The fact that philosophy is systematic—that philosophical issues are thoroughly interconnected—was a commonplace among nineteenth century idealists, then neglected by analytic philosophers throughout much of the twentieth century, and has now finally started to get some renewed attention. But other than calling attention to the fact, few philosophers have tried to say what it consists in, or what its implications are. -/- I argue that the systematicity of philosophy has disastrous epistemological implications. In particular, it implies philosophical skepticism: philosophers are (...) rationally prohibited from believing any philosophical thesis. The argument goes by way of a new principle that connects inquiry with what is rational to believe. I conclude with a discussion of the relationship between my argument and other, more well-trodden arguments for philosophical skepticism. (shrink)

Reasoning from inconclusive evidence, or ‘induction’, is central to science and any applications we make of it. For that reason alone it demands the attention of philosophers of science. This Element explores the prospects of using probability theory to provide an inductive logic, a framework for representing evidential support. Constraints on the ideal evaluation of hypotheses suggest that overall support for a hypothesis is represented by its probability in light of the total evidence, and incremental support, or confirmation, indicated by (...) an increased probability given the evidence than otherwise. This proposal is shown to have the capacity to reconstruct many canons of the scientific method and inductive inference. Along the way, significant objections are discussed, such as the challenge from inductive scepticism and the objection that the probabilistic approach makes evidential support arbitrary. (shrink)

In this paper we explore the absentminded driver problem using two different scenarios. In the first scenario we assume that the driver is capable of reasoning about his degree of absentmindedness before he hits the highway. This leads to a Savage-style model where the states are mutually exclusive and the act-state independence is in place. In the second we employ centred possibilities, by modelling the states (i.e. the events about which the driver is uncertain) as the possible final destinations indexed (...) by a time period. The optimal probability we find for continuing at an exit is different from almost all papers in the literature. In this scenario, act-state independence is still violated, but states are mutually exclusive and the driver arrives at his optimal choice probability via Bayesian updating. We show that our solution is the only one guaranteeing immunity from sure loss via a Dutch strategy, and that – despite initial appearances – it is time consistent. This raises important implications for the rationality of commitment in such scenarios. (shrink)

I propose the notion of ‘epistemic sanity’, a property of parsimony between the holding of true but not false beliefs and the consideration of our cognitive limitations. Where ‘alethic value’ is the epistemic value of holding true but not false beliefs, the ‘alethic potential’ of an agent is the amount of extra alethic value that she is expected to achieve, given her current environment, beliefs, and reasoning skills. Epistemic sanity would be related to the holding of (true or false) beliefs (...) that increase the agent's alethic potential (relevant beliefs) but not of beliefs that decrease it (this is related to cognitive parsimony). Suspension of judgment, forgetting, and clutter avoidance are the main contributors to an agent's epistemic sanity, where this paper focuses on suspension. I argue that rational suspension favors the holding of true and relevant beliefs, which is not the case for the extremes of opinionation (no suspension) and skepticism (general suspension). In the absence of evidence, opinionated agents are often forced to rely on principles such as the principle of indifference, but suspension dominates indifference in terms of alethic value in some conditions. A rational agent would only find it beneficial to adopt skepticism if she considers herself to be an anti-expert about her entire agenda, but then ‘flipping’ beliefs maximizes expected alethic value in relation to skepticism. The study of epistemic sanity results in an ‘impure’ veritism, which can deal with some limitations of veritism (e.g., explaining the existence of false but relevant beliefs). (shrink)

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)

Bayesian epistemologists support the norms of probabilism and conditionalization using Dutch book and accuracy arguments. These arguments assume that rationality requires agents to maximize practical or epistemic value in every doxastic state, which is evaluated from a subjective point of view (e.g., the agent’s expectancy of value). The accuracy arguments also presuppose that agents are opinionated. The goal of this paper is to discuss the assumptions of these arguments, including the measure of epistemic value. I have designed AI agents based (...) on the Bayesian model and a nonmonotonic framework and tested how they achieve practical and epistemic value in conditions in which an alternative set of assumptions holds. In one of the tested conditions, the nonmonotonic agent, which is not opinionated and fulfills neither probabilism nor conditionalization, outperforms the Bayesian in the measure of epistemic value that I argue for in the paper (α-value). I discuss the consequences of these results for the epistemology of rationality. (shrink)

Bayesians standardly claim that there is rational pressure for agents’ credences to cohere across time because they face bad (epistemic or practical) consequences if they fail to diachronically cohere. But as David Christensen has pointed out, groups of individual agents also face bad consequences if they fail to interpersonally cohere, and there is no general rational pressure for one agent's credences to cohere with another’s. So it seems that standard Bayesian arguments may prove too much. Here, we agree with Christensen (...) that there is no general rational pressure to diachronically cohere, but we argue that there are particular cases in which there is rational pressure to diachronically cohere, as well as particular cases in which interpersonal probabilistic coherence is rationally required. More generally, we suggest that Bayesian arguments for coherence apply whenever a collection (of agents or time slices) has a shared dimension of value and an ability to coordinate their actions in a range of cases relevant to that value. Typically, this shared value and ability to coordinate is very strong across the time slices of one human being, and very weak across different human beings, but there are special cases where these can switch—i.e., some groups of humans will have as much reason for their beliefs to cohere across a particular range of cases as the time slices of one human usually do, but some time slices of a human will have as much freedom to differ in their beliefs from the others as the members of a group usually do. (shrink)

Philosophy and Phenomenological Research, Volume 103, Issue 3, Page 620-638, November 2021.

The main conclusion is this conditional: If the principle of reflection is a valid constraint on rational credences, then it is not rational to have a uniform credence distribution on a countable outcome space. The argument is a variation on some arguments that are already in the literature, but with crucial differences. The conditional can be used for either a modus ponens or a modus tollens; some reasons for thinking that the former is most reasonable are given.

– We offer a new motivation for imprecise probabilities. We argue that there are propositions to which precise probability cannot be assigned, but to which imprecise probability can be assigned. In such cases the alternative to imprecise probability is not precise probability, but no probability at all. And an imprecise probability is substantially better than no probability at all. Our argument is based on the mathematical phenomenon of non-measurable sets. Non-measurable propositions cannot receive precise probabilities, but there is a natural (...) way for them to receive imprecise probabilities. The mathematics of non-measurable sets is arcane, but its epistemological import is far-reaching; even apparently mundane propositions are liable to be affected by non-measurability. The phenomenon of non-measurability dramatically reshapes the dialectic between critics and proponents of imprecise credence. Non-measurability offers natural rejoinders to prominent critics of imprecise credence. Non-measurability even reverses some of the critics’ arguments—by the very lights that have been used to argue against imprecise credences, imprecise credences are better than precise credences. (shrink)

When beliefs are quantified as credences, they are related to each other in terms of closeness and accuracy. The “accuracy first” approach in formal epistemology wants to establish a normative account for credences based entirely on the alethic properties of the credence: how close it is to the truth. To pull off this project, there is a need for a scoring rule. There is widespread agreement about some constraints on this scoring rule, but not whether a unique scoring rule stands (...) above the rest. The Brier score equips credences with a structure similar to metric space and induces a “geometry of reason.” It enjoys great popularity in the current debate. I point out many of its weaknesses in this article. An alternative approach is to reject the geometry of reason and accept information theory in its stead. Information theory comes fully equipped with an axiomatic approach which covers probabilism, standard conditioning, and Jeffrey conditioning. It is not based on an underlying topology of a metric space, but uses a non-commutative divergence instead of a symmetric distance measure. I show that information theory, despite initial promise, also fails to accommodate basic epistemic intuitions; and speculate on its remediation. (shrink)

Reflection and martingale principles are central to models of rational learning. They can be justified in a variety of ways. In what follows we study martingale and reflection principles in the con...

When we get evidence that tells us our belief-forming mechanisms may not be reliable this presents a thorny set of questions about whether and how to revise our original belief. This article analyzes aspects of the problem and a variety of approaches to its solution.

Rescorla (Erkenntnis, 2020) has recently pointed out that the standard arguments for Bayesian Conditionalization assume that whenever I become certain of something, it is true. Most people would reject this assumption. In response, Rescorla offers an improved Dutch Book argument for Bayesian Conditionalization that does not make this assumption. My purpose in this paper is two-fold. First, I want to illuminate Rescorla’s new argument by giving a very general Dutch Book argument that applies to many cases of updating beyond those (...) covered by Conditionalization, and then showing how Rescorla’s version follows as a special case of that. Second, I want to show how to generalise R. A. Briggs and Richard Pettigrew’s Accuracy Dominance argument to avoid the assumption that Rescorla has identified (Briggs and Pettigrew in Noûs, 2018). In both cases, these arguments proceed by first establishing a very general reflection principle. (shrink)

The central aim of this paper is to argue that there is a meaningful sense in which a concept of rationality can apply to a city. The idea will be that a city is rational to the extent that the collective practices of its people enable diverse inhabitants to simultaneously live the kinds of life they are each trying to live. This has significant implications for the varieties of social practices that constitute being more or less rational. Some of these (...) implications may be welcome to a theorist that wants to identify collective rationality with a notion of justice, while others are unwelcome. There are some significant challenges to this use of the concept of rationality, but I claim that these challenges at the city level have parallels at the individual level, and may thus help deepen our understanding of rationality at all levels. (shrink)

This chapter is a philosophical survey of some leading approaches in formal epistemology in the so-called ‘Bayesian’ tradition. According to them, a rational agent’s degrees of belief—credences—at a time are representable with probability functions. We also canvas various further putative ‘synchronic’ rationality norms on credences. We then consider ‘diachronic’ norms that are thought to constrain how credences should respond to evidence. We discuss some of the main lines of recent debate, and conclude with some prospects for future research.

Sometimes a proposition is ‘opaque’ to an agent: he doesn't know it, but he does know something about how coming to know it should affect his or her credence function. It is tempting to assume that a rational agent's credence function coheres in a certain way with his or her knowledge of these opaque propositions, and I call this the ‘Opaque Proposition Principle’. The principle is compelling but demonstrably false. I explain this incongruity by showing that the principle is ambiguous: (...) the term ‘know’ as it appears in the principle can be interpreted in two different ways, as either basic-know or super-know. I use this distinction to construct a plausible version of the principle, and then to similarly construct plausible versions of the Reflection Principle and the Sure-Thing Principle. (shrink)

Conditionalization is a widely endorsed rule for updating one’s beliefs. But a sea of complaints have been raised about it, including worries regarding how the rule handles error correction, changing desiderata of theory choice, evidence loss, self-locating beliefs, learning about new theories, and confirmation. In light of such worries, a number of authors have suggested replacing Conditionalization with a different rule — one that appeals to what I’ll call “ur-priors”. But different authors have understood the rule in different ways, and (...) these different understandings solve different problems. In this paper, I aim to map out the terrain regarding these issues. I survey the different problems that might motivate the adoption of such a rule, flesh out the different understandings of the rule that have been proposed, and assess their pros and cons. I conclude by suggesting that one particular batch of proposals, proposals that appeal to what I’ll call “loaded evidential standards”, are especially promising. (shrink)

This thesis focuses on expressively rich languages that can formalise talk about probability. These languages have sentences that say something about probabilities of probabilities, but also sentences that say something about the probability of themselves. For example: (π): “The probability of the sentence labelled π is not greater than 1/2.” Such sentences lead to philosophical and technical challenges; but can be useful. For example they bear a close connection to situations where ones confidence in something can affect whether it is (...) the case or not. The motivating interpretation of probability as an agent's degrees of belief will be focused on throughout the thesis. -/- This thesis aims to answer two questions relevant to such frameworks, which correspond to the two parts of the thesis: “How can one develop a formal semantics for this framework?” and “What rational constraints are there on an agent once such expressive frameworks are considered?”. (shrink)

This paper is about the standard Reflection Principle :235–256, 1984) and the Group Reflection Principle :478–502, 2007; Bovens and Rabinowicz in Episteme 8:281–300, 2011; Titelbaum in Quitting certainties: a Bayesian framework modeling degrees of belief, OUP, Oxford, 2012; Hedden in Mind 124:449–491, 2015). I argue that these principles are incomplete as they stand. The key point is that deference is an intensional relation, and so whether you are rationally required to defer to a person at a time can depend on (...) how that person and that time are designated. In this paper I suggest a way of completing the Reflection Principle and Group Reflection Principle, and I argue that so completed these principles are plausible. In particular, they do not fall foul of the Sleeping Beauty case :143–147, 2000), the Cable Guy Paradox :112–119, 2005), Arntzenius’ prisoner cases :356–370, 2003), or the Puzzle of the Hats :281–300, 2011). (shrink)

If an agent believes that the probability of E being true is 1/2, should she accept a bet on E at even odds or better? Yes, but only given certain conditions. This paper is about what those conditions are. In particular, we think that there is a condition that has been overlooked so far in the literature. We discovered it in response to a paper by Hitchcock (2004) in which he argues for the 1/3 answer to the Sleeping Beauty problem. (...) Hitchcock argues that this credence follows from calculating her fair betting odds, plus the assumption that Sleeping Beauty’s credences should track her fair betting odds. We will show that this last assumption is false. Sleeping Beauty’s credences should not follow her fair betting odds due to a peculiar feature of her epistemic situation. (shrink)

This paper offers two new arguments for a version of Reflection, the principle that says, roughly, that if one knew now what one would believe in the future, one ought to believe it now. The most prominent existing argument for the principle is the coherence-based Dutch Strategy argument advanced by Bas van Fraassen (and others). My two arguments are quite different. The first is a truth-based argument. On the basis of two substantive premises, that people’s beliefs generally get better over (...) time and that being a person requires having knowledge of this fact, it concludes that it is rational to treat your future selves as experts. The second argument is a transcendental one. Being a person requires being able to engage in plans and projects. But these cannot be meaningfully undertaken unless one has Reflection-like expectations about one’s future beliefs. Hence, satisfaction of Reflection is necessary for being a person. Together, the arguments show that satisfaction of Reflection is both rational and necessary for persons. (shrink)

The Reflection principle expresses a kind of epistemic deference to one's future self. There is a plausible intuitive argument to the effect that, if one believes one will reason well and gain information over time, then one ought to satisfy Reflection. There are also associated formal arguments that show that, if one's beliefs about one's current and future selves meet certain criteria, then one is committed by the axioms of probability to satisfy Reflection. The formal arguments, however, rely on an (...) assumption that has no apparent relevance to the intuitive argument: the assumption that one has perfect access to one's beliefs. This paper explains why it is advantageous to replace the perfect access assumption with a self-trust assumption. The self-trust assumption is superior from a formal point of view, since it is formally weaker than the perfect access assumption, and from an intuitive point of view, since it leads to an improved formulation of the intuitive argument. (shrink)

In this paper I present a new way of understanding Dutch Book Arguments: the idea is that an agent is shown to be incoherent iff he would accept as fair a set of bets that would result in a loss under any interpretation of the claims involved. This draws on a standard definition of logical inconsistency. On this new understanding, the Dutch Book Arguments for the probability axioms go through, but the Dutch Book Argument for Reflection fails. The question of (...) whether we have a Dutch Book Argument for Conditionalization is left open. (shrink)

I argue that while admission of one's own fallibility rationally requires one's readiness to stand corrected in the light of future evidence, it need have no consequences for one's present degrees of belief. In particular, I argue that one's fallibility in a given area gives one no reason to forego assigning credence 1 to propositions belonging to that area. I can thus be seen to take issue with David Christensen's recent claim that our fallibility has far-reaching consequences for our account (...) of rational belief and epistemic rationality. My arguments inter alia rely on the idea that in basing one's beliefs on one's evidence, one trusts both that one's evidence has the right pedigree and that one gets its probative force right, where such trust can rationally be invested without the need of any further evidence. (shrink)

One recent topic of debate in Bayesian epistemology has been the question of whether imprecise credences can be rational. I argue that one account of imprecise credences, the orthodox treatment as defended by James M. Joyce, is untenable. Despite Joyce’s claims to the contrary, a puzzle introduced by Roger White shows that the orthodox account, when paired with Bas C. van Fraassen’s Reflection Principle, can lead to inconsistent beliefs. Proponents of imprecise credences, then, must either provide a compelling reason to (...) reject Reflection or admit that the rational credences in White’s case are precise. (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 argues that several leading theories of subjunctive conditionals are incompatible with ordinary intuitions about what credences we ought to have in subjunctive conditionals. In short, our theory of subjunctives should intuitively display semantic humility, i.e. our semantic theory should deliver the truth conditions of sentences without pronouncing on whether those conditions actually obtain. In addition to describing intuitions about subjunctive conditionals, I argue that we can derive these ordinary intuitions from justified premises, and I answer a possible worry (...) for my derivation by refuting a subjunctive triviality result modeled on (Lewis 1976). I conclude that the debate over the correct theory of subjunctive conditionals requires settling meta-philosophical questions about the relative value of various virtues of first-order theories of subjunctive conditionals. (shrink)

Certain situations seem to call for acknowledging the possibility that one’s own beliefs are biased or distorted. On the other hand, certain sorts of epistemic self-doubts (such as ‘I believe it’s raining, but it’s not’) seem paradoxical. And some have put forth epistemic principles requiring rational agents to regard their own credences as so-called ‘expert functions’. This paper examines the question of whether rationality requires agents to respect their own credences in a way in which they need not respect the (...) credences of others. (shrink)

The phenomenon of disagreement has recently been brought into focus by the debate between contextualists and relativist invariantists about epistemic expressions such as ‘might’, ‘probably’, indicative conditionals, and the deontic ‘ought’. Against the orthodox contextualist view, it has been argued that an invariantist account can better explain apparent disagreements across contexts by appeal to the incompatibility of the propositions expressed in those contexts. This paper introduces an important and underappreciated phenomenon associated with epistemic expressions — a phenomenon that we call (...) reversibility. We argue that the invariantist account of disagreement is incompatible with reversibility, and we go on to show that reversible sentences cast doubt on the putative data about disagreement, even without assuming invariantism. Our argument therefore undermines much of the motivation for invariantism, and provides a new source for constraints on the proper explanation of purported data about disagreement. (shrink)

Diachronic Dutch book arguments seem to support both conditionalization and Bas van Fraassen's Reflection principle. But the Reflection principle is vulnerable to numerous counterexamples. This essay addresses two questions: first, under what circumstances should an agent obey Reflection, and second, should the counterexamples to Reflection make us doubt the Dutch book for conditionalization? In response to the first question, this essay formulates a new "Qualified Reflection" principle, which states that an agent should obey Reflection only if he or she is (...) certain that he or she will conditionalize on veridical evidence in the future. Qualified Reflection follows from the probability calculus together with a few idealizing assumptions. The essay then formulates a "Distorted Reflection" principle that approximates Reflection even in cases where the agent is not quite certain that he or she will conditionalize on veridical evidence. In response to the second question, the essay argues that contrary to a common misconception, not all Dutch books dramatize incoherence—some dramatize a less blameworthy sort of epistemic frailty that the essay calls "self-doubt." The distinction between Dutch books that dramatize incoherence and those that dramatize self-doubt cross-cuts the distinction between synchronic and diachronic Dutch books. The essay explains why the Dutch book for conditionalization reveals true incoherence, whereas the Dutch book for Reflection reveals only self-doubt. (shrink)

Simon Evnine examines various epistemic aspects of what it is to be a person. Persons are defined as finite beings that have beliefs, including second-order beliefs about their own and others' beliefs, and are agents, capable of making long-term plans. It is argued that for any being meeting these conditions, a number of epistemic consequences obtain. First, all such beings must have certain logical concepts and be able to use them in certain ways. Secondly, there are at least two principles (...) governing belief that it is rational for persons to satisfy and are such that nothing can be a person at all unless it satisfies them to a large extent. These principles are that one believe the conjunction of one's beliefs and that one treat one's future beliefs as, by and large, better than one's current beliefs. Thirdly, persons both occupy epistemic points of view on the world and show up within those views. This makes it impossible for them to be completely objective about their own beliefs. Ideals of rationality that require such objectivity, while not necessarily wrong, are intrinsically problematic for persons. This "aspectual dualism" is characteristic of treatments of persons in the Kantian tradition. In sum, these epistemic consequences support a traditional view of the nature of persons, one in opposition to much recent theorizing. (shrink)

Can self-locating beliefs be relevant to non-self-locating claims? Traditional Bayesian modeling techniques have trouble answering this question because their updating rule fails when applied to situations involving contextsensitivity. This essay develops a fully general framework for modeling stories involving context-sensitive claims. The key innovations are a revised conditionalization rule and a principle relating models of the same story with different modeling languages. The essay then applies the modeling framework to the Sleeping Beauty Problem, showing that when Beauty awakens her degree (...) of belief in heads should be one-third. This demonstrates that it can be rational for an agent who gains only self-locating beliefs between two times to alter her degree of belief in a non-self-locating claim. (shrink)

This is surely a bit of Socrates' famous irony. He draws the analogy to explain how his friends should regard poetry as they regretfully banish it from the ideal state. But lovers were no more sensible then than they are now. The advice to banish poetry, undermined already by Plato's own delight and skill in drama, is perhaps undermined still further by this evocation of a 'sensible' lover who counts love so well lost. Yet Socrates' image is one of avowed (...) rationality and prudence. The sensible lover imitates the older literary example of Ulysses' tying himself to the mast. (The example belongs therefore to the class of problems treated in Elster (1979)). Both this lover and Ulysses foresee that under certain possible future conditions, their opinions, values and preferences will or would differ from what they are now, in a very definite fashion. To what extent is such foresight possible? Correspondingly (when we do not claim foreknowledge) to what extent is such opinion reasonable, rational, coherent, or consistent in some suitably broad sense? It is not easy to understand exactly what is possible or even logically permissible in this respect. In an earlier paper, "Belief and the Will", I argued for a principle ("Reflection") to govern such deliberation. Here I will both generalize the treatment of opinion in "Belief and the Will" and respond to criticism. Critical examples mainly resembled the story of Ulysses who foresaw a period of dysfunction (at the sound 2 of the sirens) in his epistemic and/or doxastic future. Other criticism focused on the model of opinion used (precise numerical subjective probability) and on the merits of Dutch Book arguments. The present argument will not rely on Dutch Book arguments and strategies, and the Reflection principle will be formulated so as to apply also to vague opinion. (shrink)

Adam Elga takes the Sleeping Beauty example to provide a counter-example to Reflection, since on Sunday Beauty assigns probability 1/2 to H, and she is certain that on Monday she will assign probability 1/3. I will show that there is a natural way for Bas van Fraassen to defend Reflection in the case of Sleeping Beauty, building on van Fraassen’s treatment of forgetting. This will allow me to identify a lacuna in Elga’s argument for 1/3. I will then argue, however, (...) that not all is well with Reflection: there is a problem with van Fraassen’s treatment of forgetting. Ultimately I will agree with Elga’s 1/3 answer. David Lewis maintains that the answer is 1/2; I will argue that cases of forgetting can be used to show that the premiss of Lewis’s argument for 1/2 is false. (shrink)

In Belief and the Will, van Fraassen employed a diachronic Dutch Book argument to support a counterintuitive principle called Reflection. There and subsequently van Fraassen has put forth Reflection as a linchpin for his views in epistemology and the philosophy of science, and for the voluntarism (first-person reports of subjective probability are undertakings of commitments) that he espouses as an alternative to descriptivism (first-person reports of subjective probability are merely self-descriptions). Christensen and others have attacked Reflection, taking it to have (...) unpalatable consequences. We prescind from the question of the cogency of diachronic Dutch Book arguments, and focus on Reflection's proper interpretation. We argue that Reflection is not as counterintuitive as it appears — that once interpreted properly the status of the counterexamples given by Christensen and others is left open. We show also that descriptivism can make sense of Reflection, while voluntarism is not especially well suited to do so. (shrink)

The Lottery Paradox and the Preface Paradox both involve the thesis that high probability is sufficient for rational acceptability. The standard solution to these paradoxes denies that rational acceptability is deductively closed. This solution has a number of untoward consequences. The present paper suggests that a better solution to the paradoxes is to replace the thesis that high probability suffices for rational acceptability with a somewhat stricter thesis. This avoids the untoward consequences of the standard solution. The new solution will (...) be defended against a seemingly obvious objection. 1 The paradoxes of rational acceptability 2 The standard solution 3 A new solution to the paradoxes 4 Basic assumptions 5 The new solution defended 6 Conclusion 7 Appendix. (shrink)

A theory of evidential probability is developed from two assumptions:(1) the evidential probability of a proposition is its probability conditional on the total evidence;(2) one's total evidence is one's total knowledge. Evidential probability is distinguished from both subjective and objective probability. Loss as well as gain of evidence is permitted. Evidential probability is embedded within epistemic logic by means of possible worlds semantics for modal logic; this allows a natural theory of higher-order probability to be developed. In particular, it is (...) emphasized that it is sometimes uncertain which propositions are part of one's total evidence; some surprising implications of this fact are drawn out. (shrink)

How should you take into account the opinions of an advisor? When you completely defer to the advisor's judgment, then you should treat the advisor as a guru. Roughly, that means you should believe what you expect she would believe, if supplied with your extra evidence. When the advisor is your own future self, the resulting principle amounts to a version of the Reflection Principle---a version amended to handle cases of information loss. When you count an advisor as an epistemic (...) peer, you should give her conclusions the same weight as your own. Denying that view---call it the ``equal weight view''---leads to absurdity: the absurdity that you could reasonably come to believe yourself to be an epistemic superior to an advisor simply by noting cases of disagreement with her, and taking it that she made most of the mistakes. Accepting the view seems to lead to another absurdity: that one should suspend judgment about everything that one's smart and well-informed friends disagree on, which means suspending judgment about almost everything interesting. But despite appearances, the equal weight view does not have this absurd consequence. Furthermore, the view can be generalized to handle cases involving not just epistemic peers, but also epistemic superiors and inferiors. (shrink)

The most immediately appealing model for formal constraints on degrees of belief is provided by probability theory, which tells us, for instance, that the probability of P can never be greater than that of (P v Q). But while this model has much intuitive appeal, many have been concerned to provide arguments showing that ideally rational degrees of belief would conform to the calculus of probabilities. The arguments most frequently used to make this claim plausible are the so-called "Dutch Book" (...) arguments. (shrink)

How should we respond to evidence when our evidence indicates that we are rationally impaired? I will defend a novel answer based on the analogy between self-doubt and memory loss. To believe that one is now impaired and previously was not is to believe that one’s epistemic position has deteriorated. Memory loss is also a form of epistemic deterioration. I argue that agents who suffer from epistemic deterioration should return to the priors they had at an earlier time. I develop (...) this argument regarding memory loss then extend it to cases of self-doubt. (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)

Recently, several epistemologists have defended an attractive principle of epistemic rationality, which we shall call Ur-Prior Conditionalization. In this essay, I ask whether we can justify this principle by appealing to the epistemic goal of accuracy. I argue that any such accuracy-based argument will be in tension with Evidence Externalism, i.e., the view that agent's evidence may entail non-trivial propositions about the external world. This is because any such argument will crucially require the assumption that, independently of all empirical evidence, (...) it is rational for an agent to be certain that her evidence will always include truths, and that she will always have perfect introspective access to her own evidence. This assumption is in tension with Evidence Externalism. I go on to suggest that even if we don't accept Evidence Externalism, the prospects for any accuracy-based justification for Ur-Prior Conditionalization are bleak. (shrink)

In this paper, I argue for a view largely favorable to the Thirder view: when Sleeping Beauty wakes up on Monday, her credence in the coin’s landing heads is less than 1/2. Let’s call this “the Lesser view.” For my argument, I (i) criticize Strict Conditionalization as the rule for changing de se credences; (ii) develop a new rule; and (iii) defend it by Gaifman’s Expert Principle. Finally, I defend the Lesser view by making use of this new rule.

We explore the question of whether sustained rational disagreement is possible from a broadly Bayesian perspective. The setting is one where agents update on the same information, with special consideration being given to the case of uncertain information. The classical merging of opinions theorem of Blackwell and Dubins shows when updated beliefs come and stay closer for Bayesian conditioning. We extend this result to a type of Jeffrey conditioning where agents update on evidence that is uncertain but solid (hard Jeffrey (...) shifts). However, merging of beliefs does not generally hold for Jeffrey conditioning on evidence that is fluid (soft Jeffrey shifts, Field shifts). Several theorems on the asymptotic behavior of subjective probabilities are proven. Taken together they show that while a consensus nearly always emerges in important special cases, sustained rational disagreement can be expected in many other situations. (shrink)

This paper shows that any view of future contingent claims that treats such claims as having indeterminate truth values or as simply being false implies probabilistic irrationality. This is because such views of the future imply violations of reflection, special reflection and conditionalization.

The Sleeping Beauty Problem attracts so much attention because it connects to a wide variety of unresolved issues in formal epistemology, decision theory, and the philosophy of science. The problem raises unanswered questions concerning relative frequencies, objective chances, the relation between self-locating and non-self-locating information, the relation between self-location and updating, Dutch Books, accuracy arguments, memory loss, indifference principles, the existence of multiple universes, and many-worlds interpretations of quantum mechanics. After stating the problem, this article surveys its connections to all (...) of these areas. (shrink)