Epistemic decision theorists aim to justify Bayesian norms by arguing that these norms further the goal of epistemic accuracy—having beliefs that are as close as possible to the truth. The standard defense of Probabilism appeals to accuracy dominance: for every belief state that violates the probability calculus, there is some probabilistic belief state that is more accurate, come what may. The standard defense of Conditionalization, on the other hand, appeals to expected accuracy: before the evidence is in, one should expect (...) to do better by conditionalizing than by following any other rule. We present a new argument for Conditionalization that appeals to accuracy‐dominance, rather than expected accuracy. Our argument suggests that Conditionalization is a rule of coherence: plans that conflict with Conditionalization don't just prescribe bad responses to the evidence; they also give rise to inconsistent attitudes. (shrink)

Greaves and Wallace argue that conditionalization maximizes expected accuracy. In this paper I show that their result only applies to a restricted range of cases. I then show that the update procedure that maximizes expected accuracy in general is one in which, upon learning P, we conditionalize, not on P, but on the proposition that we learned P. After proving this result, I provide further generalizations and show that much of the accuracy-first epistemology program is committed to KK-like iteration principles (...) and to the existence of a class of propositions that rational agents will be certain of if and only if they are true. (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)

Epistemologists who study credences have a well-developed account of how you should change them when you learn new evidence; that is, when your body of evidence grows. What's more, they boast a diverse range of epistemic and pragmatic arguments that support that account. But they do not have a satisfactory account of when and how you should change your credences when you become aware of possibilities and propositions you have not entertained before; that is, when your awareness grows. In this (...) paper, I consider the arguments for the credal epistemologist's account of how to respond to evidence, and I ask whether they can help us generate an account of how to respond to awareness growth. The results are surprising: the arguments that all support the same norms for responding to evidence growth support a number of different norms when they are applied to awareness growth. Some of these norms seem too weak, others too strong. I ask what we should conclude from this, and argue that our credal response to awareness growth is considerably less rigorously constrained than our credal response to new evidence. (shrink)

According to accuracy-first epistemology, accuracy is the fundamental epistemic good. Epistemic norms — Probabilism, Conditionalization, the Principal Principle, etc. — have their binding force in virtue of helping to secure this good. To make this idea precise, accuracy-firsters invoke Epistemic Decision Theory (EpDT) to determine which epistemic policies are the best means toward the end of accuracy. Hilary Greaves and others have recently challenged the tenability of this programme. Their arguments purport to show that EpDT encourages obviously epistemically irrational behavior. (...) We develop firmer conceptual foundations for EpDT. First, we detail a theory of praxic and epistemic good. Then we show that, in light of their very different good-making features, EpDT will evaluate epistemic states and epistemic acts according to different criteria. So, in general, rational preference over states and acts won’t agree. Finally, we argue that based on direction-of-fit considerations, it’s preferences over the former that matter for normative epistemology, and that EpDT, properly spelt out, arrives at the correct verdicts in a range of putative problem cases. (shrink)

Jim Joyce argues for two amendments to probabilism. The first is the doctrine that credences are rational, or not, in virtue of their accuracy or “closeness to the truth” (1998). The second is a shift from a numerically precise model of belief to an imprecise model represented by a set of probability functions (2010). We argue that both amendments cannot be satisfied simultaneously. To do so, we employ a (slightly-generalized) impossibility theorem of Seidenfeld, Schervish, and Kadane (2012), who show that (...) there is no strictly proper scoring rule for imprecise probabilities. -/- The question then is what should give way. Joyce, who is well aware of this no-go result, thinks that a quantifiability constraint on epistemic accuracy should be relaxed to accommodate imprecision. We argue instead that another Joycean assumption — called strict immodesty— should be rejected, and we prove a representation theorem that characterizes all “mildly” immodest measures of inaccuracy. (shrink)

We use a theorem from M. J. Schervish to explore the relationship between accuracy and practical success. If an agent is pragmatically rational, she will quantify the expected loss of her credence with a strictly proper scoring rule. Which scoring rule is right for her will depend on the sorts of decisions she expects to face. We relate this pragmatic conception of inaccuracy to the purely epistemic one popular among epistemic utility theorists.

Accuracy arguments for the core tenets of Bayesian epistemology differ mainly in the conditions they place on the legitimate ways of measuring the inaccuracy of our credences. The best existing arguments rely on three conditions: Continuity, Additivity, and Strict Propriety. In this paper, I show how to strengthen the arguments based on these conditions by showing that the central mathematical theorem on which each depends goes through without assuming Additivity.

A widely shared view in the cognitive sciences is that discovering and assessing explanations of cognitive phenomena whose production involves uncertainty should be done in a Bayesian framework. One assumption supporting this modelling choice is that Bayes provides the best approach for representing uncertainty. However, it is unclear that Bayes possesses special epistemic virtues over alternative modelling frameworks, since a systematic comparison has yet to be attempted. Currently, it is then premature to assert that cognitive phenomena involving uncertainty are best (...) explained within the Bayesian framework. As a forewarning, progress in cognitive science may be hindered if too many scientists continue to focus their efforts on Bayesian modelling, which risks to monopolize scientific resources that may be better allocated to alternative approaches. (shrink)

The best accuracy arguments for probabilism apply only to credence functions with finite domains, that is, credence functions that assign credence to at most finitely many propositions. This is a significant limitation. It reveals that the support for the accuracy-first program in epistemology is a lot weaker than it seems at first glance, and it means that accuracy arguments cannot yet accomplish everything that their competitors, the pragmatic (Dutch book) arguments, can. In this paper, I investigate the extent to which (...) this limitation can be overcome. Building on the best arguments in finite domains, I present two accuracy arguments for probabilism that are perfectly general—they apply to credence functions with arbitrary domains. I then discuss how the arguments’ premises can be challenged. We will see that it is particularly difficult to characterize admissible accuracy measures in infinite domains. (shrink)

Famously, William James held that there are two commandments that govern our epistemic life: Believe truth! Shun error! In this paper, I give a formal account of James' claim using the tools of epistemic utility theory. I begin by giving the account for categorical doxastic states – that is, full belief, full disbelief, and suspension of judgment. Then I will show how the account plays out for graded doxastic states – that is, credences. The latter part of the paper thus (...) answers a question left open in Pettigrew. (shrink)

Unspecific evidence calls for imprecise credence. My aim is to vindicate this thought. First, I will pin down what it is that makes one's imprecise credences more or less epistemically valuable. Then I will use this account of epistemic value to delineate a class of reasonable epistemic scoring rules for imprecise credences. Finally, I will show that if we plump for one of these scoring rules as our measure of epistemic value or utility, then a popular family of decision rules (...) recommends imprecise credences. In particular, a range of Hurwicz criteria, which generalise the Maximin decision rule, recommend imprecise credences. If correct, the moral is this: an agent who adopts precise credences, rather than imprecise ones, in the face of unspecific and incomplete evidence, goes wrong by gambling with the epistemic utility of her doxastic state in too risky a fashion. Precise credences represent an overly risky epistemic bet, according to the Hurwicz criteria. (shrink)

If the laws of nature are as the Humean believes, it is an unexplained cosmic coincidence that the actual Humean mosaic is as extremely regular as it is. This is a strong and well-known objection to the Humean account of laws. Yet, as reasonable as this objection may seem, it is nowadays sometimes dismissed. The reason: its unjustified implicit assignment of equiprobability to each possible Humean mosaic; that is, its assumption of the principle of indifference, which has been attacked on (...) many grounds ever since it was first proposed. In place of equiprobability, recent formal models represent the doxastic state of total ignorance as suspension of judgment. In this paper I revisit the cosmic coincidence objection to Humean laws by assessing which doxastic state we should endorse. By focusing on specific features of our scenario I conclude that suspending judgment results in an unnecessarily weak doxastic state. First, I point out that recent literature in epistemology has provided independent justifications of the principle of indifference. Second, given that the argument is framed within a Humean metaphysics, it turns out that we are warranted to appeal to these justifications and assign a uniform and additive credence distribution among Humean mosaics. This leads us to conclude that, contrary to widespread opinion, we should not dismiss the cosmic coincidence objection to the Humean account of laws. (shrink)

Consider Phoebe and Daphne. Phoebe has credences in 1 million propositions. Daphne, on the other hand, has credences in all of these propositions, but she's also got credences in 999 million other propositions. Phoebe's credences are all very accurate. Each of Daphne's credences, in contrast, are not very accurate at all; each is a little more accurate than it is inaccurate, but not by much. Whose doxastic state is better, Phoebe's or Daphne's? It is clear that this question is analogous (...) to a question that has exercised ethicists over the past thirty years. How do we weigh a population consisting of some number of exceptionally happy and satisfied individuals against another population consisting of a much greater number of people whose lives are only just worth living? This is the question that occasions population ethics. In this paper, I go in search of the correct population ethics for credal states. (shrink)

How does logic relate to rational belief? Is logic normative for belief, as some say? What, if anything, do facts about logical consequence tell us about norms of doxastic rationality? In this paper, we consider a range of putative logic-rationality bridge principles. These purport to relate facts about logical consequence to norms that govern the rationality of our beliefs and credences. To investigate these principles, we deploy a novel approach, namely, epistemic utility theory. That is, we assume that doxastic attitudes (...) have different epistemic value depending on how accurately they represent the world. We then use the principles of decision theory to determine which of the putative logic-rationality bridge principles we can derive from considerations of epistemic utility. (shrink)

Longtermism is the thesis that in a large class of decision situations, the best thing we can do is what is best for the long-term future. The scope question for longtermism asks: how large is the class of decision situations for which this is true? In this paper, I suggest that the scope of longtermism may be narrower than many longtermists suppose. I identify a restricted version of longtermism: swamping axiological strong longtermism (swamping ASL). I identify three scope-limiting factors - (...) probabilistic and decision-theoretic phenomena which, when present, tend to reduce the prospects for swamping ASL. I argue that these scope-limiting factors are often present in human decision problems, then use two case studies from recent discussions of longtermism to show how the scope-limiting factors lead to a restricted, if perhaps nonempty, scope for swamping ASL. (shrink)

In a recent paper in this journal, James Hawthorne, Jürgen Landes, Christian Wallmann, and Jon Williamson argue that the principal principle entails the principle of indifference. In this article, I argue that it does not. Lewis’s version of the principal principle notoriously depends on a notion of admissibility, which Lewis uses to restrict its application. HLWW base their argument on certain intuitions concerning when one proposition is admissible for another: Conditions 1 and 2. There are two ways of reading their (...) argument, depending on how you understand the status of these conditions. Reading 1: The correct account of admissibility is determined independently of these two principles, and yet these two principles follow from that correct account. Reading 2: The correct account of admissibility is determined in part by these two principles, so that the principles follow from that account but only because the correct account is constrained so that it must satisfy them. HLWW show that given an account of admissibility on which Conditions 1 and 2 hold, the principal principle entails the principle of indifference. I argue that on either reading of the argument, it fails. First, I argue that there is a plausible account of admissibility on which Conditions 1 and 2 are false. That defeats Reading 1. Next, I argue that the intuitions that lead us to assent to Condition 2 also lead us to assent to other very closely related principles that are inconsistent with Condition 2. This, I claim, casts doubt on the reliability of those intuitions, and thus removes our justification for Condition 2. This defeats Reading 2 of the HLWW argument. Thus, the argument fails. 1Introduction 2Introducing the Principal Principle 3Introducing the Principle of Indifference 4The HLWW Argument 4.1Reading 1: Admissibility justifies Conditions 1 and 2 4.2Reading 2: Conditions 1 and 2 constrain admissibility 5Conclusion. (shrink)

How much does rationality constrain what we should believe on the basis of our evidence? According to this book, not very much. For most people and most bodies of evidence, there is a wide range of beliefs that rationality permits them to have in response to that evidence. The argument, which takes inspiration from William James' ideas in 'The Will to Believe', proceeds from two premises. The first is a theory about the basis of epistemic rationality. It's called epistemic utility (...) theory, and it says that what it is epistemically rational for you to believe is what it would be rational for you to choose if you were given the chance to pick your beliefs and, when picking them, you were to care only about their epistemic value. So, to say which beliefs are permitted, we must say how to measure epistemic value, and which decision rule to use when picking your beliefs. The second premise is a claim about attitudes to epistemic risk, and it says that rationality permits many different such attitudes. These attitudes can show up in epistemic utility theory in two ways: in the way you measure epistemic value; and in the decision rule you use to pick beliefs. This book explores the latter. The result is permissivism about epistemic rationality: different attitudes to epistemic risk lead to different choices of prior beliefs; given most bodies of evidence, different priors lead to different posteriors; and even once we fix your attitudes to epistemic risk, if they are at all risk-inclined, there is a range of different priors and therefore different posteriors they permit. (shrink)

I propose a general alethic theory of epistemic risk according to which the riskiness of an agent’s credence function encodes her relative sensitivity to different types of graded error. After motivating and mathematically developing this approach, I show that the epistemic risk function is a scaled reflection of expected inaccuracy. This duality between risk and information enables us to explore the relationship between attitudes to epistemic risk, the choice of scoring rules in epistemic utility theory, and the selection of priors (...) in Bayesian epistemology more generally. (shrink)

Forty years ago, Bayesian philosophers were just catching a new wave of technical innovation, ushering in an era of scoring rules, imprecise credences, and infinitesimal probabilities. Meanwhile, down the hall, Gettier’s 1963 paper [28] was shaping a literature with little obvious interest in the formal programs of Reichenbach, Hempel, and Carnap, or their successors like Jeffrey, Levi, Skyrms, van Fraassen, and Lewis. And how Bayesians might accommodate the discourses of full belief and knowledge was but a glimmer in the eye (...) of Isaac Levi. Forty years later, scoring rules, imprecise credences, and infinitesimal probabilities are all the rage. And the formal and “informal” traditions are increasingly coming together as Bayesian arguments spill over into debates about the foundations of empirical knowledge, skepticism, and more. Relatedly, Bayesian interest in full belief and knowledge has never been greater. Much more besides has happened in the last forty years of Bayesian philosophy, .. (shrink)

Don’t form beliefs on the basis of coin flips or random guesses. More generally, don’t take belief gambles: if a proposition is no more likely to be true than false given your total body of evidence, don’t go ahead and believe that proposition. Few would deny this seemingly innocuous piece of epistemic advice. But what, exactly, is wrong with taking belief gambles? Philosophers have debated versions of this question at least since the classic dispute between William Clifford and William James (...) near the end of the nineteenth century. Here I reassess the normative standing of belief gambles from the perspective of epistemic decision theory. The main lesson of the paper is a negative one: it turns out that we need to make some surprisingly strong and hard-to-motivate assumptions to establish a general norm against belief gambles within a decision-theoretic framework. I take this to pose a dilemma for epistemic decision theory: it forces us to either make seemingly unmotivated assumptions to secure a norm against belief gambles, or concede that belief gambles can be rational after all. (shrink)

In a series of papers over the past twenty years, and in a new book, Igor Douven has argued that Bayesians are too quick to reject versions of inference to the best explanation that cannot be accommodated within their framework. In this paper, I survey their worries and attempt to answer them using a series of pragmatic and purely epistemic arguments that I take to show that Bayes’ Rule really is the only rational way to respond to your evidence.

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)

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)

In a recent paper in this journal, James Hawthorne, Jürgen Landes, Christian Wallmann, and Jon Williamson argue that the principal principle entails the principle of indifference. In this paper, I argue that it does not. Lewis’s version of the principal principle notoriously depends on a notion of admissibility, which Lewis uses to restrict its application. HLWW base their argument on certain intuitions concerning when one proposition is admissible for another: Conditions 1 and 2. There are two ways of reading their (...) argument, depending on how you understand the status of these conditions. Reading 1: The correct account of admissibility is determined independently of these two principles, and yet these two principles follow from that correct account. Reading 2: The correct account of admissibility is determined in part by these two principles, so that the principles follow from that account but only because the correct account is constrained so that it must satisfy them. HLWWshow that, given an account of admissibility on which Conditions 1 and 2 hold, the principal principle entails the principle of indifference. I argue that, on either reading of the argument, it fails. First, I argue that there is a plausible account of admissibility on which Conditions 1 and 2 are false. That defeats reading 1. Next, I argue that the intuitions that lead us to assent to Condition 2 also lead us to assent to other very closely related principles that are inconsistent with Condition 2. This, I claim, casts doubt on the reliability of those intuitions, and thus removes our justification for Condition 2. This defeats the second reading of the HLWW argument. Thus, the argument fails. (shrink)

We argue that subjective Bayesians face a dilemma: they must offend against the spirit of their permissivism about rational credence or reject the principle that one should avoid accuracy dominance.

One of the most difficult problems in the foundations of physics is what gives rise to the arrow of time. Since the fundamental dynamical laws of physics are (essentially) symmetric in time, the explanation for time's arrow must come from elsewhere. A promising explanation introduces a special cosmological initial condition, now called the Past Hypothesis: the universe started in a low-entropy state. Unfortunately, in a universe where there are many copies of us (in the distant ''past'' or the distant ''future''), (...) the Past Hypothesis is not enough; we also need to postulate self-locating (de se) probabilities. However, I show that we can similarly use self-locating probabilities to strengthen its rival---the Fluctuation Hypothesis, leading to in-principle empirical underdetermination and radical epistemological skepticism. The underdetermination is robust in the sense that it is not resolved by the usual appeal to 'empirical coherence' or 'simplicity.' That is a serious problem for the vision of providing a completely scientific explanation of time's arrow. (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)

This paper highlights the role of Lewis’ Principal Principle and certain auxiliary conditions on admissibility as serving to explicate normal informal standards of what is reasonable. These considerations motivate the presuppositions of the argument that the Principal Principle implies the Principle of Indifference, put forward by Hawthorne et al.. They also suggest a line of response to recent criticisms of that argument, due to Pettigrew and Titelbaum and Hart, 621–632, 2020). The paper also shows that related concerns of Hart and (...) Titelbaum, 252–262, 2015) do not undermine the argument of Hawthorne et al.. (shrink)

This paper presents a new argument for the Principle of Indifference. This argument can be thought of in two ways: as a pragmatic argument, justifying the principle as needing to hold if one is to minimise worst-case expected loss, or as an epistemic argument, justifying the principle as needing to hold in order to minimise worst-case expected inaccuracy. The question arises as to which interpretation is preferable. I show that the epistemic argument contradicts Evidentialism and suggest that the relative plausibility (...) of Evidentialism provides grounds to prefer the pragmatic interpretation. If this is right, it extends to a general preference for pragmatic arguments for the Principle of Indifference, and also to a general preference for pragmatic arguments for other norms of Bayesian epistemology. (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)

While many philosophers have agreed that evidence of disagreement is a kind of higher-order evidence, this has not yet resulted in formally precise higher-order approaches to the problem of disagreement. In this paper, we outline a simple formal framework for determining the epistemic significance of a body of higher-order evidence, and use this framework to motivate a novel interpretation of the popular “equal weight view” of peer disagreement—we call it the Variably Equal Weight View (VEW). We show that VEW differs (...) from the standard Split the Difference (SD) interpretation of the equal weight view in almost all cases of peer disagreement, and use our formal framework to explain why SD has seemed attractive but is in fact misguided. A desirable feature of VEW, we argue, is that it gives rise to plausible instances of synergy—an effect whereby the parties to a disagreement should become more (or less) confident in the disputed proposition than any of them were prior to disagreement. Lastly, we show how VEW may be generalized to cases of non-peer disagreement. (shrink)

Epistemic decision theory (EDT) employs the mathematical tools of rational choice theory to justify epistemic norms, including probabilism, conditionalization, and the Principal Principle, among others. Practitioners of EDT endorse two theses: (1) epistemic value is distinct from subjective preference, and (2) belief and epistemic value can be numerically quantified. We argue the first thesis, which we call epistemic puritanism, undermines the second.

ABSTRACTThis book symposium onAccuracy and the Laws of Credenceconsists of an overview of the book’s argument by the author, Richard Pettigrew, together with four commentaries on different aspects of that argument. Ben Levinstein challenges the characterisation of the legitimate measures of inaccuracy that plays a central role in the arguments of the book. Julia Staffel asks whether the arguments of the book are compatible with an ontology of doxastic states that includes full beliefs as well as credences. Fabrizio Cariani raises (...) concerns about the argument offered in the book for various chance-credence principles. And Sophie Horowitz questions the assumptions at play in the book’s argument for the Principle of Indifference, as well as asking how the various laws of credence considered in the book relate to one another. (shrink)

Accuracy-first epistemology says that the rational update rule is the rule that maximizes expected accuracy. Externalism says, roughly, that we do not always know what our total evidence is. It’s been argued in recent years that the externalist faces a dilemma: Either deny that Bayesian Conditionalization is the rational update rule, thereby rejecting traditional Bayesian epistemology, or else deny that the rational update rule is the rule that maximizes expected accuracy, thereby rejecting the accuracy-first program. Call this the Bayesian Dilemma. (...) Here is roughly how the argument goes. Schoenfield (2017) has shown that following Metaconditionalization maximizes expected accuracy. But if externalism is true, Metaconditionalization is not Bayesian Conditionalization. Therefore, the externalist must choose between the rule that maximizes expected accuracy (Metaconditionalization) and Bayesian Conditionalization. I am not convinced by this argument; once we make the premises fully explicit, we see that it relies on assumptions that the externalist has every reason to reject. Still, I think that the Bayesian Dilemma is a genuine dilemma. I give a new argument—I call it the continuity argument—that doesn’t make any assumptions the externalist rejects. Roughly, I show that if you're sufficiently confident that you will correctly identify your evidence, then you'll expect adopting a rule that I call Accurate Metaconditionalization to be more accurate than adopting Bayesian Conditionalization. (shrink)

Can we extend accuracy-based epistemic utility theory to imprecise credences? There's no obvious way of proceeding: some stipulations will be necessary for either (i) the notion of accuracy or (ii) the epistemic decision rule. With some prima facie plausible stipulations, imprecise credences are always required. With others, they’re always impermissible. Care is needed to reach the familiar evidential view of imprecise credence: that whether precise or imprecise credences are required depends on the character of one's evidence. I propose an epistemic (...) utility theoretic defense of a common view about how evidence places demands on imprecise credence: that your spread of credence should cover the range of chance hypotheses left open by your evidence. I argue that objections to the form of epistemic utility theoretic argument that I use will extend to the standard motivation for epistemically mandatory imprecise credences. (shrink)

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 Principle of Indifference (POI) is a rule for rationally assigning precise degrees of confidence to possibilities among which we have no reason to discriminate. Despite criticism of the principle stemming from Bertrand's paradox, many have recently come to the defense of POI or adopted some restricted version of that principle, especially in discussions of self-locating belief. I argue that POI in both unrestricted and restricted forms is untenable, and that arguments for the more restricted principles are hostage to problems (...) similar to those that bedevil arguments for traditional POI. (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 situations where we ignore everything but the space of possibilities, we ought to suspend judgment—that is, remain agnostic—about which of these possibilities is the case. This means that we cannot sum our degrees of belief in different possibilities, something that has been formalized as an axiom of non-additivity. Consistent with this way of representing our ignorance, I defend a doxastic norm that recommends that we should nevertheless follow a certain additivity of possibilities: even if we cannot sum degrees of (...) belief in different possibilities, we should be more confident in larger groups of possibilities. It is thus shown that, in the type of situation considered (in so-called ‘classical ignorance’, i.e. “behind a thin veil of ignorance”), it is epistemically rational for advocates of suspending judgment to endorse this comparative confidence; while on the other hand it is shown that, even in classical ignorance, no stronger belief—such as a precise uniform probability distribution—is warranted. (shrink)

An important line of response to scepticism appeals to the best explanation. But anti-sceptics have not engaged much with work on explanation in the philosophy of science. I plan to investigate whether plausible assumptions about best explanations really do favour anti-scepticism. I will argue that there are ways of constructing sceptical hypotheses in which the assumptions do favour anti-scepticism, but the size of the support for anti-scepticism is small.

The principle of indifference has fallen from grace in contemporary philosophy, yet some papers have recently sought to vindicate its plausibility. This paper follows suit. In it, I articulate a version of the principle and provide what appears to be a novel argument in favour of it. The argument relies on a thought experiment where, intuitively, an agent’s confidence in any particular outcome being true should decrease with the addition of outcomes to the relevant space of possible outcomes. Put simply: (...) the greater the number of outcomes, the weaker your confidence should be in any one of those outcomes. The argument holds that this intuition favours the principle of indifference. I point out that, in contrast, the intuition is also incompatible with a major alternative to the principle which prescribes imprecise credences: the so-called wide interval view. Consequently, the argument may also be seen as an argument against the wide interval view. (shrink)

This paper presents a new argument for the Principle of Indifference. This argument can be thought of in two ways: as a pragmatic argument, justifying the principle as needing to hold if one is to minimise worst-case expected loss, or as an epistemic argument, justifying the principle as needing to hold in order to minimise worst-case expected inaccuracy. The question arises as to which interpretation is preferable. I show that the epistemic argument contradicts Evidentialism and suggest that the relative plausibility (...) of Evidentialism provides grounds to prefer the pragmatic interpretation. If this is right, it extends to a general preference for pragmatic arguments for the Principle of Indifference, and also to a general preference for pragmatic arguments for other norms of Bayesian epistemology. (shrink)

Many philosophers have challenged the ideal of value-free science on the grounds that social or moral values are relevant to inferential thresholds. But given this view, how precisely and to what extent should scientists adjust their inferential thresholds in light of nonepistemic values? We suggest that signal detection theory provides a useful framework for addressing this question. Moreover, this approach opens up further avenues for philosophical inquiry and has important implications for philosophical debates concerning inductive risk. For example, the signal (...) detection theory framework entails that considerations of inductive risk and inferential-threshold placement cannot be conducted in isolation from base-rate information. (shrink)

According to the principle of indifference, when a set of possibilities is evidentially symmetric for you – when your evidence no more supports any one of the possibilities over any other – you're required to distribute your credences uniformly among them. Despite its intuitive appeal, the principle of indifference is often thought to be unsustainable due to the problem of multiple partitions: Depending on how a set of possibilities is divided, it seems that sometimes, applying indifference reasoning can require you (...) to assign incompatible credences to equivalent possibilities. This paper defends the principle of indifference from the problem of multiple partitions by offering two guides for how to respond. The first is for permissivists about rationality, and is modeled on permissivists' arguments for the claim that a body of evidence sometimes does not uniquely determine a fully rational credence function. The second is for impermissivists about rationality, and is modeled on impermissivists' arguments for the claim that a body of evidence does always uniquely determine a fully rational credence function. What appears to be a decisive objection against the principle of indifference is in fact an instance of a general challenge taking different forms familiar to both permissivists and impermissivists. (shrink)

An important line of response to scepticism appeals to the best explanation. But anti-sceptics have not engaged much with work on explanation in the philosophy of science. I plan to investigate whether plausible assumptions about best explanations really do favour anti-scepticism. I will argue that there are ways of constructing sceptical hypotheses in which the assumptions do favour anti-scepticism, but the size of the support for anti-scepticism is small.

Richard Pettigrew has recently advanced a justification of the Principle of Indifference on the basis of a principle that he calls “cognitive conservatism,” or “extreme epistemic conservatism.” However, the credences based on the Principle of Indifference, as Pettigrew formulates it, violate another desideratum, namely, that learning from experience be possible. If it is accepted that learning from experience should be possible, this provides grounds for rejecting cognitive conservatism. Another set of criteria considered by Pettigrew, which involves a weighted mean of (...) worst-case and best-case accuracy, affords some learning, but not the sort that one would expect. This raises the question of whether accuracy-based considerations can be adapted to justify credence functions that permit induction. (shrink)