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)

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)

When faced with multiple claims to a particular good, what does distributive justice require? To answer this question, we need a substantive moral theory that will enable us assign relative moral weights to the parties' claims. But this is not all we need. Once we have assessed the moral weight of each party's claim, we still need to decide what method of distribution to employ, for there are two methods open to us. We could take the winner-take-all approach, and award (...) the good to the party with the strongest claim. On the other hand, we could divide the good proportionally, according to the relative strength of each party's claim. Because the choice between these two methods of distribution can have a dramatic impact on the resulting pattern of distribution, the choice presents a question of justice. But this is a question of justice that is often overlooked. As a result, we currently employ the principle of proportionality far less often than justice actually requires. If we focus on the question of distributive method, however, we are not only better able to understand how certain reasons enter into our all-things-considered moral judgments, we are also able to explain some perplexing but common aspects of our moral beliefs: how rights can be said to have peremptory force, yet still be balanced against other important interests; how justice can sometimes require compromise, yet sometimes require victory; and how a moral theory can avoid being too demanding while still being demanding enough. Key Words: autonomy • equality • indivisibility • inviolability • weighted lotteries • rights. (shrink)

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)

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)

How should we make distributive decisions when there is not enough of the good to go around, or at least not enough of it right now? What does fairness require in such cases? In what follows, we distinguish between cases of scarcity and bottleneck cases, and we argue that both arguments for lotteries and arguments for queues have merit, albeit for different distributive scenarios. When dealing with scarcity not everyone can get the good. A secondary good that can be distributed (...) fairly is the chances of obtaining the good. In cases of scarcity, lotteries are the best way of allocating chances of obtaining the good fairly. When dealing with bottlenecks, the secondary good that can and ought to be distributed fairly is waiting time. Queues are best suited to distribute the good of waiting time fairly. (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)

Lara Buchak argues for a version of rank-weighted utilitarianism that assigns greater weight to the interests of the worse off. She argues that our distributive principles should be derived from the preferences of rational individuals behind a veil of ignorance, who ought to be risk averse. I argue that Buchak’s appeal to the veil of ignorance leads to a particular way of extending rank-weighted utilitarianism to the evaluation of uncertain prospects. This method recommends choices that violate the unanimous (...) preferences of rational individuals and choices that guarantee worse distributions. These results, I suggest, undermine Buchak’s argument for rank-weighted utilitarianism. (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)

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)

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

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)

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)

The lottery paradox involves a set of judgments that are individually easy, when we think intuitively, but ultimately hard to reconcile with each other, when we think reflectively. Empirical work on the natural representation of probability shows that a range of interestingly different intuitive and reflective processes are deployed when we think about possible outcomes in different contexts. Understanding the shifts in our natural ways of thinking can reduce the sense that the lottery paradox reveals something problematic about (...) our concept of knowledge. However, examining these shifts also raises interesting questions about how we ought to be thinking about possible outcomes in the first place. (shrink)

In 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)

Carl Knight argues that lexical sufficientarianism, which holds that sufficientarian concerns should have lexical priority over other distributive goals, is ‘excessive’ in many distinct ways and that sufficientarians should either defend weighted sufficientarianism or become prioritarians. In this article, I distinguish three types of weighted sufficientarianism and propose a weighted sufficientarian view that meets the excessiveness objection and is preferable to both Knight’s proposal and prioritarianism. More specifically, I defend a multi-threshold view which gives weighted priority (...) to benefits directly above and below its thresholds, but gives benefits below the lowest threshold lexical priority over benefits above the highest threshold. (shrink)

This paper addresses the two extensional objections to the Humean Theory of Reasons—that it allows for too many reasons, and that it allows for too few. Although I won’t argue so here, manyof the other objections to the Humean Theoryof Reasons turn on assuming that it cannot successfully deal with these two objections.1 What I will argue, is that the force of the too many and the too few objections to the Humean Theorydepend on whether we assume that Humeans are (...) committed to a thesis about the weight of reasons—one I call Proportionalism. In particular, I’ll show how a version of the Humean Theorythat rejects Proportionalism can reasonablyhope to escape both the too many and the too few objections. This will constitute my defense of this version of the Humean Theory. But then, separately, I will argue that this defense of the Humean Theoryis not ad hoc. I’ll argue that Humeans have no reason to accept Proportionalism in the first place. Or at least, no weightyone. There are three parts to the paper. In Part 1 we introduce the Humean Theoryand the too few reasons objection. I’ll first layout the objection, and then layout the basis for a response on behalf of myfavored version of the Humean Theory. There will be an obvious objection to my defense— but it will turn out to depend on the assumption of Proportionalism. This will constitute myargument that the susceptibilityof the Humean Theoryto.. (shrink)

According to Stephen Finlay, ‘A ought to X’ means that X-ing is more conducive to contextually salient ends than relevant alternatives. This in turn is analysed in terms of probability. I show why this theory of ‘ought’ is hard to square with a theory of a reason’s weight which could explain why ‘A ought to X’ logically entails that the balance of reasons favours that A X-es. I develop two theories of weight to illustrate my point. I first look at (...) the prospects of a theory of weight based on expected utility theory. I then suggest a simpler theory. Although neither allows that ‘A ought to X’ logically entails that the balance of reasons favours that A X-es, this price may be accepted. For there remains a strong pragmatic relation between these claims. (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.

Alison Bailey’s The Weight of Whiteness: A Feminist Engagement with Privilege, Race, and Ignorance examines how whiteness misshapes our humanity, measuring the weight of whiteness in terms of its costs and losses to collective humanity. People of color feel the weight of whiteness daily. The resistant habits of whiteness and its attendant privileges, however, make it difficult for white people to feel the damage. White people are more comfortable thinking about white supremacy in terms of what privilege does for them, (...) rather than feeling what it does to them. The first half of the book focuses on the overexposed side of white privilege, the side that works to make the invisible and intangible structures of power more visible and tangible. Bailey discusses the importance of understanding privileges intersectionally, the ignorance-preserving habits of “white talk,” and how privilege and ignorance circulate in educational settings. The second part invites white readers to explore the underexposed side of white dominance, the weightless side that they would rather not feel. The final chapters are powerfully autobiographical. Bailey engages readers with a deeply personal account of what it means to hold space with the painful weight of whiteness in her own life. She also offers a moving account of medicinal genealogies, which helps to engage the weight she inherits from her settler colonial ancestors. The book illustrates how the gravitational pull of white ignorance and comfort are stronger than the clean pain required for collective liberation. The stakes are high: Failure to hold the weight of whiteness ensures that white people will continue to blow the weight of historical trauma through communities of color. -/- All rights reserved. No portion of this publication may be reproduced, stored in a retrieval system, or transmitted in any form by any means, electronic, mechanical, photocopying, recording or otherwise without the prior written permission of the publisher. -/- -/- . (shrink)

We describe a prediction method called "Attractivity Weighting" (AW). In the case of cue-based paired comparison tasks, AW's prediction is based on a weighted average of the cue values of the most successful cues. In many situations, AW's prediction is based on the cue value of the most successful cue, resulting in behavior similar to Take-the-Best (TTB). Unlike TTB, AW has a desirable characteristic called "access optimality": Its long-run success is guaranteed to be at least as great as the (...) most successful cue. While access optimality is a desirable characteristic, concerns may be raised about the short-term performance of AW. To evaluate such concerns, we here present a study of AW's short-term performance. The results suggest that there is little reason to worry about the short-run performance of AW. Our study also shows that, in random sequences of paired comparison tasks, the behavior of AW and TTB is nearly indiscernible. (shrink)

Many epistemologists have responded to the lottery paradox by proposing formal rules according to which high probability defeasibly warrants acceptance. Douven and Williamson present an ingenious argument purporting to show that such rules invariably trivialise, in that they reduce to the claim that a probability of 1 warrants acceptance. Douven and Williamson’s argument does, however, rest upon significant assumptions – amongst them a relatively strong structural assumption to the effect that the underlying probability space is both finite and uniform. (...) In this paper, I will show that something very like Douven and Williamson’s argument can in fact survive with much weaker structural assumptions – and, in particular, can apply to infinite probability spaces. (shrink)

Many authors in ethics, economics, and political science endorse the Lottery Requirement, that is, the following thesis: where different parties have equal moral claims to one indivisible good, it is morally obligatory to let a fair lottery decide which party is to receive the good. This article defends skepticism about the Lottery Requirement. It distinguishes three broad strategies of defending such a requirement: the surrogate satisfaction account, the procedural account, and the ideal consent account, and argues that (...) none of these strategies succeed. The article then discusses and discharges some remaining grounds for resistance to these skeptical conclusions, as well as the possibility of defending a weaker version of a normative lottery principle. The conclusion is that we have no reason to believe that where equal claims conflict, we are morally required to hold a lottery, as opposed to simply picking one of the parties on more subjective grounds or out of pure whim. In addition to the practical consequences of this skeptical view, the article sketches some theoretical implications for debates about saving the greater number and about axiomatic utilitarianism. (shrink)

, whereby some causes are deemed more important than others, are ubiquitous in historical studies. Drawing from influential recent work on causation, I develop a definition of causal-explanatory strength. This makes clear exactly which aspects of explanatory weighting are subjective and which objective. It also sheds new light on several traditional issues, showing for instance that: underlying causes need not be more important than proximate ones; several different causes can each be responsible for most of an effect; small causes need (...) not be less important than big ones; and non-additive interactive effects between causes present no particular difficulty. Key Words: causation • explanation • history • interaction • proximate • underlying. (shrink)

The book develops, defends, and applies a "Dual Scale" model of weighing reasons to resolve various issues in ethics. It tells you everything you ever wanted to know about weighing reasons and probably a lot of stuff you didn't want to know too. It addresses, among other things, what the general issue of weighing reasons is; what it is to weigh reasons correctly; whether reasons have more than one weight value (e.g., justifying, requiring, and/or commending weight); whether weight values are (...) context sensitive; how to tell what the weights of reasons are; how reasons for are related to reasons against; and how the weights of reasons aggregate. After addressing such issues, it explains a number of puzzling phenomena in ethics, such as the All or Nothing Problem, the normative significance of small improvements, and the intransitivity of the makes-it-permissible-to-act-against relation. (shrink)

Particularists in ethics emphasize that the normative is holistic, and invite us to infer with them that it therefore defies generalization. This has been supposed to present an obstacle to traditional moral theorizing, to have striking implications for moral epistemology and moral deliberation, and to rule out reductive theories of the normative, making it a bold and important thesis across the areas of normative theory, moral epistemology, moral psychology, and normative metaphysics. Though particularists emphasize the importance of the holism of (...) the normative, however, it is not something that they have been able to explain. In this paper I’ll show how to use a small number of simple and, I’ll argue, independently compelling assumptions in order to both predict and explain the holistic features of the normative with respect to the non-normative. The basic idea of the paper is simple. It is that normative claims are holistic because they are general, rather than because they defy generalization. (shrink)

This paper addresses the question of how the ‘weight’ or ‘strength’ of normative reasons is best understood. We argue that, given our preferred analysis of reasons as sources of normative support, this question has a straightforward answer: the weight of a normative reason is simply a matter of how much support it provides. We also critically discuss several competing views of reasons and their weight. These include views which take reasons to be normatively fundamental, views which analyze reasons as evidence (...) concerning what one ought to do, views which analyze reasons in terms of good reasoning, and views which analyze reasons as explanations of ought-facts, fittingness-facts, or goodness-facts. (shrink)

The testimonia concerning weight in early Greek atomism appear to contradict one another. Some reports assert that the atoms do have weight, while others outright deny weight as a property of the atoms. A common solution to this apparent contradiction divides the testimonia into two groups. The first group describes the atoms within a κόσμος, where they have weight; the second group describes the atoms outside of a κόσμος, where they are weightless. A key testimonium for proponents of this solution (...) is Aëtius 1.3.18. It apparently denies weight as a property of the atoms, and supposedly describes the atoms when they are outside of a κόσμος. I argue against this interpretive solution by demonstrating, first, that Aëtius 1.3.18 does not deny that weight is a property of the atoms. Second, I argue that the report does not describe the atoms when they are outside of a κόσμος. Although these are largely negative conclusions, I contend that we are not left without a solution to the present interpretive difficulty. Once our testimonia concerning weight in early Greek atomism are examined thoroughly, it is clear that there is no conflict among them. (shrink)

In this research, an Artificial Neural Network (ANN) model was developed and tested to predict Birth Weight. A number of factors were identified that may affect birth weight. Factors such as smoke, race, age, weight (lbs) at last menstrual period, hypertension, uterine irritability, number of physician visits in 1st trimester, among others, as input variables for the ANN model. A model based on multi-layer concept topology was developed and trained using the data from some birth cases in hospitals. The evaluation (...) of testing the dataset shows that the ANN model is capable of correctly predicting the birth weight with 100% accuracy. (shrink)

The study of Enrici et al. (2023) in Ecology and Society [1] is one of a few in-depth discussions of the significance of money on how people (including academics, politicians, and residents) understand the impact of humans on the environment. These insights are critical, especially given the urgency of understanding anthropogenic influences on the ecosystem in the face of the unpredictable dangers of climate catastrophe.

There are many conceivable circumstances in which some people have to be sacrificed in order to give others a chance to survive. The fair and rational method of selection is a lottery with equal chances. But why should losers comply, when they have nothing to lose in a war of all against all? A novel solution to this Compliance Problem is proposed. The lottery must be made self-enforcing by making the lots themselves the means of enforcement of the (...) outcome. This way no external authority is needed to make the losers’ compliance rational both ex ante and ex post. A fairly realistic concrete scenario is sketched to show that the solution could be made to work in practice, particularly since making it work is in everyone’s enlightened self-interest in the circumstances. (shrink)

This article discusses Keith DeRose’s treatment of the lottery problem in Chapter 5 of his recent The Appearance of Ignorance. I agree with a lot of it but also raise some critical points and questions and make some friendly proposals. I discuss different ways to set up the problem, go into the difference between knowing and ending inquiry, propose to distinguish between two different kinds of lotteries, add to the defense of the idea that one can know lottery (...) propositions, give a critical discussion of DeRose’s contextualist solution to the problem, and support his defense against an absurdity objection with additional arguments. (shrink)

It is commonly argued that values “fill the logical gap” of underdetermination of theory by evidence, namely, values affect our choice between two or more theories that fit the same evidence. The underdetermination model, however, does not exhaust the roles values play in evidential reasoning. I introduce WAVE – a novel account of the logical relations between values and evidence. WAVE states that values influence evidential reasoning by adjusting evidential weights. I argue that the weight-adjusting role of values is distinct (...) from their underdetermination gap-filling role. Values adjust weights in three ways. First, values affect our trust in the testimony of others. Second, values influence the evidential thresholds required for justified epistemic judgments. Third, values influence the relative weight of a certain type of evidence within a body of multimodal discordant evidence. WAVE explains, from an epistemic perspective, rather than psychological, how smokers, for example, can find the same evidence about the dangers of smoking less persuasive than non-smokers. WAVE allows for a wider effect of values on our accepted scientific theories and beliefs than the effect for which the underdetermination model allows alone; therefore, science studies scholars must consider WAVE in their research and analysis of evidential case studies. (shrink)

According to the permissibility solution to the lottery paradox, the paradox can be solved if we conceive of epistemic justification as a species of permissibility. Clayton Littlejohn has objected that the permissibility solution draws on a sufficient condition for permissible belief that has implausible consequences and that the solution conflicts with our lack of knowledge that a given lottery ticket will lose. The paper defends the permissibility solution against Littlejohn's objections.

The aim of this paper is to provide a detailed characterisation of some ways in which our preferences reflect our reasons. I will argue that practical reasons can be characterised along two dimensions that influence our preferences: their balance and their weight. This is analogous to a similar characterisation of the way in which probabilities reflect the balance and weight of evidence in epistemology. In this paper, I will illustrate the distinction between the balance and weight of reasons, and show (...) how this is crucial for an adequate account of preference and choice. The upshot is a more complete picture of a particular kind of decision, labelled by Isaac Levi and, more recently, Ruth Chang as ‘hard choices’. These are choices in which one option is better than another in some ways, the other is better than the first in some ways, but neither seems better overall. The distinction between the balance and weight of reasons presents a new way of understanding how hard choices vary by degree and what it is that makes them so hard. (shrink)

Minimalists, such as Paul Horwich, claim that the notions of truth, reference and satisfaction are exhausted by some very simple schemes. Unfortunately, there are subtle difficulties with treating these as schemes, in the ordinary sense. So instead, minimalists regard them as illustrating one-place functions, into which we can input propositions (when considering truth) or propositional constituents (when considering reference and satisfaction). However, Bertrand Russell's Gray's Elegy argument teaches us some important lessons about propositions and propositional constituents. When applied to minimalism, (...) these lessons show us why we should abandon it. (shrink)

This work is a complete mathematical guide to lottery games, covering all of the problems related to probability, combinatorics, and all parameters describing the lottery matrices, as well as the various playing systems. The mathematics sections describe the mathematical model of the lottery, which is in fact the essence of the lotto game. The applications of this model provide players with all the mathematical data regarding the parameters attached to the gaming events and personal playing systems. By (...) applying these data, one can find all the winning probabilities for the play with one line, and how these probabilities change with playing the various types of systems containing several lines, depending on their structure. Also, each playing system has a formula attached that provides the number of possible multiple prizes in various circumstances. Other mathematical parameters of the playing systems and the correlations between them are also presented. The generality of the mathematical model and of the obtained formulas allows their application for any existent lottery and any playing system. Each formula is followed by numerical results covering the most frequent lottery matrices worldwide and by multiple examples predominantly belonging to the 6/49 lottery. The listing of the numerical results in dozens of well-organized tables, along with instructions and examples of using them, makes possible the direct usage of this guide by players without a mathematical background. The author also discusses from a mathematical point of view the strategies of choosing involved in the lotto game. The book does not offer so-called winning strategies, but helps players to better organize their own playing systems and to confront their own convictions with the incontestable reality offered by the direct applications of the mathematical model of the lotto game. As a must-have handbook for any lottery player, this book offers essential information about the game itself and can provide the basis for gaming decisions of any kind. (shrink)

Abstract: In this research, an Artificial Neural Network (ANN) model was developed and tested to predict Birth Weight. A number of factors were identified that may affect birth weight. Factors such as smoke, race, age, weight (lbs) at last menstrual period, hypertension, uterine irritability, number of physician visits in 1st trimester, among others, as input variables for the ANN model. A model based on multi-layer concept topology was developed and trained using the data from some birth cases in hospitals. The (...) evaluation of testing the dataset shows that the ANN model is capable of correctly predicting the birth weight with 100% accuracy. (shrink)

In the last decade, analytic epistemologists have engaged in a lively debate about Equal Weight, the claim that you should give the credences of epistemic peers the same consideration as your own credences. In this paper, I explore the implications of the debate about Equal Weight for how we should respond to religious disagreement found in the diversity of models of God. I first claim that one common argument against religious exclusivism and for religious pluralism can be articulated as an (...) Equal Weight argument. I then argue that to avoid this argument, religious exclusivists must reject Equal Weight. Next, I maintain that, while the exclusivist complaint that pluralism is self-undermining is incorrect, exclusivists can rightly object that the pluralist’s Equal Weight argument is self-undermining. Thus both exclusivists and pluralists have an interest in rejecting Equal Weight. My final discussion is speculative: I suggest that the goals of those of pluralist persuasion might be better met by religious permissivism, the view that some forms of both exclusivism and pluralism are rational responses to religious disagreement. (shrink)

This paper elaborates a new solution to the lottery paradox, according to which the paradox arises only when we lump together two distinct states of being confident that p under one general label of ‘belief that p’. The two-state conjecture is defended on the basis of some recent work on gradable adjectives. The conjecture is supported by independent considerations from the impossibility of constructing the lottery paradox both for risk-tolerating states such as being afraid, hoping or hypothesizing, and (...) for risk-averse, certainty-like states. The new proposal is compared to views within the increasingly popular debate opposing dualists to reductionists with respect to the relation between belief and degrees of belief. (shrink)

We prove a representation theorem for preference relations over countably infinite lotteries that satisfy a generalized form of the Independence axiom, without assuming Continuity. The representing space consists of lexicographically ordered transfinite sequences of bounded real numbers. This result is generalized to preference orders on abstract superconvex spaces.

We present an algorithm for concept combination inspired and informed by the research in cognitive and experimental psychology. Dealing with concept combination requires, from a symbolic AI perspective, to cope with competitive needs: the need for compositionality and the need to account for typicality effects. Building on our previous work on weighted logic, the proposed algorithm can be seen as a step towards the management of both these needs. More precisely, following a proposal of Hampton [1], it combines two (...) weighted Description Logic formulas, each defining a concept, using the following general strategy. First it selects all the features needed for the combination, based on the logical distinc- tion between necessary and impossible features. Second, it determines the threshold and assigns new weights to the features of the combined concept trying to preserve the relevance and the necessity of the features. We illustrate how the algorithm works exploiting some paradigmatic examples discussed in the cognitive literature. (shrink)

Some philosophers believe that when epistemic peers disagree, each has an obligation to accord the other's assessment the same weight as her own. I first make the antecedent of this Equal-Weight View more precise, and then I motivate the View by describing cases in which it gives the intuitively correct verdict. Next I introduce some apparent counterexamples – cases of apparent peer disagreement in which, intuitively, one should not give equal weight to the other party's assessment. To defuse these apparent (...) counterexamples, an advocate of the View might try to explain how they are not genuine cases of peer disagreement. I examine David Christensen's and Adam Elga's explanations and find them wanting. I then offer a novel explanation, which turns on a distinction between knowledge from reports and knowledge from direct acquaintance. Finally, I extend my explanation to provide a handy and satisfying response to the charge of self-defeat. (shrink)

Stephen Finlay analyses ‘ought’ in terms of probability. According to him, normative ‘ought's are statements about the likelihood that an act will realize some (contextually supplied) end. I raise a problem for this theory. It concerns the relation between ‘ought’ and the balance of reasons. ‘A ought to Φ’ seems to entail that the balance of reasons favours that A Φ-es, and vice versa. Given Finlay's semantics for ‘ought’, it also makes sense to think of reasons and their weight in (...) terms of probability. In this paper, I develop such a theory of weight. It turns out, however, that it cannot explain the entailments. This leaves Finlay with a challenge: to explain these entailments in some other way consistent with his theory, or to show why the appearances deceive and there are no such entailments. (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)

In this paper it will be attempted to dissolve the lottery problem based on fallibilism, probabilism and the introduction of a so far widely neglected second context of knowledge. First, it will be argued that the lottery problem is actually an exemplification of the much wider Humean "future knowledge problem" (ch. 1). Two types of inferences and arguments will be examined, compared and evaluated in respect to their ability to fittingly describe the thought processes behind lottery/future knowledge (...) propositions (ch. 2). A second context of knowledge that underlines the importance of fallibilism and probabilism in a somewhat different manner will be introduced (ch. 3) and, based on that "two-context probabilism," the lottery/future knowledge problem will be dissolved (ch. 4). Lastly, it will be hinted at the necessity of adopting not just fallibilism including and two context minding probabilism, but, beyond that, also the even more encompassing position of both ontological and epistemological "gradualism" (ch. 5). (shrink)