I review recent empirical findings on knowledge attributions in lottery cases and report a new experiment that advances our understanding of the topic. The main novel finding is that people deny knowledge in lottery cases because of an underlying qualitative difference in how they process probabilistic information. “Outside” information is generic and pertains to a base rate within a population. “Inside” information is specific and pertains to a particular item’s propensity. When an agent receives information that (...) 99% of all lottery tickets lose (outside information), people judge that she does not know that her ticket will lose. By contrast, when an agent receives information that her specific ticket is 99% likely to lose (inside information), people judge that she knows that her ticket will lose. Despite this difference in knowledge judgments, people rate the likelihood of her ticket losing the exact same in both cases (i.e. 99%). The results shed light on other factors affecting knowledge judgments in lottery cases, including formulaic expression and participants’ own estimation of whether it is true that the ticket will lose. The results also undermine previous hypotheses offered for knowledge denial in lottery cases, including the hypotheses that people deny knowledge because they either deny justification or acknowledge a chance for error. (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)

A ‘lottery belief’ is a belief that a particular ticket has lost a large, fair lottery, based on nothing more than the odds against it winning. The lottery paradox brings out a tension between the idea that lottery beliefs are justified and the idea that that one can always justifiably believe the deductive consequences of things that one justifiably believes – what is sometimes called the principle of closure. Many philosophers have treated the lottery paradox (...) as an argument against the second idea – but I make a case here that it is the first idea that should be given up. As I shall show, there are a number of independent arguments for denying that lottery beliefs are justified. (shrink)

We conducted five experiments that reveal some main contours of the folk epistemology of lotteries. The folk tend to think that you don't know that your lottery ticket lost, based on the long odds ("statistical cases"); by contrast, the folk tend to think that you do know that your lottery ticket lost, based on a news report ("testimonial cases"). We evaluate three previous explanations for why people deny knowledge in statistical cases: the justification account, the (...) chance account, and the statistical account. None of them seems to work. We then propose a new explanation of our own, the formulaic account, according to which some people deny knowledge in statistical cases due to formulaic expression. (shrink)

Many philosophers have thought that aggregates of small, broadly dispersed evils don’t pose the same sort of challenge to theism that horrendous evils like the Nazi Holocaust do. But there are interesting arguments that purport to show that large enough aggregates of small evils are morally and axiologically equivalent to horrendous evils. Herein lies an intriguing and overlooked strategy for defending theism. In short: small evils, or aggregates of such evils, don’t provide decisive evidence against theism; there’s no relevant difference (...) between horrendous evils and aggregates of small evils; hence horrendous evils must not provide decisive evidence against theism, either. (shrink)

The word ‘extremist’ is often used pejoratively, but it’s not clear what, if anything, is wrong with extremism. My project is to give an account of moral extremism as a vice. It consists roughly in having moral convictions so intense that they cause a sort of moral tunnel vision, pushing salient competing considerations out of mind. We should be interested in moral extremism for several reasons: it’s consequential, it’s insidious – we don’t expect immorality to arise from excessive devotion to (...) morality – and it’s yet to attract much philosophical attention. I give several examples of moral extremism from history and explore their social-political implications. I also consider how we should evaluate people who miss the mark, being either too extreme in the service of a good cause or inconsistent with their righteous convictions. I compare John Brown and John Quincy Adams, who fell on either side of this spectrum, as examples. (shrink)

A number of prominent epistemologists claim that the principle of sensitivity “play[s] a starring role in the solution to some important epistemological problems”. I argue that traditional sensitivity accounts fail to explain even the most basic data that are usually considered to constitute their primary motivation. To establish this result I develop Gettier and lottery cases involving necessary truths. Since beliefs in necessary truths are sensitive by default, the resulting cases give rise to a serious explanatory problem (...) for the defenders of sensitivity accounts. It is furthermore argued that attempts to modally strengthen traditional sensitivity accounts to avoid the problem must appeal to a notion of safety—the primary competitor of sensitivity in the literature. The paper concludes that the explanatory virtues of sensitivity accounts are largely illusory. In the framework of modal epistemology, it is safety rather than sensitivity that does the heavy explanatory lifting with respect to Gettier cases, lottery examples, and other pertinent cases. (shrink)

A question, long discussed by legal scholars, has recently provoked a considerable amount of philosophical attention: ‘Is it ever appropriate to base a legal verdict on statistical evidence alone?’ Many philosophers who have considered this question reject legal reliance on bare statistics, even when the odds of error are extremely low. This paper develops a puzzle for the dominant theories concerning why we should eschew bare statistics. Namely, there seem to be compelling scenarios in which there are multiple sources of (...) incriminating statistical evidence. As we conjoin together different types of statistical evidence, it becomes increasingly incredible to suppose that a positive verdict would be impermissible. I suggest that none of the dominant views in the literature can easily accommodate such cases, and close by offering a diagnosis of my own. (shrink)

This paper defends the heretical view that, at least in some cases, we ought to assign legal liability based on purely statistical evidence. The argument draws on prominent civil law litigation concerning pharmaceutical negligence and asbestos-poisoning. The overall aim is to illustrate moral pitfalls that result from supposing that it is never appropriate to rely on bare statistics when settling a legal dispute.

According to an increasingly popular view in epistemology and philosophy of mind, beliefs are sensitive to contextual factors such as practical factors and salient error possibilities. A prominent version of this view, called credal sensitivism, holds that the context-sensitivity of belief is due to the context-sensitivity of degrees of belief or credence. Credal sensitivism comes in two variants: while credence-one sensitivism (COS) holds that maximal confidence (credence one) is necessary for belief, threshold credal sensitivism (TCS) holds that belief consists in (...) having credence above some threshold, where this threshold doesn’t require maximal confidence. In this paper, I argue that COS has difficulties in accounting for three important features about belief: i) the compatibility between believing p and assigning non-zero credence to certain error possibilities that one takes to entail not-p, ii) the fact that outright beliefs can occur in different strengths, and iii) beliefs held by unconscious subjects. I also argue that TCS can easily avoid these problems. Finally, I consider an alleged advantage of COS over TCS in terms of explaining beliefs about lotteries. I argue that lottery cases are rather more problematic for COS than TCS. In conclusion, TCS is the most plausible version of credal sensitivitism. (shrink)

[Significantly updated in Chapter 6 of Awareness and the Substructure of Knowledge] In order for a reason to justify an action or attitude it must be one that is possessed by an agent. Knowledge-centric views of possession ground our possession of reasons, at least partially, either in our knowledge of them or in our being in a position to know them. On virtually all accounts, knowing P is some kind of non-accidental true belief that P. This entails that knowing P (...) is a kind of non-accidental true representation that P. I outline a novel theory of the epistemic requirement on possession in terms of this more general state of non-accidental true representation. It is just as well placed to explain the motivations behind knowledge-centric views of possession, and it is also better placed to explain the extent of the reasons we possess in certain cases of deductive belief-updates and cases involving environmental luck. I conclude with three reflections. First, I indicate how my arguments generate a dilemma for Errol Lord’s view that possessing reasons is just a matter of being in a position to manifest one’s knowledge how to use them. Second, I explain how my view can simultaneously manage cases of environmental luck without falling prey to lottery cases. Finally, I sketch the direction for a further range of counterexamples to knowledge-centric theories of possession. (shrink)

Safety principles in epistemology are often hailed as providing us with an explanation of why we fail to have knowledge in Gettier cases and lottery examples, while at the same time allowing for the fact that we know the negations of sceptical hypotheses. In a recent paper, Sinhababu and Williams have produced an example—the Backward Clock—that is meant to spell trouble for safety accounts of knowledge. I argue that the Backward Clock case is, in fact, unproblematic for the (...) more sophisticated formulations of safety in the literature. However, I then proceed to construct two novel examples that turn out problematic for those formulations—one that provides us with a lottery-style case of safe ignorance and one that is a straightforward case of unsafe knowledge. If these examples succeed, then safety as it is usually conceived in the current debate cannot account for ignorance in all Gettier and lottery-style cases, and neither is it a necessary condition for knowledge. I conclude from these troublesome examples that modal epistemologists ought to embrace a much more simple and non-reductive version of safety, according to which the notion of similarity between possible worlds that determines in which worlds the subject must believe truly is an epistemic notion that cannot be defined or reduced to notions independent of knowledge. The resulting view is shown to also lead to desirable results with respect to lottery cases, certain quantum phenomena, and a puzzling case involving a cautious brain-in-a-vat. (shrink)

Questioning the ethical reasoning behind ways of attributing value to lives impacts philosophical dilemmas encountered in policy making and innovation in AI. For instance, this sort of reasoning requires us to determine how self-driving cars should behave when encountering real-life dilemmas such as inevitably crashing into one person as opposed to a group of people. -/- This issue will be examined with the Rocks Case, a case of conflict of interest where all the relevant parties are strangers, and we can (...) either save one person or a group of five. The two courses of action which will be discussed in this paper are: 1) “Ought to Save the Many” (OSM) and 2) “Permitted to Save the Few” (PSF). -/- The position of PSF using a weighted lottery will be argued for, rather than acting according to utilitarian or contractualist OSM reasoning, on the grounds that it would give all persons involved a fair opportunity of survival. This is judged to be a more important criterion than merely maximising the number of people to rescue. (shrink)

A theory of what we should believe should include a theory of what we should believe when we are uncertain about what we should believe and/or uncertain about the factors that determine what we should believe. In this paper, I present a novel theory of what we should believe that gives normative externalists a way of responding to a suite of objections having to do with various kinds of error, ignorance, and uncertainty. This theory is inspired by recent work in (...) ethical theory in which non-consequentialists 'consequentialize' their theories and then use the tools of decision-theory to give us an account of what we ought (in some sense) to do when we're uncertain about what we ought (in some primary sense) to do. On my proposal, because what we ought to do is acquire knowledge and avoid ignorance, we ought to believe iff the probability of coming to know is sufficiently high. This view has a number of important virtues. Among them, it gives us a unified story about how defeaters defeat (a theory developed with Julien Dutant), explains puzzling intuitions about the differences between lottery cases, preface cases, and cases of perceptual knowledge, and provides externalists (and internalists!) with a general framework for thinking about subjective normativity. It's also relatively brief. (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)

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)

This dissertation is a contribution to formal and computational philosophy. -/- In the first part, we show that by exploiting the parallels between large, yet finite lotteries on the one hand and countably infinite lotteries on the other, we gain insights in the foundations of probability theory as well as in epistemology. Case 1: Infinite lotteries. We discuss how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. The solution boils down to the (...) introduction of infinitesimal probability values, which can be achieved using non-standard analysis. Our solution can be generalized to uncountable sample spaces, giving rise to a Non-Archimedean Probability (NAP) theory. Case 2: Large but finite lotteries. 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’. -/- The second part presents a case study in social epistemology. We model a group of agents who update their opinions by averaging the opinions of other agents. Our main goal is to calculate the probability for an agent to end up in an inconsistent belief state due to updating. To that end, an analytical expression is given and evaluated numerically, both exactly and using statistical sampling. The probability of ending up in an inconsistent belief state turns out to be always smaller than 2%. (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)

The idea that knowledge can be extended by inference from what is known seems highly plausible. Yet, as shown by familiar preface paradox and lottery-type cases, the possibility of aggregating uncertainty casts doubt on its tenability. We show that these considerations go much further than previously recognized and significantly restrict the kinds of closure ordinary theories of knowledge can endorse. Meeting the challenge of uncertainty aggregation requires either the restriction of knowledge-extending inferences to single premises, or eliminating epistemic (...) uncertainty in known premises. The first strategy, while effective, retains little of the original idea—conclusions even of modus ponens inferences from known premises are not always known. We then look at the second strategy, inspecting the most elaborate and promising attempt to secure the epistemic role of basic inferences, namely Timothy Williamson’s safety theory of knowledge. We argue that while it indeed has the merit of allowing basic inferences such as modus ponens to extend knowledge, Williamson’s theory faces formidable difficulties. These difficulties, moreover, arise from the very feature responsible for its virtue- the infallibilism of knowledge. (shrink)

Harman’s lottery paradox, generalized by Vogel to a number of other cases, involves a curious pattern of intuitive knowledge ascriptions: certain propositions seem easier to know than various higher-probability propositions that are recognized to follow from them. For example, it seems easier to judge that someone knows his car is now on Avenue A, where he parked it an hour ago, than to judge that he knows that it is not the case that his car has been stolen (...) and driven away in the last hour. Contextualists have taken this pattern of intuitions as evidence that ‘knows’ does not always denote the same relationship; subject-sensitive invariantists have taken this pattern of intuitions as evidence that non-traditional factors such as practical interests figure in knowledge; still others have argued that the Harman Vogel pattern gives us a reason to abandon the principle that knowledge is closed under known entailment. This paper argues that there is a psychological explanation of the strange pattern of intuitions, grounded in the manner in which we shift between an automatic or heuristic mode of judgment and a controlled or systematic mode. Understanding the psychology behind the pattern of intuitions enables us to see that the pattern gives us no reason to abandon traditional intellectualist invariantism. The psychological account of the paradox also yields new resources for clarifying and defending the single premise closure principle for knowledge ascriptions. (shrink)

Most philosophers recognize that sometimes particular individuals have to be grateful to others who have benefited them in a way that provides reasons for treating them in a differential way. In the same way, I argue, there are cases in which society as such benefits from the actions of a person, which gives rise to collective duties of gratitude that must be expressed at the political and socio-economic levels. The political concern about merit should not be merely instrumental, but (...) also moral: a society cannot be just if it disregards its collective duties of gratitude. I criticize Rawls’ famous Natural Lottery Argument showing that it relies on a problematic understanding of the notion of moral responsibility and develop some considerations on the role that gratitude should play when designing both public institutions and policies. (shrink)

There is much to like about the idea that justification should be understood in terms of normality or normic support (Smith 2016, Goodman and Salow 2018). The view does a nice job explaining why we should think that lottery beliefs differ in justificatory status from mundane perceptual or testimonial beliefs. And it seems to do that in a way that is friendly to a broadly internalist approach to justification. In spite of its attractions, we think that the normic support (...) view faces two serious challenges. The first is that it delivers the wrong result in preface cases. These cases suggest that the view is either too sceptical or too externalist. The second is that the view struggles with certain kinds of Moorean absurdities. It turns out that these problems can easily be avoided. If we think of normality as a condition on *knowledge*, we can characterise justification in terms of its connection to knowledge and thereby avoid the difficulties discussed here. The resulting view does an equally good job explaining why we should think that our perceptual and testimonial beliefs are justified when lottery beliefs cannot be. Thus, it seems that little could be lost and much could be gained by revising the proposal and adopting a view on which it is knowledge, not justification, that depends directly upon normality. (shrink)

It is one thing to hold that merely statistical evidence is _sometimes_ insufficient for rational belief, as in typical lottery and profiling cases. It is another thing to hold that merely statistical evidence is _always_ insufficient for rational belief. Indeed, there are cases where statistical evidence plainly does justify belief. This project develops a dispositional account of the normativity of statistical evidence, where the dispositions that ground justifying statistical evidence are connected to the goals (= proper function) (...) of objects. There are strong intuitive motivations for doing this. For we can turn almost any case of _non-justifying_ merely statistical evidence into a case of _justifying_ merely statistical evidence by adding information about the dispositions and goals of the objects involved. The resulting view not only helps us understand when and why merely statistical evidence is normatively significant, but it also helps us understand how statistical evidence relates to more standard forms of evidence (perceptual, testimonial). The emerging view also has surprising applications, as it imposes limitations on the epistemic value of fine-tuning arguments for theism as well as undermines a standard class of case-based arguments for moral encroachment. (shrink)

In order to perform certain actions – such as incarcerating a person or revoking parental rights – the state must establish certain facts to a particular standard of proof. These standards – such as preponderance of evidence and beyond reasonable doubt – are often interpreted as likelihoods or epistemic confidences. Many theorists construe them numerically; beyond reasonable doubt, for example, is often construed as 90 to 95% confidence in the guilt of the defendant. -/- A family of influential cases (...) suggests standards of proof should not be interpreted numerically. These ‘proof paradoxes’ illustrate that purely statistical evidence can warrant high credence in a disputed fact without satisfying the relevant legal standard. In this essay I evaluate three influential attempts to explain why merely statistical evidence cannot satisfy legal standards. (shrink)

ABSTRACT Drawing inspiration from Fred Dretske, L. S. Carrier, John A. Barker, and Robert Nozick, we develop a tracking analysis of knowing according to which a true belief constitutes knowledge if and only if it is based on reasons that are sensitive to the fact that makes it true, that is, reasons that wouldn’t obtain if the belief weren’t true. We show that our sensitivity analysis handles numerous Gettier-type cases and lottery problems, blocks pathways leading to skepticism, and (...) validates the epistemic closure thesis that correct inferences from known premises yield knowledge of the conclusions. We discuss the plausible views of Ted Warfield and Branden Fitelson regarding cases of knowledge acquired via inference from false premises, and we show how our sensitivity analysis can account for such cases. We present arguments designed to discredit putative counterexamples to sensitivity analyses recently proffered by Tristan Haze, John Williams and Neil Sinhababu, which involve true statements made by untrustworthy informants and strange clocks that sometimes display the correct time while running backwards. Finally, we show that in virtue of employing the paradox-free subjunctive conditionals codified by Relevance Logic theorists instead of the paradox-laden subjunctive conditionals codified by Robert Stalnaker and David Lewis. (shrink)

Waiting time is widely used in health and social policy to make resource allocation decisions, yet no general account of the moral significance of waiting time exists. We provide such an account. We argue that waiting time is not intrinsically morally significant, and that the first person in a queue for a resource does not ipso facto have a right to receive that resource first. However, waiting time can and sometimes should play a role in justifying allocation decisions. First, there (...) is a duty of fairness prohibiting line-cutting where a sufficiently just queue exists. Second, waiting time has several morally attractive features that can justify its incorporation into allocation schemes. Where candidates are in relevantly similar circumstances, allocating by waiting time is relatively efficient, maximizes distribution equality relative to other Pareto efficient distributions, and treats candidates fairly. The claim that allocation using waiting time is fair is controversial. Some have claimed that formal lotteries are a fairer way to select among equal beneficiaries. We argue that lotteries are no fairer than allocation based on waiting time when it is equiprobable how a prospective queue will be ordered. In practice, lotteries share many of the disadvantages of queues; which is fairer will depend on contingent features of the allocation scenario. The upshot is that first-come, first-served is in fact a just way to allocate resources in many of the cases where it seems pre-theoretically compelling, and waiting time has unique normative properties which frequently justify its incorporation into resource allocation schemes. (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)

How does evidence figure into the reasoning of an agent? This is an intricate philosophical problem but also one we all encounter in our daily lives. In this chapter, we identify the problem and outline a possible solution to it. The problem arises, because the fact that it is up to us whether we do something makes a difference to how we should think of the evidence concerning whether we will actually do it. Otherwise we regard something that is up (...) to us as if it were not: We regard something that is up to us as if it were the outcome of a lottery. Nonetheless, we would be wrong to ignore the evidence. Otherwise we could not make a rational decision. In this chapter, we first show that a decision-theoretic approach to this problem cannot succeed. This approach does not explain how we can take evidence into account in practical reasoning without making predictions concerning matters that are up to us. It also gives rise to incoherence between our practical and our theoretical conclusions. We then argue that what is required to solve the problem is recognizing that beliefs about matters that are up to us can be grounded in practical reasoning. We argue that such beliefs are not subject to an evidential norm, because they are not meant to reflect a reality that is independent of them but instead are meant to bring about the reality they represent. Finally, we argue that, even if we are fully rational agents, we will sometimes lack practical knowledge of what we will do. That is because when it is practically rational to do something that will require resolve, we may be in a position to rationally conclude that we will do it, even though we have evidence that there is a non-negligible chance that we won’t. In such cases, our evidence serves as a defeater for our practical knowledge. (shrink)

A theory of rational belief should get the cases right. It should also reach its verdicts using the right theoretical assumptions. Leading theories seem to predict the wrong things. With only one exception, they don't accommodate principles that we should use to explain these verdicts. We offer a theory of rational belief that combines an attractive picture of epistemic desirability with plausible principles connecting desirability to rationality. On our view, it's rational to believe when it's sufficiently likely that you'd (...) know because believing when it's sufficiently likely that you'd know minimises expected objective epistemic undesirability. (shrink)

We argue that the ethical case for instituting vaccine benefit programs is justified by 2 widely recognized values: (1) reducing overall harm from COVID-19 and (2) protecting disadvantaged individuals. We then explain why they do not coerce, exploit, wrongfully distort decision-making, corrupt vaccination's moral significance, wrong those who have already been vaccinated, or destroy willingness to become vaccinated. However, their cost impacts and their effects on public perception of vaccines should be evaluated.

Suppose we can save either a larger group of persons or a distinct, smaller group from some harm. Many people think that, all else equal, we ought to save the greater number. This article defends this view (with qualifications). But unlike earlier theories, it does not rely on the idea that several people's interests or claims receive greater aggregate weight. The argument starts from the idea that due to their stakes, the affected people have claims to have a say in (...) the rescue decision. As rescuers, our primary duty is to respect these procedural claims, which we must do by doing what these people would decide, in a process where each is given an equal vote on the matter. So in cases where each votes in their own self-interest, respect for their equal right to decide, or their autonomy, will lead us to save the greater number. The argument is explained in detail, with special attention to the questions of how, exactly, it avoids aggregation, and of why majority rule is superior to lottery procedures. The view has further advantages. Especially, it explains the “partial” relevance of numbers in cases involving unequal harms, and it does so in a way that dissolves the appearance of paradox that besets theories of “partial aggregation.”. (shrink)

An influential proposal is that knowledge involves safe belief. A belief is safe, in the relevant sense, just in case it is true in nearby metaphysically possible worlds. In this paper, I introduce a distinct but complementary notion of safety, understood in terms of epistemically possible worlds. The main aim, in doing so, is to add to the epistemologist’s tool-kit. To demonstrate the usefulness of the tool, I use it to advance and assess substantive proposals concerning knowledge and justification.

John Broome has proposed a theory of fairness according to which fairness requires that agents’ claims to goods be satisfied in proportion to the relative strength of those claims. In the case of competing claims for a single indivisible good, Broome argues that what fairness requires is the use of a weighted lottery as a surrogate to satisfying the competing claims: the relative chance of each claimant's winning the lottery should be set to the relative strength of each (...) claimant's claim. In this journal, James Kirkpatrick and Nick Eastwood have objected that the use of weighted lotteries in the case of indivisible goods is unacceptable. In this article, I explain why Kirkpatrick and Eastwood's objection misses its mark. (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)

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)

It is argued that two observers with the same information may rightly disagree about the probability of an event that they are both observing. This is a correct way of describing the view of a lottery outcome from the perspective of a winner and from the perspective of an observer not connected with the winner - the outcome is improbable for the winner and not improbable for the unconnected observer. This claim is both argued for and extended by developing (...) a case in which a probabilistic inference is supported for one observer and not for another, though they relevantly differ only in perspective, not in any information that they have. It is pointed out, finally, that all probabilities are in this way dependent on perspective. (shrink)

People sometimes knowingly undermine the achievement of their own goals by, e.g., playing the lottery or borrowing from loan sharks. Are these agents acting irrationally? The standard answer is “yes.” But, in a recent award-winning paper, Jennifer Morton argues “no.” On her view, the norms of practical reasoning an agent ought to follow depend on that agent’s resource context (roughly, how rich or poor they are). If Morton is correct, the orthodox view that the same norms of practical rationality (...) apply to all agents needs revision. I argue that Morton’s arguments fail on empirical and philosophical grounds. What’s at stake? If Morton is correct, poverty relief agencies ought to re-design their incentives so resource-scarce agents can rationally respond to them. If I’m correct, resource-scarce agents do act irrationally in the cases under discussion, and we shouldn’t be shy about saying so. Instead of declaring them rational, we should try to understand the causes of their irrational behavior and help them better succeed by their own lights. (shrink)

This work develops a philosophically credible and psychologically realisable account of control that is necessary for moral responsibility. We live, think, and act in an environment of subjective uncertainty and limited information. As a result, our decisions and actions are influenced by factors beyond our control. Our ability to act freely is restricted by uncertainty, ignorance, and luck. Through three articles, I develop a naturalistic theory of control for action as a process of error minimisation that extends over time. Thus (...) conceived, control can serve to minimise the influence of luck on action and enable freedom in uncertainty. -/- In Article 1, Thor Grünbaum and I argue for a psychologically plausible account of the kind of control that is necessary for moral responsibility. We begin by establishing the relationship between agentive contribution and responsibility-level control. One way to determine whether one the right kind and degree of control to be morally responsible is to track one’s degree of contribution to an action. However, a psychologically plausible account of control in terms of agentive contribution may seem to contradict the types of functional-mechanistic explanations used in cognitive science. In cognitive psychology and cognitive neuroscience, personal-level capacities are explained by a set of sub-personal mechanisms. Often, such explanations leave no room for a contribution by the agent. By integrating insights from theories of cognitive control and incorporating them into a philosophical account of intentions, we propose a way of thinking about the distribution of cognitive control resources as something the agent does. -/- Article 2 argues that a classic argument concerning luck, originally aimed at libertarianism, generalises beyond any specific theory of free will, and regardless of whether determinism or indeterminism is true. I call this mental luck. Because we all make decisions under conditions of relative uncertainty and limited information, it is possible for an agent to make decisions that are contrary to their own motivation. In such situations, it may be a matter of luck whether the agent makes the right decision. Mentally lucky decisions are not rationally governed by attitudes within the agent's perspective, and thus, may be indistinguishable from unlucky ones. From the perspective of the agent, such decisions may resemble the outcome of a lottery. Therefore, mental luck poses a challenge to most prominent theories of free action and moral responsibility. -/- Finally, article 3 engages with the issue of resultant luck, namely luck in how things turn out. Resultant luck raises a challenge for theories of moral responsibility because its existence suggests that one may be responsible for factors beyond one’s control. Prominent responses to resultant luck led to a choice between internalism and scepticism. I argue that familiar cases of resultant luck are based on the assumption that actions are events. Instead, I propose an alternative ontology of action as an ongoing goal-directed process with a many-shots structure. Described this way, cases of resultant luck are not representative of ordinary action. The proposal of action as a many-shots process is consistent with predictive coding, a cognitive architecture which centres around error minimisation. Under this framework, cases of resultant more luck are no longer failures of action, but rather anticipated errors to be settled within the ordinary process of action. (shrink)

We consider a basic logic with two primitive uni-modal operators: one for certainty and the other for plausibility. The former is assumed to be a normal operator, while the latter is merely a classical operator. We then define belief, interpreted as “maximally plausible possibility”, in terms of these two notions: the agent believes \ if she cannot rule out \ ), she judges \ to be plausible and she does not judge \ to be plausible. We consider four interaction properties (...) between certainty and plausibility and study how these properties translate into properties of belief. We then prove that all the logics considered are minimal logics for the highlighted theorems. We also consider a number of possible interpretations of plausibility, identify the corresponding logics and show that some notions considered in the literature are special cases of our framework. (shrink)

The lottery and preface paradoxes pose puzzles in epistemology concerning how to think about the norms of reasonable or permissible belief. Contextualists in epistemology have focused on knowledge ascriptions, attempting to capture a set of judgments about knowledge ascriptions and denials in a variety of contexts (including those involving lottery beliefs and the principles of closure). This article surveys some contextualist approaches to handling issues raised by the lottery and preface, while also considering some of the difficulties (...) encountered by those approaches. (shrink)

Abstract: Lotteries have long been a source of fascination and intrigue, offering the tantalizing prospect of unexpected fortunes. In this research paper, we delve into the world of lottery predictions, employing cutting-edge AI techniques to unlock the secrets of lottery outcomes. Our dataset, obtained from Kaggle, comprises historical lottery draws, and our goal is to develop predictive models that can anticipate future winning numbers. This study explores the use of deep learning and time series analysis to achieve (...) this elusive feat. Through rigorous experimentation and data-driven approaches, we seek to determine the viability of AI in the realm of lottery predictions. Our findings reveal both the promise and limitations of AI in this context, shedding light on the complexities of lottery data and the potential need for quantum computing as a last resort. (shrink)

To resolve the lottery paradox, the “no-justification account” proposes that one is not justified in believing that one's lottery ticket is a loser. The no-justification account commits to what I call “the Harman-style skepticism”. In reply, proponents of the no-justification account typically downplay the Harman-style skepticism. In this paper, I argue that the no-justification reply to the Harman-style skepticism is untenable. Moreover, I argue that the no-justification account is epistemically ad hoc. My arguments are based on a rather (...) surprising finding that the no-justification account implies that people living in Taiwan typically suffer from the Harman-style skepticism. (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)

This article discusses how the concept of a fair finite lottery can best be extended to denumerably infinite lotteries. Techniques and ideas from non-standard analysis are brought to bear on the problem.

Shortages of new therapeutics to treat coronavirus disease (COVID-19) have forced clinicians, public health officials, and health systems to grapple with difficult questions about how to fairly allocate potentially life-saving treatments when there are not enough for all patients in need (1). Shortages have occurred with remdesivir, tocilizumab, monoclonal antibodies, and the oral antiviral Paxlovid (2) -/- Ensuring equitable allocation is especially important in light of the disproportionate burden experienced during the COVID-19 pandemic by disadvantaged groups, including Black, Hispanic/Latino and (...) Indigenous communities, individuals with certain disabilities, and low-income persons. However, many health systems have resorted to first-come, first-served approaches to allocation, which tend to disadvantage individuals with barriers in access to care (3). There is mounting evidence of racial, ethnic, and socioeconomic disparities in access to medications for COVID-19 (4, 5). -/- One potential method to promote equitable allocation is to use a weighted lottery, which is an allocation strategy that gives all eligible patients a chance to receive the scarce treatment while also allowing the assignment of higher or lower chances according to other ethical considerations (6). We sought to assess the feasibility of implementing a weighted lottery to allocate scarce COVID-19 medications in a large U.S. health system and to determine whether the weighted lottery promotes equitable allocation. (shrink)

In some lottery situations, the probability that your ticket's a loser can get very close to 1. Suppose, for instance, that yours is one of 20 million tickets, only one of which is a winner. Still, it seems that (1) You don't know yours is a loser and (2) You're in no position to flat-out assert that your ticket is a loser. "It's probably a loser," "It's all but certain that it's a loser," or even, "It's quite certain that (...) it's a loser" seem quite alright to say, but, it seems, you're in no position to declare simply, "It's a loser." (1) and (2) are closely related phenomena. In fact, I'll take it as a working hypothesis that the reason "It's a loser" is unassertable is that (a) You don't seem to know that your ticket's a loser, and (b) In flat-out asserting some proposition, you represent yourself as knowing it.1 This working hypothesis will enable me to address these two phenomena together, moving back and forth freely between them. I leave it to those who reject the hypothesis to sort out those considerations which properly apply to the issue of knowledge from those germane to that of assertability. Things are quite different when you report the results of last night's basketball game. Suppose your only source is your morning newspaper, which did not carry a story about the 1 game, but simply listed the score, "Knicks 83, at Bulls 95," under "Yesterday's Results." Now, it doesn't happen very frequently, but, as we all should suspect, newspapers do misreport scores from time to time. On several occasions, my paper has transposed a result, attributing to each team the score of its opponent. In fact, that your paper's got the present result wrong seems quite a bit more probable than that you've won the lottery of the above paragraph. Still, when asked, "Did the Bulls win yesterday?", "Probably" and "In all likelihood" seem quite unnecessary. "Yes, they did," seems just fine.. (shrink)

According to the epistemic account of request normativity, a request gives us reasons by revealing normatively relevant information. The information is normative, not the request itself. I raise a new objection to the epistemic account based on situations where we might try to avoid someone requesting something of us. The best explanation of these situations seems to be that we do not want to acquire a new reason to do something. For example, if you know I am going to ask (...) you to read a draft of my paper, you might avoid running into me so as to avoid acquiring a reason to read a draft of my paper. I then argue that the epistemic account can successfully reply to this objection and that in fact the epistemic account does a better job of accounting for cases like this than competing views of the normativity of requests. (shrink)