Duncan Pritchard's version of the safety analysis of knowledge has it that for all contingent propositions, p, S knows that p iff S believes that p, p is true, and (the “safety principle”) in most nearby worlds in which S forms his belief in the same way as in the actual world, S believes that p only if p is true. Among the other virtues claimed by Pritchard for this view is its supposed ability to solve a version of the (...) lottery puzzle. In this paper, I argue that the safety analysis of knowledge in fact fails to solve the lottery puzzle. I also argue that a revised version of the safety principle recently put forward by Pritchard fares no better. (shrink)

The lottery puzzle can elicit strong intuitions in favour of skepticism, according to which we ordinary language-users speak falsely about knowledge with shocking regularity. Various contextualist and invariantist responses to the puzzle attempt to avoid this unwelcome result and preserve the competence of ordinary speakers. I will argue that these solutions can be successful only if they respect intuitions of a certain kind, and proceed to judge competing solutions by this criterion.

The safety analysis of knowledge, due to Duncan Pritchard, has it that for all contingent propositions, p, S knows that p iff S believes that p, p is true, and (the “safety principle”) in most nearby worlds in which S forms his belief in the same way as in the actual world, S believes that p only if p is true. Among the other virtues claimed by Pritchard for this view is its supposed ability to solve a version of the (...) lottery puzzle. In this paper, I argue that the safety analysis of knowledge in fact fails to solve the lottery puzzle. I also argue that a revised version of the safety principle recently put forward by Pritchard fares no better. (shrink)

In the first chapter of his Knowledge and Lotteries, John Hawthorne argues that thinkers do not ordinarily know lottery propositions. His arguments depend on claims about the intimate connections between knowledge and assertion, epistemic possibility, practical reasoning, and theoretical reasoning. In this paper, we cast doubt on the proposed connections. We also put forward an alternative picture of belief and reasoning. In particular, we argue that assertion is governed by a Gricean constraint that makes no reference to knowledge, and (...) that practical reasoning has more to do with rational degrees of belief than with states of knowledge. (shrink)

The safety analysis of knowledge, due to Duncan Pritchard, has it that for all contingent propositions, p, S knows that p iff S believes that p, p is true, and (the “safety principle”) in most nearby worlds in which S forms his belief in the same way as in the actual world, S believes that p only if p is true. Among the other virtues claimed by Pritchard for this view is its supposed ability to solve a version of the (...) lottery puzzle. In this paper, I argue that the safety analysis of knowledge in fact fails to solve the lottery puzzle. I also argue that a revised version of the safety principle recently put forward by Pritchard fares no better. (shrink)

The safety analysis of knowledge, due to Duncan Pritchard, has it that for all contingent propositions, p, S knows that p iff S believes that p, p is true, and (the “safety principle”) in most nearby worlds in which S forms his belief in the same way as in the actual world, S believes that p only if p is true. Among the other virtues claimed by Pritchard for this view is its supposed ability to solve a version of the (...) lottery puzzle. In this paper, I argue that the safety analysis of knowledge in fact fails to solve the lottery puzzle. I also argue that a revised version of the safety principle recently put forward by Pritchard fares no better. (shrink)

In this article, I discuss three distinct but related puzzles involving lotteries: Kyburg’s lottery paradox, the statistical evidence problem, and the Harman-Vogel paradox. Kyburg’s lottery paradox is the following well-known problem: if we identify rational outright belief with a rational credence above a threshold, we seem to be forced to admit either that one can have inconsistent rational beliefs, or that one cannot rationally believe anything one is not certain of. The statistical evidence problem arises from the observation (...) that people seem to resist forming outright beliefs whenever the available evidence for the claim under consideration is purely statistical. We need explanations of whether it is in fact irrational to form such beliefs, and of whether a clear distinction can be drawn between statistical and non-statistical evidence. The Harman-Vogel paradox is usually presented as a paradox about knowledge: we tend to assume that we can know so-called ordinary propositions, such as the claim that I will be in Barcelona next spring. Yet, we hesitate to make knowledge claims regarding so-called lottery propositions, such as the claim that I won’t die in a car crash in the next few months, even if these lottery propositions are obviously entailed by the ordinary propositions we claim to know. Depending on one’s view about the relationship between rational belief and knowledge, the Harman-Vogel paradox has ramifications for a theory of rational outright belief. Formal theories of the relationship between rational credence and rational belief, such as Leitgeb’s stability theory, tend to focus mostly on handling Kyburg’s lottery paradox, but not the other two puzzles I mention. My aim in this article is to draw out relationships and differences between the puzzles, and to examine to what extent existing formal solutions to Kyburg’s lottery paradox help with answering the statistical evidence problem and the Harman-Vogel paradox. (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.

Knowledge and Lotteries is organized around an epistemological puzzle: in many cases, we seem consistently inclined to deny that we know a certain class of propositions, while crediting ourselves with knowledge of propositions that imply them. In its starkest form, the puzzle is this: we do not think we know that a given lottery ticket will be a loser, yet we normally count ourselves as knowing all sorts of ordinary things that entail that its holder will not (...) suddenly acquire a large fortune. After providing a number of specific and general characterizations of the puzzle, Hawthorne carefully examines the competing merits of candidate solutions. In so doing, he explores a number of central questions concerning the nature and importance of knowledge, including the relationship of knowledge to assertion and practical reasoning, the status of epistemic closure principles, the merits of various brands of scepticism, the prospects for a contextualist account of knowledge, and the potential for other sorts of salience-sensitive accounts. Along the way, he offers a careful treatment of pertinent issues at the foundations of semantics. His book will be of interest to anyone working in the field of epistemology, as well as to philosophers of language. (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)

Lottery puzzles involve an ordinary piece of knowledge which seems to imply knowledge of a so-called “lottery proposition,” which itself seems unknown: I might be said to know that I won’t be going on safari next year. But if I were to win the lottery, I would go, and I don’t know that I won’t win the lottery. Examples can be multiplied. Thus we seem left either with the paradoxical position of knowing certain ordinary propositions, but (...) failing to know the lottery propositions they imply, or else conceding to the skeptic. I present a version of reliabilism according to which empirical knowledge is true belief produced by a reliable process causally connecting belief and fact. According to this theory, if my ordinary belief and my belief in the lottery proposition are suitably connected to the facts that render them true, both count as knowledge. In cases where my ordinary belief and my belief in the lottery proposition are not suitably connected to the relevant facts, neither count as knowledge. Thus the paradoxical air of lottery puzzles is removed, and skepticism is avoided. (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)

I seem to know that I won't experience spaceflight but also that if I win the lottery, then I will take a flight into space. Suppose I competently deduce from these propositions that I won't win the lottery. Competent deduction from known premises seems to yield knowledge of the deduced conclusion. So it seems that I know that I won't win the lottery; but it also seems clear that I don't know this, despite the minuscule probability of (...) my winning (if I have a lottery ticket). So we have a puzzle. It seems to generalize, for analogues of the lottery-proposition threaten almost all ordinary knowledge attributions. For example, my apparent knowledge that my bike is parked outside seems threatened by the possibility that it's been stolen since I parked it, a proposition with a low but non-zero probability; and it seems that I don't know this proposition to be false. Familiar solutions to this family of puzzles incur unacceptable costs—either by rejecting deductive closure for knowledge, or by yielding untenable consequences for ordinary attributions of knowledge or of ignorance. After canvassing and criticizing these solutions, I offer a new solution free of these costs. Knowledge that p requires an explanatory link between the fact that p and the belief that p. This necessary but insufficient condition on knowledge distinguishes actual lottery cases from typical, apparently analogous ‘quasi-lottery’ cases. It does yield scepticism about my not winning the lottery and not experiencing spaceflight, but the scepticism doesn't generalize to quasi-lottery cases such as that involving my bike. (shrink)

How is it that a speaker _S_ can at once make it obvious to an audience _A_ that she intends to communicate some proposition _p_, and yet at the same time retain plausible deniability with respect to this intention? The answer is that _S_ can bring it about that _A_ has a high justified credence that ‘_S_ intended _p_’ without putting _A_ in a position to know that ‘_S_ intended _p_’. In order to achieve this _S_ has to exploit a (...) sense in which communication can be lottery-like. After defending this view of deniability I argue that it compares favorably to a rival account recently developed by Dinges and Zakkou (Mind, https://doi.org/10.1093/mind/fzac056, 2023 ). (shrink)

John Hawthorne’s recent monograph Knowledge and Lotteries1 is centred on the following puzzle: Suppose you claim to know that you will not be able to afford to summer in the Hamptons next year. Aware of your modest means, we believe you. But suppose you also claim to know that a ticket you recently purchased in a multi-million dollar lottery is a loser. Most of us have the intuition that you do not know that your ticket is a loser. (...) However, your alleged knowledge of not being able to afford to summer in the Hamptons puts you in a position to know that your ticket is a loser. For the proposition that you will not be able to afford to summer in the Hamptons entails the proposition that you will lose the lottery. And the following principle, what Hawthorne calls ‘Single Premise Closure’ ( p. 34), is very plausible: If you know that p, p entails q, and you competently deduce q from p thereby coming to believe that q (all the while retaining your knowledge of p), then you come to know q. (shrink)

This paper revisits a puzzle that arises for theories of knowledge according to which one can know on the basis of merely inductive grounds. No matter how strong such theories require inductive grounds to be if a belief based on them is to qualify as knowledge, there are certain beliefs that are based on even stronger inductive grounds, while, intuitively, they do not qualify as knowledge. This paper discusses what is often regardedas the most promising classical invariantist solution to (...) the puzzle, namely, that beliefs about the outcomes of fair lotteries do not qualify as knowledge because they are too lucky to do so, while other beliefs based on potentially weaker inductive grounds are not too lucky. A case is presented that shows that this solution to the puzzle is actually not viable. It is argued that there is no obvious alternative solution in sight and that therefore the puzzle still awaits a classical invariantist solution. (shrink)

This paper revisits a puzzle that arises for theories of knowledge according to which one can know on the basis of merely inductive grounds. No matter how strong such theories require inductive grounds to be if a belief based on them is to qualify as knowledge, there are certain beliefs (namely, about the outcome of fair lotteries) that are based on even stronger inductive grounds, while, intuitively, they do not qualify as knowledge. This paper discusses what is often regarded (...) as the most promising classical invariantist solution to the puzzle, namely, that beliefs about the outcomes of fair lotteries do not qualify as knowledge because they are too lucky to do so (or, relatedly, because they do not satisfy a safety condition on knowledge), while other beliefs based on potentially weaker inductive grounds are not too lucky (or, relatedly, because they are safe). A case is presented that shows that this solution to the puzzle is actually not viable. It is argued that there is no obvious alternative solution in sight and that therefore the puzzle still awaits a classical invariantist solution. (shrink)

This chapter examines the advantages and disadvantages of contextualism, and its application to the puzzle. Contextualism offers a compelling solution to puzzle. The contextualist allows that ordinary knowledge ascriptions often come out true, and allows the ordinary claims to the effect that lottery propositions are not known can also come true. He explains away the apparent threat to closure provided by the original puzzles. The resolution of conflicting intuitions is prima facie and extremely compelling.

This chapter introduces the epistemological puzzle to be examined in this volume. In essence, the puzzle consists of a tension between various ordinary claims to know and our apparent incapacity to know whether or not someone will lose a lottery. It discusses why we are inclined to think that lottery propositions are unknowable. These unknowable intuitions are linked to other intuitions concerning our assertoric and deliberative dispositions with regard to lottery propositions. It then discusses the (...) epistemic closure, which is vital to the force of the puzzle. (shrink)

"This talk of holding back in the face of strong temptation brings me to the climax of this column: the announcement of a Luring Lottery open to all readers and nonreaders of Scientific American. The prize of this lottery is $ 1,000,000/N, where N is the number of entries submitted. Just think: if you are the only entrant (and if you submit only one entry), a cool million is yours! Perhaps, though, you doubt this will come about. It (...) does seem a trifle iffy. If you'd like to increase your chances of winning, you are encouraged to send in multiple entries without limit. Just send in one postcard per entry. If you send in 100 entries, you'll have 100 times the chance of some poor slob who sends in just one. Come to think of it, why should you have to send in multiple entries separately? Just send one postcard with your name and address and a positive integer (telling how many entries you're making) to. (shrink)

Presents an additional one hundred philosophical puzzles that encourage readers to seek their own conclusions about a broad spectrum of moral, social, and personal issues.

Au xviiie siècle, la figure insistante de la «femme philosophe» s'articule à un imaginaire ambivalent de la différence des sexes, entre hantise d'une confusion délétère et quête d'un modèle d'harmonie. La femme travestit-elle la philosophie? Les Lumières ont-elles un genre?

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)

Arguments from "easy knowledge" are meant to refute a class of epistemological views, including foundationalism about perceptual knowledge. I present arguments from easy knowledge in their strongest form, and explain why other formulations in the literature are inferior. I criticize two features of Stewart Cohen's presentation, namely his focus on knowing that one's faculties are reliable, and his use of a Williamson-style closure principle. Rather, the issue around easy knowledge must be understood using a notion of epistemic priority. Roger White's (...) presentation is contaminated by the so-called lottery puzzle, which is best kept separate. Distinguishing basic from non-basic visual contents limits the force of the examples discussed by Cohen, White, and Crispin Wright. Finally, I present a new strategy for resisting even the best-formulated arguments from easy knowledge. (shrink)

What is the epistemological structure of situations where many small risks amount to a large one? Lottery and preface paradoxes and puzzles about quantum-mechanical blips threaten the idea that competent deduction is a way of extending our knowledge. Seemingly, everyday knowledge involves small risks, and competently deducing the conjunction of many such truths from them yields a conclusion too risky to constitute knowledge. But the dilemma between scepticism and abandoning MPC is false. In extreme cases, objectively improbable truths are (...) known. Safety is modal, not probabilistic, in structure, with closure and factiveness conditions. It is modelled using closeness of worlds. Safety is analogous to knowledge. It suggests an interpretation of possible worlds semantics for epistemic logic. To avoid logical omniscience, a relation of epistemic counterparthood between formulas is introduced. This supports a safety conception of knowledge and formalizes how extending knowledge by deduction depends on logical competence. (shrink)

I examine two species of epistemic luck that I claim are not benign and explain how they feature in the main epistemological debates. The first species of epistemic luck—what I call ‘veritic’ luck—can be handled with a modest ‘relevant alternatives’ account of knowledge that is specifically defined so that it counters this type of epistemic luck. As I explain, such a theory is essentially a version of the safety-based neo-Moorean thesis that we looked at in Ch. 3. I develop this (...) view by considering some of the main examples that are discussed in epistemology—such as Gettier examples, the ‘lottery’ puzzle, and ‘barn façade’ examples—and show how the neo-Moorean account can in each case generate the right result. Along the way the formulation of this anti-veritic-luck thesis is refined in response to potential challenges that might be presented to the view. Significantly, however, the chapter closes by arguing that there is a second species of epistemic luck—what I call ‘reflective luck’-that is epistemically problematic and that is not dealt with by the neo-Moorean account. (shrink)

Replies are given to comments, questions, and objections to The Appearance of Ignorance. The reply to Robin McKenna focuses mainly on his questions of whether, with the skeptical argument I’m focused on, a strong enough appearance of ignorance is generated to require an account of that appearance, and whether, to the extent that we do need to account for that appearance, we might do so without contextualism by adopting a solution proposed by Ernest Sosa. The reply to Michael Blome-Tillman focuses (...) mainly on a counterexample he offers to my account of the operation of the “Rule of Sensitivity.” The reply to Elke Brendel focuses mainly on objections to contextualism from the phenomena of disagreement and retraction. The reply to Peter Baumann concerns several of his comments about my treatment of the Harman lottery puzzle. (shrink)

Replies are given to comments, questions, and objections to The Appearance of Ignorance. The reply to Robin McKenna focuses mainly on his questions of whether, with the skeptical argument I’m focused on, a strong enough appearance of ignorance is generated to require an account of that appearance, and whether, to the extent that we do need to account for that appearance, we might do so without contextualism by adopting a solution proposed by Ernest Sosa. The reply to Michael Blome-Tillman focuses (...) mainly on a counterexample he offers to my account of the operation of the “Rule of Sensitivity.” The reply to Elke Brendel focuses mainly on objections to contextualism from the phenomena of disagreement and retraction. The reply to Peter Baumann concerns several of his comments about my treatment of the Harman lottery puzzle. (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)

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)

Socrates' attitude towards falsehood is quite puzzling in the Republic. Although Socrates is clearly committed to truth, at several points he discusses the benefits of falsehood. This occurs most notably in Book 3 with the "noble lie" (414d-415c) and most disturbingly in Book 5 with the "rigged sexual lottery" (459d-460c). This raises the question: What kinds of falsehoods does Socrates think are beneficial, and what kinds of falsehoods does he think are harmful? And more broadly: What can this tell (...) us about the relationship between ethics and epistemology? The key to answering these questions lies in an obscure and paradoxical passage in Book II; at 382a-d Socrates distinguishes between "true falsehoods" and "impure lies." True falsehoods are always bad, but impure lies are sometimes beneficial. Despite Socrates' insistence that he is not saying anything deep, his distinction is far from straightforward. Nevertheless, in order to determine why some falsehoods are beneficial and why some are always harmful, we must understand what exactly true falsehoods are and how they differ from impure lies. In this paper, I argue that true falsehoods are a restricted class of false beliefs about ethics; they are false beliefs about how one should live and what one should pursue. I refer to these beliefs as "normative commitments." False normative commitments are always pernicious because they create and sustain psychological disharmony. Unlike true falsehoods, impure lies can be about anything. Nevertheless, they are only beneficial when they help produce and sustain true normative commitments. I argue that the upshot of this is that practical concerns have a kind of primacy over theoretical concerns. (shrink)

Many people believe that there is a Dutch Book argument establishing that the principle of countable additivity is a condition of coherence. De Finetti himself did not, but for reasons that are at first sight perplexing. I show that he rejected countable additivity, and hence the Dutch Book argument for it, because countable additivity conflicted with intuitive principles about the scope of authentic consistency constraints. These he often claimed were logical in nature, but he never attempted to relate this idea (...) to deductive logic and its own concept of consistency. This I do, showing that at one level the definitions of deductive and probabilistic consistency are identical, differing only in the nature of the constraints imposed. In the probabilistic case I believe that R.T. Cox's ‘scale-free’ axioms for subjective probability are the most suitable candidates. 1 Introduction 2 Coherence and Consistency 3 The Infinite Fair Lottery 4 The Puzzle Resolved—But Replaced by Another 5 Countable Additivity, Conglomerability and Dutch Books 6 The Probability Axioms and Cox's Theorem 7 Truth and Probability 8 Conclusion: ‘Logical Omniscience’ CiteULike Connotea Del.icio.us What's this? (shrink)

Paradoxes are more than just intellectual puzzles - they raise substantive philosophical issues and offer the promise of increased philosophical knowledge. In this introduction to paradox and paradoxes, Doris Olin shows how seductive paradoxes can be, why they confuse and confound, and why they continue to fascinate. Olin examines the nature of paradox, outlining a rigorous definition and providing a clear and incisive statement of what does and does not count as a resolution of a paradox. The view that a (...) statement can be both true and false, that contradictions can be true, is seen to provide a challenge to the account of paradox resolution, and is explored. With this framework in place, the book then turns to an in-depth treatment of the Prediction Paradox, versions of the Preface/Fallibility Paradox, the Lottery Paradox, Newcomb's Problem, the Prisoner's Dilemma and the Sorites Paradox. Each of these paradoxes is shown to have considerable philosophical punch. Olin unpacks the central arguments in a clear and systematic fashion, offers original analyses and solutions, and exposes further unsettling implications for some of our most deep-seated principles and convictions. (shrink)

Paradoxes are more than just intellectual puzzles - they raise substantive philosophical issues and offer the promise of increased philosophical knowledge. In this introduction to paradox and paradoxes, Doris Olin shows how seductive paradoxes can be, why they confuse and confound, and why they continue to fascinate. Olin examines the nature of paradox, outlining a rigorous definition and providing a clear and incisive statement of what does and does not count as a resolution of a paradox. The view that a (...) statement can be both true and false, that contradictions can be true, is seen to provide a challenge to the account of paradox resolution, and is explored. With this framework in place, the book then turns to an in-depth treatment of the Prediction Paradox, versions of the Preface/Fallibility Paradox, the Lottery Paradox, Newcomb's Problem, the Prisoner's Dilemma and the Sorites Paradox. Each of these paradoxes is shown to have considerable philosophical punch. Olin unpacks the central arguments in a clear and systematic fashion, offers original analyses and solutions, and exposes further unsettling implications for some of our most deep-seated principles and convictions. (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)

Conditionals that contain a modality in the consequent give rise to a particular semantic phenomenon whereby the antecedent of the conditional blocks possibilities when interpreting the modality in the consequent. This explains the puzzling logical behaviour of constructions like "If you don't buy a lottery ticket, you can't win", "If you eat that poison, it is unlikely that you will survive the day" and "If you kill Harry, you ought to kill him gently". In this paper it is argued (...) that a semantic version of the Ramsey Test provides a key in the analysis of such constructions. The logic for this semantics is axiomatized and some examples are studied, among them a well-known puzzle for contrary-to-duty obligations. (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)

I present an epistemological puzzle about perceptual knowledge and its relation to the evaluation of probabilities. It involves cases, concerning a given subject S and a proposition P in a determinate context, where apparently: S has perceptual knowledge of P; the epistemic justification S has for believing Not-P is much greater than her epistemic justification for believing P. If those two theses were true, the following very plausible epistemological principle would fail: If S knows P, then the epistemic justification (...) S has for believing Not-P is not greater than her epistemic justification for believing P. I offer a solution to the puzzle, which is compatible with basic intuitions and theses of orthodox Bayesianism. (shrink)

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.

This paper presents a new decision theory for modelling choice under risk. The new theory is a two-parameter generalization of expected utility theory. The proposed theory assumes that a decision maker: behaves as if maximizing expected utility; but may experience disappointment when the utility of a lottery’s outcome falls short of the expected utility of the lottery; and may have a preference for gambling. The proposed theory can rationalize the fourfold pattern of risk attitudes; the common ratio effect (...) and the reverse thereof ; the Allais paradox in classical common consequence problems and the reverse Allais paradox—in common consequence problems with an even split of a probability mass; violations of the betweenness axiom; switching behavior in the Samuelson’s example; violations of ordinal, upper and lower cumulative independence ; and preference reversals between valuations and choice. In application to insurance, the theory can rationalize full insurance with an actuarially unfair premium and aversion to probabilistic insurance. In application to optimal portfolio investment, the theory can rationalize the equity premium puzzle. (shrink)

Cet article est la traduction française de l’introduction du livre d’Ayelet Shachar, «The Puzzle of Birthright Citizenship», avec la permission de l’éditeur, tirée de The Birthright Lottery : Citizenship and Global Inequality, Cambridge, Mass.: Harvard University Press, pp.1-18. © 2009 President and Fellows of Harvard College. Traduction de Martin Provencher.This paper is the French translation of Ayelet Shachar’s introduction, «The Puzzle of Birthright Citizenship», digitally reproduced by permission of the publisher from The Birthright Lottery : Citizenship (...) and Global Inequality, Cambridge, Mass.: Harvard University Press, pp.1-18. © 2009 by the President and Fellows of Harvard College. Translation by Martin Provencher. (shrink)

The conjunction fallacy occurs whenever probability compounds are thought of as more likely than its component probabilities alone. In the experiment we present, subjects chose between simple and compound lotteries after some practice. Depending on the condition, they were given more or less information about the nature of probability compounds. The conjunction fallacy was surprisingly robust. There was, however, a puzzling dissociation between verbal and behavioral learning: verbal responses were sensitive, but actual choices entirely insensitive, to the amount of verbal (...) instructions being provided. This might reflect a dichotomy between implicit and explicit learning. Caution must be exercised in generalizing results from what people say to what people do. (shrink)

Crafted within a knowledge-first epistemological framework, Mona Simion’s engaging and wide-ranging work ensures that both the Knowledge Norm of Assertion (KNA) and Classical Invariantism (CI) can be part of a viable and productive research program.Dissatisfied with current strategies on offer in the literature, she successfully counters objections to the pair sourced in “shiftiness intuitions”—intuitions that seem to indicate that mere changes in practical context can impact the propriety of assertions and knowledge attributions. For example, in Keith DeRose’s famous pair of (...) low stakes versus high stakes bank cases, the consequences of Keith’s acting on The bank is open on Saturday if it were false change from trivial in low stakes to catastrophic in high stakes. We are to suppose that the proposition is true, and that Keith has access to the same quantity and quality of evidence for it in both cases. In low stakes, but not in high stakes, we are inclined to think that Keith can appropriately assert to his inquiring wife “The bank is open on Saturday.” In low stakes, Keith’s knowledge ascription “I know that the bank is open on Saturday” strikes us as aptly asserted and true. In high stakes only a knowledge denial on Keith’s part strikes us as aptly asserted and true.If we want to hang on to KNA, it looks like we will have to abandon CI and concede that ‘knows’ or knowledge is sensitive to changes in practical considerations. If we want to retain CI, we can try to say that, while Keith does still know that the bank is open on Saturday in high stakes, he does not have sufficient warrant to properly assert that it is. But such a move seems to run counter to KNA. We appear to be stuck in the Shiftiness Dilemma.Keen to get us out of the dilemma and to preserve the idea that epistemically good thinking and asserting are independent of practical concerns, Simion suggests a strategy that can also be used to protect other epistemic speech-act norms and notions from similar threats of practical shiftiness. She notes that having an impact on the degree of epistemic warrant required is not enough to make a norm an epistemic one. Fair enough. If I am given strong practical reason (a million dollars, or a gun to the head) not to adopt full belief until I have gathered more evidence, there is potentially some nonepistemic norm at work in the demand for further evidence. So it is a live possibility (indeed, a plausible one, as Simion would say) that our intuitions in the Shiftiness Dilemma are being misdescribed: they are tracking all-things-considered propriety of assertion, not epistemic propriety. In high stakes, practical norms override the epistemic norm KNA. Keith’s asserting “The bank is open on Saturday” would be epistemically proper but all-things-considered improper.Simion backs up her account with an etiological-function origin story and typology for the norms of assertion. Here is her characterization of etiological function for traits, artifacts, and actions. E-function.A token of type T has the e-function of type B of producing effect E in a system S iff (1) tokens of T produced E in the past, (2) producing E resulted in benefit of type B in S/S’s ancestors, and (3) producing E’s having B-benefited S’s ancestors contributes to the explanation of why T exists in S.In this schema, norms governing an action are typed by the functions or purposes of the action, which in turn are typed by the benefits the action delivers. The epistemic norm of assertion will be the one that characteristically and reliably enables participants in the practice of assertion to secure its primary epistemic good, which Simion identifies as knowledge (testimonial knowledge in hearers generated under normal conditions by the assertions of knowledgeable speakers). Moves in a practice either directly or indirectly aim at fulfilling the goal of the practice. Assertion is a move in the practice of inquiry, which has the generation of knowledge as its aim. Hence, Simion concludes, assertion aims at generating knowledge.This account helps to explain why, in cases like high stakes, Keith all-things-considered ought not to assert “The bank is open on Saturday,” even though he knows it is true. Prudential norms of assertion override the epistemic KNA, for when multiple functions come into conflict, the ones that are more important to the survival of the organism will generate weightier normative constraints.Simion then applies her account to the general category of constatives—for example, speech acts that express a speaker’s belief and the intention that the hearer form or continue to hold the like belief. Employing the taxonomy of Bach and Harnish, she argues that, as expressions of belief and hence varieties of assertion, constatives are subject to knowledge norms as well. Bach and Harnish identify fifteen different subcategories of constatives, each characterized in terms of the kind of belief and intention they express. The norms governing a species have to be at least as strong as the norms governing the corresponding type. As species of the type assertion, each subcategory, then, is subject to at least the necessary direction of KNA. Ultimately, we arrive at a knowledge norm for every speech act on the list, such as The Knowledge Norm of Conjecture (KNC):One’s conjecture that p is epistemically permissible only if one knows that there is reason, but not sufficient reason, to believe that p. Most of the proposed interpretations of various constatives are on the whole reasonable enough, though J. L. Austin would surely be unhappy to see so many different speech acts fashioned into varieties of assertion. Simion concludes with reflections on conjecturing, telling, and moral assertion.Construing the challenge of shiftiness intuitions in terms of the Shiftiness Dilemma allows Simion to declare success when the compatibility of KNA and CI with the relevant data of intuition is secured. Ensuring empirical adequacy for an explanatory framework is an important step, but pronouncements of victory by way of inference to the best explanation would be premature.Other candidates have been shown to match KNA’s familiar explanatory successes (involving lottery propositions, Moorean statements, etc.). Unlike KNA, alternatives that require only epistemically justified or rational belief or credence can allow that a subject is epistemically proper to assert what they believe when their belief is epistemically rational, even under conditions where there are defeating reasons that they are not in a position to be aware of. Furthermore, such norms seem better suited for philosophical or heated moral discussions where there is little consensus and individuals routinely fail to know that what they assert is true. Simion sounds the alarm that the Shiftiness Dilemma threatens to generalize “to epistemic normativity as a whole” (xi–xii), but norms concerning rational credence seem particularly immune.As Simion notes, the etiological-function model of norms that she proposes could be rebuilt with a different central epistemic aim at its core. Indeed, Millikan-inspired models along these lines are appealed to in other areas in philosophy where the concept of information takes center stage—a concept that may be more amenable to rigorous definition and use in dialogue with the sciences than knowledge. We can wonder, also, what special weight the etiological-function model accords to a knowledge-first perspective on epistemic normativity when the model is malleable in this way.The effectiveness of Simion’s strategy for shielding epistemically good thinking and assertion from practical shiftiness becomes less apparent when we try to apply it to Keith’s belief or judgment that the knowledge ascription/denial he asserts is true. It is unclear whether we are to suppose that, in high stakes, Keith epistemically ought to believe/judge that his asserted knowledge denial is false, but all-things-considered he ought to believe/judge that it is true. We do not have to accept that the knowledge-first, etiological function account of normativity for assertion carries over to belief, of course, but then what progress have we made in accounting for the shiftiness in Keith’s judgment that he knows the bank is open on Saturday in low stakes but not in high stakes?Furthermore, there are other ways to generate problems for fallibilist Classical Invariantists in low versus high stakes pairs of cases. Here is a simplified version of a puzzle from the debate over pragmatic encroachment. Consider low cases where you meet the invariant standards for knowing that p, but your justified confidence falls short of certainty. Among these cases, there must be some where you also meet the invariant standards for knowing that if p is true, then among your choices of action ϕ-ing results in the best overall outcome. Say, for instance, that you have a machine with a ϕ button, and your machine, which you know to be extremely reliable, tells you what the cost or benefit will be if you push the button and p is true versus if p is false. If you ϕ (push the ϕ button) and p is true, you win one hundred dollars; if you ϕ and p is false, you lose one hundred dollars. You face the choice: to ϕ or not to ϕ. Since you know that p, and you know that if p is true, then among your choices of action ϕ-ing results in the best overall outcome, you rationally conclude that ϕ-ing results in the best overall outcome, and hence that you ought to ϕ. If you know which choice of action has the best overall outcome, that is what you all-things-considered should do. Now consider high, where the quantity and quality of your evidence for p is the same, and you still know that your machine is extremely reliable. This time, however, the machine tells you that if you push ϕ and p is true, you win one hundred dollars, but if you push ϕ and p is false, you lose $1 million. Your rational confidence in p is not high enough to justify pushing the button, so you rationally conclude that you ought not to ϕ. Since in high nothing evidentially relevant has changed (all that has changed is the machine informing you of a new, more serious cost of acting on p if p is false), the classical invariantist will have to say that you still know that ϕ, and you still know that if p is true, then among your choices of action ϕ-ing results in the best overall outcome. So, according to CI, you should still be able to reason properly as follows: you know that p, and you know that if p is true, then among your choices of action ϕ-ing results in the best overall outcome, so you know that ϕ-ing results in the best overall outcome, hence you ought to ϕ. Classical invariantists owe us an explanation concerning how we can avoid the paradox here without conceding that knowledge is practically shifty. (shrink)

The Appearance of Ignorance develops and champions contextualist solutions to the puzzles of skeptical hypotheses and of lotteries. It is argued that, at least by ordinary standards for knowledge, we do know that skeptical hypotheses are false, and that we’ve lost the lottery. Accounting for how it is that we know that skeptical hypotheses are false and why it seems that we don’t know that they’re false tells us a lot, both about what knowledge is and how knowledge attributions (...) work. Along the way, the following are all explained and defended: Moorean methodological approaches to skepticism, on which one seeks to defeat, rather than refute, the skeptic; contextualist responses to skepticism; contextualist substantive Mooreanism; the basic safety approach to knowledge and the double-safety picture of what knowledge is; insensitivity accounts of various appearances of ignorance; the closure principle for knowledge; and the claim that our knowledge that we are not brains in vats is a priori, despite its being knowledge of a deeply contingent fact. (shrink)