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)

I articulate a functional characterisation of the concept of evidence, according to which evidence is that which allows us to make inferences that extend our knowledge. This entails Williamson's equation of knowledge with evidence.

Until recently, it seemed like no theory about the relationship between rational credence and rational outright belief could reconcile three independently plausible assumptions: that our beliefs should be logically consistent, that our degrees of belief should be probabilistic, and that a rational agent believes something just in case she is sufficiently confident in it. Recently a new formal framework has been proposed that can accommodate these three assumptions, which is known as “the stability theory of belief” or “high probability cores.” (...) In this paper, I examine whether the stability theory of belief can meet two further constraints that have been proposed in the literature: that it is irrational to outright believe lottery propositions, and that it is irrational to hold outright beliefs based on purely statistical evidence. I argue that these two further constraints create a dilemma for a proponent of the stability theory: she must either deny that her theory is meant to give an account of the common epistemic notion of outright belief, or supplement the theory with further constraints on rational belief that render the stability theory explanatorily idle. This result sheds light on the general prospects for a purely formal theory of the relationship between rational credence and belief, i.e. a theory that does not take into account belief content. I argue that it is doubtful that any such theory could properly account for these two constraints, and hence play an important role in characterizing our common epistemic notion of outright belief. (shrink)

We report a series of experiments examining whether people ascribe knowledge for true beliefs based on probabilistic evidence. Participants were less likely to ascribe knowledge for beliefs based on probabilistic evidence than for beliefs based on perceptual evidence or testimony providing causal information. Denial of knowledge for beliefs based on probabilistic evidence did not arise because participants viewed such beliefs as unjustified, nor because such beliefs leave open the possibility of error. These findings rule out traditional philosophical accounts for why (...) probabilistic evidence does not produce knowledge. The experiments instead suggest that people deny knowledge because they distrust drawing conclusions about an individual based on reasoning about the population to which it belongs, a tendency previously identified by “judgment and decision making” researchers. Consistent with this, participants were more willing to ascribe knowledge for beliefs based on probabilistic evidence that is specific to a particular case. (shrink)

In this paper, I present a puzzle about epistemic rationality. It seems plausible that it should be rational to believe a proposition if you have sufficient evidential support for it. It seems plausible that it rationality requires you to conform to the categorical requirements of rationality. It also seems plausible that our first-order attitudes ought to mesh with our higher-order attitudes. It seems unfortunate that we cannot accept all three claims about rationality. I will present three ways of trying to (...) resolve this tension and argue that the best way to do this is to reject the idea that strong evidential support is the stuff rationality is made of. In the course of doing this, I shall argue that there is a special class of propositions about the requirements of rationality that we cannot make rational mistakes about and explain how this can be. (shrink)

It is a prevalent, if not popular, thesis in the metaphysics of belief that facts about an agent’s beliefs depend entirely upon facts about that agent’s underlying credal state. Call this thesis ‘credal reductivism’ and any view that endorses this thesis a ‘credal reductivist view’. An adequate credal reductivist view will accurately predict both when belief occurs and which beliefs are held appropriately, on the basis of credal facts alone. Several well-known—and some lesser known—objections to credal reductivism turn on the (...) inability of standard credal reductivist views to get the latter, normative, results right. This paper presents and defends a novel credal reductivist view according to which belief is a type of “imprecise credence” that escapes these objections by including an extreme credence of 1. (shrink)

According to the principle of epistemic closure, knowledge is closed under known implication. The principle is intuitive but it is problematic in some cases. Suppose you know you have hands and you know that ‘I have hands’ implies ‘I am not a brain-in-a-vat’. Does it follow that you know you are not a brain-in-a-vat? It seems not; it should not be so easy to refute skepticism. In this and similar cases, we are confronted with a puzzle: epistemic closure is an (...) intuitive principle, but at times, it does not seem that we know by implication. In response to this puzzle, the literature has been mostly polarized between those who are willing to do away with epistemic closure and those who think we cannot live without it. But there is a third way. Here I formulate a restricted version of the principle of epistemic closure. In the standard version, the principle can range over any proposition; in the restricted version, it can only range over those propositions that are within the limits of a given epistemic inquiry and that do not constitute the underlying assumptions of the inquiry. If we adopt the restricted version, I argue, we can preserve the advantages associated with closure, while at the same time avoiding the puzzle I’ve described. My discussion also yields an insight into the nature of knowledge. I argue that knowledge is best understood as a topic-restricted notion, and that such a conception is a natural one given our limited cognitive resources. (shrink)

This paper will articulate and defend a novel theory of epistemic justification; I characterize my view as the thesis that justification is potential knowledge . My project is an instance of the ‘knowledge-first’ programme, championed especially by Timothy Williamson. So I begin with a brief recapitulation of that programme.

Igor Douven has recently developed a challenge for accounts of justification according to which beliefs about lottery losers are never justified. This article argues that champions of such accounts can rise to Douven's challenge and, what's more, that they can turn Douven's argument around in the sense that they can legitimately take it to provide a vindication of their preferred view.

Some series can go on indefinitely, others cannot, and epistemologists want to know in which class to place epistemic chains. Is it sensible or nonsensical to speak of a proposition or belief that is justified by another proposition or belief, ad infinitum? In large part the answer depends on what we mean by “justification.” Epistemologists have failed to find a definition on which everybody agrees, and some have even advised us to stop looking altogether. In spite of this, the present (...) essay submits a few candidate definitions. It argues that, although not giving the final word, these candidates tell us something about the possibility of infinite epistemic chains. And it shows that they can short-circuit a debate about doxastic justification. (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)

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)

Adequate epistemic justification is best conceived as the appearance, over time, of knowledge to the subject. ‘Appearance’ is intended literally, not as a synonym for belief. It is argued through consideration of examples that this account gets the extension of ‘adequately justified belief’ at least roughly correct. A more theoretical reason is then offered to regard justification as the appearance of knowledge: If we have a knowledge norm for assertion, we do our best to comply with this norm when we (...) express as assertions only beliefs that appear to us to be knowledge. If we are doing our best, there is little point in further sanctions. So a norm of knowledge for assertion would lead to a secondary norm of justified belief as the appearance of knowledge, marking a point at which our assertions may be corrected but should not be blamed. (shrink)

Closure for justification is the claim that thinkers are justified in believing the logical consequences of their justified beliefs, at least when those consequences are competently deduced. Many have found this principle to be very plausible. Even more attractive is the special case of Closure known as Single-Premise Closure. In this paper, I present a challenge to Single-Premise Closure. The challenge is based on the phenomenon of rational self-doubt – it can be rational to be less than fully confident in (...) one's beliefs and patterns of reasoning. In rough outline, the argument is as follows: Consider a thinker who deduces a conclusion from a justified initial premise via an incredibly long sequence of small competent deductions. Surely, such a thinker should suspect that he has made a mistake somewhere. And surely, given this, he should not believe the conclusion of the deduction even though he has a justified belief in the initial premise. (shrink)

A popular way to relate probabilistic information to binary rational beliefs is the Lockean Thesis, which is usually formalized in terms of thresholds. This approach seems far from satisfactory: the value of the thresholds is not well-specified and the Lottery Paradox shows that the model violates the Conjunction Principle. We argue that the Lottery Paradox is a symptom of a more fundamental and general problem, shared by all threshold-models that attempt to put an exact border on something that is intrinsically (...) vague. We propose application of the language of relative analysis—a type of non-standard analysis—to formulate a new model for rational belief, called Stratified Belief. This contextualist model seems well-suited to deal with a concept of beliefs based on probabilities ‘sufficiently close to unity’ and satisfies a moderately weakened form of the Conjunction Principle. We also propose an adaptation of the model that is able to deal with beliefs that are less firm than ‘almost certainty’. The adapted version is also of interest for the epistemicist account of vagueness. (shrink)

We challenge a line of thinking at the fore of recent work on epistemic value: the line (suggested by Kvanvig in The value of knowledge and the pursuit of understanding, 2003 and others) that if the value of knowledge is “swamped” by the value of mere true belief, then we have good reason to doubt its theoretical importance in epistemology. We offer a value-driven argument for the theoretical importance of knowledge—one that stands even if the value of knowledge is “swamped” (...) by the value of true belief. Specifically, we contend that even if knowledge itself has no special epistemic value, its relationship to other items of value—cognitive abilities—gives ample reason to locate the concept at the very core of epistemology. (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)

Epistemic contextualism was originally motivated and supported by the response it provides to skeptical paradox. Although there has been much discussion of the contextualist response to skeptical paradox, not much attention has been paid to the argument from skepticism for contextualism. Contextualists argue that contextualism accounts for the plausibility and apparent inconsistency of a set of paradoxical claims better than any classical invariantist theory. In this paper I focus on and carefully examine the argument from skepticism for contextualism. I argue (...) not only that the prima facie advantage of contextualism is specious, but also that contextualism is in fact at a competitive disadvantage with respect to two classical invariantist views. I also argue that contextualism takes an arbitrary and unsatisfying strategy in its response to skepticism. That contextualism is alone in taking this arbitrary strategy marks a second competitive disadvantage for it. In addition, I argue that the contextualist response to skeptical paradox regenerates a skeptical paradox which contextualism is powerless to solve. Consequently, the argument from skepticism for contextualism fails. Furthermore, this feature of the contextualist response to skeptical paradox completely undermines the motivation and support for contextualism deriving from its treatment of skeptical paradox. I conclude that the argument from skepticism for contextualism fails, and that the contextualist response to skeptical paradox fails to motivate contextualism, pending the success of another argument for the contextualist thesis. (shrink)

Although recent epistemology has been marked by several prominent disagreements – e.g., between foundationalists and coherentists, internalists and externalists – there has been widespread agreement that some form of fallibilism must be correct. According to a rough formulation of this view, it is possible for a subject to have knowledge even in cases where the justification or grounding for the knowledge is compatible with the subject’s being mistaken. In this paper, I examine the motivation for fallibilism before providing a fully (...) general account of the view. I conclude by looking at the two major difficulties for fallibilism: the Gettier problem and the lottery paradox. (shrink)

What is the normative role of knowledge? I argue that knowledge plays an important role as a norm of assertion and action, which is explained and unified by its more fundamental role as a norm of belief. Moreover, I propose a distinctive account of what this normative role consists in. I argue that knowledge is the aim of belief, which sets a normative standard of correctness and a corresponding normative standard of justification. According to my proposal, it is correct to (...) believe, assert and act on a proposition if and only if one is in a position to know it, but one has justification to believe, assert and act on a proposition if and only if one has justification to believe that one is in a position to know it. (shrink)

In this paper I take issue with Jonathan Sutton's attempt at defending the thesis that knowledge is justified belief. I argue, first, that the arguments he adduces in support of it fail. Second, I provide independent reason to believe that knowledge and justified belief come apart.

Many epistemologists have responded to the lottery paradox by proposing formal rules according to which high probability defeasibly warrants acceptance. Douven and Williamson ([2006]) 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—among them a relatively strong structural assumption to the effect that the underlying probability space is both finite and uniform . In (...) this article, 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)

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)

In this article, I first elaborate and refine the Principle of Intention Agglomeration (PIA), which was introduced by Michael Bratman as “a natural constraint on intention”. According to the PIA, the intentions of a rational agent should be agglomerative. The proposed refinement of the PIA is not only in accordance with the spirit of Bratman’s planning theory of intention as well as consistency constraints for intentions rooted in the theory, but also reveals some deep rationales of practical rationality regarding resource-limited (...) agents. Then I defend the PIA against various objections and counterexamples, showing that the refined PIA survives attacks based on both conceptual analyses and psychological considerations. (shrink)

Elizabeth Fricker has recently proposed a principle aimed at stating the necessary and sufficient conditions for testimonial justification. Her proposal entails that a hearer is justified in believing a speaker’s testimony only if she recognizes the speaker to be trustworthy, which, given Fricker’s internalist commitments, requires the hearer to have within her epistemic purview grounds which justify belief in the speaker’s trustworthiness. We argue that, as it stands, Fricker’s principle is too demanding, and we propose some amendments to it. We (...) further discuss the viability of her internalist approach to testimony.Keywords: Testimony; Justification; Internalism; Social epistemology; Elizabeth Fricker. (shrink)

Alston, Searle, and Williamson advocate the restrictive model of assertion , according to which certain constitutive assertoric norms restrict which propositions one may assert. Sellars and Brandom advocate the dialectical model of assertion , which treats assertion as constituted by its role in the game of giving and asking for reasons. Sellars and Brandom develop a restrictive version of the dialectical model. I explore a non-restrictive version of the dialectical model. On such a view, constitutive assertoric norms constrain how one (...) must react if an interlocutor challenges one's assertion, but they do not constrain what one should assert in the first place. I argue that the non-restrictive dialectical perspective can accommodate various linguistic phenomena commonly taken to support the restrictive model. 1. (shrink)

This paper advances the debate over the question whether false beliefs may nevertheless have warrant, the property that yields knowledge when conjoined with true belief. The paper’s first main part—which spans Sections 2–4—assesses the best argument for Warrant Infallibilism, the view that only true beliefs can have warrant. I show that this argument’s key premise conflicts with an extremely plausible claim about warrant. Sections 5–6 constitute the paper’s second main part. Section 5 presents an overlooked puzzle about warrant, and uses (...) that puzzle to generate a new argument for Warrant Fallibilism, the view that false beliefs can have warrant. Section 6 evaluates this pro-Fallibilism argument, finding ultimately that it defeats itself in a surprising way. I conclude that neither Infallibilism nor Fallibilism should now constrain theorizing about warrant. (shrink)

Many have the intuition that the right response to the Lottery Paradox is to deny that one can justifiably believe of even a single lottery ticket that it will lose. The paper shows that from any theory of justification that solves the paradox in accordance with this intuition, a theory not of that kind can be derived that also solves the paradox but is more conducive to our epistemic goal than the former. It is argued that currently there is no (...) valid reason not to give preference to the derived accounts over the accounts from which they come. (shrink)

Many have the intuition that the right response to the Lottery Paradox is to deny that one can justifiably believe of even a single lottery ticket that it will lose. The paper shows that from any theory of justification that solves the paradox in accordance with this intuition, a theory not of that kind can be derived that also solves the paradox but is more conducive to our epistemic goal than the former. It is argued that currently there is no (...) valid reason not to give preference to the derived accounts over the accounts from which they come. (shrink)

When is a belief or judgment justified? One might be forgiven for thinking the search for single answer to this question to be hopeless. The concept of justification is required to fulfil several tasks: to evaluate beliefs epistemically, to fill in the gap between truth and knowledge, to describe the virtuous organization of one’s beliefs, to describe the relationship between evidence and theory (and thus relate to confirmation and probabilification). While some of these may be held to overlap, the prospects (...) for fulfilling all may well seem poor. Furthermore the internalist requires that justification be an introspectible property of beliefs and a fundamental epistemic concept, while the externalist is often happy to ignore the concept altogether or at best regard it as an embarrassing add-on to their epistemology. In the light of this one might reasonably give up on justification altogether or adopt pluralist approach, denying that justification is any single property of beliefs of judgments. (shrink)

Traditional approaches to epistemology have sought, unsuccessfully, to define knowledge in terms of justification. I follow Timothy Williamson in arguing that this is misconceived and that we should take knowledge as our fundamental epistemological notion. We can then characterise justification as a certain sort of approximation to knowledge. A judgement is justified if and only if the reason (if there is one) for a failure to know is to be found outside the subject's mental states; that is, justified judging is (...) possible knowing (where one world accessible from another if and only if they are identical with regard to a subject's antecedent mental states and judgement forming processes). This view is explained and defended. (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.

Fair lotteries offer familiar ways to pose a number of epistemological problems, prominently those of closure and of scepticism. Although these problems apply to many epistemological positions, in this paper I develop a variant of a lottery case to raise a difficulty with the reliabilist's fundamental claim that justification or knowledge is to be analyzed as a high truth-ratio (of the relevant belief-forming processes). In developing the difficulty broader issues are joined including fallibility and the relation of reliability to understanding.

In the tradition of substructural logics, it has been claimed for a long time that conjunction and inclusive disjunction are ambiguous:we should, in fact, distinguish between ‘lattice’ connectives (also called additive or extensional) and ‘group’ connectives (also called multiplicative or intensional). We argue that an analogous ambiguity affects the quantifiers. Moreover, we show how such a perspective could yield solutions for two well-known logical puzzles: McGee’s counterexample to modus ponens and the lottery paradox.

I will be arguing that a subject’s belief that p is justified if and only if he knows that p: justification is knowledge. I will start by describing two broad classes of allegedly justified beliefs that do not constitute knowledge and which, hence, cannot be what they are often taken to be if my view is correct. It is far from clear what my view is until I say a lot more about the relevant concept or concepts of justification that (...) concern me. The following section describes several concepts of justification that epistemologists have employed, and, in particular, identifies the two concepts of justification that I claim are coextensive with the concept of knowledge. One of those is the deontological conception of justification: I will be arguing that one ought not believe that p unless one knows that p. I imagine that the major opposition to my view will be that it is simply obvious that there are justified false beliefs, a feeling that I try to dispel in the lengthy section on concepts of justification before I finally get around to giving the main arguments in favor of my view. A view as unorthodox as mine demands more than a single argument: I offer four in the third section. Everyone allows that many people have many unjustified beliefs, and everyone has some unjustified beliefs, but such beliefs appear to be far more prevalent on my view than on more orthodox views. In the last section, I argue that unjustified beliefs, although widespread, are not quite as common as they might appear to be on my view. (shrink)

There are many ordinary propositions we think we know. Almost every ordinary proposition entails some lottery proposition which we think we do not know but to which we assign a high probability of being true (for instance:I will never be a multi-millionaire entails I will not win this lottery). How is this possible – given that some closure principle is true? This problem, also known as the Lottery puzzle, has recently provoked a lot of discussion. In this paper I discuss (...) one of the most promising answers to the problem: Stewart Cohens contextualist solution, which is based on ideas about the salience of chances of error. After presenting some objections to it I sketch an alternative solution which is still contextualist in spirit. (shrink)

There are many ordinary propositions we think we know. Almost every ordinary proposition entails some "lottery proposition" which we think we do not know but to which we assign a high probability of being true (for instance: “I will never be a multi-millionaire” entails “I will not win this lottery”). How is this possible - given that some closure principle is true? This problem, also known as “the Lottery puzzle”, has recently provoked a lot of discussion. In this paper I (...) discuss one of the most promising answers to the problem: Stewart Cohen’s contextualist solution which is based on ideas about the salience of chances of error. After presenting some objections to it I sketch an alternative solution which is still contextualist in spirit. (shrink)