According to a widely held norm of rationality, one should not change prior credences without new evidence. An important argument for this norm appeals to accuracy considerations, which says that changing priors doesn’t maximize expected accuracy. This is because accuracy measures are strictly proper, and thus any probabilistically coherent person regards her own priors as uniquely maximizing expected accuracy compared with other priors. -/- This paper attempts to resist the accuracy argument against changing priors. We argue that even if rational (...) epistemic decisions maximize expected accuracy according to strictly proper accuracy measures, it can still be rational to change priors sometimes. The core idea of our argument is that changing priors can be rational if one wants to maximize not just one’s current, short-term accuracy but also future, long-term accuracy. Our argument, if successful, shows that considering long-term accuracy has significant ramifications for the accuracy-first project. (shrink)

The aim of this paper is to argue for a revised and precisified version of the infamous Verifiability Criterion for the meaningfulness of declarative sentences. The argument is based on independently plausible premises concerning probabilistic confirmation and meaning as context-change potential, it is shown to be logically valid, and its ramifications for potential applications of the criterion are being discussed. Although the paper is not historical but systematic, the criterion thus vindicated will resemble the original one(s) in some important ways. (...) At the same time, it will also be more modest insofar as meaningfulness will turn out to be relativized linguistically and probabilistically, and different choices of the linguistic and probabilistic parameters may lead to different verdicts on meaningfulness. (shrink)

This paper aims to flesh out the celebrated notion of reflective equilibrium within a probabilistic framework for epistemic rationality. On the account developed here, an agent's attitudes are in reflective equilibrium when there is a certain sort of harmony between the agent's credences, on the one hand, and what the agent accepts, on the other hand. Somewhat more precisely, reflective equilibrium is taken to consist in the agent accepting, or being prepared to accept, all and only claims that follow from (...) a maximally comprehensive theory that is more probable than any other such theory. Drawing on previous work, the paper shows that when an agent is in reflective equilibrium in this sense, the set of claims they accept or are prepared to accept is bound to be logically consistent and closed under logical implication. The paper also argues that this account can explain various features of philosophical argumentation in which the notion of reflective equilibrium features centrally, such as the emphasis on evaluating philosophical theories holistically rather than in a piecemeal fashion. (shrink)

Why engage in inquiry? According to many philosophers, the goal of inquiring into some question is to come to know its answer. While this view holds considerable appeal, this paper argues that it stands in tension with another highly attractive thesis: knowledge does not require absolute certainty. Forced to choose between these two theses, I argue that we should reject the idea that inquiry aims at knowledge. I go on to develop an alternative view, according to which inquiry aims at (...) maximizing the epistemic value of our credences. This alternative view makes room for knowledge that falls shy of certainty, and it coheres nicely with a rich body of work in epistemic decision theory. I proceed to highlight the implications of this replacement for some important topics in epistemology, including the dogmatism paradox, the nature of interrogative attitudes, and the norm of practical reasoning. (shrink)

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

A core tenet of Bayesian epistemology is that rational agents update by conditionalization. Accuracy arguments in favour of this norm are well known. Meanwhile, scholars working in quantum probability and quantum state estimation have proposed multiple updating rules, all of which look prima facie like analogues of Bayesian conditionalization. The most common are Lüders conditionalization and Bayesian mean estimation (BME). Some authors also endorse a lesser-known alternative that we call retrodiction. We show how one can view Lüders and BME as (...) complementary rules, and we give expected accuracy and accuracy dominance arguments for both. By contrast, we find that retrodiction is accuracy-dominated, at least on many measures of accuracy. (shrink)

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

In the recent philosophical literature on inquiry, epistemologists point out that their subject has often begun at the point at which you already have your evidence and then focussed on identifying the beliefs for which that evidence provides justification. But we are not mere passive recipients of evidence. While some comes to us unbidden, we often actively collect it. This has long been recognised, but typically epistemologists have taken the norms that govern inquiry to be practical, not epistemic. The recent (...) literature challenges this assumption and uncovers a rich range of questions about the epistemic normativity of inquiry. In this paper, I approach these questions from the formal side of epistemology. Developing out of the philosophy of science, as it did, this branch of epistemology has long discussed inquiry. And, building on the insights of Janina Hosiasson (1931), David Blackwell (1951), and I. J. Good (1967), it has produced a reasonably well-developed framework in which to understand norms of inquiry, both epistemic and practical. In the first half of the paper, I will present the pragmatic versions of this framework due to Hosiasson, Blackwell, and Good, and the epistemic version due to Graham Oddie (1997); in the second half of the paper, I put this framework to work, turning to some of the questions from the recent debate about inquiry and asking how the framework can help us answer them. Questions include: When should we initiate an inquiry, when should we continue it, when should we conclude it, and when should we reopen it? How do epistemic norms of inquiry relate to epistemic norms of belief or credence, and can they conflict, as Jane Friedman (2020) contends? How should we resolve the apparent puzzle raised by Friedman's example of counting the windows in the Chrysler Building? How should we direct our attention, as Georgi Gardiner (2022) asks? How should we choose and reason after receiving evidence we'd rather not have received? And how should we understand the epistemic error that occurs when someone is resistant to evidence in the way Mona Simion (2023) describes? (shrink)

There is some consensus on the claim that imagination as suppositional thinking can have epistemic value insofar as it’s constrained by a principle of minimal alteration of how we know or believe reality to be – compatibly with the need to accommodate the supposition initiating the imaginative exercise. But in the philosophy of imagination there is no formally precise account of how exactly such minimal alteration is to work. I propose one. I focus on counterfactual imagination, arguing that this can (...) be modeled as simulated belief revision governed by Laplacian imaging. So understood, it can be rationally justified by accuracy considerations: it minimizes expected belief inaccuracy, as measured by the Brier score. (shrink)

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

Epistemic consequentialism is the view that epistemic goodness is more fundamental than epistemic rightness. This paper examines the relationship between epistemic consequentialism and theistic belief. I argue that, in an epistemic consequentialist framework, there is an epistemic reason to believe in God. Imagine having an unlimited amount of time to ask an omniscient being anything you wanted. The potential epistemic benefits would be enormous. Considerations like these point to an epistemic version of Pascal’s wager. I compare and contrast the epistemic (...) wager with the traditional wager, and argue that the epistemic wager has several notable advantages. (shrink)

Drawing on a passage from Ramsey's Truth and Probability, we formulate a simple, plausible constraint on evaluating the accuracy of credences: the Calibration Test. We show that any additive, continuous accuracy measure that passes the Calibration Test will be strictly proper. Strictly proper accuracy measures are known to support the touchstone results of accuracy-first epistemology, for example vindications of probabilism and conditionalization. We show that our use of Calibration is an improvement on previous such appeals by showing how it answers (...) or sidesteps problems that have been raised for previous work in this area. (shrink)

In a recent paper, Yoaav Isaacs, Alan Hájek, and John Hawthorne argue for the rational permissibility of "credal imprecision" by appealing to certain propositions associated with non-measurable spatial regions: for example, the proposition that the pointer of a spinner will come to rest within a certain non-measurable set of points on its circumference. This paper rebuts their argument by showing that its premises lead to implausible consequences in cases where one is trying to learn, by making multiple observations, whether a (...) certain outcome is associated with a non-measurable region or a measurable one. (shrink)

We can have credences in an infinite number of propositions—that is, our opinion set can be infinite. Accuracy-first epistemologists have devoted themselves to evaluating credal states with the help of the concept of ‘accuracy’. Unfortunately, under several innocuous assumptions, infinite opinion sets yield several undesirable results, some of which are even fatal, to accuracy-first epistemology. Moreover, accuracy-first epistemologists cannot circumvent these difficulties in any standard way. In this regard, we will suggest a non-standard approach, called a relativistic approach, to accuracy-first (...) epistemology and show that such an approach can successfully circumvent undesirable results while having some advantages over the standard approach. (shrink)

In this paper I’ll suggest that a certain challenge facing defeatist views about higher-order evidence cannot be met, namely, motivating principles that recommend abandoning belief in cases of higher order defeat, but do not recommend global scepticism. I’ll propose that, ultimately, the question of whether to abandon belief in response to the realization that our belief can’t be recovered from what I’ll call ‘a perspective of doubt’ can’t be answered through rational deliberation aimed at truth or accuracy.

According to evidentialist views, credence in a proposition p should be proportional to the degree of evidential support that one has in favor of p. However, empirical evidence suggests that our credences are systematically sensitive to practical factors. In this article, I provide a cost–benefit analysis of credences' practical sensitivity. The upshot of this analysis is that credences sensitive to practical factors fare better than practically insensitive ones along several dimensions. All things considered, our credences should be sensitive to practical (...) factors. (shrink)

Awareness growth—coming to entertain propositions of which one was previously unaware—is a crucial aspect of epistemic thriving. And yet, it is widely believed that orthodox Bayesianism cannot accommodate this phenomenon, since that would require employing supposedly defective catch-all propositions. Orthodox Bayesianism, it is concluded, must be amended. In this paper, I show that this argument fails, and that, on the contrary, the orthodox version of Bayesianism is particularly well-suited to accommodate awareness growth. For it entails what I call the refinement (...) view, which allows us to capture that awareness growth consists in the increase of one’s capacity of discernment. (shrink)

Had we grown up elsewhere or been educated differently, our view of the world would likely be radically different. What to make of this? This paper takes an accuracy-centered first-personal approach to the question of how to respond to the arbitrary nature in which many of our beliefs are formed. I show how considerations of accuracy motivate different responses to this sort of information depending on the type of attitude we take towards the belief in question upon subjecting the belief (...) to doubt. (shrink)

Philosophers have recently attempted to justify particular belief revision procedures by arguing that they are the optimal means towards the epistemic end of accurate credences. These attempts, however, presuppose that means should be evaluated according to classical expected utility theory; and there is a long tradition maintaining that expected utility theory is too restrictive as a theory of means–end rationality, ruling out too many natural ways of taking risk into account. In this paper, we investigate what belief-revision procedures are supported (...) by accuracy-theoretic considerations once we depart from expected utility theory to allow agents to be risk-sensitive. We argue that if accuracy-theoretic considerations tell risk-sensitive agents anything about belief-revision, they tell them the same thing they tell risk-neutral agents: they should conditionalize. (shrink)

Philosophy and Phenomenological Research, EarlyView.

Epistemic rationality is typically taken to be immodest at least in this sense: a rational epistemic state should always take itself to be doing at least as well, epistemically and by its own light, than any alternative epistemic state. If epistemic states are probability functions and their alternatives are other probability functions defined over the same collection of proposition, we can capture the relevant sense of immodesty by claiming that epistemic utility functions are (strictly) proper. In this paper I examine (...) what happens if we allow for the alternatives to an epistemic state to include probability functions with different domains. I first prove an impossibility result: on minimal assumptions, I show that there is no way of vindicating strong immodesty principles to the effect that any probability function should take itself to be doing at least as well than any alternative probability function, regardless of its domain. I then consider alternative, weaker generalizations of the traditional immodesty principle and prove some characterization results for some classes of epistemic utility functions satisfying each of the relevant principles. (shrink)

Quine taught us the difference between a theory’s ontology and its ideology. Ontology is the things a theory’s quantifiers must range over if it is true, Ideology is the primitive concepts that must be used to state the theory. This allows us to split the theoretical virtue of parsimony into two kinds: ontological parsimony and ideological parsimony. My goal is help illuminate the virtue of ideological parsimony by giving a criterion for ideological innocence—a rule for when additional ideology does not (...) count against parsimony. I propose the expressive power innocence criterion: if the ideology of theory one is expressively equivalent to that of theory two, then neither is ideologically simpler than the other. In its favor I offer the argument from accuracy, showing that any account of a theoretical virtue that is supposed to make theories that have it more likely to be true than theories that do not must respect it. Next I consider its ramifications, eliminating rival views and passing judgment on some arguments from parsimony that can be found in the literature. Finally, I consider two objections. First: I address an objection arising from the possibility of languages with a ‘primitive’ operator that allows us to list a theory’s primitives in the object-language. Second: I address an objection raised by Nelson Goodman against attempts to reckon simplicity by expressive power. Both objections fail. (shrink)

Two of the most influential arguments for Bayesian updating ("Conditionalization") -- Hilary Greaves' and David Wallace's Accuracy Argument and David Lewis' Diachronic Dutch Book Argument-- turn out to impose a strong and surprising limitation on rational uncertainty: that one can never be rationally uncertain of what one's evidence is. Many philosophers ("externalists") reject that claim, and now seem to face a difficult choice: either to endorse the arguments and give up Externalism, or to reject the arguments and lose some of (...) the best justifications of Bayesianism. The author argues that the key to resolving this conflict lies in recognizing that both arguments are plan-based, in that they argue for Conditionalization by first arguing that one should planto conditionalize. With this in view, we can identify the culprit common to both arguments: for an externalist, they misconceive the requirement to carry out a plan made at an earlier time. They should therefore not persuade us to reject Externalism. Furthermore, rethinking the nature of this requirement allows us to give two new arguments for Conditionalization that do not rule out rational uncertainty about one's evidence and that can thus serve as common ground in the debate between externalists and their opponents. (shrink)

Accuracy-first epistemology says that the rational update rule is the rule that maximizes expected accuracy. Externalism says, roughly, that we do not always know what our total evidence is. It’s been argued in recent years that the externalist faces a dilemma: Either deny that Bayesian Conditionalization is the rational update rule, thereby rejecting traditional Bayesian epistemology, or else deny that the rational update rule is the rule that maximizes expected accuracy, thereby rejecting the accuracy-first program. Call this the Bayesian Dilemma. (...) Here is roughly how the argument goes. Schoenfield (2017) has shown that following Metaconditionalization maximizes expected accuracy. But if externalism is true, Metaconditionalization is not Bayesian Conditionalization. Therefore, the externalist must choose between the rule that maximizes expected accuracy (Metaconditionalization) and Bayesian Conditionalization. I am not convinced by this argument; once we make the premises fully explicit, we see that it relies on assumptions that the externalist has every reason to reject. Still, I think that the Bayesian Dilemma is a genuine dilemma. I give a new argument—I call it the continuity argument—that doesn’t make any assumptions the externalist rejects. Roughly, I show that if you're sufficiently confident that you will correctly identify your evidence, then you'll expect adopting a rule that I call Accurate Metaconditionalization to be more accurate than adopting Bayesian Conditionalization. (shrink)

The best accuracy arguments for probabilism apply only to credence functions with finite domains, that is, credence functions that assign credence to at most finitely many propositions. This is a significant limitation. It reveals that the support for the accuracy-first program in epistemology is a lot weaker than it seems at first glance, and it means that accuracy arguments cannot yet accomplish everything that their competitors, the pragmatic (Dutch book) arguments, can. In this paper, I investigate the extent to which (...) this limitation can be overcome. Building on the best arguments in finite domains, I present two accuracy arguments for probabilism that are perfectly general—they apply to credence functions with arbitrary domains. I then discuss how the arguments’ premises can be challenged. We will see that it is particularly difficult to characterize admissible accuracy measures in infinite domains. (shrink)

The Bayesian Approach and the Classical Approach are two very different families of approaches to statistical inference. There are many different versions of each view, often with very substantial differences among them. But I will here endeavor to explain the philosophical core of each family of approaches, as well as to identify four main philosophical differences between them.

Some epistemologists think that the Bayesian ideals matter because we can approximate them. That is, our attitudes can be more or less close to the ones of our ideal Bayesian counterpart. In this paper, I raise a worry for this justification of epistemic ideals. The worry is this: In order to correctly compare agents to their ideal counterparts, we need to imagine idealized agents who have the same relevant information, knowledge, or evidence. However, there are cases in which one’s ideal (...) counterpart cannot have one’s information, knowledge, or evidence. In these situations, agents cannot compare themselves to their ideal counterpart. (shrink)

Epistemic decision theory aims to defend a variety of epistemic norms in terms of their facilitation of epistemic ends. One of the most important components of EpDT is known as a scoring rule. This thesis addresses some problems about scoring rules in EpDT. I consider scoring rules both for precise credences and for imprecise credences. For scoring rules in the context of precise credences, I examine the rationale for requiring a scoring rule to be strictly proper, and argue that no (...) satisfactory justification has been given. I then investigate one possible response to my argument and show the problems with this response. The conclusion is that there is a further need for justifying the requirement that a scoring rule should be strictly proper for precise credences. For scoring rules in the context of imprecise credences, an impossibility result has been established in the literature purporting to show that no strictly proper, continuous and real-valued scoring rule exists. However, a precise statement of the impossibility result requires precise definitions both of strict propriety and of continuity in the context of imprecise credences. Moreover, the result implies that we need to drop one of the three properties - strict propriety, continuity or being real-valued - to have a scoring rule for applying EpDT to imprecise credences. So, firstly, I offer definitions of strict propriety and of continuity and clarify the impossibility result. Then, I investigate what will happen if we drop one of the three properties. I argue that we should drop the property of being real-valued and I offer the general forms of two kinds of strictly proper, continuous and lexicographic scoring rules for imprecise credences. (shrink)

Structural requirements of rationality prohibit various things, like having inconsistent combinations of attitudes, having means-end incoherent combinations of attitudes, and so on. But what is the distinctive feature of structural requirements of rationality? And do we fall under an obligation to be structurally rational? These issues have been at the heart of significant debates over the past fifteen years. Some philosophers have recently argued that we can unify the structural requirements of rationality by analyzing what is constitutive of our attitudes (...) (Lee, 2020; Worsnip, 2018a). It has also been suggested that, in the course of good first-personal deliberation, agents should treat structurally irrational combinations of attitudes as off-limits (Worsnip, 2021). In this paper, I raise a worry for these two theses concerning structural rationality. Roughly, I argue that some imperfect epistemic agents (like us) can be disposed to have structurally irrational combinations of attitudes. Also, when these imperfect agents deliberate, they should not treat structurally irrational combinations of attitudes as off-limits. Given our imperfections, being structurally irrational can very well be the best option we have. More generally, these observations reveal that structural rationality should not always be theorized independently from more “substantive” norms, like responsiveness to reasons or expected value optimization. (shrink)

According to van Fraassen, inference to the best explanation (IBE) is incompatible with Bayesianism. To argue to the contrary, many philosophers have suggested hybrid models of scientific reasoning with both explanationist and probabilistic elements. This paper offers another such model with two novel features. First, its Bayesian component is imprecise. Second, the domain of credence functions can be extended.

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)

Sometimes you are unreliable at fulfilling your doxastic plans: for example, if you plan to be fully confident in all truths, probably you will end up being fully confident in some falsehoods by mistake. In some cases, there is information that plays the classical role of evidence—your beliefs are perfectly discriminating with respect to some possible facts about the world—and there is a standard expected‐accuracy‐based justification for planning to conditionalize on this evidence. This planning‐oriented justification extends to some cases where (...) you do not have transparent evidence, in the sense that your beliefs are not perfectly discriminating with respect to any non‐trivial facts. In other cases, accuracy considerations do not tell you to plan to conditionalize on any information at all, but rather to plan to follow a different updating rule. Even in the absence of evidence, accuracy considerations can guide your doxastic plan. (shrink)

Epistemologists who study credences have a well-developed account of how you should change them when you learn new evidence; that is, when your body of evidence grows. What's more, they boast a diverse range of epistemic and pragmatic arguments that support that account. But they do not have a satisfactory account of when and how you should change your credences when you become aware of possibilities and propositions you have not entertained before; that is, when your awareness grows. In this (...) paper, I consider the arguments for the credal epistemologist's account of how to respond to evidence, and I ask whether they can help us generate an account of how to respond to awareness growth. The results are surprising: the arguments that all support the same norms for responding to evidence growth support a number of different norms when they are applied to awareness growth. Some of these norms seem too weak, others too strong. I ask what we should conclude from this, and argue that our credal response to awareness growth is considerably less rigorously constrained than our credal response to new evidence. (shrink)

– 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 a belief has been influenced, in part or whole, by factors that, by the believer's own lights, do not bear on the truth of the believed proposition, we can say that the belief has been, in a sense, arbitrarily formed. Can such beliefs ever be rational? It might seem obvious that they can't. After all, belief, supposedly, “aims at the truth.” But many epistemologists have come to think that certain kinds of arbitrary beliefs can, indeed, be rational. In this (...) paper, I want to do two things. First, I want to show that the claim that arbitrary beliefs can be rational is inconsistent with the conjunction of two other attractive claims: one saying that rationality requires a certain kind of epistemic immodesty, and one saying that rationality forbids certain kinds of self-ascriptions of epistemic luck. Second, I want to evaluate different ways one might respond to this inconsistent triad. I won't defend any response in particular, but I'll draw out some notable costs and benefits of each response, which may help shed light on the question of whether arbitrary beliefs can be rational. (shrink)

In a series of papers over the past twenty years, and in a new book, Igor Douven has argued that Bayesians are too quick to reject versions of inference to the best explanation that cannot be accommodated within their framework. In this paper, I survey their worries and attempt to answer them using a series of pragmatic and purely epistemic arguments that I take to show that Bayes’ Rule really is the only rational way to respond to your evidence.

In this paper, we ask: how should an agent who has incoherent credences update when they learn new evidence? The standard Bayesian answer for coherent agents is that they should conditionalize; however, this updating rule is not defined for incoherent starting credences. We show how one of the main arguments for conditionalization, the Dutch strategy argument, can be extended to devise a target property for updating plans that can apply to them regardless of whether the agent starts out with coherent (...) or incoherent credences. The main idea behind this extension is that the agent should avoid updating plans that increase the possible sure loss from Dutch strategies. This happens to be equivalent to avoiding updating plans that increase incoherence according to a distance-based incoherence measure. (shrink)

We argue that there is a tension between two monistic claims that are the core of recent work in epistemic consequentialism. The first is a form of monism about epistemic value, commonly known as veritism: accuracy is the sole final objective to be promoted in the epistemic domain. The other is a form of monism about a class of epistemic scoring rules: that is, strictly proper scoring rules are the only legitimate measures of inaccuracy. These two monisms, we argue, are (...) in tension with each other. If only accuracy has final epistemic value, then there are legitimate alternatives to strictly proper scoring rules. Our argument relies on the way scoring rules are used in contexts where accuracy is rewarded, such as education. (shrink)

Sometimes we are interested in how groups are doing epistemically in aggregate. For instance, we may want to know the epistemic impact of a change in school curriculum or the epistemic impact of abolishing peer review in the sciences. Being able to say something about how groups are doing epistemically is especially important if one is interested in pursuing a consequentialist approach to social epistemology of the sort championed by Goldman. According to this approach we evaluate social practices and institutions (...) from an epistemic perspective based on how well they promote the aggregate level of epistemic value across a community. The aim of this paper is to investigate this concept of group epistemic value and defend a particular way of measuring it. (shrink)

Accuracy-first epistemology aims to show that the norms of epistemic rationality can be derived from the effective pursuit of accuracy. This paper explores the prospects within accuracy-first epistemology for vindicating “modesty”: the thesis that ideal rationality permits uncertainty about one’s own rationality. I argue that accuracy-first epistemology faces serious challenges in accommodating three forms of modesty: uncertainty about what priors are rational, uncertainty about whether one’s update policy is rational, and uncertainty about what one’s evidence is. I argue that the (...) problem stems from the representation of epistemic decision problems. The appropriate representation of decision problems, and corresponding decision rules, for (diachronic) update policies should be a generalization of decision problems and decision rules for (synchronic) coherence. I argue that extant accounts build in conflicting assumptions about which kinds of information about the believer should be used to structure epistemic decision problems. In particular, extant accounts of update build in a form of epistemic consequentialism. Related forms of epistemic consequentialism have been shown to generate problems for accuracy-first epistemology’s purported justifications of probabilism, conditionalization, and the principal principle. These results are vindicated only with nonconsequentialist epistemic decision theories. I close with suggestive examples of how, with a fully nonconsequentialist representation of epistemic decision problems, accuracy-first epistemology can allow for rational modesty. (shrink)

How much does rationality constrain what we should believe on the basis of our evidence? According to this book, not very much. For most people and most bodies of evidence, there is a wide range of beliefs that rationality permits them to have in response to that evidence. The argument, which takes inspiration from William James' ideas in 'The Will to Believe', proceeds from two premises. The first is a theory about the basis of epistemic rationality. It's called epistemic utility (...) theory, and it says that what it is epistemically rational for you to believe is what it would be rational for you to choose if you were given the chance to pick your beliefs and, when picking them, you were to care only about their epistemic value. So, to say which beliefs are permitted, we must say how to measure epistemic value, and which decision rule to use when picking your beliefs. The second premise is a claim about attitudes to epistemic risk, and it says that rationality permits many different such attitudes. These attitudes can show up in epistemic utility theory in two ways: in the way you measure epistemic value; and in the decision rule you use to pick beliefs. This book explores the latter. The result is permissivism about epistemic rationality: different attitudes to epistemic risk lead to different choices of prior beliefs; given most bodies of evidence, different priors lead to different posteriors; and even once we fix your attitudes to epistemic risk, if they are at all risk-inclined, there is a range of different priors and therefore different posteriors they permit. (shrink)

According to epistemic utility theory, epistemic rationality is teleological: epistemic norms are instrumental norms that have the aim of acquiring accuracy. What’s definitive of these norms is that they can be expected to lead to the acquisition of accuracy when followed. While there’s much to be said in favor of this approach, it turns out that it faces a couple of worrisome extensional problems involving the future. The first problem involves credences about the future, and the second problem involves future (...) credences. Examining prominent solutions to a different extensional problem for this approach reinforces the severity of the two problems involving the future. Reflecting on these problems reveals the source: the teleological assumption that epistemic rationality aims at acquiring accuracy. (shrink)

Epistemic decision theory produces arguments with both normative and mathematical premises. I begin by arguing that philosophers should care about whether the mathematical premises (1) are true, (2) are strong, and (3) admit simple proofs. I then discuss a theorem that Briggs and Pettigrew (2020) use as a premise in a novel accuracy-dominance argument for conditionalization. I argue that the theorem and its proof can be improved in a number of ways. First, I present a counterexample that shows that one (...) of the theorem’s claims is false. As a result of this, Briggs and Pettigrew’s argument for conditionalization is unsound. I go on to explore how a sound accuracy-dominance argument for conditionalization might be recovered. In the course of doing this, I prove two new theorems that correct and strengthen the result reported by Briggs and Pettigrew. I show how my results can be combined with various normative premises to produce sound arguments for conditionalization. I also show that my results can be used to support normative conclusions that are stronger than the one that Briggs and Pettigrew’s argument supports. Finally, I show that Briggs and Pettigrew’s proofs can be simplified considerably. (shrink)

(This is for the Cambridge Handbook of Analytic Philosophy, edited by Marcus Rossberg) In this handbook entry, I survey the different ways in which formal mathematical methods have been applied to philosophical questions throughout the history of analytic philosophy. I consider: formalization in symbolic logic, with examples such as Aquinas’ third way and Anselm’s ontological argument; Bayesian confirmation theory, with examples such as the fine-tuning argument for God and the paradox of the ravens; foundations of mathematics, with examples such as (...) Hilbert’s programme and Gödel’s incompleteness theorems; social choice theory, with examples such as Condorcet’s paradox and Arrow’s theorem; ‘how possibly’ results, with examples such as Condorcet’s jury theorem and recent work on intersectionality theory; and the application of advanced mathematics in philosophy, with examples such as accuracy-first epistemology. (shrink)

Accuracy arguments for the core tenets of Bayesian epistemology differ mainly in the conditions they place on the legitimate ways of measuring the inaccuracy of our credences. The best existing arguments rely on three conditions: Continuity, Additivity, and Strict Propriety. In this paper, I show how to strengthen the arguments based on these conditions by showing that the central mathematical theorem on which each depends goes through without assuming Additivity.

This paper contributes to a recent research program that extends arguments supporting elementary conditionalization to arguments supporting conditionalization with general, measure-theoretic conditional probabilities. I begin by suggesting an amendment to the framework that Rescorla (2018) has used to characterize regular conditional probabilities in terms of avoiding Dutch book. If we wish to model learning scenarios in which an agent gains complete membership knowledge about some subcollection of the events of interest to her, then we should focus on updating policies that (...) are what I shall call proper. I go on to characterize regular conditional probabilities in proper learning scenarios using what van Fraassen (1999) calls The General Reflection Principle. (shrink)