Predictable polarization is everywhere: we can often predict how people’s opinions—including our own—will shift over time. Empirical studies suggest that this is so when evidence is ambiguous. That fact is often thought to demonstrate human irrationality. It doesn’t. Bayesians will predictably polarize iff their evidence is ambiguous. And ours often is: the process of cognitive search—searching a cognitively-accessible space for an item of a particular profile—yields ambiguous evidence that can predictably polarize beliefs, despite being expected to make them more accurate. (...) A series of such rational updates can lead to polarization that is predictable, profound, and persistent. This process is not only theoretically possible, but also empirically plausible. I present an experiment supporting the polarizing effect of cognitive search, and then use models and simulations to show how such ambiguous evidence can help explain two of the core causes of polarization: confirmation bias and the group polarization effect. (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)

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)

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.

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)

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

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)

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)

Do people tend to be overconfident in their opinions? Many think so. They’ve run studies to test whether people are calibrated: whether their 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 observed over-calibration, it’s inferred that people are irrationally overconfident. My question: When—and why—is this inference warranted? Answering this question 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 to calibration research, but also reveals a flaw: the connection between being rational and being right is much weaker than is commonly assumed; as a result, 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 first predict the expected rational deviations from calibration, and then compare those predictions to people’s performance. I show how in principle this can be done—and that doing so has the potential to overturn the standard interpretation of robust empirical effects. In short: rational people can be expected to be wrong more often than you might think. (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)

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

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)

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)

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)

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.

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)

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.