Scoring Rules

In this paper, we seek a reliabilist account of justified credence. Reliabilism about justified beliefs comes in two varieties: process reliabilism (Goldman, 1979, 2008) and indicator reliabilism (Alston, 1988, 2005). Existing accounts of reliabilism about justified credence comes in the same two varieties: Jeff Dunn (2015) proposes a version of process reliabilism, while Weng Hong Tang (2016) offers a version of indicator reliabilism. As we will see, both face the same objection. If they are right about what justification is, it (...) is mysterious why we care about justification, for neither of the accounts explains how justification is connected to anything of epistemic value. We will call this the Connection Problem. I begin by describing Dunn’s process reliabilism and Tang’s indicator reliabilism. I argue that, understood correctly, they are, in fact, extensionally equivalent. That is, Dunn and Tang reach the top of the same mountain, albeit by different routes. However, I argue that both face the Connection Problem. In response, I offer my own version of reliabilism, which is both process and indicator, and I argue that it solves that problem. Furthermore, I show that it is also extensionally equivalent to Dunn’s reliabilism and Tang’s. Thus, I reach the top of the same mountain as well. (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.

Arguments for probabilism aim to undergird/motivate a synchronic probabilistic coherence norm for partial beliefs. Standard arguments for probabilism are all of the form: An agent S has a non-probabilistic partial belief function b iff (⇐⇒) S has some “bad” property B (in virtue of the fact that their p.b.f. b has a certain kind of formal property F). These arguments rest on Theorems (⇒) and Converse Theorems (⇐): b is non-Pr ⇐⇒ b has formal property F.

The goal of a partial belief is to be accurate, or close to the truth. By appealing to this norm, I seek norms for partial beliefs in self-locating and non-self-locating propositions. My aim is to find norms that are analogous to the Bayesian norms, which, I argue, only apply unproblematically to partial beliefs in non-self-locating propositions. I argue that the goal of a set of partial beliefs is to minimize the expected inaccuracy of those beliefs. However, in the self-locating framework, (...) there are two equally legitimate definitions of expected inaccuracy. And, while each gives rise to the same synchronic norm for partial beliefs, they give rise to different, inconsistent diachronic norms. I conclude that both norms are rationally permissible. En passant, I note that this entails that both Halfer and Thirder solutions to the well-known Sleeping Beauty puzzle are rationally permissible. (shrink)

In this paper, I provide an accuracy-based argument for conditionalization (via reflection) that does not rely on norms of maximizing expected accuracy. -/- (This is a draft of a paper that I wrote in 2013. It stalled for no very good reason. I still believe the content is right).

According to accuracy-first epistemology, accuracy is the fundamental epistemic good. Epistemic norms — Probabilism, Conditionalization, the Principal Principle, etc. — have their binding force in virtue of helping to secure this good. To make this idea precise, accuracy-firsters invoke Epistemic Decision Theory (EpDT) to determine which epistemic policies are the best means toward the end of accuracy. Hilary Greaves and others have recently challenged the tenability of this programme. Their arguments purport to show that EpDT encourages obviously epistemically irrational behavior. (...) We develop firmer conceptual foundations for EpDT. First, we detail a theory of praxic and epistemic good. Then we show that, in light of their very different good-making features, EpDT will evaluate epistemic states and epistemic acts according to different criteria. So, in general, rational preference over states and acts won’t agree. Finally, we argue that based on direction-of-fit considerations, it’s preferences over the former that matter for normative epistemology, and that EpDT, properly spelt out, arrives at the correct verdicts in a range of putative problem cases. (shrink)

Standard accuracy-based approaches to imprecise credences have the consequence that it is rational to move between precise and imprecise credences arbitrarily, without gaining any new evidence. Building on the Educated Guessing Framework of Horowitz (2019), we develop an alternative accuracy-based approach to imprecise credences that does not have this shortcoming. We argue that it is always irrational to move from a precise state to an imprecise state arbitrarily, however it can be rational to move from an imprecise state to a (...) precise state arbitrarily. (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)

There is a well-known equivalence between avoiding accuracy dominance and having probabilistically coherent credences (see, e.g., de Finetti 1974, Joyce 2009, Predd et al. 2009, Pettigrew 2016). However, this equivalence has been established only when the set of propositions on which credence functions are defined is finite. In this paper, I establish connections between accuracy dominance and coherence when credence functions are defined on an infinite set of propositions. In particular, I establish the necessary results to extend the classic accuracy (...) argument for probabilism to certain classes of infinite sets of propositions including countably infinite partitions. (shrink)

Unspecific evidence calls for imprecise credence. My aim is to vindicate this thought. First, I will pin down what it is that makes one's imprecise credences more or less epistemically valuable. Then I will use this account of epistemic value to delineate a class of reasonable epistemic scoring rules for imprecise credences. Finally, I will show that if we plump for one of these scoring rules as our measure of epistemic value or utility, then a popular family of decision rules (...) recommends imprecise credences. In particular, a range of Hurwicz criteria, which generalise the Maximin decision rule, recommend imprecise credences. If correct, the moral is this: an agent who adopts precise credences, rather than imprecise ones, in the face of unspecific and incomplete evidence, goes wrong by gambling with the epistemic utility of her doxastic state in too risky a fashion. Precise credences represent an overly risky epistemic bet, according to the Hurwicz criteria. (shrink)

Some of the most interesting recent work in formal epistemology has focused on developing accuracy-based approaches to justifying Bayesian norms. These approaches are interesting not only because they offer new ways to justify these norms, but because they potentially offer a way to justify all of these norms by appeal to a single, attractive epistemic goal: having accurate beliefs. Recently, Easwaran & Fitelson (2012) have raised worries regarding whether such “all-accuracy” or “purely alethic” approaches can accommodate and justify evidential Bayesian (...) norms. In response, proponents of purely alethic approaches, such as Pettigrew (2013b) and Joyce (2016), have argued that scoring rule arguments provide us with compatible and purely alethic justifications for the traditional Bayesian norms, including evidential norms. In this paper I raise several challenges to this claim. First, I argue that many of the justifications these scoring rule arguments provide are not compatible. Second, I raise worries for the claim that these scoring rule arguments provide purely alethic justifications. Third, I turn to assess the more general question of whether purely alethic justifications for evidential norms are even possible, and argue that, without making some contentious assumptions, they are not. Fourth, I raise some further worries for the possibility of providing purely alethic justifications for content-sensitive evidential norms, like the Principal Principle. (shrink)

In a recent paper, Pettigrew (2021) reports a generalization of the celebrated accuracy-dominance theorem due to Predd et al. (2009). But Pettigrew’s proof is incorrect. I will explain the mistakes and provide a correct proof.

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.

Michael Rescorla (2020) has recently pointed out that the standard arguments for Bayesian Conditionalization assume that whenever you take yourself to learn something with certainty, it's 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 Briggs and Pettigrew's Accuracy Dominance argument to avoid the assumption that Rescorla has identified (Briggs & Pettigrew 2018). (shrink)

The short abstract: Epistemic utility theory + permissivism about attitudes to epistemic risk => permissivism about rational credences. The longer abstract: I argue that epistemic rationality is permissive. More specifically, I argue for two claims. First, a radical version of interpersonal permissivism about rational credence: for many bodies of evidence, there is a wide range of credal states for which there is some individual who might rationally adopt that state in response to that evidence. Second, a slightly less radical version (...) of intrapersonal permissivism about rational credence: for many bodies of evidence and for many individuals, there is a narrower but still wide range of credal states that the individual might rationally adopt in response to that evidence. My argument proceeds from two premises: (1) epistemic utility theory; and (2) permissivism about attitudes to epistemic risk. Epistemic utility theory says this: What it is epistemically rational for you to believe is what it would be rational for you to choose if you got to pick your beliefs and, when picking them, you cared only for their purely epistemic value. So, to say which credences it is epistemically rational for you to have, we must say how you should measure purely epistemic value, and which decision rule it is appropriate for you to use when you face the hypothetical choice between the possible credences you might adopt. Permissivism about attitudes to epistemic risk says that rationality permits many different attitudes to epistemic risk. These attitudes can show up in epistemic utility theory in two ways: in the way that you measure epistemic value; and in the decision rule that you use to pick your credences. I explore what happens if we encode our attitudes to epistemic risk in our epistemic decision rule. The result is the interpersonal and intrapersonal permissivism described above: different attitudes to epistemic risk lead to different choices of priors; given most bodies of evidence you might acquire, 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. The essay ends by considering a range of objections to the sort of permissivism for which I’ve argued. (shrink)

Hilary Greaves and David Wallace argue that conditionalization maximizes expected accuracy and so is a rational requirement, but their argument presupposes a particular picture of the bridge between rationality and accuracy: the Best-Plan-to-Follow picture. And theorists such as Miriam Schoenfield and Robert Steel argue that it's possible to motivate an alternative picture—the Best-Plan-to-Make picture—that does not vindicate conditionalization. I show that these theorists are mistaken: it turns out that, if an update procedure maximizes expected accuracy on the Best-Plan-to-Follow picture, it's (...) guaranteed to maximize expected accuracy on the Best-Plan-to-Make picture as well, in which case moving from the former to the latter can't help us avoid the conclusion that conditionalization is a rational requirement. If there's a problem with Greaves and Wallace’s argument, it must lie elsewhere. (shrink)

Considerations of accuracy – the epistemic good of having credences close to truth-values – have led to the justification of a host of epistemic norms. These arguments rely on specific ways of measuring accuracy. In particular, the accuracy measure should be strictly proper. However, the main argument for strict propriety supports only weak propriety. But strict propriety follows from weak propriety given strict truth directedness and additivity. So no further argument is necessary.

There is an ongoing debate about which rule we ought to use for scoring probability estimates. Much of this debate has been premised on scoring-rule monism, according to which there is exactly one best scoring rule. In previous work, I have argued against this position. The argument given there was based on purely a priori considerations, notably the intuition that scoring rules should be sensitive to truthlikeness relations if, and only if, such relations are present among whichever hypotheses are at (...) issue. The present paper offers a new, quasi-empirical argument against scoring-rule monism. This argument uses computational simulations to show that different scoring rules can have different economical consequences, depending on the context of use. (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)

Dutch book and accuracy arguments are used to justify certain rationality constraints on credence functions. Underlying these Dutch book and accuracy arguments are associated theorems, and I show that the interpretation of these theorems can vary along a range of dimensions. Given that the theorems can be interpreted in a variety of different ways, what is the status of the associated arguments? I consider three possibilities: we could aggregate the results of the differently interpreted theorems in some way, and motivate (...) rationality constraints based on this aggregation; we could be permissive, and accept the conclusions of the Dutch book and accuracy arguments under all interpretations of the associated theorems; or we could select one uniquely correct interpretation of the Dutch book or accuracy theorem, and use that to justify certain rationality constraints. I show that each possibility faces problems, and conclude that Dutch book and accuracy theorems cannot be used to justify any principle of rationality. (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)

Many have claimed that epistemic rationality sometimes requires us to have imprecise credal states (i.e. credal states representable only by sets of credence functions) rather than precise ones (i.e. credal states representable by single credence functions). Some writers have recently argued that this claim conflicts with accuracy-centered epistemology, i.e., the project of justifying epistemic norms by appealing solely to the overall accuracy of the doxastic states they recommend. But these arguments are far from decisive. In this essay, we prove some (...) new results, which show that there is little hope for reconciling the rationality of credal imprecision with accuracy-centered epistemology. (shrink)

How should we adjust our beliefs in light of the testimony of those who are in a better epistemic position than ourselves, such as experts and other epistemic superiors? In this paper, I develop and defend a deference model of epistemic authority. The paper attempts to resolve the debate between the preemption view and the total evidence view of epistemic authority by taking an accuracy-first approach to the issue of how we should respond to authoritative and expert testimony. I argue (...) that when we look at the debate through the lens of accuracy, it becomes clear that matters are more complicated than either the preemption view or the total evidence view are able to account for. Consequently, a deference model, outlined within a credence-based framework, does a better job of capturing the relevant phenomena, and explaining how we should update our beliefs in response to epistemically authoritative testimony. (shrink)

The epistemology of self-locating belief concerns itself with how rational agents ought to respond to certain kinds of indexical information. I argue that those who endorse the thesis of Time-Slice Rationality ought to endorse a particular view about the epistemology of self-locating belief, according to which ‘essentially indexical’ information is never evidentially relevant to non-indexical matters. I close by offering some independent motivations for endorsing Time-Slice Rationality in the context of the epistemology of self-locating belief.

Given the standard dominance conditions used in accuracy theories for outright belief, epistemologists must invoke epistemic conservatism if they are to avoid licensing belief in both a proposition and its negation. Florian Steinberger (2019) charges the committed accuracy monist — the theorist who thinks that the only epistemic value is accuracy — with being unable to motivate this conservatism. I show that the accuracy monist can avoid Steinberger’s charge by moving to a subtly different set of dominance conditions. Having done (...) so, they no longer need to invoke conservatism. I briefly explore some ramifications of this shift. (shrink)

to appear in Szabó Gendler, T. & J. Hawthorne (eds.) Oxford Studies in Epistemology volume 6 We often ask for the opinion of a group of individuals. How strongly does the scientific community believe that the rate at which sea levels are rising increased over the last 200 years? How likely does the UK Treasury think it is that there will be a recession if the country leaves the European Union? What are these group credences that such questions request? And (...) how do they relate to the individual credences assigned by the members of the particular group in question? According to the credal judgment aggregation principle, Linear Pooling, the credence function of a group should be a weighted average or linear pool of the credence functions of the individuals in the group. In this paper, I give an argument for Linear Pooling based on considerations of accuracy. And I respond to two standard objections to the aggregation principle. (shrink)

Conditionalization is one of the central norms of Bayesian epistemology. But there are a number of competing formulations, and a number of arguments that purport to establish it. In this paper, I explore which formulations of the norm are supported by which arguments. In their standard formulations, each of the arguments I consider here depends on the same assumption, which I call Deterministic Updating. I will investigate whether it is possible to amend these arguments so that they no longer depend (...) on it. As I show, whether this is possible depends on the formulation of the norm under consideration. (shrink)

Fitelson and McCarthy have proposed an accuracy measure for confidence orders which favors probability measures and Dempster-Shafer belief functions as accounts of degrees of belief and excludes ranking functions. Their accuracy measure only penalizes mistakes in confidence comparisons. We propose an alternative accuracy measure that also rewards correct confidence comparisons. Thus we conform to both of William James’ maxims: “Believe truth! Shun error!” We combine the two maxims, penalties and rewards, into one criterion that we call prioritized accuracy optimization. That (...) is, PAO punishes wrong comparisons and rewards right comparisons. And it requires to prioritize being right und avoiding to be wrong in a specific way. Thus PAO is both, a scoring rule and a decision rule. It turns out that precisely confidence orders representable by two-sided ranking functions satisfy PAO. The point is not to argue that PAO is the better accuracy goal. The point is only that ranking theory can also be supported by accuracy considerations. Thus, those considerations by themselves cannot decide about rational formats for degrees of belief, but are part and parcel of an overall normative assessment of those formats. (shrink)

Local proper scoring rules provide convenient tools for measuring subjective probabilities. Savage, 783–801, 1971) has shown that the only local proper scoring rule for more than two exclusive events is the logarithmic family. We generalize Savage by relaxing the properness and the domain, and provide simpler proof.

I propose a general alethic theory of epistemic risk according to which the riskiness of an agent’s credence function encodes her relative sensitivity to different types of graded error. After motivating and mathematically developing this approach, I show that the epistemic risk function is a scaled reflection of expected inaccuracy. This duality between risk and information enables us to explore the relationship between attitudes to epistemic risk, the choice of scoring rules in epistemic utility theory, and the selection of priors (...) in Bayesian epistemology more generally. (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)

The Lockean Thesis says that you must believe p iff you’re sufficiently confident of it. On some versions, the 'must' asserts a metaphysical connection; on others, it asserts a normative one. On some versions, 'sufficiently confident' refers to a fixed threshold of credence; on others, it varies with proposition and context. Claim: the Lockean Thesis follows from epistemic utility theory—the view that rational requirements are constrained by the norm to promote accuracy. Different versions of this theory generate different versions of (...) Lockeanism; moreover, a plausible version of epistemic utility theory meshes with natural language considerations, yielding a new Lockean picture that helps to model and explain the role of beliefs in inquiry and conversation. Your beliefs are your best guesses in response to the epistemic priorities of your context. Upshot: we have a new approach to the epistemology and semantics of belief. And it has teeth. It implies that the role of beliefs is fundamentally different than many have thought, and in fact supports a metaphysical reduction of belief to credence. (shrink)

Accuracy-based arguments for conditionalization and probabilism appear to have a significant advantage over their Dutch Book rivals. They rely only on the plausible epistemic norm that one should try to decrease the inaccuracy of one’s beliefs. Furthermore, conditionalization and probabilism apparently follow from a wide range of measures of inaccuracy. However, we argue that there is an under-appreciated diachronic constraint on measures of inaccuracy which limits the measures from which one can prove conditionalization, and none of the remaining measures allow (...) one to prove probabilism. That is, among the measures in the literature, there are some from which one can prove conditionalization, others from which one can prove probabilism, but none from which one can prove both. Hence at present, the accuracy-based approach cannot underwrite both conditionalization and probabilism. (shrink)

Recently several authors have argued that accuracy-first epistemology ends up licensing problematic epistemic bribes. They charge that it is better, given the accuracy-first approach, to deliberately form one false belief if this will lead to forming many other true beliefs. We argue that this is not a consequence of the accuracy-first view. If one forms one false belief and a number of other true beliefs, then one is committed to many other false propositions, e.g., the conjunction of that false belief (...) with any of the true beliefs. Once we properly account for all the falsehoods that are adopted by the person who takes the bribe, it turns out that the bribe does not increase accuracy. (shrink)

Shuford, Albert and Massengill proved, a half century ago, that the logarithmic scoring rule is the only proper measure of inaccuracy determined by a differentiable function of probability assigned the actual cell of a scored partition. In spite of this, the log rule has gained less traction in applied disciplines and among formal epistemologists that one might expect. In this paper we show that the differentiability criterion in the Shuford et. al. result is unnecessary and use the resulting simplified characterization (...) of the logarithmic rule to give novel arguments in favor of it. (shrink)

Two different programmes are in the business of explicating accuracy—the truthlikeness programme and the epistemic utility programme. Both assume that truth is the goal of inquiry, and that among inquiries that fall short of realizing the goal some get closer to it than others. Truthlikeness theorists have been searching for an account of the accuracy of propositions. Epistemic utility theorists have been searching for an account of the accuracy of credal states. Both assume we can make cognitive progress in an (...) inquiry even while falling short of the target. I show that the prospects for combining these two programmes are bleak. A core accuracy principle, proximity, that is universally embraced within the truthlikeness programme turns out to be incompatible with a central principle within the epistemic utility programme, namely propriety. 1Truthlikeness and Epistemic Utility 2Inquiries 3Accuracy for Propositions 4Proximity 5Accuracy for Credal States 6Propriety 7Proximity for Credal States 8Extensionality 9Admissible Weightings 10Propriety Violates Proximity 11Possible Responses 11.1Retreat to convexity 11.2Reject boundedness 11.3Reject additivity 12The Upshot. (shrink)

We often ask for the opinion of a group of individuals. How strongly does the scientific community believe that the rate at which sea levels are rising has increased over the last 200 years? How likely does the UK Treasury think it is that there will be a recession if the country leaves the European Union? What are these group credences that such questions request? And how do they relate to the individual credences assigned by the members of the particular (...) group in question? According to the credal judgement aggregation principle, linear pooling, the credence function of a group should be a weighted average or linear pool of the credence functions of the individuals in the group. In this chapter, I give an argument for linear pooling based on considerations of accuracy. And I respond to two standard objections to the aggregation principle. (shrink)

Accuracy‐first epistemology is an approach to formal epistemology which takes accuracy to be a measure of epistemic utility and attempts to vindicate norms of epistemic rationality by showing how conformity with them is beneficial. If accuracy‐first epistemology can actually vindicate any epistemic norms, it must adopt a plausible account of epistemic value. Any such account must avoid the epistemic version of Derek Parfit's “repugnant conclusion.” I argue that the only plausible way of doing so is to say that accurate credences (...) in certain propositions have no, or almost no, epistemic value. I prove that this is incompatible with standard accuracy‐first arguments for probabilism, and argue that there is no way for accuracy‐first epistemology to show that all credences of all agents should be coherent. (shrink)

Traditional definitions of lying require that a speaker believe that what she asserts is false. Sam Fox Krauss seeks to jettison the traditional belief requirement in favour of a necessary condition given in a credence-accuracy framework, on which the liar expects to impose the risk of increased inaccuracy on the hearer. He argues that this necessary condition importantly captures nearby cases as lies which the traditional view neglects. I argue, however, that Krauss's own account suffers from an identical drawback of (...) being unable to explain nearby cases; and even worse, that account fails to distinguish cases of telling lies from cases of telling the truth. (shrink)

One of the main goals of Bayesian epistemology is to justify the rational norms credence functions ought to obey. Accuracy arguments attempt to justify these norms from the assumption that the source of value for credences relevant to their epistemic status is their accuracy. This assumption and some standard decision-theoretic principles are used to argue for norms like Probabilism, the thesis that an agent’s credence function is rational only if it obeys the probability axioms. We introduce an example that shows (...) that the accuracy arguments for Probabilism given by Joyce and Pettigrew fail, and that Probabilism in fact turns out to be false given Pettigrew’s way of conceiving of the goal of having accurate credences. Finally, we use our discussion of Pettigrew’s framework to draw an important general lesson about normative theorizing that relies on the positing of ideal agents. (shrink)

This paper addresses a largely neglected question in ongoing debates over disagreement: what is the relation, if any, between disagreements involving credences and disagreements involving outright beliefs? The first part of the paper offers some desiderata for an adequate account of credal and full disagreement. The second part of the paper argues that both phenomena can be subsumed under a schematic definition which goes as follows: A and B disagree if and only if the accuracy conditions of A's doxastic attitude (...) are such that, if they were fulfilled, this would ipso facto make B's doxastic attitude inaccurate, or vice-versa. (shrink)

Consider Phoebe and Daphne. Phoebe has credences in 1 million propositions. Daphne, on the other hand, has credences in all of these propositions, but she's also got credences in 999 million other propositions. Phoebe's credences are all very accurate. Each of Daphne's credences, in contrast, are not very accurate at all; each is a little more accurate than it is inaccurate, but not by much. Whose doxastic state is better, Phoebe's or Daphne's? It is clear that this question is analogous (...) to a question that has exercised ethicists over the past thirty years. How do we weigh a population consisting of some number of exceptionally happy and satisfied individuals against another population consisting of a much greater number of people whose lives are only just worth living? This is the question that occasions population ethics. In this paper, I go in search of the correct population ethics for credal states. (shrink)

This article proposes a new interpretation of mutual information. We examine three extant interpretations of MI by reduction in doubt, by reduction in uncertainty, and by divergence. We argue that the first two are inconsistent with the epistemic value of information assumed in many applications of MI: the greater is the amount of information we acquire, the better is our epistemic position, other things being equal. The third interpretation is consistent with EVI, but it is faced with the problem of (...) measure sensitivity and fails to justify the use of MI in giving definitive answers to questions of information. We propose a fourth interpretation of MI by reduction in expected inaccuracy, where inaccuracy is measured by a strictly proper monotonic scoring rule. It is shown that the answers to questions of information given by MI are definitive whenever this interpretation is appropriate, and that it is appropriate in a wide range of applications with epistemic implications. _1_ Introduction _2_ Formal Analyses of the Three Interpretations _2.1_ Reduction in doubt _2.2_ Reduction in uncertainty _2.3_ Divergence _3_ Inconsistency with Epistemic Value of Information _4_ Problem of Measure Sensitivity _5_ Reduction in Expected Inaccuracy _6_ Resolution of the Problem of Measure Sensitivity _6.1_ Alternative measures of inaccuracy _6.2_ Resolution by strict propriety _6.3_ Range of applications _7_ Global Scoring Rules _8_ Conclusion. (shrink)

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

Epistemic utility theory (EUT) is generally coupled with \emph{veritism}. Veritism is the view that truth is the sole fundamental epistemic value. Veritism, when paired with EUT, entails a methodological commitment: Norms of epistemic rationality are justified only if they can be derived from considerations of accuracy alone. According to EUT, then, believing truly has epistemic value, while believing falsely has epistemic disvalue. This raises the question as to how the rational believer should balance the prospect of true belief against the (...) risk of error. A strong intuitive case can be made for a kind of epistemic \emph{conservatism}---that we should disvalue error more than we value true belief. I argue that none of the ways in which advocates of veritist EUT have sought to motivate conservatism can be squared with their methodological commitments. Short of any such justification, they must therefore either abandon their most central methodological principle or else adopt a permissive line with respect to epistemic risk. (shrink)

Pettigrew offers new axiomatic constraints on legitimate measures of inaccuracy. His axiom called ‘Decomposition’ stipulates that legitimate measures of inaccuracy evaluate a credence function in part based on its level of calibration at a world. I argue that if calibration is valuable, as Pettigrew claims, then this fact is an explanandum for accuracy-rst epistemologists, not an explanans, for three reasons. First, the intuitive case for the importance of calibration isn’t as strong as Pettigrew believes. Second, calibration is a perniciously global (...) property that both contravenes Pettigrew’s own views about the nature of credence functions themselves and undercuts the achievements and ambitions of accuracy-rst epistemology. Finally, Decomposition introduces a new kind of value compatible with but separate from accuracy-proper in violation of Pettigrew’s alethic monism. introduction. (shrink)

Permissivism about rationality is the view that there is sometimes more than one rational response to a given body of evidence. In this paper I discuss the relationship between permissivism, deference to rationality, and peer disagreement. I begin by arguing that—contrary to popular opinion—permissivism supports at least a moderate version of conciliationism. I then formulate a worry for permissivism. I show that, given a plausible principle of rational deference, permissive rationality seems to become unstable and to collapse into unique rationality. (...) I conclude with a formulation of a way out of this problem on behalf of the permissivist. (shrink)