The Hamiltonian for the Einstein equations is constructed on a outgoing null cone with the help of the usual null tetrad. The resulting null surface constraints are shown to be second class in the terminology of Dirac. These second class constraints are eliminated by use of the “starring” procedure of Bergmann and Komar.

The canonical formalism for the Maxwell field on a null surface has been revisited. A new pair of gauge-independent canonical variables is introduced. It is shown that these variables are derivable from a Hamillon-Jacobi functional. The construction of the appropriate C * algebra is carried out in preparation for quantization. The resulting quantum theory is similar to a previous result. It is then shown that one can construct the T-variables of Rovelli and Smolin on the null surface. The Poisson bracket (...) algebra exhibits causal relations along the null rays, but is nonsingular if the loops are restricted to those whose projections along the null rays are not tangent and one-to-one. Finally, there is a brief discussion of the relevance of this work to general relativity. (shrink)

American men experience worse outcomes on a wide range of health and well-being variables compared to women, including disease, educational problems, violence, addiction, suicide, unemployment, and life expectancy. Because of this, organizations have created programs that focus on helping men both psychologically and spiritually; however, it is important to assess the effectiveness of these programs. The Crucible Project, founded in 2002, attempts to facilitate the development of integrity, courage, and grace in men using a weekend retreat format. The purpose of (...) this pilot study was to explore the effect of the weekend retreat on participants’ authenticity, assertiveness, and willingness to forgive. Participants completed measures before the weekend retreat, immediately after the weekend retreat, and at a 1-month follow-up. Results indicate that weekend retreat participants demonstrated a significant increase in scores on measures of authenticity and willingness to forgive and a trend toward increased scores on the measure of assertiveness over time. We conclude by discussing limitations of the study, areas for future research, and implications for spiritual and character development. (shrink)

The lung allocation score system in the United States and several European countries gives more weight to risk of death without transplantation than to survival following transplantation. As a result, centers transplant sicker patients, leading to increased length of initial hospitalization. The care of patients who have accumulated functional deficits or additional organ dysfunction during their prolonged stay can be ethically complex. Disagreement occurs between the transplant team, patients and families, and non-transplant health care professionals over the burdens of ongoing (...) intensive intervention. These cases highlight important ethical issues in organ transplantation, including the nature and requirements of transplant informed consent, the limits of physician prognostication, patient autonomy and decision-making capacity following transplant, obligations to organ donors and to other potential recipients, and the impact of program metrics on individualized recipient care. We outline general ethical principles for the care of lung transplant recipients with prolonged hospitalization and give regulatory, research, and patient-centered recommendations for these cases. (shrink)

Until recently, psychologists have conceptualised and studied trust in God (TIG) largely in isolation from contemporary work in theology, philosophy, history, and biblical studies that has examined the topic with increasing clarity. In this article, we first review the primary ways that psychologists have conceptualised and measured TIG. Then, we draw on conceptualizations of TIG outside the psychology of religion to provide a conceptual map for how TIG might be related to theorised predictors and outcomes. Finally, we provide a research (...) agenda for future empirical work in this area, as well as practical applications for counsellors and religious leaders. (shrink)

The empirical study of grace, a relational virtue, is in its beginning stages. The purpose of this study was to provide rich, context-based, qualitative data to describe Mainline Protestants’ (a) experiences of, and (b) beliefs about, divine grace. Interviews were conducted with 28 community adults who were affiliated with Mainline Protestant Churches. Results indicated that Mainline Protestant Christians have varying beliefs about divine grace and how it is related to both the present moment and the afterlife. Divine grace was often (...) defined as, or associated with, other relational virtues (e.g., forgiveness and love), and participants occasionally defined grace as a gift. In addition, divine grace was also reported to be difficult to accept at times for a variety of reasons, but the effects of divine grace have direct associations with participants’ overall well-being. Divine grace was also associated with beliefs about heaven or the afterlife, yet participants had varying beliefs about how grace is applied to non-Christians. Limitations and future directions for research are discussed in light of the present empirical literature on divine grace. (shrink)

Photonic Crystals is the first book to address one of the newest and most exciting developments in physics--the discovery of photonic band-gap materials and their use in controlling the propagation of light. Recent discoveries show that many of the properties of an electron in a semiconductor crystal can apply to a particle of light in a photonic crystal. This has vast implications for physicists, materials scientists, and electrical engineers and suggests such possible developments as an entirely optical computer. Combining cutting-edge (...) research with the basic theoretical concepts behind photonic crystals, the authors present to undergraduates and researchers a concise, readable, and comprehensive text on these novel materials and their applications. The first chapters develop the theoretical tools of photonic crystals in a broad, intuitive fashion, starting from nothing more than Maxwell's equations and Fourier analysis, and include analogies to traditional solid-state physics and quantum theory. There follows an investigation of the unique phenomena that take place within photonic crystals, at defect sites, and at surfaces and interfaces. The authors offer a new treatment of the traditional multilayer film (a one-dimensional photonic crystal), which allows for the extension to higher dimensions and more complex geometries. After exploring the capabilities of photonic crystals to guide and localize light, the authors demonstrate how these notions can be put to work. (shrink)

Bibliography of works in experimental philosophy.

DBS Think Tank IX was held on August 25–27, 2021 in Orlando FL with US based participants largely in person and overseas participants joining by video conferencing technology. The DBS Think Tank was founded in 2012 and provides an open platform where clinicians, engineers and researchers can freely discuss current and emerging deep brain stimulation technologies as well as the logistical and ethical issues facing the field. The consensus among the DBS Think Tank IX speakers was that DBS expanded in (...) its scope and has been applied to multiple brain disorders in an effort to modulate neural circuitry. After collectively sharing our experiences, it was estimated that globally more than 230,000 DBS devices have been implanted for neurological and neuropsychiatric disorders. As such, this year’s meeting was focused on advances in the following areas: neuromodulation in Europe, Asia and Australia; cutting-edge technologies, neuroethics, interventional psychiatry, adaptive DBS, neuromodulation for pain, network neuromodulation for epilepsy and neuromodulation for traumatic brain injury. (shrink)

New materialism is one of the most important emerging trends in the humanities and social sciences, but it is also one of the least understood. This is because, as a term of ongoing contest...

Writing in 1999, legal ethics scholar Brad Wendel noted that “[v]ery little empirical work has been done on the moral decision making of lawyers.” Indeed, since the mid-1990s, few empirical studies have attempted to explore how attorneys deliberate about ethical dilemmas they encounter in their practice. Moreover, while past research has explored some of the ethical issues confronting lawyers practicing in certain specific areas of practice, no published data exists probing the moral mind of health care lawyers. As signaled by (...) the creation of a regular column “devoted to ethical issues arising in the practice of health law” in the Journal of Law, Medicine & Ethics, the time to address the empirical gap in the professional ethics literature is now. Accordingly, this article presents data collected from 120 health care lawyers. Presenting this population with a number of hypothetical scenarios relating to how they would respond when confronting an ethical dilemma without an obvious solution or when facing a situation in which their personal values were in tension with their professional obligations, this article represents a first step toward better understanding how lawyers who practice in health care settings understand and resolve the moral discomfort they encounter in their professional lives. (shrink)

The empirical literature exploring lawyers and their moral decision making is limited despite the “crisis” of unethical and unprofessional behavior in the bar that has been well documented for over a decade. In particular we are unaware of any empirical studies that investigate the moral landscape of the health lawyer’s practice. In an effort to address this gap in the literature, an interdisciplinary team of researchers at Vanderbilt University designed an empirical study to gather preliminary evidence regarding the moral reasoning (...) of health care attorneys. The primary research question was how health lawyers respond when they encounter ethical or moral dilemmas in their practice for which the law fails to offer a bright-line solution. In exploring this question, we sought to understand better what motivations or influences guide action when health lawyers confront ethical quandaries, and whether there are specific differences, e.g., gender, experience, or religiosity, that are associated with specific responses to situations testing ethical or moral boundaries. (shrink)

There has long been interest in identifying and studying ‘‘successful psychopaths.” This study sampled psychologists with an interest in law, attorneys, and clinical psychology professors to obtain descriptions of individuals considered to be psychopaths who were also successful in their endeavors. The results showed a consistent description across professions and convergence with descriptions of traditional psychopathy, though the successful psychopathy profile had higher scores on conscientiousness, as measured within the five-factor model (FFM). These results are useful in documenting the existence (...) of successful psychopathy, demonstrating the potential benefit of informant methodology, and providing an FFM description that distinguishes successful psychopaths from unsuccessful psychopaths studied more routinely within prison settings. (shrink)

The Hamiltonian for the Einstein equations is constructed on an outgoing null cone with the help of the usual null tetrad used in the study of the asymptotical gravitational radiation field.

This volume is a collection of essays by various contributors in honor of the late Laurence Berns, Richard Hammond Elliot Tutor Emeritus at St. John's College, Annapolis. The essays address the literary, political, theological, and philosophical themes of his life's work as a scholar, teacher, and constant companion of the "great books.".

In online social networks, the audience size commanded by an organization or an individual is a critical measure of that entity’s popularity and this measure has important economic and/or political implications. Such efforts to measure popularity of users or exploit knowledge about their audience are complicated by the presence of fake profiles on these networks. In this study, analysis of 62 million publicly available Twitter user profiles was conducted and a strategy to identify automatically generated fake profiles was established. Using (...) a combination of a pattern-matching algorithm on screen-names and an analysis of update times, a reasonable number of highly reliable fake user accounts were identified. Analysis of profile creation times and URLs of these fake accounts revealed their distinct behavior relative to a ground truth data set. The characteristics of friends and followers of users in the two data sets further revealed the very different nature of the two groups. The ratio of number of followers-to-friends for ground truth users was ∼1, consistent with past observations, while the fake profiles had a median ratio ∼30, indicating that the fake users we identified were primarily focused on gathering friends. An analysis of the temporal evolution of accounts over 2 years showed that the friends-to-followers ratio increased over time for fake profiles while they decreased for ground truth users. Our results, thus, suggest that a profile-based approach can be used for identifying a core set of fake online social network users in a time-efficient manner. (shrink)

This book reveals and discusses the foundations of law and justice. Fifteen leading lawyers and philosophers of law, representing thirteen nations and fifteen different philosophical schools examine the value and purpose of law, and the nature and requirements of law and justice. Some of the world's most learned and provocative legal scholars address the ultimate questions of legal and social philosophy from all angles and the broadest possible perspective, with special reference to the work of Mortimer Newlin Stead Sellers, and (...) the republican, liberal, and analytical schools of legal thought. The conclusions reached here are not fully unanimous, congruent or conclusive, but they represent the pinnacle of legal scholarship as it exists today and furnish the necessary basis for any future study of law, justice, or the ultimate requirements of just, effective and legitimate law and society. (shrink)

Responding to recent concerns about the reliability of the published literature in psychology and other disciplines, we formed the X-Phi Replicability Project to estimate the reproducibility of experimental philosophy. Drawing on a representative sample of 40 x-phi studies published between 2003 and 2015, we enlisted 20 research teams across 8 countries to conduct a high-quality replication of each study in order to compare the results to the original published findings. We found that x-phi studies – as represented in our sample (...) – successfully replicated about 70% of the time. We discuss possible reasons for this relatively high replication rate in the field of experimental philosophy and offer suggestions for best research practices going forward. (shrink)

Appendix 1 was incomplete in the initial online publication. The original article has been corrected.

We estimate that 208,000 deep brain stimulation (DBS) devices have been implanted to address neurological and neuropsychiatric disorders worldwide. DBS Think Tank presenters pooled data and determined that DBS expanded in its scope and has been applied to multiple brain disorders in an effort to modulate neural circuitry. The DBS Think Tank was founded in 2012 providing a space where clinicians, engineers, researchers from industry and academia discuss current and emerging DBS technologies and logistical and ethical issues facing the field. (...) The emphasis is on cutting edge research and collaboration aimed to advance the DBS field. The Eighth Annual DBS Think Tank was held virtually on September 1 and 2, 2020 (Zoom Video Communications) due to restrictions related to the COVID-19 pandemic. The meeting focused on advances in: (1) optogenetics as a tool for comprehending neurobiology of diseases and on optogenetically-inspired DBS, (2) cutting edge of emerging DBS technologies, (3) ethical issues affecting DBS research and access to care, (4) neuromodulatory approaches for depression, (5) advancing novel hardware, software and imaging methodologies, (6) use of neurophysiological signals in adaptive neurostimulation, and (7) use of more advanced technologies to improve DBS clinical outcomes. There were 178 attendees who participated in a DBS Think Tank survey, which revealed the expansion of DBS into several indications such as obesity, post-traumatic stress disorder, addiction and Alzheimer’s disease. This proceedings summarizes the advances discussed at the Eighth Annual DBS Think Tank. (shrink)

This paper introduces a framework for thinking about ontological questions—in particular, the Special Composition Question—and shows how the framework might help support something like an account of restricted composition. The framework takes the form of an account of natural objects, in analogy with David Lewis’s account of natural properties. Objects, like properties, come in various metaphysical grades, from the fundamental, fully objective, perfectly natural objects to the nomologically otiose, maximally gerrymandered, perfectly non-natural objects. The perfectly natural objects, I argue, are (...) the mereological simples, and (roughly) a collection composes an object of degree-n naturalness if and only if its members are arranged F-wise, for some property F that appears in the degree-n natural laws. Arbitrary composites turn out to be perfectly non-natural objects and are metaphysical bystanders. Ordinary composite objects fall in between. Some—e.g., atoms—are very (though not perfectly) natural; others—e.g., tables—are highly non-natural. (shrink)

A singular thought about an object o is one that is directly about o in a characteristic way—grasp of that thought requires having some special epistemic relation to the object o, and the thought is ontologically dependent on o. One account of the nature of singular thought exploits a Russellian Structured Account of Propositions, according to which contents are represented by means of structured n-tuples of objects, properties, and functions. A proposition is singular, according to this framework, if and only (...) if it contains an object as a constituent. One advantage of the framework of Russellian Structured propositions is that it promises to provide a metaphysical basis for the notion of a singular thought about an object, grounding it in terms of constituency. In this paper, we argue that the attempt to ground the peculiar features of singular thoughts in terms of metaphysical constituency fails, and draw some consequences of our discussion for other debates. (shrink)

How might law address the multiple crises of meaning intrinsic to global crises of climate, poverty, mass displacements, ecological breakdown, species extinctions and technological developments that increasingly complicate the very notion of 'life' itself? How can law embrace -- in other words --the 'posthuman' condition -- a condition in which non-human forces such as climate change and Covid-19 signal the impossibility of clinging to the existing imaginaries of Western legal systems and international law? This carefully curated book addresses these and (...) related questions, bringing 'law beyond the human' (drawing on Indigenous legalities, life ways and ontologies) and New Materialist and Posthuman/ist approaches into stimulating proximity to each other. Bold and astute, it draws an invigorating and lively mix of participants into its conversation: soils, urban animals, rivers, rights, Indigenous legalities, property as habitat, swarms, 'unusual posthuman capacities', decolonial critiques, eco-feedback, arts, affective encounters and more besides. Ultimately, this pivotal work shows how law currently fails to respond to the challenges and realities it faces, while demonstrating that law can also be a co-emergence of 'something else', more responsive, relational and prefigurative. Lively and engaging, Posthuman Legalities will prove an imperative read for students and scholars with a keen interest in breaking down barriers to address emerging challenges in environmental law, climate law, and human rights law, in conversation with new approaches to planetary justice. (shrink)

Emerging research has highlighted the utility of measuring individual differences in decision-making competence (DMC), showing that consistently following normatively rational principles is associated with positive psychosocial and health behaviors. From another level of analysis, functional theories of personality suggest that broad trait dimensions represent variation in underlying self-regulatory systems, providing a mechanistic account for robust associations between traits and similar life outcomes. Yet, the degree to which broad dispositional personality dimensions predict global tendencies to respond rationally is less understood. In (...) a large online community sample (N = 804), we tested the associations between HEXACO personality dimensions, a 6-factor structural trait model, and a subset of DMC indicators (Applying Decision Rules, Resistance to Framing, Recognizing Social Norms, and Consistency in Risk Perception). Additionally, we examined gender differences across the DMC, first considering the potential for measurement non-invariance across groups for the DMC. We observed partial measurement invariance between men and women; only the Applying Decision Rules scale showed evidence of differential functioning across groups. Controlling for these differences, analyses revealed that higher Conscientiousness, Honesty/Humility, and Openness were associated with higher DMC scores. In contrast, Emotionality and Extraversion demonstrated gender-specific associations. Speci... (shrink)

Decision Making Competence (DMC) reflects individual differences in rational responding across several classic behavioral decision-making tasks. Although it has been associated with real-world risk behavior, less is known about the degree to which DMC contributes to specific components of risk attitudes. Utilizing a psychological risk-return framework, we examined the associations between risk attitudes and DMC. Italian community residents (n = 804) completed an online DMC measure, using a subset of the original Adult-DMC battery (A-DMC; Bruine de Bruin, Parker, & Fischhoff, (...) 2007). Participants also completed a self-reported risk attitude measure for three components of risk attitudes (risk-taking, risk perceptions, and expected benefits) across six risk domains. Overall, greater performance on the DMC component scales were inversely, albeit modestly, associated with risk-taking tendencies. Structural equation modeling results revealed that DMC was associated with lower perceived expected benefits for all domains. In contrast, its association with perceived risks was more domain-specific. These analyses also revealed stronger indirect effects for the DMC  expected benefits  risk-taking than the DMC  perceived risk  risk-taking path, especially for risk behaviors that may be considered more antisocial in nature. These results suggest that DMC performance differentially impacts specific components of risk attitudes, and may be more strongly related to the evaluation of expected value of the given behavior. (shrink)

Background: Recent literature on addiction and judgments about the characteristics of agents has focused on the implications of adopting a ‘brain disease’ versus ‘moral weakness’ model of addiction. Typically, such judgments have to do with what capacities an agent has (e.g., the ability to abstain from substance use). Much less work, however, has been conducted on the relationship between addiction and judgments about an agent’s identity, including whether or to what extent an individual is seen as the same person after (...) becoming addicted. Methods: We conducted a series of vignette-based experiments (total N = 3,620) to assess lay attitudes concerning addiction and identity persistence, systematically manipulating key characteristics of agents and their drug of addiction. Conclusions: In Study 1, we found that US participants judged an agent who became addicted to drugs as being closer to ‘a completely different person’ than ‘completely the same person’ as the agent who existed prior to the addiction. In Studies 2-6, we investigated the intuitive basis for this result, finding that lay judgments of altered identity as a consequence of drug use and addiction are driven primarily by perceived negative changes in the moral character of drug users, who are seen as having deviated from their good true selves. (shrink)

Previous examinations of the scope of moral concern have focused on aggregate attributions of moral worth. However, because trade‐offs exist in valuing different kinds of entities, tabulating total amounts of moral expansiveness may conceal significant individual differences in the relative proportions of moral valuation ascribed to various entities. We hypothesized that some individuals (“tree‐huggers”) would ascribe greater moral worth to animals and ecosystems than to humans from marginalized or stigmatized groups, while others (“human‐lovers”) would ascribe greater moral worth to outgroup (...) members than to the natural world. Additionally, because moral valuation is often treated as being zero‐sum, we hypothesized that there would be no difference in aggregate levels of moral concern between tree‐huggers and human‐lovers. Finally, because attributions of mental capacities substantially contribute to moral valuation, we predicted that tree‐huggers and human‐lovers would show different patterns of mind attribution for animals versus humans. Three studies (N = 985) yielded evidence in support of our hypotheses. First, over one‐third of participants valued nature over outgroups. Second, extending moral value to animals and nature was not indicative of more expansive moral concern overall; instead, tree‐huggers and human‐lovers were identical in their aggregate ascriptions of moral worth. Third, tree‐huggers had relatively amplified tendencies to attribute mental capacities to animals and relatively reduced tendencies to attribute mental capacities to outgroup members—thus having elevated rates of both anthropomorphism and dehumanization. These findings necessitate a reconceptualization of both the extension of moral worth and the attribution of minds. (shrink)

This article aims to provide an a posteriori argument for the veracity of the Christian conception of the Abrahamic religion that centres on God’s action of sending a divine and atoning prophet—the ‘Messianic Prophet’—into the world, who we can identify as the person of Jesus of Nazareth. This specific argument will be presented through Richard Swinburne’s (modified) explanatory framework, which focuses on assessing the prior and posterior evidence in support of this identification. This, however, will be done in light of (...) the work of Historical Jesus and NT scholars John P. Meier, N.T. Wright, Richard Bauckham and Larry Hurtado—which, in combination, will provide a means to ward off two important objections against Swinburne's methodology, and ultimately allow one to establish the veracity of the ‘Christian Position’, on firm historical grounds. (shrink)

Public discourse is often caustic and conflict-filled. This trend seems to be particularly evident when the content of such discourse is around moral issues (broadly defined) and when the discourse occurs on social media. Several explanatory mechanisms for such conflict have been explored in recent psychological and social-science literatures. The present work sought to examine a potentially novel explanatory mechanism defined in philosophical literature: Moral Grandstanding. According to philosophical accounts, Moral Grandstanding is the use of moral talk to seek social (...) status. For the present work, we conducted six studies, using two undergraduate samples (Study 1, N = 361; Study 2, N = 356); a sample matched to U.S. norms for age, gender, race, income, Census region (Study 3, N = 1,063); a YouGov sample matched to U.S. demographic norms (Study 4, N = 2,000); and a brief, one-month longitudinal study of Mechanical Turk workers in the U.S. (Study 5, Baseline N = 499, follow-up n = 296), and a large, one-week YouGov sample matched to U.S. demographic norms (Baseline N = 2,519, follow-up n = 1,776). Across studies, we found initial support for the validity of Moral Grandstanding as a construct. Specifically, moral grandstanding motivation was associated with status-seeking personality traits, as well as greater political and moral conflict in daily life. (shrink)

A consequence relation is strongly classical if it has all the theorems and entailments of classical logic as well as the usual meta-rules (such as Conditional Proof). A consequence relation is weakly classical if it has all the theorems and entailments of classical logic but lacks the usual meta-rules. The most familiar example of a weakly classical consequence relation comes from a simple supervaluational approach to modelling vague language. This approach is formally equivalent to an account of logical consequence according (...) to which α1, ..., αn entails β just in case □α1, ..., □αn entails □β in the modal logic S5. This raises a natural question: If we start with a different underlying modal logic, can we generate a strongly classical logic? This paper explores this question. In particular, it discusses four related technical issues: (1) Which base modal logics generate strongly classical logics and which generate weakly classical logics? (2) Which base logics generate themselves? (3) How can we directly characterize the logic generated from a given base logic? (4) Given a logic that can be generated, which base logics generate it? The answers to these questions have philosophical interest. They can help us to determine whether there is a plausible supervaluational approach to modelling vague language that yields the usual meta-rules. They can also help us to determine the feasibility of other philosophical projects that rely on an analogous formalism, such as the project of defining logical consequence in terms of the preservation of an epistemic status. (shrink)

The present work posits that social motives, particularly status seeking in the form of moral grandstanding, are likely at least partially to blame for elevated levels of affective polarization and ideological extremism in the U.S. In Study 1, results from both undergraduates (N = 981; Mean age = 19.4; SD = 2.1; 69.7% women) and a cross-section of U.S. adults matched to 2010 census norms (N = 1,063; Mean age = 48.20, SD = 16.38; 49.8% women) indicated that prestige-motived grandstanding (...) was consistently and robustly related to more extreme ideological views on a variety of issues. In Study 2, results from a weighted, nationally-representative cross-section of U.S. adults (N = 2,519; Mean age = 47.5, SD = 17.8; 51.4% women) found that prestige motivated grandstanding was reliably related to both ideological extremism and affective polarization. (shrink)

This article aims to provide a theory of atonement, termed the "Agápēic Theory," which is formulated within a philosophical framework that has the aim of humans flourishing to the maximum level through partaking in an everlasting relationship of love with God. The Agápēic Theory will be formulated by using a certain conception of love, introduced by Alexander Pruss, into the field of applied ethics, and also various elements from other existing theories of the Atonement found within the fields of analytic (...) theology, in the work of Richard Swinburne, Eleonore Stump and Robin Collins, and systematic/biblical theology, in the work of Karl Barth and N.T Wright, which will both help to ground the Agápēic Theory on firm philosophical and theological grounds and ultimately provide a robust theory of the Atonement. (shrink)

In a fair finite lottery with n tickets, the probability assigned to each ticket winning is 1/n and no other answer. That is, 1/n is unique. Now, consider a fair lottery over the natural numbers. What probability is assigned to each ticket winning in this lottery? Well, this probability value must be smaller than 1/n for all natural numbers n. If probabilities are real-valued, then there is only one answer: 0, as 0 is the only real and non-negative value that (...) is smaller than 1/n for all natural numbers n. However, this answer seems counter-intuitive, as it violates Regularity: for all possible events A that are assigned a probability, A is assigned a positive probability. It is possible for ticket i to win in the second lottery. So, the set {i} should be assigned a positive probability and not 0. Consequently, in order to satisfy Regularity, probabilities must be allowed to take on `non-real' values, e.g. a positive infinitesimal x that is smaller than 1/n for all natural numbers n. So, what regular probability is assigned to {i} in the second lottery? This probability value must be positive but smaller than 1/n for all natural numbers n. Given the definition of x, x is a correct answer. But x isn't unique, because every other positive infinitesimal is a correct answer as well and there are uncountably many positive infinitesimals. After all, every positive infinitesimal is strictly between 0 and 1/n for all natural numbers n. Nothing about a fair lottery over the natural numbers uniquely determines x as the correct answer and nothing about the lottery rules out other positive infinitesimals as a correct answer as well. What probability to assign to {i} is underdetermined. -/- In this thesis, I explore this difference between fair finite lotteries and fair infinite lotteries. The constraints governing the former uniquely determine the probabilities assigned to events in those lotteries, but this isn't true for the latter lotteries, when Regularity is a constraint on probabilities. Now, although there are uncountably many correct probability values that can be assigned to {i} in the second lottery, there are some applications of probability theory, for which at least one correct probability value must be chosen in order to accomplish that application, e.g. calculation of expected utilities. In this thesis, I spell out sufficient conditions for when a choice like that is problematic. These conditions apply to precise probabilities, imprecise probabilities, and qualitative probabilities. So, I will consider Benci et al. (2018)'s and Pruss (2021)'s suggestion of allowing probabilities to be imprecise, as well as resorting to qualitative probabilities, to overcome the choice problem. I will argue that both don't solve the problem. Furthermore, there's a hitherto unnoticed difficulty in deriving imprecise probabilities by supervaluating over precise `non-real' probability values. To avoid this difficulty, precise probability values should be real-valued. Thus, Regularity cannot be a constraint on probabilities. But as it turns out, dropping Regularity as a constraint and requiring precise probabilities to be real-valued solve the choice problem. (shrink)