduce false evidence into our views and that why the alleged advantage of worldly internalism in resisting sceptical pressures is illusory. (shrink)

Sometimes you are unreliable at fulfilling your doxastic plans: for example, if you plan to be fully confident in all truths, probably you will end up being fully confident in some falsehoods by mistake. In some cases, there is information that plays the classical role of *evidence*—your beliefs are perfectly discriminating with respect to some possible facts about the world—and there is a standard expected-accuracy-based justification for planning to *conditionalize* on this evidence. This planning-oriented justification extends to some cases where (...) you do not have transparent evidence, in the sense that your beliefs are not perfectly discriminating with respect to any non-trivial facts. In other cases, accuracy considerations do not tell you to plan to conditionalize on any information at all, but rather to plan to follow a different updating rule. Even in the absence of evidence, accuracy considerations can guide your doxastic plan. (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)

This paper argues that the agent concerned to have accurate (outright) beliefs will have a consistent and multi-premise closed belief set, and not a (merely) single-premise closed and (merely) pairwise consistent belief set, as has often been thought. This argument rests on the fact that we need a notion of accuracy coherence for belief that is belief-sensitive; sensitive to one's perspective, in a way that the standard belief-insensitive notion of accuracy coherence is not. The choice of the belief-sensitive over belief-insensitive (...) notion is defended, as is the choice of this particular belief-sensitive kind of accuracy coherence over other belief-sensitive rivals. Our conclusion is that accurate believers are deductively cogent. (shrink)

The externalist says that your evidence could fail to tell you what evidence you do or not do have. In that case, it could be rational for you to be uncertain about what your evidence is. This is a kind of uncertainty which orthodox Bayesian epistemology has difficulty modeling. For, if externalism is correct, then the orthodox Bayesian learning norms of conditionalization and reflection are inconsistent with each other. I recommend that an externalist Bayesian reject conditionalization. In its stead, I (...) provide a new theory of rational learning for the externalist. I defend this theory by arguing that its advice will be followed by anyone whose learning dispositions maximize expected accuracy. I then explore some of this theory’s consequences for the rationality of epistemic akrasia, peer disagreement, undercutting defeat, and uncertain evidence. (shrink)

A handful of well-known arguments (the 'diachronic Dutch book arguments') rely upon theorems establishing that, in certain circumstances, you are immune from sure monetary loss (you are not 'diachronically Dutch bookable') if and only if you adopt the strategy of conditionalizing (or Jeffrey conditionalizing) on whatever evidence you happen to receive. These theorems require non-trivial assumptions about which evidence you might acquire---in the case of conditionalization, the assumption is that, if you might learn that e, then it is not the (...) case that you might learn something else that is consistent with e. These assumptions may not be relaxed. When they are, not only will non-(Jeffrey) conditionalizers be immune from diachronic Dutch bookability, but (Jeffrey) conditionalizers will themselves be diachronically Dutch bookable. I argue: 1) that there are epistemic situations in which these assumptions are violated; 2) that this reveals a conflict between the premise that susceptibility to sure monetary loss is irrational, on the one hand, and the view that rational belief revision is a function of your prior beliefs and the acquired evidence alone, on the other; and 3) that this inconsistency demonstrates that diachronic Dutch book arguments for (Jeffrey) conditionalization are invalid. (shrink)

My topic is how to make decisions when you possess foreknowledge of the consequences of your choice. Many have thought that these kinds of decisions pose a distinctive and novel problem for causal decision theory (CDT). My thesis is that foreknowledge poses no new problems for CDT. Some of the purported problems are not problems. Others are problems, but they are not problems for CDT. Rather, they are problems for our theories of subjunctive supposition. Others are problems, but they are (...) not new problems. They are old problems transposed into a new key. Nonetheless, decisions made with foreknowledge illustrate important lessons about the instrumental value of our choices. Once we've appreciated these lessons, we are left with a version of CDT which faces no novel threats from foreknowledge. (shrink)

Philosophy and Phenomenological Research, EarlyView.

Belief and credence are often characterized in three different ways—they ought to govern our actions, they ought to be governed by our evidence, and they ought to aim at the truth. If one of these roles is to be central, we need to explain why the others should be features of the same mental state rather than separate ones. If multiple roles are equally central, then this may cause problems for some traditional arguments about what belief and credence must be (...) like. I read the history of formal and traditional epistemology through the lens of these functional roles, and suggest that considerations from one literature might have a role in the other. The similarities and differences between these literatures may suggest some more general ideas about the nature of epistemology in abstraction from the details of credence and belief in particular. (shrink)

The Lockean Thesis says that you must believe p iff you’re sufficiently confident of it. On some versions, the 'must' asserts a metaphysical connection; on others, it asserts a normative one. On some versions, 'sufficiently confident' refers to a fixed threshold of credence; on others, it varies with proposition and context. Claim: the Lockean Thesis follows from epistemic utility theory—the view that rational requirements are constrained by the norm to promote accuracy. Different versions of this theory generate different versions of (...) Lockeanism; moreover, a plausible version of epistemic utility theory meshes with natural language considerations, yielding a new Lockean picture that helps to model and explain the role of beliefs in inquiry and conversation. Your beliefs are your best guesses in response to the epistemic priorities of your context. Upshot: we have a new approach to the epistemology and semantics of belief. And it has teeth. It implies that the role of beliefs is fundamentally different than many have thought, and in fact supports a metaphysical reduction of belief to credence. (shrink)

Many have claimed that whenever an investigation might provide evidence for a claim, it might also provide evidence against it. Similarly, many have claimed that your credence should never be on the edge of the range of credences that you think might be rational. Surprisingly, both of these principles imply that you cannot rationally be modest: you cannot be uncertain what the rational opinions are.

In this paper, we ask: how should an agent who has incoherent credences update when they learn new evidence? The standard Bayesian answer for coherent agents is that they should conditionalize; however, this updating rule is not defined for incoherent starting credences. We show how one of the main arguments for conditionalization, the Dutch strategy argument, can be extended to devise a target property for updating plans that can apply to them regardless of whether the agent starts out with coherent (...) or incoherent credences. The main idea behind this extension is that the agent should avoid updating plans that increase the possible sure loss from Dutch strategies. This happens to be equivalent to avoiding updating plans that increase incoherence according to a distance-based incoherence measure. (shrink)

In this essay, I cast doubt on an apparent truism: namely, that if evidence is available for gathering and use at a negligible cost, then it's always instrumentally rational for us to gather that evidence and use it for making decisions. Call this thesis Value of Information. I show that Value of Information conflicts with two other plausible theses. The first is the view that an agent's evidence can entail non-trivial propositions about the external world. The second is the view (...) that epistemic rationality requires us to update our credences by conditionalization. These two theses, given some plausible assumptions, make room for rationally biased inquiries where Value of Information fails. I go on to argue that this is bad news for defenders of Value of Information. (shrink)

According to Bayesian orthodoxy, an agent should update---or at least should plan to update---her 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 (...) view that an agent's evidence can entail non-trivial propositions about the external world. I argue that this tension casts doubt on the idea that diachronic Dutch books can be used to justify or vindicate updating plans. (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)

Recently, several epistemologists have defended an attractive principle of epistemic rationality, which we shall call Ur-Prior Conditionalization. In this essay, I ask whether we can justify this principle by appealing to the epistemic goal of accuracy. I argue that any such accuracy-based argument will be in tension with Evidence Externalism, i.e., the view that agent's evidence may entail non-trivial propositions about the external world. This is because any such argument will crucially require the assumption that, independently of all empirical evidence, (...) it is rational for an agent to be certain that her evidence will always include truths, and that she will always have perfect introspective access to her own evidence. This assumption is in tension with Evidence Externalism. I go on to suggest that even if we don't accept Evidence Externalism, the prospects for any accuracy-based justification for Ur-Prior Conditionalization are bleak. (shrink)

What is structural rationality? Specifically, what is the distinctive feature of structural requirements of rationality? Some philosophers have argued, roughly, that the distinctive feature of structural requirements is coherence. But what does coherence mean, exactly? Or, at least, what do structuralists about rationality have in mind when they claim that structural rationality is coherence? This issue matters for making progress in various active debates concerning rationality. In this paper, I analyze three strategies for figuring out what coherence means in the (...) debates on structural rationality. I argue that these strategies face problems. (shrink)

Some epistemologists think that the Bayesian ideals matter because we can approximate them. That is, our attitudes can be more or less close to the ones of our ideal Bayesian counterpart. In this paper, I raise a worry for this justification of epistemic ideals. The worry is this: In order to correctly compare agents to their ideal counterparts, we need to imagine idealized agents who have the same relevant information, knowledge, or evidence. However, there are cases in which one’s ideal (...) counterpart cannot have one’s information, knowledge, or evidence. In these situations, agents cannot compare themselves to their ideal counterpart. (shrink)

Structural requirements of rationality prohibit various things, like having inconsistent combinations of attitudes, having means-end incoherent combinations of attitudes, and so on. But what is the distinctive feature of structural requirements of rationality? And do we fall under an obligation to be structurally rational? These issues have been at the heart of significant debates over the past fifteen years. Some philosophers have recently argued that we can unify the structural requirements of rationality by analyzing what is constitutive of our attitudes. (...) It has also been suggested that, in the course of good first-personal deliberation, agents should treat structurally irrational combinations of attitudes as off-limits. In this paper, I raise a worry for these two theses concerning structural rationality. Roughly, I argue that some imperfect epistemic agents can be disposed to have structurally irrational combinations of attitudes. Also, when these imperfect agents deliberate, they should not treat structurally irrational combinations of attitudes as off-limits. Given our imperfections, being structurally irrational can very well be the best option we have. More generally, these observations reveal that structural rationality should not always be theorized independently from more “substantive” norms, like responsiveness to reasons or expected value optimization. (shrink)

Accuracy-first epistemology aims to show that the norms of epistemic rationality can be derived from the effective pursuit of accuracy. This paper explores the prospects within accuracy-first epistemology for vindicating “modesty”: the thesis that ideal rationality permits uncertainty about one’s own rationality. I argue that accuracy-first epistemology faces serious challenges in accommodating three forms of modesty: uncertainty about what priors are rational, uncertainty about whether one’s update policy is rational, and uncertainty about what one’s evidence is. I argue that the (...) problem stems from the representation of epistemic decision problems. The appropriate representation of decision problems, and corresponding decision rules, for (diachronic) update policies should be a generalization of decision problems and decision rules for (synchronic) coherence. I argue that extant accounts build in conflicting assumptions about which kinds of information about the believer should be used to structure epistemic decision problems. In particular, extant accounts of update build in a form of epistemic consequentialism. Related forms of epistemic consequentialism have been shown to generate problems for accuracy-first epistemology’s purported justifications of probabilism, conditionalization, and the principal principle. These results are vindicated only with nonconsequentialist epistemic decision theories. I close with suggestive examples of how, with a fully nonconsequentialist representation of epistemic decision problems, accuracy-first epistemology can allow for rational modesty. (shrink)

Philosophers have recently attempted to justify particular belief revision procedures by arguing that they are the optimal means towards the epistemic end of accurate credences. These attempts, however, presuppose that means should be evaluated according to classical expected utility theory; and there is a long tradition maintaining that expected utility theory is too restrictive as a theory of means–end rationality, ruling out too many natural ways of taking risk into account. In this paper, we investigate what belief-revision procedures are supported (...) by accuracy-theoretic considerations once we depart from expected utility theory to allow agents to be risk-sensitive. We argue that if accuracy-theoretic considerations tell risk-sensitive agents anything about belief-revision, they tell them the same thing they tell risk-neutral agents: they should conditionalize. (shrink)

Self-locating beliefs cause a problem for conditionalization. Miriam Schoenfield offers a solution: that on learning E, agents should update on the fact that they learned E. However, Schoenfield is not explicit about whether the fact that they learned E is self-locating. I will argue that if the fact that they learned E is self-locating then the original problem has not been addressed, and if the fact that they learned E is not self-locating then the theory generates implausible verdicts which Schoenfield (...) explicitly rejects. (shrink)

Good’s theorem is the apparent platitude that it is always rational to ‘look before you leap’: to gather information before making a decision when doing so is free. We argue that Good’s theorem is not platitudinous and may be false. And we argue that the correct advice is rather to ‘make your act depend on the answer to a question’. Looking before you leap is rational when, but only when, it is a way to do this.

In response to two trenchant objections, radical subjective Bayesianism has been widely rejected. In this paper, I seek, if not to rehabilitate subjectivism, at least to show its critic what is attractive about the position. I argue that what is at stake in the subjectivism/anti-subjectivism debate is not, as is commonly thought, which norms of rationality are true, but rather, the conception of rationality that we adopt: there is an alternative approach to the widespread telic approach to rationality, which I (...) call the poric approach, on which subjectivism is an attractive position. I then argue that the poric approach—and therefore subjectivism—cannot be easily dismissed. (shrink)

Hilary Greaves and David Wallace argue that conditionalization maximizes expected accuracy and so is a rational requirement, but their argument presupposes a particular picture of the bridge between rationality and accuracy: the Best-Plan-to-Follow picture. And theorists such as Miriam Schoenfield and Robert Steel argue that it's possible to motivate an alternative picture—the Best-Plan-to-Make picture—that does not vindicate conditionalization. I show that these theorists are mistaken: it turns out that, if an update procedure maximizes expected accuracy on the Best-Plan-to-Follow picture, it's (...) guaranteed to maximize expected accuracy on the Best-Plan-to-Make picture as well, in which case moving from the former to the latter can't help us avoid the conclusion that conditionalization is a rational requirement. If there's a problem with Greaves and Wallace’s argument, it must lie elsewhere. (shrink)

Defined narrowly, epistemology is the study of knowledge and justified belief. As the study of knowledge, epistemology is concerned with the following questions: What are the necessary and sufficient conditions of knowledge? What are its sources? What is its structure, and what are its limits? As the study of justified belief, epistemology aims to answer questions such as: How we are to understand the concept of justification? What makes justified beliefs justified? Is justification internal or external to one's own mind? (...) Understood more broadly, epistemology is about issues having to do with the creation and dissemination of knowledge in particular areas of inquiry. This article will provide a systematic overview of the problems that the questions above raise and focus in some depth on issues relating to the structure and the limits of knowledge and justification. (shrink)

Some of the most interesting recent work in formal epistemology has focused on developing accuracy-based approaches to justifying Bayesian norms. These approaches are interesting not only because they offer new ways to justify these norms, but because they potentially offer a way to justify all of these norms by appeal to a single, attractive epistemic goal: having accurate beliefs. Recently, Easwaran & Fitelson (2012) have raised worries regarding whether such “all-accuracy” or “purely alethic” approaches can accommodate and justify evidential Bayesian (...) norms. In response, proponents of purely alethic approaches, such as Pettigrew (2013b) and Joyce (2016), have argued that scoring rule arguments provide us with compatible and purely alethic justifications for the traditional Bayesian norms, including evidential norms. In this paper I raise several challenges to this claim. First, I argue that many of the justifications these scoring rule arguments provide are not compatible. Second, I raise worries for the claim that these scoring rule arguments provide purely alethic justifications. Third, I turn to assess the more general question of whether purely alethic justifications for evidential norms are even possible, and argue that, without making some contentious assumptions, they are not. Fourth, I raise some further worries for the possibility of providing purely alethic justifications for content-sensitive evidential norms, like the Principal Principle. (shrink)

On at least one of its uses, ‘higher-order evidence’ refers to evidence about what opinions are rationalized by your evidence. This chapter surveys the foundational epistemological questions raised by such evidence, the methods that have proven useful for answering them, and the potential consequences and applications of such answers.

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)

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.