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)

It is natural to regard understanding as having a rational dimension, in the sense that understanding seems to require having justification for holding certain beliefs about the world. Some philosophers however argue that justification is not required to gain understanding of phenomena. In the present paper, my intention is to provide a critical examination of the arguments that have been offered against the view that understanding requires justification in order to show that, contrary to what they purport to establish, justification (...) remains a plausible requirement on understanding. (shrink)

In legal proceedings, a fact-finder needs to decide whether a defendant is guilty or not based on probabilistic evidence. We defend the thesis that the defendant should be found guilty just in case it is rational for the fact-finder to believe that the defendant is guilty. We draw on Leitgeb’s stability theory for an appropriate notion of rational belief and show how our thesis solves the problem of statistical evidence. Finally, we defend our account of legal proof against challenges from (...) Staffel and compare it to a recent competitor put forth by Moss. (shrink)

Philosophy and Phenomenological Research, Volume 104, Issue 1, Page 19-49, January 2022.

I will present a novel account of justification in terms of knowledge on which one is justified in believing p just in case one could know that p. My main aim is to unravel some of the formal properties that justification has in virtue of its connection to knowledge. Assuming that safety is at least a necessary condition for knowledge, I show that justification doesn’t iterate trivially; isn’t a luminous condition; is closed under a certain kind of multi-premise closure principle, (...) but; surprisingly one can nevertheless believe with justification a set of claims that’s jointly inconsistent. This last feature allows for a rather satisfying solution to the preface paradox. Finally, I contrast my account with other knowledge-first accounts of justification. (shrink)

This paper defends the view, put roughly, that to think that p is to guess that p is the answer to the question at hand, and that to think that p rationally is for one’s guess to that question to be in a certain sense non-arbitrary. Some theses that will be argued for along the way include: that thinking is question-sensitive and, correspondingly, that ‘thinks’ is context-sensitive; that it can be rational to think that p while having arbitrarily low credence (...) that p; that, nonetheless, rational thinking is closed under entailment; that thinking does not supervene on credence; and that in many cases what one thinks on certain matters is, in a very literal sense, a choice. Finally, since there are strong reasons to believe that thinking just is believing, there are strong reasons to think that all this goes for belief as well. (shrink)

The terms “model” and “model-building” have been used to characterize the field of formal philosophy, to evaluate philosophy’s and philosophical logic’s progress and to define philosophical logic itself. A model is an idealization, in the sense of being a deliberate simplification of something relatively complex in which several important aspects are left aside, but also in the sense of being a view too perfect or excellent, not found in reality, of this thing. Paraconsistent logic is a branch of philosophical logic. (...) It is however not clear how paraconsistent logic can be seen as model-building. What exactly is modeled? In this paper I adopt the perspective of looking at a particular instance of paraconsistent logic—paranormal modal logic—which might be seen as a model of a specific kind of agent: inductive agents. After ntroducing what I call the highlevel and low-level models of inductive agents, I analyze the extent to which the above-mentioned idealizing features of model-building appear in paranormal modal logic and how they affect its philosophical significance. (shrink)

Is self-knowledge a requirement of rationality, like consistency, or means-ends coherence? Many claim so, citing the evident impropriety of asserting, and the alleged irrationality of believing, Moore-paradoxical propositions of the form < p, but I don't believe that p>. If there were nothing irrational about failing to know one's own beliefs, they claim, then there would be nothing irrational about Moore-paradoxical assertions or beliefs. This article considers a few ways the data surrounding Moore's paradox might be marshaled to support rational (...) requirements to know one's beliefs, and finds that none succeed. (shrink)

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)

Denying the conclusion of a valid argument is not generally permissible if one suspends on one premise of the argument and believes the other premise. This can happen when one’s only critique of an argument is to undermine one premise. There is incoherence there. Here I examine how this is relevant to the debate on evolutionary debunking of our moral knowledge. I argue that one significant line of response to the debunker is unsuccessful: merely undermining the debunker’s empirical claim. It (...) is not rational to respond this way and believe one has moral knowledge. First I present evidence that prominent critics of the debunking argument merely undermine the debunker’s empirical claim. Then I argue for two premises: merely undermining a premise can only justify a middling amount of doubt towards the premise and we should have no more doubt about the conclusion of a valid argument than we do about the premises. Implications of the argument are explored. (shrink)

In mathematics, any form of probabilistic proof obtained through the application of a probabilistic method is not considered as a legitimate way of gaining mathematical knowledge. In a series of papers, Don Fallis has defended the thesis that there are no epistemic reasons justifying mathematicians’ rejection of probabilistic proofs. This paper identifies such an epistemic reason. More specifically, it is argued here that if one adopts a conception of mathematical knowledge in which an epistemic subject can know a mathematical proposition (...) based solely on a probabilistic proof, one is then forced to admit that such an epistemic subject can know several lottery propositions based solely on probabilistic evidence. Insofar as knowledge of lottery propositions on the basis of probabilistic evidence alone is denied by the vast majority of epistemologists, it is concluded that this constitutes an epistemic reason for rejecting probabilistic proofs as a means of acquiring mathematical knowledge. (shrink)

Some theories of rational belief assume that beliefs should be closed under conjunction. I motivate the rejection of the conjunction closure, and point out that the consequences of this rejection are not as severe as it is usually thought. An often raised objection is that without the conjunction closure people are unable to reason. I outline an approach in which we can – in usual cases – reason using conjunctions without accepting the closure in its whole generality. This solution is (...) based on the notion of confidence levels, which can be defined using probabilities. Moreover, on this approach, reasoning has a scalable computational complexity adaptable to cognitive abilities of both rationally bounded and perfectly rational agents. I perform a simulation to assess its error rate, and compare it to reasoning with conjunction closure. (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)

We propose a new account of indicative conditionals, giving acceptability and logical closure conditions for them. We start from Adams’ Thesis: the claim that the acceptability of a simple indicative equals the corresponding conditional probability. The Thesis is widely endorsed, but arguably false and refuted by empirical research. To fix it, we submit, we need a relevance constraint: we accept a simple conditional 'If φ, then ψ' to the extent that (i) the conditional probability p(ψ|φ) is high, provided that (ii) (...) φ is relevant for ψ. How (i) should work is well-understood. It is (ii) that holds the key to improve our understanding of conditionals. Our account has (i) a probabilistic component, using Popper functions; (ii) a relevance component, given via an algebraic structure of topics or subject matters. We present a probabilistic logic for simple indicatives, and argue that its (in)validities are both theoretically desirable and in line with empirical results on how people reason with conditionals. (shrink)

Statistical evidence—say, that 95% of your co-workers badmouth each other—can never render resenting your colleague appropriate, in the way that other evidence (say, the testimony of a reliable friend) can. The problem of statistical resentment is to explain why. We put the problem of statistical resentment in several wider contexts: The context of the problem of statistical evidence in legal theory; the epistemological context—with problems like the lottery paradox for knowledge, epistemic impurism and doxastic wrongdoing; and the context of a (...) wider set of examples of responses and attitudes that seem not to be appropriately groundable in statistical evidence. Regrettably, we do not come up with a fully general, fully adequate, fully unified account of all the phenomena discussed. But we give reasons to believe that no such account is forthcoming, and we sketch a somewhat messier account that may be the best that can be had here. (shrink)

Formal models of appearance and reality have proved fruitful for investigating structural properties of perceptual knowledge. This paper applies the same approach to epistemic justification. Our central goal is to give a simple account of The Preface, in which justified belief fails to agglomerate. Following recent work by a number of authors, we understand knowledge in terms of normality. An agent knows p iff p is true throughout all relevant normal worlds. To model The Preface, we appeal to the normality (...) of error. Sometimes, it is more normal for reality and appearance to diverge than to match. We show that this simple idea has dramatic consequences for the theory of knowledge and justification. Among other things, we argue that a proper treatment of The Preface requires a departure from the internalist idea that epistemic justification supervenes on the appearances and the widespread idea that one knows most when free from error. (shrink)

I argue that we should solve the Lottery Paradox by denying that rational belief is closed under classical logic. To reach this conclusion, I build on my previous result that (a slight variant of) McGee’s election scenario is a lottery scenario (see Lissia 2019). Indeed, this result implies that the sensible ways to deal with McGee’s scenario are the same as the sensible ways to deal with the lottery scenario: we should either reject the Lockean Thesis or Belief Closure. After (...) recalling my argument to this conclusion, I demonstrate that a McGee-like example (which is just, in fact, Carroll’s barbershop paradox) can be provided in which the Lockean Thesis plays no role: this proves that denying Belief Closure is the right way to deal with both McGee’s scenario and the Lottery Paradox. A straightforward consequence of my approach is that Carroll’s puzzle is solved, too. (shrink)

Instability occurs when the very fact of choosing one particular possible option rather than another affects the expected values of those possible options. In decision theory: An act is stable iff given that it is actually performed, its expected utility is maximal. When there is no stable choice available, the resulting instability can seem to pose a dilemma of practical rationality. A structurally very similar kind of instability, which occurs in cases of anti-expertise, can likewise seem to create dilemmas of (...) epistemic rationality. One possible line of response to such cases of instability, suggested by both Jeffrey (1983) and Sorensen (1987), is to insist that a rational agent can simply refuse to accept that such instability applies to herself in the first place. According to this line of thought it can be rational for a subject to discount even very strong empirical evidence that the anti-expertise condition obtains. I present a new variety of anti-expertise condition where no particular empirical stage-setting is required, since the subject can deduce a priori that an anti-expertise condition obtains. This kind of anti-expertise case is therefore not amenable to the line of response that Jeffrey and Sorensen recommend. (shrink)

What does logic tells us how about we ought to reason? If P entails Q, and I believe P, should I believe Q? I will argue that we should embed the issue in an independently motivated contextualist semantics for ‘ought’, with parameters for a standard and set of propositions. With the contextualist machinery in hand, we can defend a strong principle expressing how agents ought to reason while accommodating conflicting intuitions. I then show how our judgments about blame and guidance (...) can be handled by this machinery. (shrink)

Suppositions can be introduced in either the indicative or subjunctive mood. The introduction of either type of supposition initiates judgments that may be either qualitative, binary judgments about whether a given proposition is acceptable or quantitative, numerical ones about how acceptable it is. As such, accounts of qualitative/quantitative judgment under indicative/subjunctive supposition have been developed in the literature. We explore these four different types of theories by systematically explicating the relationships canonical representatives of each. Our representative qualitative accounts of indicative (...) and subjunctive supposition are based on the belief change operations provided by AGM revision and KM update respectively; our representative quantitative ones are offered by conditionalization and imaging. This choice is motivated by the familiar approach of understanding supposition as `provisional belief revision' wherein one temporarily treats the supposition as true and forms judgments by making appropriate changes to their other opinions. To compare the numerical judgments recommended by the quantitative theories with the binary ones recommended by the qualitative accounts, we rely on a suitably adapted version of the Lockean thesis. Ultimately, we establish a number of new results that we interpret as vindicating the often-repeated claim that conditionalization is a probabilistic version of revision, while imaging is a probabilistic version of update. (shrink)

According to the principle of Conjunction Closure, if one has justification for believing each of a set of propositions, one has justification for believing their conjunction. The lottery and preface paradoxes can both be seen as posing challenges for Closure, but leave open familiar strategies for preserving the principle. While this is all relatively well-trodden ground, a new Closure-challenging paradox has recently emerged, in two somewhat different forms, due to Backes :3773–3787, 2019a) and Praolini :715–726, 2019). This paradox synthesises elements (...) of the lottery and the preface and is designed to close off the familiar Closure-preserving strategies. By appealing to a normic theory of justification, I will defend Closure in the face of this new paradox. Along the way I will draw more general conclusions about justification, normalcy and defeat, which bear upon what Backes :2877–2895, 2019b) has dubbed the ‘easy defeat’ problem for the normic theory. (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)

Suppose that I hold a ticket in a fair lottery and that I believe that my ticket will lose [L] on the basis of its extremely high probability of losing. What is the appropriate epistemic appraisal of me and my belief that L? Am I justified in believing that L? Do I know that L? While there is disagreement among epistemologists over whether or not I am justified in believing that L, there is widespread agreement that I do not know (...) that L. I defend the two-pronged view that I am justified in believing that my ticket will lose and that I know that it will lose. Along the way, I discuss four different but related versions of the lottery paradox—The Paradox for Rationality, The Paradox for Knowledge, The Paradox for Fallibilism, and The Paradox for Epistemic Closure—and offer a unified resolution of each of them. (shrink)

Vann McGee has presented a putative counterexample to modus ponens. I show that (a slightly modified version of) McGee’s election scenario has the same structure as a famous lottery scenario by Kyburg. More specifically, McGee’s election story can be taken to show that, if the Lockean Thesis holds, rational belief is not closed under classical logic, including classical-logic modus ponens. This conclusion defies the existing accounts of McGee’s puzzle.

I show that the Lottery Paradox is just a version of the Sorites, and argue that this should modify our way of looking at the Paradox itself. In particular, I focus on what I call “the Cut-off Point Problem” and contend that this problem, well known by Sorites scholars, ought to play a key role in the debate on Kyburg’s puzzle. Very briefly, I show that, in the Lottery Paradox, the premises “ticket n°1 will lose”, “ticket n°2 will lose”… “ticket (...) n°1000 will lose” are equivalent to soritical premises of the form “~(the winning ticket is in {…, (tn)}) ⊃ ~(the winning ticket is in {…, tn, (tn + 1)})” (where “⊃” is the material conditional, “~” is the negation symbol, “tn” and “tn + 1” are “ticket n°n” and “ticket n°n + 1” respectively, and “{}” identify the elements of the lottery tickets’ set. The brackets in “(tn)” and “(tn + 1)” are meant to point out that in the antecedent of the conditional we do not always have a “tn” (and, as a result, a “tn + 1” in the consequent): consider the conditional “~(the winning ticket is in {}) ⊃ ~(the winning ticket is in {t1})”). As a result, failing to believe, for some ticket, that it will lose comes down to introducing a cut-off point in a chain of soritical premises. In this paper I explore the consequences of the different ways of blocking the Lottery Paradox with respect to the Cut-off Point Problem. A heap variant of the Lottery Paradox is especially relevant for evaluating the different solutions. One important result is that the most popular way out of the puzzle, i.e., denying the Lockean Thesis, becomes less attractive. Moreover, I show that, along with the debate on whether rational belief is closed under classical logic, the debate on the validity of modus ponens should play an important role in discussions on the Lottery Paradox. -/- . (shrink)

This paper is about the statics and dynamics of belief states that are represented by pairs consisting of an agent's credences (represented by a subjective probability measure) and her categorical beliefs (represented by a set of possible worlds). Regarding the static side, we argue that the latter proposition should be coherent with respect to the probability measure and that its probability should reach a certain threshold value. On the dynamic side, we advocate Jeffrey conditionalisation as the principal mode of changing (...) one's belief state. This updating method fits the idea of the Lockean Thesis better than plain Bayesian conditionalisation, and it affords a flexible method for adding and withdrawing categorical beliefs. We show that it fails to satisfy the traditional principles of Inclusion and Preservation for belief revision and the principle of Recovery for belief withdrawals{, as well as the Levi and Harper identities. We take this to be a problem for the latter principles rather than for the idea of coherent belief change. (shrink)

To understand something involves some sort of commitment to a set of propositions comprising an account of the understood phenomenon. Some take this commitment to be a species of belief; others, such as Elgin and I, take it to be a kind of cognitive policy. This paper takes a step back from debates about the nature of understanding and asks when this commitment involved in understanding is epistemically appropriate, or ‘acceptable’ in Elgin’s terminology. In particular, appealing to lessons from the (...) lottery and preface paradoxes, it is argued that this type of commitment is sometimes acceptable even when it would be rational to assign arbitrarily low probabilities to the relevant propositions. This strongly suggests that the relevant type of commitment is sometimes acceptable in the absence of epistemic justification for belief, which in turn implies that understanding does not require justification in the traditional sense. The paper goes on to develop a new probabilistic model of acceptability, based on the idea that the maximally informative accounts of the understood phenomenon should be optimally probable. Interestingly, this probabilistic model ends up being similar in important ways to Elgin’s proposal to analyze the acceptability of such commitments in terms of ‘reflective equilibrium’. (shrink)

Given plausible assumptions about the nature of evidence and undercutting defeat, many believe that the force of the evidential problem of evil depends on sceptical theism’s being false: if evil is...

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)

It is well-known that versions of the lottery paradox and of the preface paradox show that the following three principles are jointly inconsistent: (Sufficiency) very probable propositions are justifiably believable; (Conjunction Closure) justified believability is closed under conjunction introduction; (No Contradictions) propositions known to be contradictory are not justifiably believable. This paper shows that there is a hybrid of the lottery and preface paradoxes that does not require Sufficiency to arise, but only Conjunction Closure and No Contradictions; and it argues (...) that, given any plausible solution to this paradox, if one is not ready to deny Conjunction Closure (and analogous consistency principles), then one must endorse the thesis that justified believability is factive. (shrink)

I am concerned with epistemic closure—the phenomenon in which some knowledge requires other knowledge. In particular, I defend a version of the closure principle in terms of analyticity; if an agent S knows that p is true, then S knows that all analytic parts of p are true as well. After targeting the relevant notion of analyticity, I argue that this principle accommodates intuitive cases and possesses the theoretical resources to avoid the preface paradox. I close by arguing that contextualists (...) who maintain that knowledge attributions are closed within—but not between—linguistic contexts are tacitly committed to this principle’s truth. (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)

In this paper, I offer an analysis of the radical disagreement over the adequacy of string theory. The prominence of string theory despite its notorious lack of empirical support is sometimes explained as a troubling case of science gone awry, driven largely by sociological mechanisms such as groupthink (e.g. Smolin 2006). Others, such as Dawid (2013), explain the controversy by positing a methodological revolution of sorts, according to which string theorists have quietly turned to nonempirical methods of theory assessment given (...) the technological inability to directly test the theory. The appropriate response, according to Dawid, is to acknowledge this development and widen the canons of acceptable scientific methods. As I’ll argue, however, the current situation in fundamental physics does not require either of these responses. Rather, as I’ll suggest, much of the controversy stems from a failure to properly distinguish the “context of justification” from the “context of pursuit”. Both those who accuse string theorists of betraying the scientific method and those who advocate an enlarged conception of scientific methodology objectionably conflate epistemic justification with judgements of pursuit-worthiness. Once we get clear about this distinction and about the different norms governing the two contexts, the current situation in fundamental physics becomes much less puzzling. After defending this diagnosis of the controversy, I’ll show how the argument patterns that have been posited by Dawid as constituting an emergent methodological revolution in science are better off if reworked as arguments belonging to the context of pursuit. (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)

I explore how rational belief and rational credence relate to evidence. I begin by looking at three cases where rational belief and credence seem to respond differently to evidence: cases of naked statistical evidence, lotteries, and hedged assertions. I consider an explanation for these cases, namely, that one ought not form beliefs on the basis of statistical evidence alone, and raise worries for this view. Then, I suggest another view that explains how belief and credence relate to evidence. My view (...) focuses on the possibilities that the evidence makes salient. I argue that this makes better sense of the difference between rational credence and rational belief than other accounts. (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)

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)

In this paper, we compare and contrast two methods for the revision of qualitative beliefs. The first method is generated by a simplistic diachronic Lockean thesis requiring coherence with the agent’s posterior credences after conditionalization. The second method is the orthodox AGM approach to belief revision. Our primary aim is to determine when the two methods may disagree in their recommendations and when they must agree. We establish a number of novel results about their relative behavior. Our most notable finding (...) is that the inverse of the golden ratio emerges as a non-arbitrary bound on the Bayesian method’s free-parameter—the Lockean threshold. This “golden threshold” surfaces in two of our results and turns out to be crucial for understanding the relation between the two methods. (shrink)

Thomas Kroedel argues that the lottery paradox can be solved by identifying epistemic justification with epistemic permissibility rather than epistemic obligation. According to his permissibility solution, we are permitted to believe of each lottery ticket that it will lose, but since permissions do not agglomerate, it does not follow that we are permitted to have all of these beliefs together, and therefore it also does not follow that we are permitted to believe that all tickets will lose. I present two (...) objections to this solution. First, even if justification itself amounts to no more than epistemic permissibility, the lottery paradox recurs at the level of doxastic obligations unless one adopts an extremely permissive view about suspension of belief that is in tension with our practice of doxastic criticism. Second, even if there are no obligations to believe lottery propositions, the permissibility solution fails because epistemic permissions typically agglomerate, and the lottery case provides no exception to this rule. (shrink)

This paper is about conjunctions and disjunctions in the scope of non-doxastic atti- tude verbs. These constructions generate a certain type of ignorance implicature. I argue that the best way to account for these implicatures is by appealing to a notion of contex- tual redundancy (Schlenker, 2008; Fox, 2008; Mayr and Romoli, 2016). This pragmatic approach to ignorance implicatures is contrasted with a semantic account of disjunctions under `wonder' that appeals to exhausti cation (Roelofsen and Uegaki, 2016). I argue that (...) exhausti cation-based theories cannot handle embedded conjunctions, so a pragmatic account of ignorance implicatures is superior. (shrink)

The primary objective of this paper is to introduce a new epistemic paradox that puts pressure on the claim that justification is closed under multi premise deduction. The first part of the paper will consider two well-known paradoxes—the lottery and the preface paradox—and outline two popular strategies for solving the paradoxes without denying closure. The second part will introduce a new, structurally related, paradox that is immune to these closure-preserving solutions. I will call this paradox, The Paradox of the Pill. (...) Seeing that the prominent closure-preserving solutions do not apply to the new paradox, I will argue that it presents a much stronger case against the claim that justification is closed under deduction than its two predecessors. Besides presenting a more robust counterexample to closure, the new paradox also reveals that the strategies that were previously thought to get closure out of trouble are not sufficiently general to achieve this task as they fail to apply to similar closure-threatening paradoxes in the same vicinity. (shrink)

What is it to believe something might be the case? We develop a puzzle that creates difficulties for standard answers to this question. We go on to propose our own solution, which integrates a Bayesian approach to belief with a dynamic semantics for epistemic modals. After showing how our account solves the puzzle, we explore a surprising consequence: virtually all of our beliefs about what might be the case provide counterexamples to the view that rational belief is closed under logical (...) implication. (shrink)

The moral of Buridan's Ass is that it can sometimes be rational to perform one action rather than another even though one lacks stronger reason to do so. Yet it is also commonly believed that it cannot ever be rational to believe one proposition rather than another if one lacks stronger reason to do so. This asymmetry has been taken to indicate a deep difference between epistemic and practical rationality. According to the view articulated here, the asymmetry should instead be (...) explained by the difference between rational intentions and rational actions. Thus, it turns out, Buridan's Ass-style cases do not indicate an asymmetry between epistemic and practical rationality as such. (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)

The Knower paradox purports to place surprising a priori limitations on what we can know. According to orthodoxy, it shows that we need to abandon one of three plausible and widely-held ideas: that knowledge is factive, that we can know that knowledge is factive, and that we can use logical/mathematical reasoning to extend our knowledge via very weak single-premise closure principles. I argue that classical logic, not any of these epistemic principles, is the culprit. I develop a consistent theory validating (...) all these principles by combining Hartry Field's theory of truth with a modal enrichment developed for a different purpose by Michael Caie. The only casualty is classical logic: the theory avoids paradox by using a weaker-than-classical K3 logic. I then assess the philosophical merits of this approach. I argue that, unlike the traditional semantic paradoxes involving extensional notions like truth, its plausibility depends on the way in which sentences are referred to--whether in natural languages via direct sentential reference, or in mathematical theories via indirect sentential reference by Gödel coding. In particular, I argue that from the perspective of natural language, my non-classical treatment of knowledge as a predicate is plausible, while from the perspective of mathematical theories, its plausibility depends on unresolved questions about the limits of our idealized deductive capacities. (shrink)

So-called “traditional epistemology” and “Bayesian epistemology” share a word, but it may often seem that the enterprises hardly share a subject matter. They differ in their central concepts. They differ in their main concerns. They differ in their main theoretical moves. And they often differ in their methodology. However, in the last decade or so, there have been a number of attempts to build bridges between the two epistemologies. Indeed, many would say that there is just one branch of philosophy (...) here—epistemology. There is a common subject matter after all. In this paper, we begin by playing the role of a “bad cop,” emphasizing many apparent points of disconnection, and even conflict, between the approaches to epistemology. We then switch role, playing a “good cop” who insists that the approaches are engaged in common projects after all. We look at various ways in which the gaps between them have been bridged, and we consider the prospects for bridging them further. We conclude that this is an exciting time for epistemology, as the two traditions can learn, and have started learning, from each other. (shrink)

According to deontological approaches to justification, we can analyze justification in deontic terms. In this paper, I try to advance the discussion of deontological approaches by applying recent insights in the semantics of deontic modals. Specifically, I use the distinction between weak necessity modals and strong necessity modals to make progress on a question that has received surprisingly little discussion in the literature, namely: ‘What’s the best version of a deontological approach?’ The two most obvious hypotheses are the Permissive View, (...) according to which justified expresses permission, and the Obligatory View, according to which justified expresses some species of obligation. I raise difficulties for both of these hypotheses. In light of these difficulties, I propose a new position, according to which justified expresses a property I call faultlessness, defined as the dual of weak necessity modals. According to this view, an agent is justified in phi-ing iff it’s not the case that she should [/ought] not phi. I argue that this ‘Faultlessness View’ gives us precisely what’s needed to avoid the problems facing the Permissive and Obligatory Views. (shrink)

According to Michael Friedman’s theory of explanation, a law X explains laws Y1, Y2, …, Yn precisely when X unifies the Y’s, where unification is understood in terms of reducing the number of independently acceptable laws. Philip Kitcher criticized Friedman’s theory but did not analyze the concept of independent acceptability. Here we show that Kitcher’s objection can be met by modifying an element in Friedman’s account. In addition, we argue that there are serious objections to the use that Friedman makes (...) of the concept of independent acceptability. (shrink)