We present a formal system, E, which provides a faithful model of the proofs in Euclid's Elements, including the use of diagrammatic reasoning.

The ability of very wealthy individuals (or, as I will call them, the ‘super-rich’) to turn their economic power into political power has been—and remains—an important cause of political inequality. In response, this paper advocates an original solution. Rather than solving the problem through implementing a comprehensive conception of political equality, or through enforcing complex rules about financial disclosure etc., I argue that we should impose a choice on the super-rich. The super-rich must choose between (i) forfeiting the things that (...) make them super-rich, i.e., pay a 100 % tax on their wealth above a certain level, or, (ii) they must forfeit some of their political rights. These rights include entitlements to fund political parties; to stand for office; and to work or volunteer for political parties. The right to vote, though, is not limited. I defend my proposal against non-consequentialist and consequentialist objections. I also argue that it avoids two problems that many attempts to reduce political inequality face; these are the political egalitarian’s dilemma and the problem of political equality’s relative moral importance. (shrink)

This article argues against the claim that democracy is a necessary condition of political legitimacy. Instead, I propose a weaker set of conditions. First, I explain the case for the necessity of democracy. This is that only democracy can address the ‘egalitarian challenge’, i.e. ‘if we are all equal, why should only some of us wield political power?’. I show that if democracy really is a necessary condition of political legitimacy, then (what I label) the problems of domestic justice and (...) of international legitimacy become intractable. I then argue that the egalitarian challenge is addressed where the requirements of (1) horizontal equality, (2) acceptable vertical inequality, and (3) publicity, are met and where (4) citizens have some institutionalized opportunity for a voice in decisions. I show that these conditions can be realized in non-democratic form and conclude by explaining how the four conditions can be employed to make the problems of domestic justice and of international legitimacy more tractable. Overall, my ambitions are limited. I do not offer an all-things-considered case against democracy but I do show that (some) forms of non-democratic government are permissible. (shrink)

The dominated convergence theorem implies that if is a sequence of functions on a probability space taking values in the interval [0, 1], and converges pointwise a.e., then converges to the integral of the pointwise limit. Tao [26] has proved a quantitative version of this theorem: given a uniform bound on the rates of metastable convergence in the hypothesis, there is a bound on the rate of metastable convergence in the conclusion that is independent of the sequence and the underlying (...) space. We prove a slight strengthening of Tao’s theorem which, moreover, provides an explicit description of the second bound in terms of the first. Specifically, we show that when the first bound is given by a continuous functional, the bound in the conclusion can be computed by a recursion along the tree of unsecured sequences. We also establish a quantitative version of Egorov’s theorem, and introduce a new mode of convergence related to these notions. (shrink)

The US neutrino community gathered at the Workshop on the Intermediate Neutrino Program at Brookhaven National Laboratory February 4-6, 2015 to explore opportunities in neutrino physics over the next five to ten years. Scientists from particle, astroparticle and nuclear physics participated in the workshop. The workshop examined promising opportunities for neutrino physics in the intermediate term, including possible new small to mid-scale experiments, US contributions to large experiments, upgrades to existing experiments, R&D plans and theory. The workshop was organized into (...) two sets of parallel working group sessions, divided by physics topics and technology. Physics working groups covered topics on Sterile Neutrinos, Neutrino Mixing, Neutrino Interactions, Neutrino Properties and Astrophysical Neutrinos. Technology sessions were organized into Theory, Short-Baseline Accelerator Neutrinos, Reactor Neutrinos, Detector R&D and Source, Cyclotron and Meson Decay at Rest sessions.This report summarizes discussion and conclusions from the workshop. (shrink)

Despite a large and multifaceted effort to understand the vast landscape of phenotypic data, their current form inhibits productive data analysis. The lack of a community-wide, consensus-based, human- and machine-interpretable language for describing phenotypes and their genomic and environmental contexts is perhaps the most pressing scientific bottleneck to integration across many key fields in biology, including genomics, systems biology, development, medicine, evolution, ecology, and systematics. Here we survey the current phenomics landscape, including data resources and handling, and the progress that (...) has been made to accurately capture relevant data descriptions for phenotypes. We present an example of the kind of integration across domains that computable phenotypes would enable, and we call upon the broader biology community, publishers, and relevant funding agencies to support efforts to surmount today's data barriers and facilitate analytical reproducibility. (shrink)

Corporate political action committees (PACs) play a prominent role in the political strategies of U.S. organizations, and the ability of firms to influence political outcomes is highly controversial. To the extent that PACs enable groups of firms to pursue corporate agendas at the expense of the social good, they promote socially suboptimal outcomes. This study examines the impact of corporate PACs on entry restriction in manufacturing industries and finds a negative relationship between corporate PAC spending and the entry of new (...) firms. Results suggest that PACs are used to shape industry structure to the economic benefit of incumbents. (shrink)

Psychology training programs emphasize competencies like professional behavior, interpersonal skills, and emotional intelligence. Some students, known as students with problems of professional competence (SPPC), struggle in these areas. This study explored SPPC characteristics and educator experiences in managing them through semi-structured interviews with twelve Australian psychology educators. Thematic analysis revealed that SPPC often struggle with professional attitudes, feedback integration, reflective skills, and mental health, placing demands on resources and contributing to educator stress. The role of educators as gatekeepers, assessors, and (...) evaluators also raises concerns about maintaining ethical standards. Findings highlight the need for better understanding, support, and strategies for managing SPPC to uphold ethical standards. (shrink)

Tom Andersen’s reflecting team process, which allowed families to witness and respond to the talk of professionals during therapy sessions, has been described as revolutionary in the field of family therapy. Reflecting teams are prominent in a number of family therapy approaches, more recently in narrative and dialogical therapies. This way of working is considered more a philosophy than a technique, and has been received positively by both therapists and service users. This paper describes how dialogical therapists conceptualise the reflective (...) process, how they work to engage families in reflective dialogues and how this supports change. We conducted semi-structured, reflective interviews with 12 dialogical therapists with between 2 and 20 years of experience. Interpretative Phenomenological analysis of transcribed interviews identified varying conceptualisations of the reflecting process and descriptions of therapist actions that support reflective talk among network members. We adopted a dialogical approach to interpretation of this data. In this sense, we did not aim to condense accounts into consensus but instead to describe variations and new ways of understanding dialogical reflecting team practices. Four themes were identified: Lived experience as expertise; Listening to the self and hearing others; Relational responsiveness and fostering connection; and Opening space for something new. We applied these themes to psychotherapy process literature both within family therapy literature and more broadly to understand more about how reflecting teams promote helpful and healing conversations in practice. (shrink)

Quantitative researchers often discuss research ethics as if specific ethical problems can be reduced to abstract normative logics (e.g., virtue ethics, utilitarianism, deontology). Such approaches overlook how values are embedded in every aspect of quantitative methods, including ‘observations,’ ‘facts,’ and notions of ‘objectivity.’ We describe how quantitative research practices, concepts, discourses, and their objects/subjects of study have always been value-laden, from the invention of statistics and probability in the 1600s to their subsequent adoption as a logic made to appear as (...) if it exists prior to, and separate from, ethics and values. This logic, which was embraced in the Academy of Management from the 1960s, casts management researchers as ethical agents who ought to know about a reality conceptualized as naturally existing in the image of statistics and probability (replete with ‘constructs’), while overlooking that S&P logic and practices, which researchers made for themselves, have an appreciable role in making the world appear this way. We introduce a different way to conceptualize reality and ethics, wherein the process of scientific inquiry itself requires an examination of its own practices and commitments. Instead of resorting to decontextualized notions of ‘rigor’ and its ‘best practices,’ quantitative researchers can adopt more purposeful ways to reason about the ethics and relevance of their methods and their science. We end by considering implications for addressing ‘post truth’ and ‘alternative facts’ problems as collective concerns, wherein it is actually the pluralistic nature of description that makes defending a collectively valuable version of reality so important and urgent. (shrink)

This article describes some potential uses of Bayesian estimation for time-series and panel data models by incorporating information from prior probabilities (i.e., priors) in addition to observed data. Drawing on econometrics and other literatures we illustrate the use of informative “shrinkage” or “small variance” priors (including so-called “Minnesota priors”) while extending prior work on the general cross-lagged panel model (GCLM). Using a panel dataset of national income and subjective well-being (SWB) we describe three key benefits of these priors. First, they (...) shrink parameter estimates toward zero or toward each other for time-varying parameters, which lends additional support for an income → SWB effect that is not supported with maximum likelihood (ML). This is useful because, second, these priors increase model parsimony and the stability of estimates (keeping them within more reasonable bounds) and thus improve out-of-sample predictions and interpretability, which means estimated effect should also be more trustworthy than under ML. Third, these priors allow estimating otherwise under-identified models under ML, allowing higher-order lagged effects and time-varying parameters that are otherwise impossible to estimate using observed data alone. In conclusion we note some of the responsibilities that come with the use of priors which, departing from typical commentaries on their scientific applications, we describe as involving reflection on how best to apply modeling tools to address matters of worldly concern. (shrink)

We find that E. J. Lowe’s resolution to David Lewis’s problem of temporary intrinsics is wrong, but not quite for the reasons adduced by Lewis himself. Our discussion hinges on a connection between state-independent properties and intrinsic properties.

Background: When adolescent boys experience close, secure relationships with their parents and peers, the implications are potentially far reaching, including lower levels of mental health problems in adolescence and young adulthood. Here we use rare prospective intergenerational data to extend our understanding of the impact of adolescent attachments on subsequent postpartum mental health problems in early fatherhood.Methods: At age 17–18 years, we used an abbreviated Inventory of Parent and Peer Attachment to assess trust, communication, and alienation reported by 270 male (...) participants in their relationships with mothers, fathers, and peers. More than a decade later, we assessed the adult males, now fathers, at 12 months postpartum for symptoms of depression, anxiety, and stress. Logistic regression was used to examine the extent to which attachment dimensions predicted paternal postpartum mental health, adjusting for potential confounding, and with assessment for interactions between parent and peer attachments.Results: Trust in mothers and peers, and good communication with fathers during adolescence, were associated with 5 to 7 percentage point reductions in postpartum mental health symptoms in early fatherhood. Weak evidence of parent-peer interactions suggested secure attachments with either parent or peer may compensate for an insecure attachment with the other.Conclusions: Our results suggest that fostering trust and communication in relationships that adolescent boys have with parents and peers may have substantial effects on rates of paternal postpartum mental health problems. The protective benefits may be preventative in intergenerational cycles of risk for mental health problems. (shrink)

Recent publications by several leading philosophers of chemistry have focused on the definition, scope, utility, and nomenclature of issues dealing with acidity and basicity. In this paper, molecular orbital theory is used to explain all acid–base reactions, concluding that the interaction of the highest occupied molecular orbital (HOMO) of one substrate, “the base,” with the lowest unoccupied molecular orbital (LUMO) of a second substrate, “the acid,” determines the reactivity of such systems. This paradigm provides an understanding of all acid–base reactions (...) as well as other reactions which, on the surface, may not seem like acid–base reactions but which have fundamental underpinnings of that kind of chemistry. Rather than being unable to determine a unified understanding of acidity and basicity as suggested in the philosophy of chemistry literature, we propose that acidity and basicity fit securely in a classification of many other reactions that, using classical chemistry knowledge, pre-quantum chemistry, would not be possible. We strongly support the use of all scientific knowledge and experience in the development of the ideas in the philosophy science. We further suggest increased interactions between philosophers of science and scientists, so that all scholars benefit from the values, knowledge, and perspectives of other disciplines. (shrink)

Democracy can be a means to independently valuable ends and/or it can be intrinsically (or non-instrumentally) valuable. One powerful non-instrumental defence of democracy is based on the idea that only it can publicly justify political authority. I contend that this is an argument about the reasonable acceptability of political authority and about the requirements of publicity and that satisfying these requirements has nothing to do with whether a society is democratic or not. Democracy, then, plays no role in publicly justifying (...) political authority. I also show that any non-instrumental defence of democracy must make claims about what justice requires and make several further claims that require substantial justification. (shrink)

We analyze the pointwise convergence of a sequence of computable elements of L1 in terms of algorithmic randomness. We consider two ways of expressing the dominated convergence theorem and show that, over the base theory RCA0, each is equivalent to the assertion that every Gδ subset of Cantor space with positive measure has an element. This last statement is, in turn, equivalent to weak weak Königʼs lemma relativized to the Turing jump of any set. It is also equivalent to the (...) conjunction of the statement asserting the existence of a 2-random relative to any given set and the principle of Σ2 collection. (shrink)

BackgroundDespite five decades of increasingly elegant studies aimed at advancing the pathophysiology and treatment of mental illness, the results have not met expectations. Diagnoses are still based on observation, the clinical history, and an outmoded diagnostic system that stresses the historic goal of disease specificity. Psychotropic drugs are still based on molecular targets developed decades ago, with no increase in efficacy. Numerous biomarkers have been proposed, but none have the requisite degree of sensitivity and specificity, and therefore have no usefulness (...) in the clinic. The obvious lack of progress in psychiatry needs exploration.MethodsThe historical goals of psychiatry are reviewed, including parity with medicine, a focus on diagnostic reliability rather than validity, and an emphasis on reductionism at the expense of socioeconomic issues. Data are used from Thomas Picketty and others to argue that our failure to advance clinical care may rest in part on the rise in social and economic inequality that began in the 1970s, and in part on our inability to move beyond the medical model of specificity of disease and treatment.ResultsIt is demonstrated herein that the historical goal of specificity of disease and treatment has not only impeded the advance of diagnosis and treatment of mental illness, but, in combination with a rapid increase in socioeconomic inequality, has led to poorer outcomes and rising mortality rates in a number of disorders, including schizophrenia, anxiety, and depression.ConclusionsIt is proposed that Psychiatry should recognize the fact of socioeconomic inequality and its effects on mental disorders. The medical model, with its emphasis on diagnostic and treatment specificity, may not be appropriate for investigation of the brain, given its complexity. The rise of scientific inequality, with billions allocated to connectomics and genetics, may shift attention away from the need for improvements in clinical care. Unfortunately, the future prospects of those suffering from mental illness appear dim. (shrink)

The ‘byproduct account’ of female orgasm, a subject of renewed debate since Lloyd (The case of the female orgasm, Harvard University Press, Cambridge, 2005), is universally attributed to Symons (The evolution of human sexuality, Oxford University Press, Oxford, 1979). While this is correct to the extent that he linked it to the adaptive value of male orgasm, I argue that the attribution of the theory as we understand it to Symons is based on a serious and hitherto unrecognised misinterpretation. Symons (...) had a different explanation of why women can orgasm, and beneath this explanation lies an obscure line of argument, including a particularly obscure use of the word ‘homologous’. (shrink)

We address how the leaders of a Catholic business school can articulate and assess how well their schools implement the following six principles drawn from Catholic social teaching : produce goods and services that are authentically good; foster solidarity with the poor by serving deprived and marginalized populations; advance the dignity of human work as a calling; exercise subsidiarity; promote responsible stewardship over resources; and acquire and allocate resources justly. We first discuss how the CST principles give substantive content and (...) meaning to the Good Goods, Good Work, and Good Wealth framework in The Vocation of the Business Leader and then discuss their congruencies and tensions with the UNGC and UNPRME principles. Next, we describe the Catholic Identity Matrix, an assessment tool that provides a quantitative and qualitative portrait of how well a Catholic business school integrates, within the scope of its mission and capacities, the three goods and related CST principles in its strategies, policies, activities, and processes. The concluding section discusses implications for ongoing UNGC and UNPRME assessment, reporting, and development efforts, and addresses the generalizability of our approach to business schools who draw their inspiration and moral principles from other faith-based or secular traditions. (shrink)

Este artigo analisa a importância do papel desempenhado pelo diplomata George Frost Kennan na elaboração da política externa dos Estados Unidos durante a Guerra Fria. Ao final da Segunda Guerra Mundial, no contexto marcado pelas apreensões relativas às rivalidades globais entre os EUA e a URSS, Kennan recomendou uma estratégia com a intenção de conter as potenciais tendências expansionistas da União Soviética. Em sua consideração, a principal ameaça posta pela União Soviética não era militar, mas sua capacidade de influência ideológica, (...) veiculada pelos partidos comunistas e seus seguidores no interior das sociedades democráticas ocidentais. Desta hipótese precedente, Kennan arquitetou a Doutrina de Contenção, uma estratégia crucial da política externa dos Estados Unidos durante a Guerra Fria. Como um diplomata de carreira e grande autoridade nos estudos relacionados à sociedade Soviética, Kennan escreveu durante a sua vida uma extraordinária obra relacionada à diplomacia dos EUA e aos seus desafios colossais no ambiente do conflito global. No entanto, desde o início da segunda Administração Truman, Kennan observou que a estratégia estadunidense em relação à Guerra Fria havia se tornado mais militarista e intensificado a corrida armamentista. Ao assumir uma posição crítica em relação a essas diretrizes, que, de acordo com a sua perspectiva, levava à distorção da sua concepção original da teoria da Contenção, Kennan foi marginalizado pelo novo Secretário de Estado, Dean Acheson e deslocado do núcleo de elaboração política do governo. Posteriormente, ele questionou a adopção da Doutrina Truman, a criação da OTAN e o envolvimento dos Estados Unidos nas guerras da Coréia e do Vietnam.George Frost Kennan and the architecture of U.S. Foreign Policy in the genesis of the Cold War This article analyzes the major role performed by diplomat George Frost Kennan in the United States Foreign Policy during the Cold War. By the end of World War II, amidst apprehensions concerning the U.S. and the USSR global rivalries, Kennan recommended a strategy intending to contain the potential expansionist tendencies of the Soviet Union. In his consideration, the core threat upraised by Soviet Union was not military, but its ideological influence conveyed by Communist parties and fellow travelers inside the western democratic societies. From this preceding hypothesis, Kennan designed the doctrine of containment, a crucial strategy of U.S. foreign policy during the Cold War. As a career diplomat and major authority on Soviet society, Kennan wrote during his lifetime an remarkable work related to U.S. diplomacy and its colossal challenges in the environment of that global conflict. Nonetheless, since the inauguration of the second Truman administration, Kennan observed that U.S. Cold War strategy had become more militaristic and that it had strengthened the arms race. For assuming a critical position towards this path, which, according to his perspective, was a distortion of his original containment theory, Kennan was marginalized by the new Secretary of State, Dean Acheson, and displaced from core government power. Subsequently, he stood up against the adoption of the Truman Doctrine, the creation of NATO and the commitment of the United States in the Korean and Vietnam wars. Resumen George Frost Kennan y la arquitectura de la política externa de los EUA en el origen de la Guerra Fría Este artículo analiza la importancia del papel desempeñado por el diplomático George Frost Kennan en la elaboración de la política externa de los Estados Unidos durante la Guerra Fría. Al finalizar la Segunda Guerra Mundial, en el contexto marcado por las aprehensiones vinculadas a las rivalidades globales entre los EUA y la URSS, Kennan recomendó una estrategia con la intención de contener las potenciales tendencias expansionistas de la Unión Soviética. En su entendimiento, la principal amenaza de la Unión Soviética no era militar, y sí su capacidad de influencia ideológica, vehiculada por los partidos comunistas y sus seguidores en el interior de las sociedades democráticas occidentales. Partiendo de esta hipótesis, Kennan ideó la Doctrina de Contención, una estrategia crucial de la política externa de los EEUU durante la Guerra Fría. Como diplomático de carrera y una autoridad en estudios relacionados a la Unión Soviética, Kennan escribió durante su vida una extraordinaria obra relacionada a la diplomacia estadounidense y sus desafíos colosales en el ambiente del conflicto global. Sin embargo, desde el inicio de la segunda administración Truman, Kennan observó que la estrategia de los EUA en relación a la Guerra Fría se había tornado más militarista, intensificándose la carrera armamentista. Al asumir una posición crítica en relación a estas directrices que, de acuerdo a su perspectiva, conducía a la distorsión de su original teoría de la Contención, Kennan fue marginado por el nuevo Secretario de Estado, Dean Acheson, y desplazado del núcleo de elaboración política del gobierno. Posteriormente, él cuestionó la adopción de la Doctrina Truman, la creación de la OTAN y la participación de Estados Unidos en las guerras de Corea y de Vietnam. (shrink)

Human trafficking is increasingly recognized as an outcome of economic insecurity, gender inequality, and conflict, all significant factors in the region of southern Africa. This paper examines policy responses to human trafficking in southern Africa and finds that there has been a diffusion of international norms to the regional and domestic levels. This paper finds that policy change is most notable in the strategies and approaches that differ at each level: international and regional agreements emphasize prevention measures and survivor assistance, (...) but national policies emphasize prosecution measures. Leaders across the region have adapted these policy norms to fit regionally specific conditions, including HIV/AIDS, conflict, traditional leaders, and prostitution. Yet, national policies often fail to incorporate preventative solutions to address gender inequality, human rights, and economic development. Until appropriate funding and preventative measures are introduced, the underlying issues that foster human trafficking will continue. (shrink)

An autobiographic instinct may be as old as Man Writing; but only since 1800 has Western Man placed a premium on autobiography. A bibliography of all autobiographic writing prior to that time would be a small fascicule; a bibliography since 1800 a thick tome. The ground behind this simpleminded assertion of a quantitative measure cannot be explained away by easy reference to the mass literacy of the modern world or the greater ease of publishing. It is as much a fact (...) of cultural conditions as is the significant relation of rhetoric to the intense public mindedness of classical men, the relative insignificance of tragedy in a thoroughly Christianized world view, the disappearance of epic from a nonaristocratic world, or the powerful assertion of the novel in an age of burghers. The usage of the term "autobiography" itself is suggestive, although this mode of historical explanation is always defective in the sense that such older terms as "hypomnemata," "commentarii," "vita," "confessions," or "memoirs" may well have covered the functions subsequently encapsulated in a newly fashionable term. In German the term makes its appearance shortly before 1800; the Oxford English Dictionary attributes first English usage to Southey in an article on Portuguese literature from the year 1809. Karl J. Weintraub, Thomas E. Donnelley Professor of History and dean of the Division of the Humanities at the University of Chicago, is the author of Visions of Culture and numerous articles. His introduction to a new edition of Goethe's Autobiography will prove of special interest to our readers. (shrink)

In this volume, I have given attention to what I consider to be some of the central problems and topics in the philosophical thought of SJ2jren Kierkegaard. Some of the chapters have been previously publish ed but were revised for their appearance here. Others were written expressly for this book. I have tried to focus on issues which have not been customarily dealt with or emphasized in the scholarship on Kierkegaard with the exception of the writings of David Swenson and (...) Paul L. Holmer to which (and to whom) I am greatly indebted. Some of the positions for which I have argued in this volume (especially in Chapters IV and V) may be controversial. I am grateful to all those who enabled me to carry out or influenced me in my studies of Kierkegaard or who assisted with regard to the research for or preparation of this volume. Among these are: Professors Paul L. Holmer, F. Arthur Jacobson, and Dennis A. Rohatyn; Dean Wallace A. Russell and Vice President Daniel J. Zaffarano of Iowa State University. (shrink)

Paul Cohen’s method of forcing, together with Saul Kripke’s related semantics for modal and intuitionistic logic, has had profound effects on a number of branches of mathematical logic, from set theory and model theory to constructive and categorical logic. Here, I argue that forcing also has a place in traditional Hilbert-style proof theory, where the goal is to formalize portions of ordinary mathematics in restricted axiomatic theories, and study those theories in constructive or syntactic terms. I will discuss the aspects (...) of forcing that are useful in this respect, and some sample applications. The latter include ways of obtaining conservation results for classical and intuitionistic theories, interpreting classical theories in constructive ones, and constructivizing model-theoretic arguments. (shrink)

Distributional models of semantics learn word meanings from contextual co‐occurrence patterns across a large sample of natural language. Early models, such as LSA and HAL (Landauer & Dumais, 1997; Lund & Burgess, 1996), counted co‐occurrence events; later models, such as BEAGLE (Jones & Mewhort, 2007), replaced counting co‐occurrences with vector accumulation. All of these models learned from positive information only: Words that occur together within a context become related to each other. A recent class of distributional models, referred to as (...) neural embedding models, are based on a prediction process embedded in the functioning of a neural network: Such models predict words that should surround a target word in a given context (e.g., word2vec; Mikolov, Sutskever, Chen, Corrado, & Dean, 2013). An error signal derived from the prediction is used to update each word's representation via backpropagation. However, another key difference in predictive models is their use of negative information in addition to positive information to develop a semantic representation. The models use negative examples to predict words that should not surround a word in a given context. As before, an error signal derived from the prediction prompts an update of the word's representation, a procedure referred to as negative sampling. Standard uses of word2vec recommend a greater or equal ratio of negative to positive sampling. The use of negative information in developing a representation of semantic information is often thought to be intimately associated with word2vec's prediction process. We assess the role of negative information in developing a semantic representation and show that its power does not reflect the use of a prediction mechanism. Finally, we show how negative information can be efficiently integrated into classic count‐based semantic models using parameter‐free analytical transformations. (shrink)

The early twentieth century was a lively time for the foundations of mathematics. This ensuing debates were, in large part, a reaction to the settheoretic and nonconstructive methods that had begun making their way into mathematical practice around the turn of the twentieth century. The controversy was exacerbated by the discovery that overly na¨ıve formulations of the fundamental principles governing the use of sets could result in contradictions. Many of the leading mathematicians of the day, including Hilbert, Henri Poincar´e, ´.

Omnipresent calls for more women in university administration assume these women will prioritize using resources and power to increase female representation, especially in STEM fields where women are most underrepresented. However, empirical evidence is lacking for systematic differences in female versus male administrators’ attitudes. Do female administrators agree on which strategies are best, and do men see things differently? To answer this question, we explored United States college and university administrators’ opinions regarding policies, strategies, and structural changes in their organizations (...) designed to increase women professors’ representation and retention in STEM fields. A comprehensive review of past research yielded a database of potentially-effective, recommended policies (e.g., increasing emphasis on teaching, service, and administration during promotion reviews; stopping the tenure clock for childbearing; providing on-campus childcare; couples-hiring; sharing tenure lines; having more women chair search committees; setting gender quotas for promotion). A survey based on these recommended policies was sent to provosts, deans, associate deans, and department chairs of STEM fields at 96 public and private research universities (formerly called R1s) across the U.S. These administrators were asked to rate the quality and feasibility of each recommended policy; 474 provided data, of which 334 contained complete numerical data used in the analyses, so our results are based on a large, geographically diverse group of administrators at research universities. Our data revealed that female administrators perceived the 44 strategies to be higher in quality overall than did male administrators--but not higher in feasibility--with 9 policies perceived differently when rated by women versus men administrators, after imposing conservative statistical controls. There was broad general agreement on the relative rankings of the 44 policies in terms of their perceived quality. Overall, our national survey of U.S. administrators supported the assertion that placing women in administrative roles creates greater emphasis on the importance of enacting policies to attract and retain women in STEM. Topics of disagreement between women and men regarding strategy quality are important focuses of future policy and planning, because female administrators may have insights into how to retain women professors that male administrators do not share. (shrink)

An efficient variant of the double-negation translation explains the relationship between Shoenfield’s and G¨odel’s versions of the Dialectica interpretation.

We address the general problem of determining the validity of boolean combinations of equalities and inequalities between real-valued expressions. In particular, we consider methods of establishing such assertions using only restricted forms of distributivity. At the same time, we explore ways in which “local'’ decision or heuristic procedures for fragments of the theory of the reals can be amalgamated into global ones. Let $Tadd[QQ]$ be the first-order theory of the real numbers in the language with symbols $0, 1, +, -.

From ancient times to the beginning of the nineteenth century, mathematics was commonly viewed as the general science of quantity, with two main branches: geometry, which deals with continuous quantities, and arithmetic, which deals with quantities that are discrete. Mathematical logic does not fit neatly into this taxonomy. In 1847, George Boole [1] offered an alternative characterization of the subject in order to make room for this new discipline: mathematics should be understood to include the use of any symbolic calculus (...) “whose laws of combination are known and general, and whose results admit of a consistent interpretation.” Depending on the laws chosen, symbols can just as well be used to represent propositions instead of quantities; in that way, one can consider calculations with propositions on par with more familiar arithmetic calculations. Despite Boole’s efforts, logic has always held an uncertain place in the mathematical community. This can partially be attributed to its youth; while number theory and geometry have their origins in antiquity, mathematical logic did not emerge as a recognizable discipline until the latter half of the nineteenth century, and so lacks the provenance and prestige of its elder companions. Furthermore, the nature of the subject matter serves to set it apart; as objects of mathematical study, formulas and proofs do not have the same character as groups, topological spaces, and measures. Even distinctly mathematical branches of contemporary logic, like model theory and set theory, tend to employ linguistic classifications and measures of complexity that are alien to other mathematical disciplines. The Birth of Model Theory, by Calixto Badesa, describes a seminal step in the emergence of logic as a mature mathematical discipline. As its title suggests, the focus is on one particular result, now referred to as the L¨owenheim-Skolem theorem, as presented in a paper by L¨owenheim in 1915. But the book is, more broadly, about the story of the logic community’s gradual coming to the modern distinction between syntax and semantics, that is, between systems of symbolic expressions and the meanings that can be assigned to them.. (shrink)

By the middle of the nineteenth century, it had become clear to mathematicians that the study of finite field extensions of the rational numbers is indispensable to number theory, even if one’s ultimate goal is to understand properties of diophantine expressions and equations in the ordinary integers. It can happen, however, that the “integers” in such extensions fail to satisfy unique factorization, a property that is central to reasoning about the ordinary integers. In 1844, Ernst Kummer observed that unique factorization (...) fails for the cyclotomic integers with exponent 23, i.e. the ring Z[ζ] of integers of the field Q(ζ), where ζ is a primitive twenty-third root of unity. In 1847, he published his theory of “ideal divisors” for cyclotomic integers with prime exponent. This was to remedy the situation by introducing, for each such ring of integers, an enlarged domain of divisors, and showing that each integer factors uniquely as a product of these. He did not actually construct these integers, but, rather, showed how one could characterize their behavior qua divisibility in terms of ordinary operations on the associated ring of integers. (shrink)

This article outlines a training activity that can enable both business and governmental professionals to translate the principles in a code of ethics to a specific list of company-related behaviors ranging from highly ethical to highly unethical. It also explores how this list can become a concrete model to follow in making ethical decisions. The article begins with a discussion as to what will improve ethical decision making in business and government. This leads us to explore the factors that can (...) most easily lead to improvement, namely a comprehensive code of conduct and employee training. From there we look at the Critical Incident Technique as a training strategy that has the potential for identifying those behaviors that distinguish really outstanding behaviors from those that go by the book, and can be used to encourage more independent thinking and to set expectations for future decisions. If employees are given the skills and examples that will enable them to make better decisions, they can apply them to any situation. (shrink)