In lieu of an abstract, here is a brief excerpt of the content:328 HUME, MIRACLES AND LOTTERIES This paper addresses recent criticisms of Hume's skepticism with regard to miracles, by 1 2 Sorensen and Hambourger who argue that there are counterexamples, illustrated by lotteries, to Hume's account of how the truth of reports of improbable events (either first or second hand) must be evaluated. They believe these counterexamples are sufficient to prove that Hume's argument against the believability of miracles, defined (...) as violations of laws of nature caused by God, is unsound. Their arguments merit consideration not only in their own right but also on the basis of historical precedent, since they have in common an assumption that is found in Butler's criticism of Hume's predecessors in this debate. The bulk of my paper deals with Hambourger, who presents the most detailed version of the 'Butler' criticism. Sorensen's version can be answered in light of the evaluation of Hambourger 's argument. Hume's Argument Hume's argument is not against the possibility of miracles but against the possibility that it could ever be reasonable to believe a miracle 4 had occurred. His argument can be summed up as follows: in judging the credibility of a report of an improbable event, the probability of the event must be weighed against the probability that the report could be mistaken. The probability of an event is determined by the degree to which it conforms to known laws of nature. Laws of nature are formulated on the basis of uniform experience. Assuming that a miracle is a violation of laws of nature, any judgment that an event is miraculous presupposes a 329 judgment that there exists a uniform pattern of causation to which it is opposed, which pattern would constitute empirical proof against the miracle's occurrence. Testimony, on the other hand, is shown by experience not to be uniformly reliable. Consequently, no report of a miracle will have credibility since there will always be a uniform experience that is full proof against it, which therefore outweighs whatever merits testimony may have. In Hume's words, [N]o testimony is sufficient to establish a miracle, unless the testimony be of such a kind, that its falsehood would be more miraculous, than the fact, which it endeavors to establish.... When anyone tells me, that he saw a dead man restored to life, I immediately consider with myself, whether it be more probable, that this person should either deceive or be deceived, or that the fact, which he relates, should really have happened.... If the falsehood of his testimony would be more miraculous, than the event which he relates; then, and not till- then, can he pretend to command my belief or opinion (E 115-116). Hambourger 's Criticism Hambourger maintains that Hume's argument depends on a principle which he calls the "principle of relative likelihood." He restates this principle as follows: Suppose that someone or, perhaps, a group of people testify to the truth of a proposition P that, considered by itself, is improbable. Then to evaluate the testimony, one must weight (sic) the probability that P is true against the probability that the informants are lying or mistaken. If it is more likely that P is true than that the informants are lying or mistaken, then, on balance, the 330 testimony renders P more likely than not, and it may be reasonable for one to believe that P. However, if it is as likely, or even more likely, that the informants are lying or mistaken than it is that P is true, then, on balance, the testimony does not render P more likely true than false, and it would not be,reasonable for one to believe that P. As a counterexample to this principle, Hambourger asks us to suppose that a lottery is held in which there are one million entrants, each of whom has a one in a million chance of winning, and that a reliable newspaper, the New York Times, reports that the winner of the lottery is Smith. He further asks us to suppose that the Times errs only once out of every 10,000 times. Thus, the probability that the Times ' report is wrong is... (shrink)

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?

The home learning environment includes what parents do to stimulate children’s literacy and numeracy skills at home and their overall beliefs and attitudes about children’s learning. The home literacy and numeracy environments are two of the most widely discussed aspects of the home learning environment, and past studies have identified how socioeconomic status and parents’ own abilities and interest in these domains also play a part in shaping children’s learning experiences. However, these studies are mostly from the West, and there (...) has been little focus on the situation of homes in Asia, which captures a large geographical area and a wide diversity of social, ethnic, and linguistic groups. Therefore, this paper aims to review extant studies on the home literacy and numeracy environments that have been conducted in different parts of Asia, such as China, the Philippines, India, Iran, Turkey, and the United Arab Emirates. Specifically, we explore how parents in these places perceive their roles in children’s early literacy and numeracy development, the methods they regard as effective for promoting young children’s literacy and numeracy learning, and the frequency with which they engage their young children in different types of home literacy and numeracy activities. We also examine studies on the relationship of the home literacy and numeracy environment with young children’s developmental outcomes, and the effectiveness of parent training programs to improve the home literacy and numeracy environments in these contexts. By examining potential trends in findings obtained in different geographical areas, we can initially determine whether there are characteristics that are potentially unique to contexts in Asia. We propose future research directions that acknowledge the role of cultural values and social factors in shaping the home learning environment, and, by extension, in facilitating children’s early literacy and numeracy development. (shrink)

We show how the use of a Laver function in the proof of the consistency, relative to the existence of a supercompact cardinal, of both the Proper Forcing Axiom and the Semiproper Forcing Axiom can be eliminated via the use of lottery sums of the appropriate partial orderings.

ABSTRACTWe examine Marx's critiques of language, politics, and capitalist political economy and show how these anticipated critical discourse and argumentation analysis and ‘cultural political economy’. Marx studied philology and rhetoric at university and applied their lessons critically. We illustrate this from three texts. The German Ideology critically explores language as practical consciousness, the division of manual and mental labor, the state, hegemony, intellectuals, and specific ideologies. The Eighteenth Brumaire studies the semantics and pragmatics of political language and how it represents (...) the class content of politics and contributes to social transformation. Capital deconstructs the categories of classical political economy and their constitutive role in capitalist social relations. This is one aspect of CPE. Capital also highlights the structural and agential aspects of these relations, their contradictory dynamic, and their crisis-prone character. We comment on this aspect too. This said, Marx held that social transformation is mediated through political imaginaries and highlighted the need for the proletariat to develop a ‘poetry’ of the future. We then consider the misleading ‘base-superstructure’ metaphor and note how, against the thrust of Marx's work, it tends to reify culture. The article concludes that Marx contributed to the critique of semiotic as well as political economy. (shrink)

According to Thomas Kuhn, the entrenchment of a paradigm, especially in the critical stages when facing anomalies, requires the further suppression of competing ideas. This essay addresses the unconscious entrenchment of European modernist aesthetics in the everyday, especially in the American suburbs of the 1950s, and its popular and cultural manifestations. Taking Levittown as a starting point, modernist architectural principles have since its construction radiated into the mass-housing market and materialized in housing development projects that have led to the rise (...) of suburbia and, more recently, the New Urbanism. Despite the conventional separations of modernism from the more criticized mass-housing development, the same principles of security, shelter, community, and utopia are present in each. Presented by some architects as a postmodernist aesthetic, the central tenets of modernism are still pursued and reimagined as timeless principles in the building of new housing communities, recycled and reconstituted to meet the dreams and desires of the public—a utopia that is both avant-garde and kitsch. (shrink)

No research thus far has attempted to examine ethical decision- making in corporate entrepreneurial organizations. Results of such study would provide management executives with insights on what action, if any, is essential for achieving business ethics and corporate entrepreneurship simultaneously. This paper argues, theoretically, that the work characteristics, organizational characteristics, and some individual characteristics in a corporate entrepreneurial organization are conducive to ethical decisions. These characteristics help mitigate the adverse impact of the turbulent environments on ethical decision- making behavior. Based (...) on these arguments, a tentative model of ethical decison-making in corporate entrepreneurial organization is constructed. (shrink)

Physical literacy has received considerable attention in the field of physical education and physical activity worldwide. According to recent studies, the level of physical fitness among Chinese university students is gradually decreasing. This study aims to examine the impact of the PF level on PA and PL, as well as the relationships among PF, PA, and PL, in Chinese university students. Participants comprised 798 university students in Chongqing, China. Participants completed the tests of vital capacity, cardiorespiratory fitness, muscular strength, and (...) flexibility, according to the National Physical Fitness Measurement Standards Manual, as well as questionnaires on PA and PL. The independent t-tests were conducted to examine sex differences in the evaluated variables, and the Pearson’s correlation between each PF test and PL attributes and PA was calculated according to sex. In addition, the independent t-tests were conducted to determine whether the PF level had an effect on PL attributes and PA at various intensities. Significant sex differences were found in the PF domains of vital capacity, muscular strength, and aerobic fitness, with higher scores in men than in women, but not in the PF domain of flexibility and total PL score. Furthermore, the PF domains of muscular strength and aerobic fitness were significantly and positively correlated with the PL attributes of confidence and physical competence in both men and women, while the PF domains of vital capacity and aerobic fitness were significantly and positively correlated with the PL attribute of motivation in men. In addition, PL was significantly and positively associated with cardiorespiratory fitness, vital capacity, muscular strength, and flexibility among participants in the fit group. These findings support advocating for increased participation in PA in university students and using PL as a tool to improve PF components. (shrink)

Many are calling for concrete mechanisms of oversight for health research involving artificial intelligence (AI). In response, institutional review boards (IRBs) are being turned to as a familiar model of governance. Here, we examine the IRB model as a form of ethics oversight for health research that uses AI. We consider the model's origins, analyze the challenges IRBs are facing in the contexts of both industry and academia, and offer concrete recommendations for how these committees might be adapted in order (...) to provide an effective mechanism of oversight for health‐related AI research. (shrink)

Aims: To examine the extent of social stigma toward diabetes among Singapore's multi-ethnic general population and determine whether this differs across socio-demographic sub-groups.Methods: Data for this study came from a nationwide cross-sectional study. A diabetes stigma questionnaire comprising Social Distance Scale and Negative Attitudes and Stereotyping Scale was administered to those respondents who had not been diagnosed with diabetes. Exploratory factor analysis was conducted to determine the dimensionality of the instruments and validated using confirmatory factor analysis. Multiple linear regression analysis (...) was conducted to examine associations between socio-demographic factors and measures of diabetes stigma.Results: In all, 2,895 participants were recruited from the general population giving a response rate of 66.2%. Factor analyses found that a one-factor model resulted in an acceptable fit for both stigma scales, which measured social distance and negative attitudes and stereotyping, respectively. Multiple linear regression analyses identified Indian ethnicity, higher personal income and having close friends or family members who had been diagnosed with diabetes to be significantly associated with lower social distance scores while those aged 50–64 years and those with secondary and vocational education were significantly associated with higher social distance scores. Those with a personal income of SG$2,000–3,999 and SGD $6,000 and above, and those with close friends or family members diagnosed with diabetes were significantly associated with lower negative attitudes and stereotyping scores. In contrast those aged 35 years and above, those with primary education and below, and those of Malay ethnicity were significantly associated with higher negative attitudes and stereotyping scores.Conclusions: The study found a relatively low level of stigma toward diabetes in the general population of Singapore, although some stigmatizing beliefs emerged. While greater knowledge of diabetes could reduce stigma, anti-stigma messaging should be incorporated into the “War on Diabetes” programme in Singapore. (shrink)

The essay discusses the presumption of one's singularity, the uniqueness of one's time, the picturesqueness of one actions, and the capacity of human beings, whether corporately or individually, to begin everything or indeed anything again from scratch. Such presumptions are indeed present in some varieties of contemporary fanaticism, but, more to the point, it is suggested that the feeling of doing something for the first time is the oldest feeling in the world.

If are such that δ is indestructibly supercompact and γ is measurable, then it must be the case that level by level inequivalence between strong compactness and supercompactness fails. We prove a theorem which points to this result being best possible. Specifically, we show that relative to the existence of cardinals such that κ1 is λ‐supercompact and λ is inaccessible, there is a model for level by level inequivalence between strong compactness and supercompactness containing a supercompact cardinal in which κ’s (...) strong compactness, but not supercompactness, is indestructible under κ‐directed closed forcing. In this model, κ is the least strongly compact cardinal, and no cardinal is supercompact up to an inaccessible cardinal. (shrink)

Non-Archimedean probability functions allow us to combine regularity with perfect additivity. We discuss the philosophical motivation for a particular choice of axioms for a non-Archimedean probability theory and answer some philosophical objections that have been raised against infinitesimal probabilities in general. _1_ Introduction _2_ The Limits of Classical Probability Theory _2.1_ Classical probability functions _2.2_ Limitations _2.3_ Infinitesimals to the rescue? _3_ NAP Theory _3.1_ First four axioms of NAP _3.2_ Continuity and conditional probability _3.3_ The final axiom of NAP (...) _3.4_ Infinite sums _3.5_ Definition of NAP functions via infinite sums _3.6_ Relation to numerosity theory _4_ Objections and Replies _4.1_ Cantor and the Archimedean property _4.2_ Ticket missing from an infinite lottery _4.3_ Williamson’s infinite sequence of coin tosses _4.4_ Point sets on a circle _4.5_ Easwaran and Pruss _5_ Dividends _5.1_ Measure and utility _5.2_ Regularity and uniformity _5.3_ Credence and chance _5.4_ Conditional probability _6_ General Considerations _6.1_ Non-uniqueness _6.2_ Invariance Appendix. (shrink)

In this note, I provide an axiomatic characterization of the relative utilitarian bargaining solution to Nash bargaining problems. The solution is obtained when Nash’s independence of irrelevant alternatives axiom is replaced by the weak linearity axiom, while retaining the other three axioms. RU maximizes the sum of proportional gains, or, equivalently, minimizes the sum of proportional losses. RU is scale invariant and compared to the Nash and Kalai and Smorodinsky solutions, it is ex ante efficient when the bargaining problem is (...) considered as a lottery of future bargaining problems. (shrink)

We study the representation of attitudes to risk in Jeffrey’s decision-theoretic framework suggested by Stefánsson and Bradley :602–625, 2015; Br J Philos Sci 70:77–102, 2017) and Bradley :231–248, 2016; Decisions theory with a human face, Cambridge University Press, Cambridge, 2017). We show that on this representation, the value of any prospect may be expressed as a sum of two components, the prospect’s instrumental value and the prospect’s intrinsic value. Both components have an expectational form. We also make a distinction between (...) a prospect’s overall intrinsic value and a prospect’s conditional intrinsic value given each one of its possible outcomes and argue that this distinction has great explanatory power. We explore the relation between these two types of intrinsic values and show that they are determined at the level of preferences. Finally, we explore the relation between the intrinsic values of different prospects and point to a strong restriction on this relation that is implicit in Jeffrey’s axioms. We suggest a natural interpretation to this restriction. (shrink)

The Gouldian argument for evolutionary contingency found in Wonderful Life can be dissected into three premises: palaeontological, macro-evolutionary, and developmental. Discussions of evolutionary contingency have revolved primarily around the developmental. However, a shift in methodological practice and new palaeontological evidence subsequent to the book’s publication appears to threaten the palaeontological premise that asserts high Cambrian disparity, or, roughly, that morphological differences between the Cambrian species were high. This presents a prima facie problem: Did the Cambrian consist of enough anatomical variety (...) to fuel a different outcome upon a replay of the tape of life? I investigate the role that disparity plays in the Gouldian argument for evolutionary contingency and conclude that the reduced disparity view does not undermine the argument, per se. As for the macro-evolutionary premise, Gould never offers any explicit justification for the idea that species sorting was indiscriminate or ‘lottery-like’ (though he certainly gestures at it). Putting aside the exegetical, I consider certain empirical avenues for underwriting the macro-evolutionary premise and argue that the most plausible route is to appeal to the special status of mass extinctions, a move that is not entirely unfamiliar to macro-evolutionists. That is, mass extinctions can be good sources of contingency due to their being ‘chancy’ in at least three respects. In sum, I update the palaeontological and macro-evolutionary premises as to reconstrue the Gouldian argument for evolutionary contingency in its strongest form. (shrink)

Egalitarians sometimes analogize socioeconomic opportunities to starting gates, playing fields, and the results of a lottery. A fair game is one in which all have an equal opportunity to succeed; egalitarians propose that the same is true of a fair society. A second type of argument for egalitarianism appeals to intuitions about the distribution of found resources. A just division of manna discovered on a strange planet seems to be an equal one. Both types of argument share a crucial (...) feature: they concern the once-off division of a fixed sum of goods. I argue that the most compelling reasons to depart from an equal division of goods derive from the economic activity involved in producing more of those goods, e.g., Pareto improvements due to efficiency gains that result from incentives that encourage production. We cannot conclude that game analogies and found resources cases arbitrate in favour of equality against non-egalitarian principles because they exclude precisely those considerations that provide the strongest reasons to reject equality. (shrink)

Since the modern era, the discourse of punishment has cycled through three sets of questions. The first, born of the Enlightenment itself, asked: On what ground does the sovereign have the right to punish? Nietzsche most forcefully, but others as well, argued that the question itself begged its own answer. The right to punish, they suggested, is what defines sovereignty, and as such, can never serve to limit sovereign power. With the birth of the social sciences, this skepticism gave rise (...) to a second set of questions: What then is the true function of punishment? What is it that we do when we punish? From Durkheim to the Frankfurt School to Michel Foucault, twentieth century moderns explored social organization, economic production, political legitimacy, and the construction of the self_turning punishment practices upside down, dissecting not only their repressive functions but more importantly their role in constructing society and the contemporary subject. A series of further critiques_of meta_narratives, of functionalism, of scientific objectivity_softened this second line of inquiry and helped shape a third set of questions: What does punishment tell us about ourselves and our culture? What is the cultural meaning of our punishment practices? These three sets of questions set the contours of our modern discourse on crime and punishment.What happens now_ now that we have seen what lies around the cultural bend and realize that the same critiques apply with equal force to any interpretation of social meaning that we could possibly read into our contemporary punishment practices? Should we continue to labor on this third and final set of questions, return to an earlier set, or, as all our predecessors did, craft a new line of inquiry? What question shall we_children of the twenty_first century_pose of our punishment practices and institutions?This essay suggests that the form of the question never really mattered. In all the modern texts, there always came this moment when the empirical facts ran out or the deductions of principle reached their limit_or both_and yet the reasoning continued. There was always this moment, ironically, when the moderns took a leap of faith. And it was always there, at that precise moment, that we learned the most: that we could read from the text and decipher a vision of just punishment that was never entirely rational, never purely empirical, and never fully determined by the theoretical premises of the author. In each and every case, the modern text let slip a leap of faith_an ethical choice about how to resolve a gap, an ambiguity, an indeterminacy in an argument of principle or fact.It is time to abandon the misguided project of modernity. Rather than continue to take these leaps of faith, it is time once and for all to recognize the critical limits of reason, and whenever we reach them, to rely instead on randomization. Where our facts run out, where our principles no longer guide us, we should leave the decision_making to the coin toss, the roll of the dice, the lottery draw_in sum, to chance. This essay begins to explore what that would mean in the field of crime and punishment. (shrink)

The lottery paradox can be solved if epistemic justification is assumed to be a species of permissibility. Given this assumption, the starting point of the paradox can be formulated as the claim that, for each lottery ticket, I am permitted to believe that it will lose. This claim is ambiguous between two readings, depending on the scope of ‘permitted’. On one reading, the claim is false; on another, it is true, but, owing to the general failure of permissibility (...) to agglomerate, does not generate the paradox. The solution generalizes to formulations of the paradox in terms of rational acceptability and doxastic rationality. (shrink)

In a recent article, Douven and Williamson offer both (i) a rebuttal of various recent suggested sufficient conditions for rational acceptability and (ii) an alleged ‘generalization’ of this rebuttal, which, they claim, tells against a much broader class of potential suggestions. However, not only is the result mentioned in (ii) not a generalization of the findings referred to in (i), but in contrast to the latter, it fails to have the probative force advertised. Their paper does however, if unwittingly, bring (...) us a step closer to a precise characterization of an important class of rationally unacceptable propositions—the class of lottery propositions for equiprobable lotteries. This helps pave the way to the construction of a genuinely lottery-paradox-proof alternative to the suggestions criticized in (i). (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)

The lottery paradox plays an important role in arguments for various norms of assertion. Why is it that, prior to information on the results of a draw, assertions such as, “My ticket lost,” seem inappropriate? This paper is composed of two projects. First, I articulate a number of problems arising from Timothy Williamson’s analysis of the lottery paradox. Second, I propose a relevant alternatives theory, which I call the Non-Destabilizing Alternatives Theory , that better explains the pathology of (...) asserting lottery propositions, while permitting assertions of what I call fallible propositions such as, “My car is in the driveway.” Le paradoxe de la loterie joue un rôle important dans l’argumentation visant à défendre diverses normes de l’assertion. Comment se fait-il que, avant que les résultats d’un tirage soient connus, des assertions comme «Mon billet a perdu» semblent inappropriées? Cet article se compose de deux projets. Premièrement, je relève certains problèmes issus de l’analyse du paradoxe de la loterie par Timothy Williamson. Deuxièmement, je propose une théorie des alternatives pertinentes que j’appelle la «théorie des alternatives non-déstabilisantes» , et qui explique d’une meilleure façon la pathologie de l’assertion de propositions concernant la loterie, tout en permettant des assertions faillibles, telles que «Ma voiture est dans l’entrée». (shrink)

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

Jim buys a ticket in a million-ticket lottery. He knows it is a fair lottery, but, given the odds, he believes he will lose. When the winning ticket is chosen, it is not his. Did he know his ticket would lose? It seems that he did not. After all, if he knew his ticket would lose, why would he have bought it? Further, if he knew his ticket would lose, then, given that his ticket is no different in (...) its chances of winning from any other ticket, it seems that by parity of reasoning he should also know that every other ticket would lose. But of course he doesn’t know that; in fact, he knows that not every ticket will lose. (shrink)

The lottery paradox shows seemingly plausible principles of rational acceptance to be incompatible. It has been argued that we shouldn’t be concerned by this clash, since the concept of (categorical) belief is otiose, to be supplanted by a quantitative notion of partial belief, in terms of which the paradox cannot even be formulated. I reject this eliminativist view of belief, arguing that the ordinary concept of (categorical) belief has a useful function which the quantitative notion does not serve. I (...) then propose a solution to the paradox it engenders. (shrink)

This paper defends the permissibility solution to the lottery paradox against an objection by Anna-Maria Asunta Eder. Eder argues that the permissibility solution should also be applicable to the preface paradox, but conflicts with a plausible principle about epistemic permissions when so applied. This paper replies by first criticizing Eder’s considerations in defense of her principle; in particular, it argues that the plausibility of her principle is to a large extent parasitic on the spurious plausibility of the principle of (...) factual detachment. The paper then presents a direct argument against Eder’s principle, which shows that her principle conflicts with a Pareto-style condition on permissible belief. (shrink)

The opportunities to become a good person are not the same for everyone. Modern European ethical theory, especially Kantian ethics, assumes the same virtues are accessible to all who are capable of rational choice. Character development, however, is affected by circumstances, such as those of wealth and socially constructed categories of gender, race, and sexual orientation, which introduce factors beyond the control of individuals. Implications of these influences for morality have, since the work of Williams and Nagel in the seventies, (...) raised questions in philosophy about the concept of moral luck. In The Unnatural Lottery, Claudia Card examines how luck enters into moral character and considers how some of those who are oppressed can develop responsibility. Luck is often best appreciated by those who have known relatively bad luck and have been unable to escape steady comparison of their lot with those of others. The author takes as her paradigms the luck of middle and lower classes of women who face violence and exploitation, of lesbians who face continuing pressure to hide or self-destruct, of culturally Christian whites who have ethnic privilege, and of adult survivors of child abuse. How have such people been affected by luck in who they are and can become, the good lives available to them, the evils they may be liable to embody? Other philosophers have explored the luck of those who begin from privileged positions and then suffer reversals of fortune. Claudia Card focuses on the more common cases of those who begin from socially disadvantaged positions, and she considers some who find their good luck troubling when its source is the unnatural lottery of social injustice. (shrink)

In this paper, we present the results of two surveys that investigate subjects’ judgments about what can be known or justifiably believed about lottery outcomes on the basis of statistical evidence, testimonial evidence, and “mixed” evidence, while considering possible anchoring and priming effects. We discuss these results in light of seven distinct hypotheses that capture various claims made by philosophers about lay people’s lottery judgments. We conclude by summarizing the main findings, pointing to future research, and comparing our (...) findings to recent studies by Turri and Friedman. (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)

One of the problems that Bayesian regularity, the thesis that all contingent propositions should be given probabilities strictly between zero and one, faces is the possibility of random processes that randomly and uniformly choose a number between zero and one. According to classical probability theory, the probability that such a process picks a particular number in the range is zero, but of course any number in the range can indeed be picked. There is a solution to this particular problem on (...) the books: a measure that assigns the same infinitesimal probability to each number between zero and one. I will show that such a measure, while mathematically interesting, is pathological for use in confirmation theory, for the same reason that a measure that assigns an infinitesimal probability to each possible outcome in a countably infinite lottery is pathological. The pathology is that one can force someone to assign a probability within an infinitesimal of one to an unlikely event. (shrink)

One result of this note is about the nonconstructivity of countably infinite lotteries: even if we impose very weak conditions on the assignment of probabilities to subsets of natural numbers we cannot prove the existence of such assignments constructively, i.e., without something such as the axiom of choice. This is a corollary to a more general theorem about large-small filters, a concept that extends the concept of free ultrafilters. The main theorem is that proving the existence of large-small filters requires (...) a nonconstructive axiom like AC. (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)

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

It can often be heard in the hallways, and occasionally read in print, that reliabilism runs into special trouble regarding lottery cases. My main aim in this paper is to argue that this is not so. Nevertheless, lottery cases do force us to pay close attention to the relation between justification and probability.

Thomas Kroedel argues that we can solve a version of the lottery paradox if we identify justified beliefs with permissible beliefs. Since permissions do not agglomerate, we might grant that someone could justifiably believe any ticket in a large and fair lottery is a loser without being permitted to believe that all the tickets will lose. I shall argue that Kroedel’s solution fails. While permissions do not agglomerate, we would have too many permissions if we characterized justified belief (...) as sufficiently probable belief. If we reject the idea that justified beliefs can be characterized as sufficiently probably beliefs, Kroedel’s solution is otiose because the paradox can be dissolved at the outset. (shrink)

We analyze the results from three different risk attitude elicitation methods. First, the broadly used test by Holt and Laury, HL, second, the lottery-panel task by Sabater-Grande and Georgantzis, SG, and third, responses to a survey question on self-assessment of general attitude towards risk. The first and the second task are implemented with real monetary incentives, while the third concerns all domains in life in general. Like in previous studies, the correlation of decisions across tasks is low and usually (...) statistically non-significant. However, when we consider only subjects whose behavior across the panels of the SG task is compatible with constant relative risk aversion, the correlation between HL and self-assessed risk attitude becomes significant. Furthermore, the correlation between HL and SG also increases for CRRA-compatible subjects, although it remains statistically non-significant. (shrink)