What propositions are rational for one to believe? With what confidence is it rational for one to believe these propositions? Answering the first of these questions requires an epistemology of beliefs, answering the second an epistemology of degrees of belief.

My aim in this paper is to develop and defend a novel answer to a question that has recently generated a considerable amount of controversy. The question concerns the normative significance of peer disagreement. Suppose that you and I have been exposed to the same evidence and arguments that bear on some proposition: there is no relevant consideration which is available to you but not to me, or vice versa. For the sake of concreteness, we might picture.

Conditional sentences are among the most intriguing and puzzling features of language, and analysis of their meaning and function has important implications for, and uses in, many areas of philosophy. Jonathan Bennett, one of the world's leading experts, distils many years' work and teaching into this Philosophical Guide to Conditionals, the fullest and most authoritative treatment of the subject. An ideal introduction for undergraduates with a philosophical grounding, it also offers a rich source of illumination and stimulation for graduate students (...) and professional philosophers. (shrink)

This paper explores an initially attractive principle connecting beliefs in general with beliefs about what beliefs are rational. The principle turns out to be violated by intuitively rational beliefs in some situations. The paper lays out some options for reacting to this fact.

It is common orthodoxy among internalists and externalists alike that knowledge is lost or defeated in situations involving misleading evidence of a suitable kind. But making sense of defeat has seemed to present a particular challenge for those who reject an internalist justification condition on knowledge. My main aim here is to argue that externalists ought to take seriously a view on which knowledge can be retained even in the face of strong seemingly defeating evidence. As an instructive example, I (...) first discuss whether a theory on which knowledge is belief that is safe from error has the resources for accommodating defeat. I argue that beliefs retained in defeat cases need not be unsafe or true in some accidental way. I then discuss externalist strategies for explaining why we have incorrect intuitions about defeat. The notion of an epistemically reasonable subject plays a central role in my theory. Reasonable subjects adopt general strategies that are good for acquiring true belief and knowledge across a wide range of normal cases, but stubbornly retaining belief in the face of new evidence does not reflect such policies. I argue that though the methods employed by subjects who fail to adjust their beliefs in defeat cases may be perfectly good, they are not good methods to adopt, as their adoption is accompanied by bad dispositions. What emerges is a view on which a subject can know despite being unreasonable, and despite failing to manifest dispositions to know across normal cases. Unreasonable subjects are genuinely criticisable, but like almost anything, knowledge can sometimes be achieved in the absence of a good general strategy. (shrink)

In this paper I will present a puzzle about epistemic akrasia, and I will use that puzzle to motivate accepting some non-standard views about the nature of epistemological judgment. The puzzle is that while it seems obvious that epistemic akrasia must be irrational, the claim that epistemic akrasia is always irrational amounts to the claim that a certain sort of justified false belief—a justified false belief about what one ought to believe—is impossible. But justified false beliefs seem to be possible (...) in any domain, and it’s hard to see why beliefs about what one ought to believe should be an exception. I will argue that when we get clearer about what sort of psychological state epistemic akrasia is, we can resolve the puzzle in favor of the intuitive view that epistemic akrasia is always irrational. (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)

Richard Pettigrew offers an extended investigation into a particular way of justifying the rational principles that govern our credences. The main principles that he justifies are the central tenets of Bayesian epistemology, though many other related principles are discussed along the way. Pettigrew looks to decision theory in order to ground his argument. He treats an agent's credences as if they were a choice she makes between different options, gives an account of the purely epistemic utility enjoyed by different sets (...) of credences, and then appeals to the principles of decision theory to show that, when epistemic utility is measured in this way, the credences that violate the principles listed above are ruled out as irrational. The account of epistemic utility set out here is the veritist's: the sole fundamental source of epistemic utility for credences is their accuracy. Thus, Pettigrew conducts an investigation in the version of epistemic utility theory known as accuracy-first epistemology. (shrink)

First published in 2000. Routledge is an imprint of Taylor & Francis, an informa company.

I treat you as a thermometer when I use your belief states as more or less reliable indicators of the facts. Should I treat myself in a parallel way? Should I think of the outputs of my faculties and yours as like the readings of two thermometers the way a third party would? I explore some of the difficulties in answering these questions. If I am to treat myself as well as others as thermometers in this way, it would appear (...) that I cannot reasonably trust my own convictions over yours unless I have antecedent reason to suppose that I am more likely than you to get things right. I appeal to some probabilistic considerations to suggest that our predicament as thermometers might not actually be as bad as it seems. (shrink)

I treat you as a thermometer when I use your belief states as more or less reliable indicators of the facts. Should I treat myself in a parallel way? Should I think of the outputs of my faculties and yours as like the readings of two thermometers the way a third party would? I explore some of the difficulties in answering these questions. If I am to treat myself as well as others as thermometers in this way, it would appear (...) that I cannot reasonably trust my own convictions over yours unless I have antecedent reason to suppose that I am more likely than you to get things right. I appeal to some probabilistic considerations to suggest that our predicament as thermometers might not actually be as bad as it seems. (shrink)

A rational person doesn’t believe just anything. There are limits on what it is rational to believe. How wide are these limits? That’s the main question that interests me here. But a secondary question immediately arises: What factors impose these limits? A first stab is to say that one’s evidence determines what it is epistemically permissible for one to believe. Many will claim that there are further, non-evidentiary factors relevant to the epistemic rationality of belief. I will be ignoring the (...) details of alternative answers in order to focus on the question of what kind of rational constraints one’s evidence puts on belief. Our main question concerns how far epistemic permission and obligation can come apart.1 Suppose I am epistemically permitted to believe P, i.e., it would not be irrational for me to believe it. Am I thereby obliged to believe P, or are other options rationally available to me?2 Might I be equally rational in remaining agnostic about P, or even believing not-P? Or could even a slightly stronger or weaker degree of confidence be just as reasonable? (shrink)

How should one react when one has a belief, but knows that other people—who have roughly the same evidence as one has, and seem roughly as likely to react to it correctly—disagree? This paper argues that the disagreement of other competent inquirers often requires one to be much less confident in one’s opinions than one would otherwise be.

Many have claimed that unspecific evidence sometimes demands unsharp, indeterminate, imprecise, vague, or interval-valued probabilities. Against this, a variant of the diachronic Dutch Book argument shows that perfectly rational agents always have perfectly sharp probabilities.

For many epistemologists, and for many philosophers more broadly, it is axiomatic that rationality requires you to take the doxastic attitudes that your evidence supports. Yet there is also another current in our talk about rationality. On this usage, rationality is a matter of the right kind of coherence between one's mental attitudes. Surprisingly little work in epistemology is explicitly devoted to answering the question of how these two currents of talk are related. But many implicitly assume that evidence -responsiveness (...) guarantees coherence, so that the rational impermissibility of incoherence will just fall out of the putative requirement to take the attitudes that one's evidence supports, and so that coherence requirements do not need to be theorized in their own right, apart from evidential reasons. In this paper, I argue that this is a mistake, since coherence and evidence -responsiveness can in fact come into conflict. More specifically, I argue that in cases of misleading higher-order evidence, there can be a conflict between believing what one's evidence supports and satisfying a requirement that I call “inter-level coherence ”. This illustrates why coherence requirements and evidential reasons must be separated and theorized separately. (shrink)

Improbable knowing is knowing something even though it is almost certain on one’s evidence at the time that one does not know that thing. Once probabilities on the agent’s evidence are introduced into epistemic logic in a very natural way, it is easy to construct models of improbable knowing, some of which have realistic interpretations, for instance concerning agents like us with limited powers of perceptual discrimination. Improbable knowing is an extreme case of failure of the KK principle, that is, (...) of a case of knowing something even though one does not know at the time that one knows that thing. A generalization of the argument yields cases of improbable rationality, in which it is rational for one to do something even though it is almost certain on one’s evidence at the time that it is not rational for one to do that thing. When the models are elaborated to represent appearances and beliefs as well as knowledge, they turn out to contain Gettier cases. Neglect of the possibility of improbable knowing may cause some sceptical claims and claims of the non-closure of knowledge under competent deduction to look more plausible than they deserve to. A formal appendix explores the closely related question of the conditions under which a reflection principle is violated. The principle says that the evidential probability of a proposition conditional on the evidential probability of that proposition’s being c is itself c. (shrink)

What is the connection between justification and the kind of consequence relations that are studied by logic? In this essay, I shall try to provide an answer, by proposing a general conception of the kind of inference that counts as justified or rational.

Should learning we disagree about p lead you to reduce confidence in p? Some who think so want to except beliefs in which you are rationally highly confident. I argue that this is wrong; we should reject accounts that rely on this intuitive thought. I then show that quite the opposite holds: factors that justify low confidence in p also make disagreement about p less significant. I examine two such factors: your antecedent expectations about your peers’ opinions and the difficulty (...) of evaluating your evidence. I close by proposing a different way of thinking about disagreement. (shrink)

We often hear such casual accusations: you just believe that because you are a liberal, a Christian, an American, a woman… When such charges are made they are meant to sting—not just emotionally, but epistemically. But should they? It can be disturbing to learn that one's beliefs reflect the influence of such irrelevant factors. The pervasiveness of such influence has led some to worry that we are not justified in many of our beliefs. That same pervasiveness has led others to (...) doubt whether there is any worry here at all. I argue that evidence of irrelevant belief influence is sometimes, but not always, undermining. My proposal picks out ordinary, non-skeptical cases in which we get evidence of error. It says that, in those cases, evidence of irrelevant influence is epistemically significant. It shows how respecting evidence of error is compatible with the epistemic lives we see ourselves living. We are fallible creatures, yes, but we are also capable and intelligent ones. We can recognize and correct for our own error so as to improve our imperfect, yet nevertheless robust, epistemic lives. (shrink)

This article defends the Fixed Point Thesis: that it is always a rational mistake to have false beliefs about the requirements of rationality. The Fixed Point Thesis is inspired by logical omniscience requirements in formal epistemology. It argues to the Fixed Point Thesis from the Akratic Principle: that rationality forbids having an attitude while believing that attitude is rationally forbidden. It then draws out surprising consequences of the Fixed Point Thesis, for instance that certain kinds of a priori justification are (...) indefeasible and that misleading all-things-considered evidence about rational requirements is impossible. Finally, the Fixed Point Thesis is applied to defend the Right Reasons position on peer disagreement, according to which an agent who has drawn the correct conclusion from her evidence should retain belief in that conclusion even in the face of disagreeing peers. (shrink)

The Self-Intimation thesis has it that whatever justificatory status a proposition has, i.e., whether or not we are justified in believing it, we are justified in believing that it has that status. The Infallibility thesis has it that whatever justificatory status we are justified in believing that a proposition has, the proposition in fact has that status. Jointly, Self-Intimation and Infallibility imply that the justificatory status of a proposition closely aligns with the justification we have about that justificatory status. Self-Intimation (...) has two noteworthy implications. First, assuming that we never have sufficient justification for a proposition and for its negation, we can derive Infallibility from Self-Intimation. Interestingly, there seems to be no equivalently simple way to derive Self-Intimation from Infallibility. This asymmetry provides reason for thinking that bottom-level justification rather than top-level justification drives the explanation for why the levels of justification align. Second, Self-Intimation suggests a counterintuitive treatment of information concerning what justificatory status a proposition has. It follows from Self-Intimation that we always have justification for the truth about whether a proposition is justified for us, and therefore, that higher-order evidence could change what we should believe on this matter only by misleading us. This permits forming beliefs about whether a proposition is justified for us without regard to higher-order evidence, and thus reveals a reason for thinking that top-level justification is evidentially inert. (shrink)

The aim of the paper is to draw a connection between a semantical theory of conditional statements and the theory of conditional probability. First, the probability calculus is interpreted as a semantics for truth functional logic. Absolute probabilities are treated as degrees of rational belief. Conditional probabilities are explicitly defined in terms of absolute probabilities in the familiar way. Second, the probability calculus is extended in order to provide an interpretation for counterfactual probabilities--conditional probabilities where the condition has zero probability. (...) Third, conditional propositions are introduced as propositions whose absolute probability is equal to the conditional probability of the consequent on the antecedent. An axiom system for this conditional connective is recovered from the probabilistic definition. Finally, the primary semantics for this axiom system, presented elsewhere, is related to the probabilistic interpretation. (shrink)

This paper argues that justification is accessible in the sense that one has justification to believe a proposition if and only if one has higher-order justification to believe that one has justification to believe that proposition. I argue that the accessibility of justification is required for explaining what is wrong with believing Moorean conjunctions of the form, ‘p and I do not have justification to believe that p.’.

Does rationality require logical omniscience? Our best formal theories of rationality imply that it does, but our ordinary evaluations of rationality seem to suggest otherwise. This paper aims to resolve the tension by arguing that our ordinary evaluations of rationality are not only consistent with the thesis that rationality requires logical omniscience, but also provide a compelling rationale for accepting this thesis in the first place. This paper also defends an account of apriori justification for logical beliefs that is designed (...) to explain the rational requirement of logical omniscience. On this account, apriori justification for beliefs about logic has its source in logical facts, rather than psychological facts about experience, reasoning, or understanding. This account has important consequences for the epistemic role of experience in the logical domain. In a slogan, the epistemic role of experience in the apriori domain is not a justifying role, but rather an enabling and disabling role. (shrink)

Plausibly, you should believe what your total evidence supports. But cases of misleading higher-order evidence—evidence about what your evidence supports—present a challenge to this thought. In such cases, taking both first-order and higher-order evidence at face value leads to a seemingly irrational incoherence between one’s first-order and higher-order attitudes: you will believe P, but also believe that your evidence doesn’t support P. To avoid sanctioning tension between epistemic levels, some authors have abandoned the thought that both first-order and higher-order evidence (...) have rational bearing. This sacrifice is both costly and unnecessary. We propose a principle, Evidential Calibration, which requires rational agents to accommodate first-order evidence correctly, while allowing rational uncertainty about what to believe. At the same time, it rules out irrational tensions between epistemic levels. We show that while there are serious problems for some views on which we can rationally believe, “P, but my evidence doesn’t support P”, Evidential Calibration avoids these problems. An important upshot of our discussion is a new way to think about the relationship between epistemic levels: why first-order and higher-order attitudes should generally be aligned, and why it is sometimes—though not always—problematic when they diverge. (shrink)

Timothy Williamson has famously argued that the principle should be rejected. We analyze Williamson's argument and show that its key premise is ambiguous, and that when it is properly stated this premise no longer supports the argument against. After canvassing possible objections to our argument, we reflect upon some conclusions that suggest significant epistemological ramifications pertaining to the acquisition of knowledge from prior knowledge by deduction.

In this paper, I begin by defending permissivism: the claim that, sometimes, there is more than one way to rationally respond to a given body of evidence. Then I argue that, if we accept permissivism, certain worries that arise as a result of learning that our beliefs were caused by the communities we grew up in, the schools we went to, or other irrelevant influences dissipate. The basic strategy is as follows: First, I try to pinpoint what makes irrelevant influences (...) worrying and I come up with two candidate principles. I then argue that one principle should be rejected because it is inconsistent with permissivism. The principle we should accept implies that it is sometimes rational to maintain our beliefs, even upon learning that they were caused by irrelevant influences. (shrink)

This paper is about the connection between rationality and accuracy. I show that one natural picture about how rationality and accuracy are connected emerges if we assume that rational agents are rationally omniscient. I then develop an alternative picture that allows us to relax this assumption, in order to accommodate certain views about higher order evidence.

The aim of this paper is to describe a problem for calibrationism: a view about higher order evidence according to which one's credences should be calibrated to one's expected degree of reliability. Calibrationism is attractive, in part, because it explains our intuitive judgments, and provides a strong motivation for certain theories about higher order evidence and peer disagreement. However, I will argue that calibrationism faces a dilemma: There are two versions of the view one might adopt. The first version, I (...) argue, has the implausible consequence that, in a wide range of cases, calibrationism is the only constraint on rational belief. The second version, in addition to having some puzzling consequences, is unmotivated. At the end of the paper I sketch a possible solution. (shrink)

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

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

Famous results by David Lewis show that plausible-sounding constraints on the probabilities of conditionals or evaluative claims lead to unacceptable results, by standard probabilistic reasoning. Existing presentations of these results rely on stronger assumptions than they really need. When we strip these arguments down to a minimal core, we can see both how certain replies miss the mark, and also how to devise parallel arguments for other domains, including epistemic “might,” probability claims, claims about comparative value, and so on. A (...) popular reply to Lewis's results is to claim that conditional claims, or claims about subjective value, lack truth conditions. For this strategy to have a chance of success, it needs to give up basic structural principles about how epistemic states can be updated—in a way that is strikingly parallel to the commitments of the project of dynamic semantics. (shrink)

I develop a general framework with a rationality constraint that shows how coherently to represent and deal with second-order information about one's own judgmental reliability. It is a rejection of and generalization away from the typical Bayesian requirements of unconditional judgmental self-respect and perfect knowledge of one's own beliefs, and is defended by appeal to the Principal Principle. This yields consequences about maintaining unity of the self, about symmetries and asymmetries between the first- and third-person, and a principled way of (...) knowing when to stop second-guessing oneself. Peer disagreement is treated as a special case where one doubts oneself because of news that an intellectual equal disagrees. This framework, and variants of it, imply that the typically stated belief that an equally reliably peer disagrees is incoherent, and thus that pure rationality constraints without further substantive information cannot give an answer as to what to do. The framework also shows that treating both ourselves and others as thermometers in the disagreement situation does not imply the Equal Weight view. (shrink)

There is a widespread view that in order to be rational we must mostly know what we believe. In the probabilistic tradition this is defended by arguments that a person who failed to have this knowledge would be vulnerable to sure loss, or probabilistically incoherent. I argue that even gross failure to know one's own beliefs need not expose one to sure loss, and does not if we follow a generalization of the standard bridge principle between first-order and second-order beliefs. (...) This makes it possible for a subject to use probabilistic decision theory to manage in a rational way cases of potential failure of this self-knowledge, as we find in implicit bias. Through such cases I argue that it is possible for uncertainty about what our beliefs are to be not only rationally permissible but advantageous. (shrink)

Discusses how to capture the link between the probability of indicative conditionals and conditional probability using a classical semantics for conditionals.

Beliefs come in different strengths. An agent's credence in a proposition is a measure of the strength of her belief in that proposition. Various norms for credences have been proposed. Traditionally, philosophers have tried to argue for these norms by showing that any agent who violates them will be lead by her credences to make bad decisions. In this article, we survey a new strategy for justifying these norms. The strategy begins by identifying an epistemic utility function and a decision-theoretic (...) norm; we then show that the decision-theoretic norm applied to the epistemic utility function yields the norm for credences that we wish to justify. We survey results already obtained using this strategy, and we suggest directions for future research. (shrink)