People with the kind of preferences that give rise to the St. Petersburg paradox are problematic---but not because there is anything wrong with infinite utilities. Rather, such people cannot assign the St. Petersburg gamble any value that any kind of outcome could possibly have. Their preferences also violate an infinitary generalization of Savage's Sure Thing Principle, which we call the *Countable Sure Thing Principle*, as well as an infinitary generalization of von Neumann and Morgenstern's Independence axiom, which we call *Countable (...) Independence*. In violating these principles, they display foibles like those of people who deviate from standard expected utility theory in more mundane cases: they choose dominated strategies, pay to avoid information, and reject expert advice. We precisely characterize the preference relations that satisfy Countable Independence in several equivalent ways: a structural constraint on preferences, a representation theorem, and the principle we began with, that every prospect has a value that some outcome could have. (shrink)

Predictable polarization is everywhere: we can often predict how people’s opinions, including our own, will shift over time. Extant theories either neglect the fact that we can predict our own polarization, or explain it through irrational mechanisms. They needn’t. Empirical studies suggest that polarization is predictable when evidence is ambiguous, that is, when the rational response is not obvious. I show how Bayesians should model such ambiguity and then prove that—assuming rational updates are those which obey the value of evidence—ambiguity (...) is necessary and sufficient for the rationality of predictable polarization. The main theoretical result is that there can be a series of such updates, each of which is individually expected to make you more accurate, but which together will predictably polarize you. Polarization results from asymmetric increases in accuracy. This mechanism is not only theoretically possible, but empirically plausible. I argue that cognitive search—searching a cognitively accessible space for a particular item—often yields asymmetrically ambiguous evidence, I present an experiment supporting its polarizing effects, and I use simulations to show how it can explain two of the core causes of polarization: confirmation bias and the group polarization effect. (shrink)

Many theories of rational belief give a special place to logic. They say that an ideally rational agent would never be uncertain about logical facts. In short: they say that ideal rationality requires "logical omniscience." Here I argue against the view that ideal rationality requires logical omniscience on the grounds that the requirement of logical omniscience can come into conflict with the requirement to proportion one’s beliefs to the evidence. I proceed in two steps. First, I rehearse an influential line (...) of argument from the "higher-order evidence" debate, which purports to show that it would be dogmatic, even for a cognitively infallible agent, to refuse to revise her beliefs about logical matters in response to evidence indicating that those beliefs are irrational. Second, I defend this "anti-dogmatism" argument against two responses put forth by Declan Smithies and David Christensen. Against Smithies’ response, I argue that it leads to irrational self-ascriptions of epistemic luck, and that it obscures the distinction between propositional and doxastic justification. Against Christensen’s response, I argue that it clashes with one of two attractive deontic principles, and that it is extensionally inadequate. Taken together, these criticisms will suggest that the connection between logic and rationality cannot be what it is standardly taken to be—ideal rationality does not require logical omniscience. (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)

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)

Cases of inexact observations have been used extensively in the recent literature on higher-order evidence and higher-order knowledge. I argue that the received understanding of inexact observations is mistaken. Although it is convenient to assume that such cases can be modeled statically, they should be analyzed as dynamic cases that involve change of knowledge. Consequently, the underlying logic should be dynamic epistemic logic, not its static counterpart. When reasoning about inexact knowledge, it is easy to confuse the initial situation, the (...) observation process, and the result of the observation; I analyze the three separately. This dynamic approach has far reaching implications: Williamson’s influential argument against the KK principle loses its force, and new insights can be gained regarding synchronic and diachronic introspection principles. (shrink)

It is natural to think that rationality imposes some relationship between what a person believes, and what she believes about what she’s rational to believe. Epistemic akrasia—for example, believing P while believing that P is not rational to believe in your situation—is often seen as intrinsically irrational. This paper argues otherwise. In certain cases, akrasia is intuitively rational. Understanding why akratic beliefs in those case are indeed rational provides a deeper explanation how typical akratic beliefs are irrational—an explanation that does (...) not flow from akrasia per se. This understanding also allows us to diagnose where general anti-akratic arguments go wrong. We can then see why even principles designed to allow only moderate akrasia fail, and also why recognizing the possibility of rational akratic beliefs does not call for finding some other epistemic defect in agents who believe akratically. Believing akratically, in itself, is nothing to apologize for. (shrink)

It is natural to think that rationality imposes some relationship between what a person believes, and what she believes about what she’s rational to believe. Epistemic akrasia—for example, believing P while believing that P is not rational to believe in your situation—is often seen as intrinsically irrational. This paper argues otherwise. In certain cases, akrasia is intuitively rational. Understanding why akratic beliefs in those case are indeed rational provides a deeper explanation how typical akratic beliefs are irrational—an explanation that does (...) not flow from akrasia per se. This understanding also allows us to diagnose where general anti-akratic arguments go wrong. We can then see why even principles designed to allow only moderate akrasia fail, and also why recognizing the possibility of rational akratic beliefs does not call for finding some other epistemic defect in agents who believe akratically. Believing akratically, in itself, is nothing to apologize for. (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.

Is more information always better? Or are there some situations in which more information can make us worse off? Good (1967) argues that expected utility maximizers should always accept more information if the information is cost-free and relevant. But Good's argument presupposes that you are certain you will update by conditionalization. If we relax this assumption and allow agents to be uncertain about updating, these agents can be rationally required to reject free and relevant information. Since there are good reasons (...) to be uncertain about updating, rationality can require you to prefer ignorance. (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.

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)

When can a shift from a prior to a posterior be represented by conditionalization? A well-known result, known as “superconditioning” and going back to work by Diaconis and Zabell, gives a sharp answer. This paper extends the result and connects it to the reflection principle and common priors. I show that a shift from a prior to a set of posteriors can be represented within a conditioning model if and only if the prior and the posteriors are connected via a (...) general form of the reflection principle. Common priors can be characterized by principles that require a certain kind of coherence between distinct sets of posteriors. I discuss the implications these results have for diachronic and synchronic modes of updating, learning experiences, the common prior assumption of game theory, and time-slice epistemology. (shrink)

My dissertation is about Bayesian rationality for non-ideal agents. I show how to derive subjective probabilities from preferences using much weaker rationality assumptions than other standard representation theorems. I argue that non-ideal agents might be uncertain about how they will update on new information and consider two consequences of this uncertainty: such agents should sometimes reject free information and make choices which, taken together, yield sure loss. The upshot is that Bayesian rationality for non-ideal agents makes very different normative demands (...) than ideal Bayesian rationality. (shrink)

You have higher-order uncertainty iff you are uncertain of what opinions you should have. I defend three claims about it. First, the higher-order evidence debate can be helpfully reframed in terms of higher-order uncertainty. The central question becomes how your first- and higher-order opinions should relate—a precise question that can be embedded within a general, tractable framework. Second, this question is nontrivial. Rational higher-order uncertainty is pervasive, and lies at the foundations of the epistemology of disagreement. Third, the answer is (...) not obvious. The Enkratic Intuition---that your first-order opinions must “line up” with your higher-order opinions---is incorrect; epistemic akrasia can be rational. If all this is right, then it leaves us without answers---but with a clear picture of the question, and a fruitful strategy for pursuing it. (shrink)

We show how to extend any finite probability space into another finite one which satisfies the conditional construal of conditional probability for the original propositions, given some maximal allowed degree of nesting of the conditional. This mitigates the force of the well-known triviality results.

Is it ever rational to suspend judgment about whether a particular doxastic attitude of ours is rational? An agent who suspends about whether her attitude is rational has serious doubts that it is. These doubts place a special burden on the agent, namely, to justify maintaining her chosen attitude over others. A dilemma arises. Providing justification for maintaining the chosen attitude would commit the agent to considering the attitude rational—contrary to her suspension on the matter. Alternatively, in the absence of (...) such justification, the attitude would be arbitrary by the agent's own lights, and therefore irrational from the agent's own perspective. So, suspending about whether an attitude of ours is rational does not cohere with considering it rationally preferable to other attitudes, and leads to a more familiar form of epistemic akrasia otherwise. (shrink)

This paper proposes a novel answer to the question of what attitude agents should adopt when they receive misleading higher-order evidence that avoids the drawbacks of existing views. The answer builds on the independently motivated observation that there is a difference between attitudes that agents form as conclusions of their reasoning, called terminal attitudes, and attitudes that are formed in a transitional manner in the process of reasoning, called transitional attitudes. Terminal and transitional attitudes differ both in their descriptive and (...) in their normative properties. When an agent receives higher-order evidence that they might have reasoned incorrectly to a belief or credence towards p, then their attitude towards p is no longer justified as a terminal attitude towards p, but it can still be justified as a transitional attitude. This view, which I call the unmooring view, allows us to capture the rational impact of misleading higher-order evidence in a way that integrates smoothly with a natural picture of epistemic justification and the dynamics of deliberation. (shrink)

Should you always be certain about what you should believe? In other words, does rationality demand higher-order certainty? First answer: Yes! Higher-order uncertainty can’t be rational, since it breeds at least a mild form of epistemic akrasia. Second answer: No! Higher-order certainty can’t be rational, since it licenses a dogmatic kind of insensitivity to higher-order evidence. Which answer wins out? The first, I argue. Once we get clearer about what higher-order certainty is, a view emerges on which higher-order certainty does (...) not, in fact, license any kind of insensitivity to higher-order evidence. The view as I will describe it has plenty of intuitive appeal. But it is not without substantive commitments: it implies a strong form of internalism about epistemic rationality, and forces us to reconsider standard ways of thinking about the nature of evidential support. Yet, the view put forth promises a simple and elegant solution to a surprisingly difficult problem in our understanding of rational belief. (shrink)

How should we understand validity? A standard way to characterize validity is in terms of the preservation of truth (or truth in a model). But there are several problems facing such characterizations. An alternative approach is to characterize validity epistemically, for instance in terms of the preservation of an epistemic status. In this paper, I raise a problem for such views. First, I argue that if the relevant epistemic status is factive, such as being in a position to know or (...) having conclusive evidence for, then the account runs into trouble if we endorse certain familiar logical principles. Second, I argue that if the relevant epistemic status is non-factive, such as is rationally committed to or has justification for believing, then a similar problem arises if we endorse the logical principles as well as a sufficiently strong epistemic “level-bridging” principle. Finally, I argue that an analogous problem arises for the most natural characterization of validity in terms of rational credence. (shrink)

Stalnaker's Thesis about indicative conditionals is, roughly, that the probability one ought to assign to an indicative conditional equals the probability that one ought to assign to its consequent conditional on its antecedent. The thesis seems right. If you draw a card from a standard 52-card deck, how confident are you that the card is a diamond if it's a red card? To answer this, you calculate the proportion of red cards that are diamonds -- that is, you calculate the (...) probability of drawing a diamond conditional on drawing a red card. Skyrms' Thesis about counterfactual conditionals is, roughly, that the probability that one ought to assign to a counterfactual equals one's rational expectation of the chance, at a relevant past time, of its consequent conditional on its antecedent. This thesis also seems right. If you decide not to enter a 100-ticket lottery, how confident are you that you would have won had you bought a ticket? To answer this, you calculate the prior chance--that is, the chance just before your decision not to buy a ticket---of winning conditional on entering the lottery. The central project of this article is to develop a new uniform theory of conditionals that allows us to derive a version of Skyrms' Thesis from a version of Stalnaker's Thesis, together with a chance-deference norm relating rational credence to beliefs about objective chance. (shrink)

This article shows that there is a liar-like paradox that arises for rational credence that relies only on very weak logical and credal principles. The paradox depends on a weak rational reflection principle, logical principles governing conjunction, and principles governing the relationship between rational credence and proof. To respond to this paradox, we must either reject even very weak rational reflection principles or reject some highly plausible logical or credal principle.

A familiar complaint about conciliatory approaches to disagreement is that they are self-defeating or incoherent because they ‘call for their own rejection’. This complaint seems to be influential but it isn’t clear whether conciliatory views call for their own rejection or what, if anything, this tells us about the coherence of such views. We shall look at two ways of developing this self-defeat objection and we shall see that conciliatory views emerge unscathed. A simple version of the self-defeat objection leaves (...) conciliatory views untouched. A subtle version of the objection contains a subtle but overlooked flaw. If the conciliatory view is right, it might be right to be dogmatically conciliatory (i.e., to continue to be conciliatory however objectionable this might seem to ourselves and to others). (shrink)

Chance both guides our credences and is an objective feature of the world. How and why we should conform our credences to chance depends on the underlying metaphysical account of what chance is. I use considerations of accuracy (how close your credences come to truth-values) to propose a new way of deferring to chance. The principle I endorse, called the Trust Principle, requires chance to be a good guide to the world, permits modest chances, tells us how to listen to (...) chance even when the chances are modest, and entails but is not entailed by the New Principle. As I show, a rational agent will obey this principle if and only if she expects chance to be at least as accurate as she is on every good way of measuring accuracy. Much of the discussion, and the technical results, extend beyond chance to deference to any kind of expert. Indeed, you will trust someone about a particular question just in case you expect that person to be more accurate than you are about that question. (shrink)

Critical race theorists and standpoint epistemologists argue that agents who are members of dominant social groups are often in a state of ignorance about the extent of their social dominance, where this ignorance is explained by these agents' membership in a socially dominant group (e.g., Mills 2007). To illustrate this claim bluntly, it is argued: 1) that many white men do not know the extent of their social dominance, 2) that they remain ignorant as to the extent of their dominant (...) social position even where this information is freely attainable, and 3) that this ignorance is due in part to the fact that they are white men. We argue that on Buchak's (2010, 2013) model of risk averse instrumental rationality, ignorance of one's privileges can be rational. This argument yields a new account of elite-group ignorance, why it may occur, and how it might be alleviated. (shrink)

Epistemologists spend a great deal of time thinking about how we should respond to our evidence. They spend far less time thinking about the ways that evidence can be acquired in the first place. This is an oversight. Some ways of acquiring evidence are better than others. Many normative epistemologies struggle to accommodate this fact. In this article I develop one that can and does. I identify a phenomenon – epistemic feedback loops – in which evidence acquisition has gone awry, (...) with the result that even beliefs based on the evidence are irrational. Examples include evidence acquired under the influence of confirmation bias and evidence acquired under the influence of cognitively penetrated experiences caused by implicit bias. I then develop a theoretical framework which enables us to understand why beliefs that are the outputs of epistemic feedback loops are irrational. Finally, I argue that many popular approaches to epistemic normativity may need to be abandoned on the grounds that they cannot comfortably explain feedback loops. The scope of this last claim is broad: it includes almost all contemporary theories of justified/rational belief and of the epistemology of cognitive penetration. (shrink)

There has been considerable puzzlement over how to respond to higher-order evidence. The existing dilemmas can be defused by adopting a ‘two-dimensional’ representation of doxastic attitudes which incorporates not only substantive uncertainty about which first-order state of affairs obtains but also the degree of conviction with which we hold the attitude. This makes it possible that in cases of higher-order evidence the evidence sometimes impacts primarily on our conviction, rather than our substantive uncertainty. I argue that such a two-dimensional representation (...) is naturally developed by making use of imprecise probabilities. (shrink)

Metacognitive mental states are mental states about mental states. For example, I may be uncertain whether my belief is correct. In social discourse, an interlocutor’s metacognitive certainty may constitute evidence about the reliability of their testimony. For example, if a speaker is certain that their belief is correct, then we may take this as evidence in favour of their belief, or its content. This paper argues that, if metacognitive certainty is genuine evidence, then it is disproportionate evidence for extreme beliefs. (...) In support of the argument, we report findings from five studies with different participant samples, designs, and measures. These studies show that, the more extreme an agent’s belief (positive or negative), the more certain they are about it, and vice versa. This relationship might contribute to moralism, virtue signalling, and polarisation, which in turn may be epistemically and morally problematic. Therefore, we caution against taking metacognitive certainty as genuine evidence. (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)

Higher-order evidence is evidence about what is rational to think in light of your evidence. Many have argued that it is special – falling into its own evidential category, or leading to deviations from standard rational norms. But it is not. Given standard assumptions, almost all evidence is higher-order evidence.

A norm of local expert deference says that your credence in an arbitrary proposition A, given that the expert's probability for A is n, should be n. A norm of global expert deference says that your credence in A, given that the expert's entire probability function is E, should be E(A). Gaifman (1988) taught us that these two norms are not equivalent. Stalnaker (2019) conjectures that Gaifman's example is "a loophole". Here, I substantiate Stalnaker's suspicions by providing characterisation theorems which (...) tell us precisely when the norms give different advice. They tell us that, in a good sense, Gaifman's example is the only case where the two norms differ. I suggest that the lesson of the theorems is that Bayesian epistemologists need not concern themselves with the differences between these two kinds of norms. While they are not strictly speaking equivalent, they are equivalent for all philosophical purposes. (shrink)

Do people tend to be overconfident? Many think so. They’ve run studies on whether people are calibrated: whether their average confidence in their opinions matches the proportion of those opinions that are true. Under certain conditions, people are systematically ‘over-calibrated’—for example, of the opinions they’re 80% confident in, only 60% are true. From this empirical over-calibration, it’s inferred that people are irrationally overconfident. My question: When and why is this inference warranted? Answering it requires articulating a general connection between being (...) rational and being right—something extant studies have not done. I show how to do so using the notion of deference. This provides a theoretical foundation for calibration research, but also reveals a flaw: the connection between being rational and being right is much weaker than is standardly assumed, since rational people can often be expected to be miscalibrated. Thus we can’t test whether people are overconfident by simply testing whether they are over-calibrated; instead, we must try to predict the rational deviations from calibration, and then compare those predictions to people’s performance. I show how this can be done—and that doing so complicates the interpretation of robust empirical effects. (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.

There are many things—call them ‘experts’—that you should defer to in forming your opinions. The trouble is, many experts are modest: they’re less than certain that they are worthy of deference. When this happens, the standard theories of deference break down: the most popular (“Reflection”-style) principles collapse to inconsistency, while their most popular (“New-Reflection”-style) variants allow you to defer to someone while regarding them as an anti-expert. We propose a middle way: deferring to someone involves preferring to make any decision (...) using their opinions instead of your own. In a slogan, deferring opinions is deferring decisions. Generalizing the proposal of Dorst (2020a), we first formulate a new principle that shows exactly how your opinions must relate to an expert’s for this to be so. We then build off the results of Levinstein (2019) and Campbell-Moore (2020) to show that this principle is also equivalent to the constraint that you must always expect the expert’s estimates to be more accurate than your own. Finally, we characterize the conditions an expert’s opinions must meet to be worthy of deference in this sense, showing how they sit naturally between the too-strong constraints of Reflection and the too-weak constraints of New Reflection. (shrink)

Principles of expert deference say that you should align your credences with those of an expert. This expert could be your doctor, the objective chances, or your future self, after you've learnt something new. These kinds of principles face difficulties in cases in which you are uncertain of the truth-conditions of the thoughts in which you invest credence, as well as cases in which the thoughts have different truth-conditions for you and the expert. For instance, you shouldn't defer to your (...) doctor by aligning your credence in the de se thought 'I am sick' with the doctor's credence in that same de se thought. Here, I generalise principles of expert deference to handle these kinds of problem cases. (shrink)

‘Bayesian epistemology’ became an epistemological movement in the 20th century, though its two main features can be traced back to the eponymous Reverend Thomas Bayes (c. 1701-61). Those two features are: (1) the introduction of a formal apparatus for inductive logic; (2) the introduction of a pragmatic self-defeat test (as illustrated by Dutch Book Arguments) for epistemic rationality as a way of extending the justification of the laws of deductive logic to include a justification for the laws of inductive logic. (...) The formal apparatus itself has two main elements: the use of the laws of probability as coherence constraints on rational degrees of belief (or degrees of confidence) and the introduction of a rule of probabilistic inference, a rule or principle of conditionalization. (shrink)

This paper explores the idea that it is instrumentally valuable to learn normative truths. We consider an argument for "normative hedging" based on this principle, and examine the structure of decision-making under moral uncertainty that arises from it. But it also turns out that the value of normative information is inconsistent with the principle that learning *empirical* truths is instrumentally valuable. We conclude with a brief comment on "metanormative regress.".