It is widely believed that the so-called knowledge account of assertion best explains why sentences such as “It’s raining in Paris but I don’t believe it” and “It’s raining in Paris but I don’t know it” appear odd to us. I argue that the rival rational credibility account of assertion explains that fact just as well. I do so by providing a broadly Bayesian analysis of the said type of sentences which shows that such sentences cannot express rationally held beliefs. (...) As an interesting aside, it will be seen that these sentences also harbor a lesson for Bayesian epistemology itself. (shrink)

This book explores a question central to philosophy--namely, what does it take for a belief to be justified or rational? According to a widespread view, whether one has justification for believing a proposition is determined by how probable that proposition is, given one's evidence. In this book this view is rejected and replaced with another: in order for one to have justification for believing a proposition, one's evidence must normically support it--roughly, one's evidence must make the falsity of that proposition (...) abnormal in the sense of calling for special, independent explanation. This conception of justification bears upon a range of topics in epistemology and beyond. Ultimately, this way of looking at justification guides us to a new, unfamiliar picture of how we should respond to our evidence and manage our own fallibility. This picture is developed here. (shrink)

Doxastic TheoriesThe application of formal tools to questions related to epistemology is of course not at all new. However, there has been a surge of interest in the field now known as “formal epistemology” over the past decade, with two annual conference series and an annual summer school at Carnegie Mellon University, in addition to many one-off events devoted to the field. A glance at the programs of these series illustrates the wide-ranging set of topics that have been grouped under (...) this name, ranging from rational choice theory and the foundations of statistics, to logics of knowledge and formal measures of coherence, with much more besides.In this paper I will ignore most of these topics, and just trace some parts of the history of two ideas about belief whose current interaction may lead to future progress. One idea is the idea of belief, disbelief, and suspension of judgment as a meaningful tripartite dis .. (shrink)

This essay develops a joint theory of rational (all-or-nothing) belief and degrees of belief. The theory is based on three assumptions: the logical closure of rational belief; the axioms of probability for rational degrees of belief; and the so-called Lockean thesis, in which the concepts of rational belief and rational degree of belief figure simultaneously. In spite of what is commonly believed, this essay will show that this combination of principles is satisfiable (and indeed nontrivially so) and that the principles (...) are jointly satisfied if and only if rational belief is equivalent to the assignment of a stably high rational degree of belief. Although the logical closure of belief and the Lockean thesis are attractive postulates in themselves, initially this may seem like a formal “curiosity”; however, as will be argued in the rest of the essay, a very reasonable theory of rational belief can be built around these principles that is not ad hoc and that has various philosophical features that are plausible independently. In particular, this essay shows that the theory allows for a solution to the Lottery Paradox, and it has nice applications to formal epistemology. The price that is to be paid for this theory is a strong dependency of belief on the context, where a context involves both the agent's degree of belief function and the partitioning or individuation of the underlying possibilities. But as this essay argues, that price seems to be affordable. (shrink)

semantic minimalism and moderte contextualism.

As the ongoing literature on the paradoxes of the Lottery and the Preface reminds us, the nature of the relation between probability and rational acceptability remains far from settled. This article provides a novel perspective on the matter by exploiting a recently noted structural parallel with the problem of judgment aggregation. After offering a number of general desiderata on the relation between finite probability models and sets of accepted sentences in a Boolean sentential language, it is noted that a number (...) of these constraints will be satisfied if and only if acceptable sentences are true under all valuations in a distinguished non-empty set W. Drawing inspiration from distance-based aggregation procedures, various scoring rule based membership conditions for W are discussed and a possible point of contact with ranking theory is considered. The paper closes with various suggestions for further research. (shrink)

Epistemologists have proposed various norms of assertion to explain when a speaker is in an epistemic position to assert a proposition. In this article I propose a distinct necessary condition on assertibility: that a speaker should assert only what she sensitively believes, where a subject's belief is sensitive just in case the subject would not hold it if it were false. I argue that the Sensitivity Rule underwrites simple explanations for three key features of assertibility that pose explanatory challenges to (...) other prominent proposals: the fact that assertibility is open under known entailment, the general impropriety of assertions that a lottery ticket has lost made purely on the basis of the speaker's knowledge of the odds, and the fact that assertibility varies widely with features of the conversational context. I close by considering three distinct roles the Sensitivity Rule might play in the overall theory of assertibility. (shrink)

The thesis that high probability suffices for rational belief, while initially plausible, is known to face the Lottery Paradox. The present paper proposes an amended version of that thesis which escapes the Lottery Paradox. The amendment is argued to be plausible on independent grounds.

There are currently two robust traditions in philosophy dealing with doxastic attitudes: the tradition that is concerned primarily with all-or-nothing belief, and the tradition that is concerned primarily with degree of belief or credence. This paper concerns the relationship between belief and credence for a rational agent, and is directed at those who may have hoped that the notion of belief can either be reduced to credence or eliminated altogether when characterizing the norms governing ideally rational agents. It presents a (...) puzzle which lends support to two theses. First, that there is no formal reduction of a rational agent’s beliefs to her credences, because belief and credence are each responsive to different features of a body of evidence. Second, that if our traditional understanding of our practices of holding each other responsible is correct, then belief has a distinctive role to play, even for ideally rational agents, that cannot be played by credence. The question of which avenues remain for the credence-only theorist is considered. (shrink)

Say that two goals are normatively coincident just in case one cannot aim for one goal without automatically aiming for the other. While knowledge and justification are distinct epistemic goals, with distinct achievement conditions, this paper begins from the suggestion that they are nevertheless normatively coincident—aiming for knowledge and aiming for justification are one and the same activity. A number of surprising consequences follow from this—both specific consequences about how we can ascribe knowledge and justification in lottery cases and more (...) general consequences about the nature of justification and the relationship between justification and evidential probability. Many of these consequences turn out to be at variance with conventional, prevailing views. (shrink)

Decision-making typically requires judgments about causal relations: we need to know the causal effects of our actions and the causal relevance of various environmental factors. We investigate how several individuals' causal judgments can be aggregated into collective causal judgments. First, we consider the aggregation of causal judgments via the aggregation of probabilistic judgments, and identify the limitations of this approach. We then explore the possibility of aggregating causal judgments independently of probabilistic ones. Formally, we introduce the problem of causal-network aggregation. (...) Finally, we revisit the aggregation of probabilistic judgments when this is constrained by prior aggregation of qualitative causal judgments. (shrink)

Epistemology is the study of knowledge and justified belief. Belief is thus central to epistemology. It comes in a qualitative form, as when Sophia believes that Vienna is the capital of Austria, and a quantitative form, as when Sophia's degree of belief that Vienna is the capital of Austria is at least twice her degree of belief that tomorrow it will be sunny in Vienna. Formal epistemology, as opposed to mainstream epistemology (Hendricks 2006), is epistemology done in a formal way, (...) that is, by employing tools from logic and mathematics. The goal of this entry is to give the reader an overview of the formal tools available to epistemologists for the representation of belief. A particular focus will be the relation between formal representations of qualitative belief and formal representations of quantitative degrees of belief. (shrink)

I propose a relevance-based independence axiom on how to aggregate individual yes/no judgments on given propositions into collective judgments: the collective judgment on a proposition depends only on people’s judgments on propositions which are relevant to that proposition. This axiom contrasts with the classical independence axiom: the collective judgment on a proposition depends only on people’s judgments on the same proposition. I generalize the premise-based rule and the sequential-priority rule to an arbitrary priority order of the propositions, instead of a (...) dichotomous premise/conclusion order resp. a linear priority order. I prove four impossibility theorems on relevance-based aggregation. One theorem simultaneously generalizes Arrow’s Theorem (in its general and indifference-free versions) and the well-known Arrow-like theorem in judgment aggregation. (shrink)

According to so-called epistemic theories of conditionals, the assertability/acceptability/acceptance of a conditional requires the existence of an epistemically significant relation between the conditional’s antecedent and its consequent. This paper points to some linguistic data that our current best theories of the foregoing type appear unable to explain. Further, it presents a new theory of the same type that does not have that shortcoming. The theory is then defended against some seemingly obvious objections.

This essay discusses the difficulty to reconcile two paradigms about beliefs: the binary or categorical paradigm of yes/no beliefs and the probabilistic paradigm of degrees of belief. The possibility for someone to hold both types of belief simultaneously is challenged by the lottery paradox, and more recently by a general impossibility theorem by Dietrich and List (2018, 2021). The nature, relevance, and implications of the tension are explained and assessed.

Much of the literature on the relationship between belief and credence has focused on the reduction question: that is, whether either belief or credence reduces to the other. This debate, while important, only scratches the surface of the belief-credence connection. Even on the anti-reductive dualist view, belief and credence could still be very tightly connected. Here, I explore questions about the belief-credence connection that go beyond reduction. This paper is dedicated to what I call the independence question: just how independent (...) are belief and credence? I look at this question from two angles: a descriptive one (as a psychological matter, how much can belief and credence come apart?) and a normative one (for a rational person, how closely connected are belief and credence?) Ultimately, I suggest that the two attitudes are more independent than one might think. (shrink)

We call attention to certain cases of epistemic akrasia, arguing that they support belief-credence dualism. Belief-credence dualism is the view that belief and credence are irreducible, equally fundamental attitudes. Consider the case of an agent who believes p, has low credence in p, and thus believes that they shouldn’t believe p. We argue that dualists, as opposed to belief-firsters (who say credence reduces to belief) and credence-firsters (who say belief reduces to credence) can best explain features of akratic cases, including (...) the observation that akratic beliefs seem to be held despite possessing a defeater for those beliefs, and that, in akratic cases, one can simultaneously believe and have low confidence in the very same proposition. (shrink)

This guide accompanies the following article(s): Jackson, E., Philosophy Compass 15/6 (2020) pp. 1-13 10.1111/phc3.12668.x.

According to the Rational Threshold View, a rational agent believes p if and only if her credence in p is equal to or greater than a certain threshold. One of the most serious challenges for this view is the problem of statistical evidence: statistical evidence is often not sufficient to make an outright belief rational, no matter how probable the target proposition is given such evidence. This indicates that rational belief is not as sensitive to statistical evidence as rational credence. (...) The aim of this paper is twofold. First, we argue that, in addition to playing a decisive role in rationalizing outright belief, non-statistical evidence also plays a preponderant role in rationalizing credence. More precisely, when both types of evidence are present in a context, non-statistical evidence should receive a heavier weight than statistical evidence in determining rational credence. Second, based on this result, we argue that a modified version of the Rational Threshold View can avoid the problem of statistical evidence. We conclude by suggesting a possible explanation of the varying sensitivity to different types of evidence for belief and credence based on the respective aims of these attitudes. (shrink)

Sometimes epistemologists theorize about belief, a tripartite attitude on which one can believe, withhold belief, or disbelieve a proposition. In other cases, epistemologists theorize about credence, a fine-grained attitude that represents one’s subjective probability or confidence level toward a proposition. How do these two attitudes relate to each other? This article explores the relationship between belief and credence in two categories: descriptive and normative. It then explains the broader significance of the belief-credence connection and concludes with general lessons from the (...) debate thus far. (shrink)

This paper explains and defends a belief-first view of the relationship between belief and credence. On this view, credences are a species of beliefs, and the degree of credence is determined by the content of what is believed. We begin by developing what we take to be the most plausible belief-first view. Then, we offer several arguments for it. Finally, we show how it can resist objections that have been raised to belief-first views. We conclude that the belief-first view is (...) more plausible than many have previously supposed. (shrink)

This paper elaborates a new solution to the lottery paradox, according to which the paradox arises only when we lump together two distinct states of being confident that p under one general label of ‘belief that p’. The two-state conjecture is defended on the basis of some recent work on gradable adjectives. The conjecture is supported by independent considerations from the impossibility of constructing the lottery paradox both for risk-tolerating states such as being afraid, hoping or hypothesizing, and for risk-averse, (...) certainty-like states. The new proposal is compared to views within the increasingly popular debate opposing dualists to reductionists with respect to the relation between belief and degrees of belief. (shrink)

Belief is a familiar attitude: taking something to be the case or regarding it as true. But we are more confident in some of our beliefs than in others. For this reason, many epistemologists appeal to a second attitude, called credence, similar to a degree of confidence. This raises the question: how do belief and credence relate to each other? On a belief-first view, beliefs are more fundamental and credences are a species of beliefs, e.g. beliefs about probabilities. On a (...) credence-first view, credences are more fundamental and beliefs are a species of credence, e.g. credence above some threshold. In this thesis, I develop and defend a third view that I call belief-credence dualism. On this view, belief and credence are independent, equally fundamental attitudes, and neither reduces to the other. I begin by motivating the project: why should we care about the relationship between belief and credence? I argue it has broad implications for many debates in epistemology and beyond. Then, I defend dualism, arguing that it can explain features of our mental lives that a credence-first view and a belief-first view cannot. I also argue that dualism has attractive, interesting implications when applied to the pragmatic encroachment debate. Finally, I explore implications of dualism, both for the nature of evidence and how faith might go beyond the evidence but nonetheless be epistemically rational. I conclude that the human mind is, in some ways, complex, but we should be happy with this conclusion also long as each mental state we posit has a clear role to play. (shrink)

The lottery paradox involves a set of judgments that are individually easy, when we think intuitively, but ultimately hard to reconcile with each other, when we think reflectively. Empirical work on the natural representation of probability shows that a range of interestingly different intuitive and reflective processes are deployed when we think about possible outcomes in different contexts. Understanding the shifts in our natural ways of thinking can reduce the sense that the lottery paradox reveals something problematic about our concept (...) of knowledge. However, examining these shifts also raises interesting questions about how we ought to be thinking about possible outcomes in the first place. (shrink)

Agents are often assumed to have degrees of belief (“credences”) and also binary beliefs (“beliefs simpliciter”). How are these related to each other? A much-discussed answer asserts that it is rational to believe a proposition if and only if one has a high enough degree of belief in it. But this answer runs into the “lottery paradox”: the set of believed propositions may violate the key rationality conditions of consistency and deductive closure. In earlier work, we showed that this problem (...) generalizes: there exists no local function from degrees of belief to binary beliefs that satisfies some minimal conditions of rationality and non-triviality. “Locality” means that the binary belief in each proposition depends only on the degree of belief in that proposition, not on the degrees of belief in others. One might think that the impossibility can be avoided by dropping the assumption that binary beliefs are a function of degrees of belief. We prove that, even if we drop the “functionality” restriction, there still exists no local relation between degrees of belief and binary beliefs that satisfies some minimal conditions. Thus functionality is not the source of the impossibility; its source is the condition of locality. If there is any non-trivial relation between degrees of belief and binary beliefs at all, it must be a “holistic” one. We explore several concrete forms this “holistic” relation could take. (shrink)

Belief-credence dualism is the view that we have both beliefs and credences and neither attitude is reducible to the other. Pragmatic encroachment is the view that practical stakes can affect the epistemic rationality of states like knowledge or justified belief. In this paper, I argue that dualism offers a unique explanation of pragmatic encroachment cases. First, I explain pragmatic encroachment and what motivates it. Then, I explain dualism and outline a particular argument for dualism. Finally, I show how dualism can (...) explain the intuitions that underlie pragmatic encroachment. My basic proposal is that in high-stakes cases, it is not that one cannot rationally believe that p; instead, one ought not to rely on one's belief that p. One should rather rely on one's credence in p. I conclude that we need not commit ourselves to pragmatic encroachment in order to explain the intuitiveness of the cases that motivate it. (shrink)

The article proceeds upon the assumption that the beliefs and degrees of belief of rational agents satisfy a number of constraints, including: consistency and deductive closure for belief sets, conformity to the axioms of probability for degrees of belief, and the Lockean Thesis concerning the relationship between belief and degree of belief. Assuming that the beliefs and degrees of belief of both individuals and collectives satisfy the preceding three constraints, I discuss what further constraints may be imposed on the aggregation (...) of beliefs and degrees of belief. Some possibility and impossibility results are presented. The possibility results suggest that the three proposed rationality constraints are compatible with reasonable aggregation procedures for belief and degree of belief. (shrink)

According to the Lockean thesis, a proposition is believed just in case it is highly probable. While this thesis enjoys strong intuitive support, it is known to conflict with seemingly plausible logical constraints on our beliefs. One way out of this conflict is to make probability 1 a requirement for belief, but most have rejected this option for entailing what they see as an untenable skepticism. Recently, two new solutions to the conflict have been proposed that are alleged to be (...) non-skeptical. We compare these proposals with each other and with the Lockean thesis, in particular with regard to the question of how much we gain by adopting any one of them instead of the probability 1 requirement, that is, of how likely it is that one believes more than the things one is fully certain of. (shrink)

In this paper, I argue that the relationship between belief and credence is a central question in epistemology. This is because the belief-credence relationship has significant implications for a number of current epistemological issues. I focus on five controversies: permissivism, disagreement, pragmatic encroachment, doxastic voluntarism, and the relationship between doxastic attitudes and prudential rationality. I argue that each debate is constrained in particular ways, depending on whether the relevant attitude is belief or credence. This means that epistemologists should pay attention (...) to whether they are framing questions in terms of belief or in terms of credence and the success or failure of a reductionist project in the belief-credence realm has significant implications for epistemology generally. (shrink)

What is the relationship between degrees of belief and binary beliefs? Can the latter be expressed as a function of the former—a so-called “belief-binarization rule”—without running into difficulties such as the lottery paradox? We show that this problem can be usefully analyzed from the perspective of judgment-aggregation theory. Although some formal similarities between belief binarization and judgment aggregation have been noted before, the connection between the two problems has not yet been studied in full generality. In this paper, we seek (...) to fill this gap. The paper is organized around a baseline impossibility theorem, which we use to map out the space of possible solutions to the belief-binarization problem. Our theorem shows that, except in limiting cases, there exists no belief-binarization rule satisfying four initially plausible desiderata. Surprisingly, this result is a direct corollary of the judgment-aggregation variant of Arrow’s classic impossibility theorem in social choice theory. (shrink)

Many epistemologists have responded to the lottery paradox by proposing formal rules according to which high probability defeasibly warrants acceptance. Douven and Williamson present an ingenious argument purporting to show that such rules invariably trivialise, in that they reduce to the claim that a probability of 1 warrants acceptance. Douven and Williamson’s argument does, however, rest upon significant assumptions – amongst them a relatively strong structural assumption to the effect that the underlying probability space is both finite and uniform. In (...) this paper, I will show that something very like Douven and Williamson’s argument can in fact survive with much weaker structural assumptions – and, in particular, can apply to infinite probability spaces. (shrink)

According to a captivating picture, epistemic justification is essentially a matter of epistemic or evidential likelihood. While certain problems for this view are well known, it is motivated by a very natural thought—if justification can fall short of epistemic certainty, then what else could it possibly be? In this paper I shall develop an alternative way of thinking about epistemic justification. On this conception, the difference between justification and likelihood turns out to be akin to the more widely recognised difference (...) between ceteris paribus laws and brute statistical generalisations. I go on to discuss, in light of this suggestion, issues such as classical and lottery-driven scepticism as well as the lottery and preface paradoxes. (shrink)

There is consensus among computer scientists, logicians, and philosophers that good reasoning with qualitative beliefs must have the structural property of cumulative transitivity or, for short, cut. This consensus is typically explicitly argued for partially on the basis of practical and mathematical considerations. But the consensus is also implicit in the approach philosophers take to almost every puzzle about reasoning that involves multiple steps: philosophers typically assume that if each step in reasoning is acceptable considered on its own, the whole (...) chain of reasoning must also acceptable. In this paper I focus on whether there are good philosophical reasons for thinking that the consensus that good reasoning must satisfy cut is true. My central claim is that we should not accept the consensus—good reasoning might not satisfy cut. In particular, I consider four arguments for the consensus and explain why they are unpersuasive. (§2-5). I then show that the issue of whether good reasoning is cut turns on a substantive yet until now unnoticed question in epistemology (§6). (shrink)

Theories of epistemic justification are commonly assessed by exploring their predictions about particular hypothetical cases – predictions as to whether justification is present or absent in this or that case. With a few exceptions, it is much less common for theories of epistemic justification to be assessed by exploring their predictions about logical principles. The exceptions are a handful of ‘closure’ principles, which have received a lot of attention, and which certain theories of justification are well known to invalidate. But (...) these closure principles are only a small sample of the logical principles that we might consider. In this paper, I will outline four further logical principles that plausibly hold for justification and two which plausibly do not. While my primary aim is just to put these principles forward, I will use them to evaluate some different approaches to justification and (tentatively) conclude that a ‘normic’ theory of justification best captures its logic. (shrink)

The following thesis discusses a range of central aspects in Timothy Williamson’s so-called «knowledge-first» epistemology. In particular, it adresses whether this kind of epistemological framework is apt to answer the challenges of scepticism.

Forty years ago, Bayesian philosophers were just catching a new wave of technical innovation, ushering in an era of scoring rules, imprecise credences, and infinitesimal probabilities. Meanwhile, down the hall, Gettier’s 1963 paper [28] was shaping a literature with little obvious interest in the formal programs of Reichenbach, Hempel, and Carnap, or their successors like Jeffrey, Levi, Skyrms, van Fraassen, and Lewis. And how Bayesians might accommodate the discourses of full belief and knowledge was but a glimmer in the eye (...) of Isaac Levi. Forty years later, scoring rules, imprecise credences, and infinitesimal probabilities are all the rage. And the formal and “informal” traditions are increasingly coming together as Bayesian arguments spill over into debates about the foundations of empirical knowledge, skepticism, and more. Relatedly, Bayesian interest in full belief and knowledge has never been greater. Much more besides has happened in the last forty years of Bayesian philosophy, .. (shrink)

List and Pettit have stated an impossibility theorem about the aggregation of individual opinion states. Building on recent work on the lottery paradox, this paper offers a variation on that result. The present result places different constraints on the voting agenda and the domain of profiles, but it covers a larger class of voting rules, which need not satisfy the proposition-wise independence of votes.

The volume analyses and develops David Makinson’s efforts to make classical logic useful outside its most obvious application areas. The book contains chapters that analyse, appraise, or reshape Makinson’s work and chapters that develop themes emerging from his contributions. These are grouped into major areas to which Makinsons has made highly influential contributions and the volume in its entirety is divided into four sections, each devoted to a particular area of logic: belief change, uncertain reasoning, normative systems and the resources (...) of classical logic. Among the contributions included in the volume, one chapter focuses on the “inferential preferential method”, i.e. the combined use of classical logic and mechanisms of preference and choice and provides examples from Makinson’s work in non-monotonic and defeasible reasoning and belief revision. One chapter offers a short autobiography by Makinson which details his discovery of modern logic, his travels across continents and reveals his intellectual encounters and inspirations. The chapter also contains an unusually explicit statement on his views on the role of logic in philosophy. (shrink)

Fitch’s paradox shows, from fairly innocent-looking assumptions, that if there are any unknown truths, then there are unknowable truths. This is generally thought to deliver a blow to antirealist positions that imply that all truths are knowable. The present paper argues that a probabilistic version of antirealism escapes Fitch’s result while still offering all that antirealists should care for.

Many philosophers have argued that "degree of belief" or "credence" is a more fundamental state grounding belief. Many other philosophers have been skeptical about the notion of "degree of belief", and take belief to be the only meaningful notion in the vicinity. This paper shows that one can take belief to be fundamental, and ground a notion of "degree of belief" in the patterns of belief, assuming that an agent has a collection of beliefs that isn't dominated by some other (...) collection in terms of the overall balance of truth and falsity that it could contain. (shrink)

The Lottery Paradox is generally thought to point at a conflict between two intuitive principles, to wit, that high probability is sufficient for rational acceptability, and that rational acceptability is closed under logical derivability. Gilbert Harman has offered a solution to the Lottery Paradox that allows one to stick to both of these principles. The solution requires the principle that acceptance licenses conditionalization. The present study shows that adopting this principle alongside the principle that high probability is sufficient for rational (...) acceptability gives rise to another paradox. (shrink)

Bradley has argued that a truth-conditional semantics for conditionals is incompatible with an allegedly very weak and intuitively compelling constraint on the interpretation of conditionals. I argue that the example Bradley offers to motivate this constraint can be explained along pragmatic lines that are compatible with the correctness of at least one popular truth-conditional semantics for conditionals.

The lottery paradox shows that the following three individually highly plausible theses are jointly incompatible: highly probable propositions are justifiably believable, justified believability is closed under conjunction introduction, known contradictions are not justifiably believable. This paper argues that a satisfactory solution to the lottery paradox must reject as versions of the paradox can be generated without appeal to either or and proposes a new solution to the paradox in terms of a novel account of justified believability.

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)

– 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)

External world skeptics are typically opposed to admitting as evidence anything that goes beyond the purely phenomenal, and equally typically, they disown the use of rules of inference that might enable one to move from premises about the phenomenal alone to a conclusion about the external world. This seems to bar any a posteriori resolution of the skepticism debate. This paper argues that the situation is not quite so hopeless, and that an a posteriori resolution of the debate becomes possible (...) once it is recognized that the skeptic holds overly defensive and ill-motivated positions vis-à-vis both evidence and inference, and that more reasonable ones are available. In stating these more reasonable positions, as well as in showing how they make possible an a posteriori resolution of the skepticism debate, the paper draws on the machinery of Bayesian epistemology. (shrink)

How does rationality bind the agnostic, that is, the one who suspends judgment about whether a given proposition is true? In this paper I explore two alternative ways of establishing what the rational requirements of agnosticism are: the Lockean–Bayesian framework and the doxastic logic framework. Each of these proposals faces strong objections. Fortunately, however, there is a rich kernel of requirements of agnosticism that are vindicated by both of them. One can then endorse the requirements that belong to that kernel (...) without thereby committing oneself to the problematic implications that stem from either of the aforementioned proposals. (shrink)