We introduce a family of rules for adjusting one's credences in response to learning the credences of others. These rules have a number of desirable features. 1. They yield the posterior credences that would result from updating by standard Bayesian conditionalization on one's peers' reported credences if one's likelihood function takes a particular simple form. 2. In the simplest form, they are symmetric among the agents in the group. 3. They map neatly onto the familiar (...) Condorcet voting results. 4. They preserve shared agreement about independence in a wide range of cases. 5. They commute with conditionalization and with multiple peer updates. Importantly, these rules have a surprising property that we call synergy - peer testimony of credences can provide mutually supporting evidence raising an individual's credence higher than any peer's initial prior report. At first, this may seem to be a strike against them. We argue, however, that synergy is actually a desirable feature and the failure of other updating rules to yield synergy is a strike against them. (shrink)

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)

The strategy of updating credences by minimizing the relative entropy has been questioned by many authors, most strongly by means of the Judy Benjamin puzzle. I present a new analysis of Judy Benjamin–like forms of new information and defend the thesis that in general the rational posterior is indeterminate, meaning that a family of posterior credence functions rather than a single one is the rational response when that type of information becomes available. The proposed thesis extends naturally to (...) all cases in which new information is traditionally handled by minimizing the relative entropy. (shrink)

Traditional procedures for rational updating fail when it comes to self-locating opinions, such as your credences about where you are and what time it is. This paper develops an updating procedure for rational agents with self-locating beliefs. In short, I argue that rational updating can be factored into two steps. The first step uses information you recall from your previous self to form a hypothetical credence distribution, and the second step changes this hypothetical distribution to reflect (...) information you have genuinely learned as time has passed. While the second step resembles traditional procedures of updating by conditionalization, the first is best understood by analogy to traditional models of how agents transmit self-locating opinions through ordinary interpersonal communication. (shrink)

A plea: If you're going to propose a Bayesian framework for updating self-locating degrees of belief, please read this piece first. I've tried to survey all the extant formalisms, group them by their general approach, then describe challenges faced by every formalism employing a given approach. Hopefully this survey will prevent further instances of authors' re-inventing updating rules already proposed elsewhere in the literature.

David Lewis' "Principal Principle" is a purported principle of rationality connecting credence and objective chance. Almost all of the discussion of the Principal Principle in the philosophical literature assumes classical probability theory, which is unfortunate since the theory of modern physics that, arguably, speaks most clearly of objective chance is the quantum theory, and quantum probabilities are not classical probabilities. This paper develops an account of how chance works in quantum theory that reveals a connection between credence and quantum chance (...) quite unlike what is envisioned in the philosophical literature: as a theorem of quantum probability, updating a completely additive chance function on a knowledge of chance brings credence into line with chance. The account also suggests a way of construing the Humean supervenience of chance that has the virtue of dissolving some puzzles about the "undermining" of chances. A number of interpretative moves in quantum theory are needed to generate the account of quantum chance on offer here, and they can all be disputed. But engaging in these disputes is part and parcel of naturalized metaphysics, and as such it can be more productive than engaging in the battle of intuitions among analytical metaphysicians about how chance ought to work this and other possible worlds. -/- . (shrink)

Triviality results threaten plausible principles governing our credence in epistemic modal claims. This paper develops a new account of modal credence which avoids triviality. On the resulting theory, probabilities are assigned not to sets of worlds, but rather to sets of information state-world pairs. The theory avoids triviality by giving up the principle that rational credence is closed under conditionalization. A rational agent can become irrational by conditionalizing on new evidence. In place of conditionalization, the paper develops a new account (...) of updating: conditionalization with normalization. (shrink)

This essay gives an account of epistemic deference for agents with imprecise credences. I look at the two main imprecise deference principles in the literature, known as Identity Reflection and Pointwise Reflection (Moss, 2021). I show that Pointwise Reflection is strictly weaker than Identity Reflection, and argue that, if you are certain you will update by conditionalisation, you should defer to your future self according to Identity Reflection. Then I give a more general justification for Pointwise and Identity Reflection (...) from the assumption that you defer to someone whenever you consider their doxastic state to be better than yours, in the sense of leading to better decision-making. (shrink)

We tackle two open questions from Leitgeb and Pettigrew (2010b) regarding what the belief update framework described in that paper mandates as correct responses to two problems. One of them concerns credences in overlapping propositions and is known in the literature as the “simultaneous update problem”. The other is the well known “Judy Benjamin” problem concerning conditional credences. We argue that our results concerning the problems point to deficiencies of the framework. More generally, we observe that the method (...) of minimizing inverse relative entropy seems to work better than (or at least equally well as) its competitors in many situations. (shrink)

Quine challenged traditional views of the a priori by appealing to two key premises: that any statement may be held true “come what may” and that no statement is immune to revision in light of new experience. Chalmers has recently developed a seemingly compelling response to each of these claims. The critique is particularly threatening because it seems to rest on the Bayesian premise that upon acquiring evidence E, a rational agent will update her credence in any statement S to (...) equal her prior conditional credence in S given E. We argue that Chalmers’s criticisms misfire. When properly understood, Quine’s two theses are largely consistent with Bayesianism. (shrink)

In this paper, I use a framework from computational linguistics, the Rational Speech Act framework, to model deceptive probabilistic communication. This account allows agents to discount for the biases they perceive their interlocutors to have. This way, agents can update their credences with the perceived interests of others in mind.

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)

David Lewis' "Principal Principle" is a purported principle of rationality connecting credence and objective chance. Almost all of the discussion of the Principal Principle in the philosophical literature assumes classical probability theory, which is unfortunate since the theory of modern physics that, arguably, speaks most clearly of objective chance is the quantum theory, and quantum probabilities are not classical probabilities. Given the generally accepted updating rule for quantum probabilities, there is a straight forward sense in which the Principal Principle (...) is a theorem of quantum probability theory for any credence function satisfying a suitable additivity requirement. No additional principle of rationality is needed to bring credence into line with objective chance. (shrink)

Scoring rules measure the accuracy or epistemic utility of a credence assignment. A significant literature uses plausible conditions on scoring rules on finite sample spaces to argue for both probabilism—the doctrine that credences ought to satisfy the axioms of probabilism—and for the optimality of Bayesian update as a response to evidence. I prove a number of formal results regarding scoring rules on infinite sample spaces that impact the extension of these arguments to infinite sample spaces. A common condition in (...) the arguments for probabilism and Bayesian update is strict propriety: that according to each probabilistic credence, the expected accuracy of any other credence is worse. Much of the discussion needs to divide depending on whether we require finite or countable additivity of our probabilities. I show that in a number of natural infinite finitely additive cases, there simply do not exist strictly proper scoring rules, and the prospects for arguments for probabilism and Bayesian update are limited. In many natural infinite countably additive cases, on the other hand, there do exist strictly proper scoring rules that are continuous on the probabilities, and which support arguments for Bayesian update, but which do not support arguments for probabilism. There may be more hope for accuracy-based arguments if we drop the assumption that scores are extended-real-valued. I sketch a framework for scoring rules whose values are nets of extended reals, and show the existence of a strictly proper net-valued scoring rules in all infinite cases, both for f.a. and c.a. probabilities. These can be used in an argument for Bayesian update, but it is not at present known what is to be said about probabilism in this case. (shrink)

'Fundamentals of Bayesian Epistemology' provides an accessible introduction to the key concepts and principles of the Bayesian formalism. This volume introduces degrees of belief as a concept in epistemology and the rules for updating degrees of belief derived from Bayesian principles.--.

In a recent paper, Pettigrew argues that the pragmatic and epistemic arguments for Bayesian updating are based on an unwarranted assumption, which he calls deterministic updating, and which says that your updating plan should be deterministic. In that paper, Pettigrew did not consider whether the symmetry arguments due to Hughes and van Fraassen make the same assumption Scientific inquiry in philosophical perspective. University Press of America, Lanham, pp. 183–223, 1987). In this note, I show that they do.

In this paper, I argue that some plausible principles concerning which credences are rationally permissible for agents given information about one another’s epistemic and credal states have some surprising consequences for which credences an agent ought to have in light of self-locating information. I provide a framework that allows us to state these constraints and draw out these consequences precisely. I then consider and assess the prospects for rejecting these prima facie plausible principles.

Lin and Kelly :957–981, 2012) and Leitgeb :1338–1389, 2013, Philos Rev 123:131–171, 2014), offer similar solutions to the Lottery Paradox, defining acceptance rules which determine a rational agent’s beliefs in terms of broader features of her credal state than just her isolated credences in individual propositions. I express each proposal as a method for obtaining an ordering over a partition from a credence function, and then a belief set from the ordering. Although these proposals avoid the original Lottery Paradox, (...) I raise a diachronic case which illustrates that neither satisfies both Lin and Kelly’s constraint that the update on orderings track the update on credence functions, and the intuitive constraint that credence of at least 0.5 is necessary for rational belief. I conclude by suggesting that we reformulate these proposals in terms of orderings over entire algebras based on partitions rather than orderings just over the partitions themselves. Reformulating both rules in this way yields acceptance rules which avoid the Lottery Paradox while satisfying both the tracking and likeliness constraints. (shrink)

There are some candidates that have been thought to measure the degree to which evidence incrementally confirms a hypothesis. This paper provides an argument for one candidate—the log-likelihood ratio measure. For this purpose, I will suggest a plausible requirement that I call the Requirement of Collaboration. And then, it will be shown that, of various candidates, only the log-likelihood ratio measure \(l\) satisfies this requirement. Using this result, Jeffrey conditionalization will be reformulated so as to disclose explicitly what determines new (...) credences after experience. (shrink)

You may think the following proposals are thought experiments that's fine, as such they still make the point in question. I happen to think of them as real, highly desirable, possibilities for the foreseeable future. For me they are a solution to the annoying certainty that we will be overtaken in every area by future superintelligent machines, and will be excluded from all the really interesting developments unless we keep up, personally and intimately, with the technologies of thought. That these (...) ideas raise and clarify some interesting metaphysical questions is a bonus. (shrink)

Ethics consultation has become an integral part of the fabric of U.S. health care delivery. This article summarizes the second edition of the Core Competencies for Health Care Ethics Consultation report of the American Society for Bioethics and Humanities. The core knowledge and skills competencies identified in the first edition of Core Competencies have been adopted by various ethics consultation services and education programs, providing evidence of their endorsement as health care ethics consultation (HCEC) standards. This revised report was prompted (...) by thinking in the field that has evolved since the original report. Patients, family members, and health care providers who encounter ethical questions or concerns that ethics consultants could help address deserve access to efficient, effective, and accountable HCEC services. All individuals providing such services should be held to the standards of competence and quality described in the revised report. (shrink)

In “Judy Benjamin is a Sleeping Beauty” (2010) Bovens recognises a certain similarity between the Sleeping Beauty (SB) and the Judy Benjamin (JB). But he does not recognise the dissimilarity between underlying protocols (as spelled out in Shafer (1985). Protocols are expressed in conditional probability tables that spell out the probability of coming to learn various propositions conditional on the actual state of the world. The principle of total evidence requires that we not update on the content of the proposition (...) learned but rather on the fact that we learn the proposition in question. Now attention to protocols drives a wedge between the SB and the JB. We have shown that the solution to a close variant of the SB which involves a clear protocol is P*(Heads) = 1/3 and since Beauty’s has precisely the same information at her disposal in the original SB at the time that she is asked to state her credence for Heads, the same solution should hold. The solution to the JB, on the other hand, is dependent on Judy’s probability distribution over protocols. One reasonable protocol yields P(Red) = 1/2, but Judy could also defend alternative values or a range of values in the interval [1/3, 1/2] depending on her probability distribution over protocols. (shrink)

The Puzzle of the Hats is a betting arrangement which seems to show that a Dutch book can be made against a group of rational players with common priors who act in the common interest and have full trust in the other players’ rationality. But we show that appearances are misleading—no such Dutch book can be made. There are four morals. First, what can be learned from the puzzle is that there is a class of situations in which credences (...) and betting rates diverge. Second, there is an analogy between ways of dealing with situations of this kind and different policies for sequential choice. Third, there is an analogy with strategic voting, showing that the common interest is not always served by expressing how things seem to you in social decision-making. And fourth, our analysis of the Puzzle of the Hats casts light on a recent controversy about the Dutch book argument for the Sleeping Beauty. (shrink)

What sort of doxastic response is rational to learning that one disagrees with an epistemic peer who has evaluated the same evidence? I argue that even weak general recommendations run the risk of being incompatible with a pair of real epistemic phenomena, what I call evidential attenuation and evidential amplification. I focus on a popular and intuitive view of disagreement, the equal weight view. I take it to state that in cases of peer disagreement, a subject ought to end up (...) equally confident that her own opinion is correct as that the opinion of her peer is. I say why we should regard the equal weight view as a synchronic constraint on (prior) credence functions. I then spell out a trilemma for the view: it violates what are intuitively correct updates (also leading to violations of conditionalisation), it poses implausible restrictions on prior credence functions, or it is non-substantive. The sorts of reasons why the equal weight view fails apply to other views as well: there is no blanket answer to the question of how a subject should adjust her opinions in cases of peer disagreement. (shrink)

Roger White objects to interval-valued credence theories because they produce a counterintuitive “dilation” effect in a story he calls the Coin Game. We respond that results in the Coin Game were bound to be counterintuitive anyway, because the story involves an agent who learns a biconditional. Biconditional updates produce surprising results whether the credences involved are ranged or precise, so White's story is no counterexample to ranged credence theories.

When P(E) > 0, conditional probabilities P(H|E)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$(H|E)$$\end{document} are given by the ratio formula. An agent engages in ratio conditionalization when she updates her credences using conditional probabilities dictated by the ratio formula. Ratio conditionalization cannot eradicate certainties, including certainties gained through prior exercises of ratio conditionalization. An agent who updates her credences only through ratio conditionalization risks permanent certainty in propositions against which she has overwhelming evidence. To avoid this (...) undesirable consequence, I argue that we should supplement ratio conditionalization with Kolmogorov conditionalization, a strategy for updating credences based on propositions E such that P(E) = 0. Kolmogorov conditionalization can eradicate certainties, including certainties gained through prior exercises of conditionalization. Adducing general theorems and detailed examples, I show that Kolmogorov conditionalization helps us model epistemic defeat across a wide range of circumstances. (shrink)

How should a group with different opinions (but the same values) make decisions? In a Bayesian setting, the natural question is how to aggregate credences: how to use a single credence function to naturally represent a collection of different credence functions. An extension of the standard Dutch-book arguments that apply to individual decision-makers recommends that group credences should be updated by conditionalization. This imposes a constraint on what aggregation rules can be like. Taking conditionalization as a basic constraint, (...) we gather lessons from the established work on credence aggregation, and extend this work with two new impossibility results. We then explore contrasting features of two kinds of rules that satisfy the constraints we articulate: one kind uses fixed prior credences, and the other uses geometric averaging, as opposed to arithmetic averaging. We also prove a new characterisation result for geometric averaging. Finally we consider applications to neighboring philosophical issues, including the epistemology of disagreement. (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)

_Philosophy of Probability: Contemporary Readings_ is the first anthology to collect essential readings in this important area of philosophy. Featuring the work of leading philosophers in the field such as Carnap, Hájek, Jeffrey, Joyce, Lewis, Loewer, Popper, Ramsey, van Fraassen, von Mises, and many others, the book looks in depth at the following key topics: subjective probability and credence probability updating: conditionalization and reflection Bayesian confirmation theory classical, logical, and evidential probability frequentism physical probability: propensities and objective chances. The (...) book features a useful primer on the mathematics of probability, and each section includes an introduction by the editor, as well as a guide to further reading. A broad-ranging and highly accessible exploration of the subject, _Philosophy of Probability_ is ideal for any student of formal epistemology, philosophy of science, metaphysics, or philosophy of mathematics. (shrink)

An infinite lottery experiment seems to indicate that Bayesian conditionalization may be inconsistent when the prior credence function is finitely additive because, in that experiment, it conflicts with the principle of reflection. I will show that any other form of updating credences would produce the same conflict, and, furthermore, that the conflict is not between conditionalization and reflection but, instead, between finite additivity and reflection. A correct treatment of the infinite lottery experiment requires a careful treatment of finite (...) additivity. I will show that the results of the experiment, paradoxical though they may be, are not inconsistent, but that they conflict with one particular version of reflection . I will reject that version and I will propose a slight modification of a different version of reflection such that the modified version does maintain the mutual consistency of finite additivity, reflection and conditionalization. As a result, I will strengthen the case for finite additivity by showing that Bayesian conditionalization is fully consistent with it. (shrink)

The Puzzle of the Hats is a puzzle in social epistemology. It describes a situation in which a group of rational agents with common priors and common goals seems vulnerable to a Dutch book if they are exposed to different information and make decisions independently. Situations in which this happens involve violations of what might be called the Group-Reflection Principle. As it turns out, the Dutch book is flawed. It is based on the betting interpretation of the subjective probabilities, but (...) ignores the fact that this interpretation disregards strategic considerations that might influence betting behavior. A lesson to be learned concerns the interpretation of probabilities in terms of fair bets and, more generally, the role of strategic considerations in epistemic contexts. Another lesson concerns Group-Reflection, which in its unrestricted form is highly counter-intuitive. We consider how this principle of social epistemology should be re-formulated so as to make it tenable. (shrink)

For epistemic subjects like us, updating our credences incurs epistemic costs. Expending our limited processing power and working memory to properly update our credences by some information can come at the cost of not responding to other available information. It is thus desirable to flesh out and compare alternative ways of taking information into account in light of cognitive shortcomings like our own. This paper is a preliminary attempt to do so. I argue that it is better, (...) in a range of circumstances and from the point of view of expected credal accuracy, for epistemic subjects like us not to update on available information that bears on propositions for which substantial evidence has been gathered than it is to update on information as it presents itself. In order to clarify the argument, and enable comparisons between information-response policies more generally, I develop a queue-theoretic model of learning for subjects with cognitive limitations. The model characterizes how policies for responding to information interact with a subject’s limitations to yield confidences. Finally, I discuss implications of the discussion for work on confidence, outright belief, and the relationship between those two states. The comparison of information-response policies helps to explain how some of the “biases” revealed by psychological research might be cognitively valuable, clarify views that take outright belief to be a kind of epistemic plan that resists reconsideration, and assuage certain “demandingness” worries for the hypothesis that we are credal reasoners. (shrink)

We argue that social deliberation may increase an agent’s confidence and credence under certain circumstances. An agent considers a proposition H and assigns a probability to it. However, she is not fully confident that she herself is reliable in this assignment. She then endorses H during deliberation with another person, expecting him to raise serious objections. To her surprise, however, the other person does not raise any objections to H. How should her attitudes toward H change? It seems plausible that (...) she should increase the credence she assigns to H and, at the same time, increase the reliability she assigns to herself concerning H. A Bayesian model helps us to investigate under what conditions, if any, this is rational. (shrink)

According to an increasingly popular epistemological view, people need outright beliefs in addition to credences to simplify their reasoning. Outright beliefs simplify reasoning by allowing thinkers to ignore small error probabilities. What is outright believed can change between contexts. It has been claimed that thinkers manage shifts in their outright beliefs and credences across contexts by an updating procedure resembling conditionalization, which I call pseudo-conditionalization (PC). But conditionalization is notoriously complicated. The claim that thinkers manage their beliefs (...) via PC is thus in tension with the view that the function of beliefs is to simplify our reasoning. I propose to resolve this puzzle by rejecting the view that thinkers employ PC. Based on this solution, I furthermore argue for a descriptive and a normative claim. The descriptive claim is that the available strategies for managing beliefs and credences across contexts that are compatible with the simplifying function of outright beliefs can generate synchronic and diachronic incoherence in a thinker’s attitudes. Moreover, I argue that the view of outright belief as a simplifying heuristic is incompatible with the view that there are ideal norms of coherence or consistency governing outright beliefs that are too complicated for human thinkers to comply with. (shrink)

Dogmatism is sometimes thought to be incompatible with Bayesian models of rational learning. I show that the best model for updating imprecise credences is compatible with dogmatism.

This paper develops an information-sensitive theory of the semantics and probability of conditionals and statements involving epistemic modals. The theory validates a number of principles linking probability and modality, including the principle that the probability of a conditional If A, then C equals the probability of C, updated with A. The theory avoids so-called triviality results, which are standardly taken to show that principles of this sort cannot be validated. To achieve this, we deny that rational agents update their (...) class='Hi'>credences via conditionalization. We offer a new rule of update, Hyperconditionalization, which agrees with Conditionalization whenever nonmodal statements are at stake but differs for modal and conditional sentences. (shrink)

According to certain normative theories in epistemology, rationality requires us to be logically omniscient. Yet this prescription clashes with our ordinary judgments of rationality. How should we resolve this tension? In this paper, I focus particularly on the logical omniscience requirement in Bayesian epistemology. Building on a key insight by Hacking :311–325, 1967), I develop a version of Bayesianism that permits logical ignorance. This includes: an account of the synchronic norms that govern a logically ignorant individual at any given time; (...) an account of how we reduce our logical ignorance by learning logical facts and how we should update our credences in response to such evidence; and an account of when logical ignorance is irrational and when it isn’t. At the end, I explain why the requirement of logical omniscience remains true of ideal agents with no computational, processing, or storage limitations. (shrink)

Approximate coherentism suggests that imperfectly rational agents should hold approximately coherent credences. This norm is intended as a generalization of ordinary coherence. I argue that it may be unable to play this role by considering its application under learning experiences. While it is unclear how imperfect agents should revise their beliefs, I suggest a plausible route is through Bayesian updating. However, Bayesian updating can take an incoherent agent from relatively more coherent credences to relatively less coherent (...) credences, depending on the data observed. Thus, comparative rationality judgments among incoherent agents are unduly sensitive to luck. (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)

According to the thesis of doxastic wronging, our beliefs can non-derivatively wrong others. A recent criticism of this view claims that proponents of the doxastic wronging thesis have no principled grounds for denying that credences can likewise non-derivatively wrong, so they must countenance pervasive conflicts between morality and epistemic rationality. This paper defends the thesis of doxastic wronging from this objection by arguing that belief bears distinctive relationships to inquiry and blame that can explain why beliefs, but not (...) class='Hi'>credences, can non-derivatively wrong. First, forming a belief (but not updating one’s credence) closes inquiry, and suspending judgment (but not updating one’s credence) opens inquiry. Consequently, beliefs can distinctively wrong others by prematurely closing inquiry or inappropriately opening inquiry. Second, beliefs (but not credences) can constitute blame. Unfittingly blaming someone can wrong them, and hence beliefs which constitute unfitting blame can distinctively wrong. In addition to defending the claim that only beliefs can non-derivatively wrong, this paper gestures towards an ethics of belief which attends to the relationship between belief and attitudes such as inquiry, faith, trust, and blame. (shrink)

Many philosophers regard the imprecise credence framework as a more realistic model of probabilistic inferences with imperfect empirical information than the traditional precise credence framework. Hence, it is surprising that the literature lacks any discussion on how to update one’s imprecise credences when the given evidence itself is imprecise. To fill this gap, I consider two updating principles. Unfortunately, each of them faces a serious problem. The first updating principle, which I call “generalized conditionalization,” sometimes forces an (...) agent to change her imprecise degrees of belief even though she does not have new evidence. The second updating principle, which I call “the generalized dynamic Keynesian model,” may result in a very precise credal state although the agent does not have sufficiently strong evidence to justify such an informative doxastic state. This means that it is much more difficult to come up with an acceptable updating principle for the imprecise credence framework than one might have thought it would be. (shrink)

A vexing question in Bayesian epistemology is how an agent should update on evidence which she assigned zero prior credence. Some theorists have suggested that, in such cases, the agent should update by Kolmogorov conditionalization, a norm based on Kolmogorov’s theory of regular conditional distributions. However, it turns out that in some situations, a Kolmogorov conditionalizer will plan to always assign a posterior credence of zero to the evidence she learns. Intuitively, such a plan is irrational and easily Dutch bookable. (...) In this paper, we propose a revised norm, Kolmogorov-Blackwell conditionalization, which avoids this problem. We prove a Dutch book theorem and converse Dutch book theorem for this revised norm, and relate our results to those of Rescorla (2018). (shrink)

The Sleeping Beauty puzzle has dramatized the divisive question of how de se beliefs should be integrated into formal theories of rational belief change. In this paper, I look ahead to a related question: how should de se beliefs be integrated into formal theories of rational choice? I argue that standard decision theoretic frameworks fail in special cases of de se uncertainty, like Sleeping Beauty. The nature of the failure reveals that sometimes rational choices are determined independently of one’s (...) class='Hi'>credences in the kinds of ‘narrow’ de se propositions that Sleepy Beauty has set in relief. Consequently, in addition to pinpointing a failure of standard decision theoretic frameworks, this result casts doubt on a large class of strategies for determining principles for the rationally updating de se beliefs in cases like Sleeping Beauty, and also calls into question the importance of making such a determination at all. (shrink)

In the Sleeping Beauty problem, Beauty is woken once if a coin lands heads or twice if the coin lands tails but promptly forgets each waking on returning to sleep. Philosophers have divided over whether her waking credence in heads should be a half or a third. Beauty has centered beliefs about her world and about her location in that world. When given new information about her location she should update her worldly beliefs before updating her locative beliefs. When (...) she conditionalizes in this way, her credence in heads is a half before and after being told it is Monday. In applications of Dutch Book arguments to the Sleeping Beauty problem, the probability of a particular outcome has often been confounded with consequences of that outcome. Heads and tails are equally likely but twice as much is at stake if the coin falls tails because Beauty is fated to make the same choice twice. As a consequence, the possibility of tails should be given twice the weight of the possibility of heads when deciding whether to bet on heads even though heads and tails are equally likely. (shrink)

The heart of my dissertation project is the proposal of a new updating rule for responding to learning experiences consisting of continuous streams of evidence. I suggest characterizing this kind of learning experience as a continuous stream of stipulated credal derivatives, and show that Continuous Probability Kinematics is the uniquely coherent response to such a stream which satisfies a continuous analogue of Rigidity – the core property of both Bayesian and Jeffrey conditionalization. In the first chapter, I define neighborhood (...) norms of rationality with reference to Kenny Easwaran’s definition of neighborhood properties. I summarize and comment on some of the key arguments in the dispute between time-slice epistemologists, who argue that there are no fundamentally diachronic norms of rationality, and the proponents of diachronic norms. I am sympathetic to two of the key motivations often given in support of the synchronist position: mentalist internalism and the idea that metaphysical disputes about the identity of persons in bizarre puzzle cases should not play a central role in epistemologists’ assessments of the rationality of agents. However, I argue that time-slice epistemology cannot adequately address the rationality of temporally-extended processes like reasoning and learning. Neighborhood norms present a viable third way between these two positions, capturing much of the spirit of the previously-discussed synchronist motivations while still providing just enough temporal structure to meaningfully guide and evaluate temporally-extended rational processes. Continuous Probability Kinematics is an example of one such neighborhood norm. In the second chapter, I develop my updating rule CPK and establish many of its core properties. Of special note here are the deep connections to Jeffrey’s Probability Kinematics, as well as some key differences. The net result of any CPK updating process will always be representable as a Jeffrey shift on the refined partition generated by the propositions that the agent is receiving direct evidence concerning. However, one crucial difference is that CPK provides an intuitive account of how to combine the effects of learning experiences that are each about fundamentally different underlying partitions. In CPK’s formalism, an agent can receive simultaneous evidence streams about an arbitrary (finite) number of propositions, which can themselves be evidentially related in any way. At any given instant, the result of the combination is a simple sum of the effects that learning about the individual propositions would have separately. CPK is concerned with a novel kind of learning experience and involves a novel characterization of evidence. The third and final chapter of this dissertation is concerned with explaining what this characterization of evidence means and with arguing that it can be the basis for genuine learning. I begin by characterizing learning experiences in terms of the Value of Information, and prove a Value of Information theorem for CPK learning experiences under the assumption of a Martingale constraint on the agent’s prior distribution over the signals that they might receive. I examine Timothy Williamson’s arguments that evidence must be propositional and express my skepticism. I then explore two different routes to model agents who update by CPK as if they are learning some propositional content and updating the rest of their credences by Bayesian conditionalization on this content. The second of these two routes provides a very interesting lens to reexamine the evidential commitments that underwrite updating by CPK, which I analyze. (shrink)

In the literature one finds two non-equivalent responses to forecasts; deference and updating. Herein it is demonstrated that, under certain conditions, both responses are entirely determined by one’s beliefs as regards the calibration of the forecaster. Further it is argued that the choice as to whether to defer to, or update on, a forecast is determined by the aim of the recipient of that forecast. If the aim of the recipient is to match their credence with the prevailing objective (...) chances, they should defer to the forecast; if it is to maximize the veritistic value of their beliefs, they should update on the forecast. (shrink)

How should we update de dicto beliefs in the face of de se evidence? The Sleeping Beauty problem divides philosophers into two camps, halfers and thirders. But there is some disagreement among halfers about how their position should generalize to other examples. A full generalization is not always given; one notable exception is the Halfer Rule, under which the agent updates her uncentered beliefs based on only the uncentered part of her evidence. In this brief article, I provide a simple (...) example for which the Halfer Rule prescribes credences that, I argue, cannot be reasonably held by anyone. In particular, these credences constitute an egregious violation of the Reflection Principle. I then discuss the consequences for halfing in general. (shrink)

In this article, 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 ‘value of information’ (VOI). I show that VOI 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 VOI fails. I go on to argue that this is bad news for defenders of VOI. (shrink)