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)

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)

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)

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)

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)

Epistemology should take seriously the possibility of rationally evaluable changes in conceptual resources. Epistemic decision theory compares belief states in terms of epistemic value. But it's standardly restricted to belief states that don't differ in their conceptual resources. I argue that epistemic decision theory should be generalized to make belief states with differing concepts comparable. I characterize some possible constraints on epistemic utility functions. Traditionally, the epistemic utility of a total belief state has been understood as a function of the (...) epistemic utility of individual (partial) beliefs. The most natural ways of generalizing this account generate a kind of repugnant conclusion. I characterize some possible alternatives, reflecting different epistemic norms. (shrink)

It’s been argued that there are no diachronic norms of epistemic rationality. These arguments come partly in response to certain kinds of counterexamples to Conditionalization, but are mainly motivated by a form of internalism that appears to be in tension with any sort of diachronic coherence requirements. I argue that there are, in fact, fundamentally diachronic norms of rationality. And this is to reject at least a strong version of internalism. But I suggest a replacement for Conditionalization that salvages internalist (...) intuitions, and carves a middle ground between conservatism and evidentialism. (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)

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)

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)

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)

The Sleeping Beauty problem is presented in a formalized framework which summarizes the underlying probability structure. The two rival solutions proposed by Elga and Lewis differ by a single parameter concerning her prior probability. They can be supported by considering, respectively, that Sleeping Beauty is “fuzzy-minded” and “blank-minded”, the first interpretation being more natural than the second. The traditional absent -minded driver problem is reinterpreted in this framework and sustains Elga’s solution.

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)

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)

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)

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)

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)

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)

Expert probability forecasts can be useful for decision making . But levels of uncertainty escalate: however the forecaster expresses the uncertainty that attaches to a forecast, there are good reasons for her to express a further level of uncertainty, in the shape of either imprecision or higher order uncertainty . Bayesian epistemology provides the means to halt this escalator, by tying expressions of uncertainty to the propositions expressible in an agent’s language . But Bayesian epistemology comes in three main varieties. (...) Strictly subjective Bayesianism and empirically-based subjective Bayesianism have difficulty in justifying the use of a forecaster’s probabilities for decision making . On the other hand, objective Bayesianism can justify the use of these probabilities, at least when the probabilities are consistent with the agent’s evidence . Hence objective Bayesianism offers the most promise overall for explaining how testimony of uncertainty can be useful for decision making. Interestingly, the objective Bayesian analysis provided in Sect. 5 can also be used to justify a version of the Principle of Reflection. (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)

The Cable Guy will definitely come between 8 a.m. and 4 p.m., and I can bet on one of two possibilities: that he will arrive between 8 and 12, or between 12 and 4. Since I have no more information, it seems (eminently) plausible to suppose the two bets are equally attractive. Yet Hajek has presented a tantalising argument that purports to show that the later interval is, initial appearances to the contrary, more choice-worthy. In this paper, I rebut the (...) argument. (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)

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)

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)

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)

The current debate about peer disagreement has so far mainly focused on the question of whether peer disagreements provide genuine counterevidence to which we should respond by revising our credences. By contrast, comparatively little attention has been devoted to the question by which process, if any, such revision should be brought about. The standard assumption is that we update our credences by conditionalizing on the evidence that peer disagreements provide. In this paper, we argue that non-dogmatist views have good reasons (...) to reject conditionalization. Instead, peer disagreements should be understood to call for a revision of our prior conditional probabilities: rather than merely adding to our original evidence, they pose a challenge to the thought that we have properly assessed the probative force of our original evidence. (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)

Conditionalization is a norm that governs the rational reallocation of credence. I distinguish between factive and non-factive formulations of Conditionalization. Factive formulations assume that the conditioning proposition is true. Non-factive formulations allow that the conditioning proposition may be false. I argue that non-factive formulations provide a better foundation for philosophical and scientific applications of Bayesian decision theory. I furthermore argue that previous formulations of Conditionalization, factive and non-factive alike, have almost universally ignored, downplayed, or mishandled a crucial causal aspect of (...) Conditionalization. To formulate Conditionalization adequately, one must explicitly address the causal structure of the transition from old credences to new credences. I offer a formulation of Conditionalization that takes these considerations into account, and I compare my preferred formulation with some prominent formulations found in the literature. (shrink)

RÉSUMÉ: Bas van Fraassen soutient que le «Principe de Réflexion» constitue une contrainte sur la rationalité et il rattache ce principe à une sorte de volontarisme épistémologique, c’est-à-dire la doctrine selon laquelle la croyance est affaire de volonté. Je soutiens que la version du volontarisme qui est compatible à la fois avec le Principe de Réflexion et avec l’idée de van Fraassen que les jugements épistémiques constituent une forme d’engagement, est tout à fait différente du volontarisme qu’envisageaient William James ou (...) Blaise Pascal. En fait, la prétention de van Fraassen d’avoir établi une théorie libératrice et pragmatique de la connaissance est mise en question par sa propre thèse selon laquelle le Principe de Réflexion sert d’appui à son volontarisme. Van Fraassen ne peut sauver le Principe de Réflexion que dans le cadre d’une théorie de la connaissance plus restrictive que celle qu’il envisage. (shrink)

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

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

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 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)

David Christensen and others argue that Dutch Strategies are more like peer disagreements than Dutch Books, and should not count against agents‘ conformity to ideal rationality. I review these arguments, then show that Dutch Books, Dutch Strategies, and peer disagreements are only possible in the case of what computer scientists call Byzantine Failures—uncorrected Byzantine Faults which update arbitrary values. Yet such Byzantine Failures make agents equally vulnerable to all three kinds of epistemic inconsistencies, so there is no principled basis for (...) claiming that only avoidance of true Dutch Books characterizes ideally rational agents. Agents without Byzantine Failures can be ideally rational in a very strong sense, but are not normative for humans. (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)

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)

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)

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)

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 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)

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. However, merging (...) of beliefs does not generally hold for Jeffrey conditioning on evidence that is fluid. 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)

I discuss two ways of justifying reflection principles. First, I propose that an undogmatic reading of dynamic Dutch book arguments provides them with a sound foundation. Second, I show also that minimizing expected inaccuracy leads to a novel argument for reflection principles. The required inaccuracy measures comprise a natural class of functions that can be derived from a generalization of a condition known as propriety or immodesty. This shows that reflection principles are an essential feature not just of consistent degrees (...) of belief but also of degrees of belief that approximate truth. (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...

In the Sleeping Beauty problem, Beauty is uncertain whether the outcome of a certain coin toss was heads or tails. One argument suggests that her degree of belief in heads should be 1/3, while a second suggests that it should be 1/2. Prima facie, the argument for 1/2 appears to be stronger. I offer a diachronic Dutch Book argument in favor of 1/3. Even for those who are not routinely persuaded by diachronic Dutch Book arguments, this one has some important (...) morals. (shrink)

I re-examine Coherence Arguments (Dutch Book Arguments, No Arbitrage Arguments) for diachronic constraints on Bayesian reasoning. I suggest to replace the usual game–theoretic coherence condition with a new decision–theoretic condition ('Diachronic Sure Thing Principle'). The new condition meets a large part of the standard objections against the Coherence Argument and frees it, in particular, from a commitment to additive utilities. It also facilitates the proof of the Converse Dutch Book Theorem. I first apply the improved Coherence Argument to van Fraassen's (...) (1984) Reflection principle. I then point out the failure of a Coherence Argument that is intended to support Conditionalization as a naive, universal, update rule. I also point out that Reflection is incompatible with the universal use of Conditionalization thus interpreted. The Coherence Argument therefore defeats the naive view on Bayesian learning that it was originally designed to justify. (shrink)

We use “I’ll be glad I did it” reasoning all the time. For example, last night I was trying to decide whether to work on this paper or go out to a movie. I realized that if I worked on the paper, then today I would be glad I did it. Whereas, if I went out to the movie, today I would regret it. This enabled me to see that I should work on the paper rather than going out to (...) a movie. This looks like excellent reasoning: Paper argument: 1. If I work on my paper, I’ll be glad I did it. 2. Therefore, I should work on my paper. When we’re having trouble making a big life decision, we often try to picture what will happen each way we might choose, and imagine how we’ll feel in that outcome. When choosing between two jobs, we might use this reasoning. Suppose you are choosing between two jobs and you know quite a lot about what the two jobs will be like. In one, you will make a lot of money but have to work eighty-hour weeks and see little of your family. In the other, you will make considerably less money—though enough to support yourself and your family. You’ll have much more time for your family. The money is attractive. But overall, you realize you’ll be glad to have the time with your family if you take the second job—you’ll be glad you made that choice. It seems this is a good way of realizing that you should take the second job. (shrink)

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.

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)