The Loeb space construction in nonstandard analysis is applied to the theory of processes to reveal basic phenomena which cannot be treated using classical methods. An asymptotic interpretation of results established here shows that for a triangular array (or a sequence) of random variables, asymptotic uncorrelatedness or asymptotic pairwise independence is necessary and sufficient for the validity of appropriate versions of the law of large numbers. Our intrinsic characterization of almost sure pairwise independence leads to the equivalence of (...) various multiplicative properties of random variables. (shrink)

Adults increase the certainty of their inductive inferences by observing more diverse instances. However, most young children fail to do so. The present study tested the hypothesis that children's sensitivity to instance diversity is determined by three variables: ability to discriminate among instances ( Discrimination ); an intuition that large numbers of instances increase the strength of conclusion ( Monotonicity ); ability to detect subcategories and evaluate numerical differences between the subcategories, or Extraction . A total of 219 (...) Chinese children aged 6 to 11 were tested for sensitivity to diversity by means of Discrimination, Monotonicity, and Extraction. The results indicated that children at all ages were able to discriminate instances and attend to set size. However, only 9- and 11-year-olds demonstrated Extraction and sensitivity to diversity. Furthermore, among all children diversity scores increased linearly with the level of Extraction. These results suggest that the law of large numbers plays a role in children's diversity-based reasoning. (shrink)

Six-month-old infants discriminate between large sets of objects on the basis of numerosity when other extraneous variables are controlled, provided that the sets to be discriminated differ by a large ratio (8 vs. 16 but not 8 vs. 12). The capacities to represent approximate numerosity found in adult animals and humans evidently develop in human infants prior to language and symbolic counting.

Despite their importance in public discourse, numbers in the range of 1 million to 1 trillion are notoriously difficult to understand. We examine magnitude estimation by adult Americans when placing large numbers on a number line and when qualitatively evaluating descriptions of imaginary geopolitical scenarios. Prior theoretical conceptions predict a log-to-linear shift: People will either place numbers linearly or will place numbers according to a compressive logarithmic or power-shaped function (Barth & Paladino, ; Siegler & (...) Opfer, ). While about half of people did estimate numbers linearly over this range, nearly all the remaining participants placed 1 million approximately halfway between 1 thousand and 1 billion, but placed numbers linearly across each half, as though they believed that the number words “thousand, million, billion, trillion” constitute a uniformly spaced count list. Participants in this group also tended to be optimistic in evaluations of largely ineffective political strategies, relative to linear number-line placers. The results indicate that the surface structure of number words can heavily influence processes for dealing with numbers in this range, and it can amplify the possibility that analogous surface regularities are partially responsible for parallel phenomena in children. In addition, these results have direct implications for lawmakers and scientists hoping to communicate effectively with the public. (shrink)

Maurice Merleau-Ponty argued that the seeing of things together (focal figure and background objects) accounted for the sense that things possess unseen depth: they are three-dimensional entities, not facades. I compare this idea to the law of large numbers. In both cases, single entities take on substance, depth, or meaning when assimilated into a large body of comparable instances. Thinking along these lines, Erwin Schrödinger proposed that living processes achieve order by virtue of the multiplicity of their (...) constituent parts, any of which, when considered individually, militate against perception and understanding. He further suggested that those parts take their place as things to be perceived even as they constitute our perceiving faculties, and this is why uncertainty occasions their reality. Thus he offers an instance of Merleau-Ponty’s notion of chiasmic intertwining, which allows for world-body interchange or reversibility beyond the reach of unequivocal apprehension. (shrink)

In the children's book ``The Phantom Tollbooth'' by Norton Juster one can find the following passage:``Yes, please,'' said Milo. ``Can you show me the biggest number there is?''.

Is there some large number of very mild hangnail pains, each experienced by a separate person, which would be worse than two years of excruciating torture, experienced by a single person? Many people have the intuition that the answer to this question is No. However, a host of philosophers have argued that, because we have no intuitive grasp of very large numbers, we should not trust such intuitions. I argue that there is decent intuitive support for the (...) No answer, which does not depend on our intuitively grasping or imagining very large numbers. (shrink)

Von Mises defined a "physical" probability as a strict limit of the relative frequency of occurrence of an event in repeated trials. As a result of a number of criticisms of von Mises's approach, the more favored approach became the "propensity" interpretation. It is argued here that this interpretation is not compelling and that the only problem in von Mises's approach is the assumption that the relative frequency converges in a strict sense. This problem is then remedied by deducing the (...) axioms of probability theory from the assumption that the relative frequency converges only in the sense of the weak law of large numbers. (shrink)

This paper presents the metaphysics of liberal rights reasoning on one hand and that of demographic reasoning on the other, as exemplifying two worldviews that both compete and complement each other in the contemporary German public debate on demographic decline. First, this essay outlines the way in which liberal theorists of various outlooks, perfectionist and neutralist alike, assume that a wide range of rights serves not only the interests of those individuals who possess them, but that it constitutes the foundations (...) of a just and stable political order in general and therefore is to the advantage of everyone. Second, the essay explains how demographic reasoning questions the assumption of harmony shared by the liberal approaches. Third, it provides an impression of the way in which demographic arguments have been deployed in the public sphere in Germany in the last few years. These arguments associate the autonomy of women with the demise of Germany. They claim that by encouraging women to pursue self-realization as self-interested individuals, the modern secular ethos of Germany as a democratic welfare society may be self-destructive in the long run, since it leads to sub-replacement fertility. Finally, the essay stresses that liberal and demographic perspectives share a “blindness” of historical events. In response, the conclusion brings history back in, by historicizing both demographic reasoning and demographic developments in Germany, with the aim of defusing some of the anxieties that may have been aroused by the current debate. (shrink)

During the COVID-19 pandemic, the race to find an effective vaccine or treatment saw an ‘extraordinary number’ of clinical trials being conducted. While there were some key success stories, not all trials produced results that informed patient care. There was a significant amount of waste in clinical research during the pandemic which is said to have hampered an evidence-based response. Conducting trials which could have been predicted to fail to answer the research question (e.g. because they are not large (...) enough to provide a definitive result) is not only a waste of resources but also a breach of research participants’ trust and a violation of research ethics. The issues seen in COVID-19 clinical trials are symptomatic of a wider trial design crisis where many trials do not provide informative results. This paper examines the roles of key stakeholders in delivering ethical and informative trials and whether guidance published by ‘The Good Clinical Trials Collaborative’ could be used to align key stakeholder groups and enable a joined-up approach to improve clinical trial design. (shrink)

> Future people count. There could be a lot of them. We can make their lives better. > > -- William MacAskill, What We Owe The Future > > [Longtermism is] quite possibly the most dangerous secular belief system in the world today. > > -- Émile P. Torres, Against Longtermism Philosophers,1 2 psychologists,3 4 politicians5 and even some tech billionaires6 have sounded the alarm about artificial intelligence (AI) and the dangers it may pose to the long-term future of humanity. (...) Some believe it poses an existential risk (X-Risk)7 to our species, potentially causing our extinction or bringing about the collapse of human civilisation as we know it. The above quote from philosopher Will MacAskill captures the key tenets of ‘longtermism’, an ethical standpoint that places the onus on current generations to prevent AI-related—and other—X-Risks for the sake of people living in the future.1 2 Developing from an adjacent social movement commonly associated with utilitarian philosophy, ‘effective altruism’, longtermism has amassed following of its own. Its supporters argue that preventing X-Risks is at least as morally significant as addressing current challenges like global poverty. However, critics are concerned that such a distant-future focus will sideline efforts to tackle the many pressing moral issues facing humanity now.8 9 Indeed, according to ‘strong’ longtermism,10 future needs arguably should take precedence over present ones. In essence, the claim is that there is greater expected utility to allocating available resources to prevent human extinction in the future than there is to focusing on present lives, since doing so stands to benefit the incalculably large number of people in later generations who will far outweigh existing populations.1 Taken to the extreme, this view suggests it would be morally permissible, or even required, to actively neglect, harm or destroy large swathes of humanity as …. (shrink)

Belief in the divine origin of the universe began to wane most markedly in the nineteenth century, when scientific accounts of creation by natural law arose to challenge traditional religious doctrines. Most of the credit - or blame - for the victory of naturalism has generally gone to Charles Darwin and the biologists who formulated theories of organic evolution. Darwinism undoubtedly played the major role, but the supporting parts played by naturalistic cosmogonies should also be acknowledged. Chief among these was (...) the nebular hypothesis proposed by Pierre Simon Laplace in 1796, which explained the origin of the solar system as a natural development over extended periods of time. Ronald Numbers focuses on Laplace's theory as it affected American scientific thought. he first traces the history of Laplace's cosmogony chronologically, from its European inception to its demise about 1900. the last three chapters explore some of the theological and scientific consequences resulting from the acceptance of this cosmogony. Most significant was the change in the status of supernatural doctrine. When the nebular hypothesis lost credence at the end of the nineteenth century, those who had before tried to accommodate natural theory with supernatural doctrine no longer felt compelled to do so when faced with succeeding theories. The nebular hypothesis, it seems, had established natural law in the heavens. (shrink)

Friedrich Nietzsche’s intellectual autobiography Ecce Homo has always been a controversial book. Nietzsche prepared it for publication just before he became incurably insane in early 1889, but it was held back until after his death, and finally appeared only in 1908. For much of the first century of its reception, Ecce Homo met with a sceptical response and was viewed as merely a testament to its author’s incipient madness. This was hardly surprising, since he is deliberately outrageous with the ‘megalomaniacal’ (...) self-advertisement of his chapter titles, and brazenly claims ‘I am not a man, I am dynamite’ as he attempts to explode one preconception after another in the Western philosophical tradition. In recent decades there has been increased interest in the work, especially in the English-speaking world, but the present volume is the first collection of essays in any language devoted to the work. Most of the essays are selected from the proceedings of an international conference held in London to mark the centenary of the first publication of Ecce Homo in 2008. They are supplemented by a number of specially commissioned essays. Contributors include established and emerging Nietzsche scholars from the UK and USA, Germany and France, Portugal, Sweden and the Netherlands. (shrink)

Australia is second only to Israel in being the world’s most culturally diverse nation, based largely on high levels of immigration in the second part of the 20th century. From the 1970s onwards, Australia formally recognized the massive social changes brought about by postwar immigration, and provided legislation to incorporate cultural diversity into everyday lives. One such ‘legislative’ enactment saw the establishment of multicultural broadcasting in Australia, as arguably a world-first, both in its comprehensiveness and diversity. Today, Australia has a (...) public sector corporation, the Special Broadcasting Service, administering five radio services in 68 languages. Also, the Community Radio sector produces multicultural programming in 100 languages through a number of its 330 broadcast and 207 narrowcast stations. This article examines the relationship between radio and its communities. It argues that despite the ‘profile’ of SBS television, radio is much closer to its constituent communities, and therefore plays a greater role in enabling those communities to speak their own histories, beyond the confines of a consensual Anglophile paradigm. (shrink)

Kant argues against the ontological argument for the existence of God but replaces it with a moral theism. This article analyses Kant’s moral proof with emphasis on the Critique of the Power of Judgement, and his historical and political writings. It argues that at the heart of this argument is the idea of progress. The concrete content of the moral law is the idea of a just world. Such a just world would be impossible without the idea of God, since (...) there would be no harmony between nature and freedom. It contrasts Kant’s concept of time and history with Heidegger’s. The difference between them is a reversal of modality. For Kant, actuality determines possibility. If I cannot imagine a just word as actual, then I would fall into moral despair. The idea of God grounds this actuality. For Heidegger, possibility is higher than actuality. Since history has no teleology, then no idea of God is required. (shrink)

In the TACITUS project for using commonsense knowledge in the understanding of texts about mechanical devices and their failures, we have been developing various commonsense theories that are needed to mediate between the way we talk about the behavior of such devices and causal models of their operation. Of central importance in this effort is the axiomatization of what might be called commonsense metaphysics. This includes a number of areas that figure in virtually every domain of discourse, such as granularity, (...) scales, time, space, material, physical objects, shape, causality, functionality, and force. Our effort has been to construct core theories of each of these areas, and then to define, or at least characterize, a large number of lexical items in terms provided by the core theories. In this paper we discuss our methodological principles and describe the key ideas in the various domains we are investigating. (shrink)

A new axiomatic characterization with a minimum of conditions for entropy as a function on the set of states in quantum mechanics is presented. Traditionally unspoken assumptions are unveiled and replaced by proven consequences of the axioms. First the Boltzmann–Planck formula is derived. Building on this formula, using the Law of Large Numbers—a basic theorem of probability theory—the von Neumann formula is deduced. Axioms used in older theories on the foundations are now derived facts.

In this paper, I suggest that infinite numbers are large finite numbers, and that infinite numbers, properly understood, are 1) of the structure omega + (omega* + omega)Ө + omega*, and 2) the part is smaller than the whole. I present an explanation of these claims in terms of epistemic limitations. I then consider the importance, part of which is demonstrating the contradiction that lies at the heart of Cantorian set theory: the natural numbers are (...) too large to be counted by any finite number, but too small to be counted by any infinite number – there is no number of natural numbers. (shrink)

Both the theory that traumatic childhood memories can be repressed, and the reliability of the techniques used to retrieve these memories are challenged in this paper. Questions are raised about the robustness of the theory and the literature that purports to provide scientific evidence for it. Evidence to this end is provided by the demographic and qualitative results of a research study conducted by the authors which surveyed New Zealand families in which one member had accused another of sexual abuse (...) on the basis of recovered memories. It is shown that a number of these allegations involve very low probability events. Since memory repression theory is not currently scientifically substantiated it is argued that care needs to be taken in the mental health, legal and insurance compensation arenas. Memories recalled during therapy may be treated as metaphorical but, in the absence of corroborative evidence, should not be considered factually true. Clinicians who wish to use memory recovery techniques should inform patients of their experimental and controversial nature, point out potential adverse effects, and obtain consent before proceeding. (shrink)

The escalating number of pending cases is a growing concern worldwide. Recent advancements in digitization have opened up possibilities for leveraging artificial intelligence (AI) tools in the processing of legal documents. Adopting a structured representation for legal documents, as opposed to a mere bag-of-words flat text representation, can significantly enhance processing capabilities. With the aim of achieving this objective, we put forward a set of diverse attributes for criminal case proceedings. To enhance the effectiveness of automatically extracting these attributes from (...) legal documents within a sequence labeling framework, we propose the utilization of a few-shot learning approach based on Large Language Models (LLMs). Moreover, we demonstrate the efficacy of the extracted attributes in downstream tasks, such aslegal judgment prediction and legal statute prediction. (shrink)

Periodic systems are considered whose increments in quantum energy grow with quantum number. In the limit of large quantum number, systems are found to give correspondence in form between classical and quantum frequency-energy dependences. Solely passing to large quantum numbers, however, does not guarantee the classical spectrum. For the examples cited, successive quantum frequencies remain separated by the incrementhI −1, whereI is independent of quantum number. Frequency correspondence follows in Planck's limit,h → 0. The first example is (...) that of a particle in a cubical box with impenetrable walls. The quantum emission spectrum is found to be uniformly discrete over the whole frequency range. This quality holds in the limitn → ∞. The discrete spectrum due to transitions in the high-quantum-number bound states of a particle in a box with penetrable walls is shown to grow uniformly discrete in the limit that the well becomes infinitely deep. For the infinitely deep spherical well, on the other hand, correspondence is found to be obeyed both in emission and configuration. In all cases studied the classical ensemble gives a continuum of frequencies. (shrink)

Rosenberg applies current thinking in philosophy of science to neoclassical economics in order to assess its claims to scientific standing. Although philosophers have used history and psychology as paradigms for the examination of social science, there is good reason to believe that economics is a more appropriate subject for analysis: it is the most systematized and quantified of the social sciences; its practitioners have reached a measure of consensus on important aspects of their subject; and it encompasses a large (...) number of apparently law-like propositions. (shrink)

In this paper, we will review research done by the Large-Scale Integrated Photonics group at HP Laboratories, and in particular we will discuss applications of optical resonances in dielectric microstructures and nanostructures to future classical and quantum information technologies. Our goal is to scale photonic technologies over the next decade in much the same way as electronics over the past five, thereby establishing a Moore’s Law for optics.

An acceptable empiricist account of laws of nature would havesignificant implications for a number of philosophical projects. For example, such an account may vitiate argumentsthat the fundamental constants of nature are divinelydesigned so that laws produce a life permittinguniverse. On an empiricist account, laws do not produce the universe but are designed by us to systematize theevents of a universe which does in fact contain life; so any ``fine tuning'' of natural law has a naturalistic explanation.But there are problems for (...) the empiricist project. This paper develops a ``perspectival'' version of the Humean bestsystem approach and argues that this version solves the standard problems faced by the empiricist project.Furthermore, the paper argues, this version is best able to answer the proponents of divine design while leaving scientificlaw a suitably objective matter.[I]t is possible tocondense the enormous mass of results to a large extent – that is to find laws which summarize...Richard Feynman It has become fashionable in some circles to argue thatscience is ultimately a sham, that we scientists read order into nature, not out of nature, and that the laws of physicsare our laws, not nature's. I believe this is arrant nonsense. You would be hard-pressed to convince a physicist thatNewton's inverse square law of gravitation is a purely cultural concoction. The laws of physics, I submit, reallyexist in the world out there, and the job of the scientist is to uncover them, not invent them. True, at any giventime, the laws you find in the textbooks are tentative and approximate, but they mirror, albeit imperfectly, a reallyexisting order in the physical world. Of course, many scientists do not recognize that in accepting the reality of anorder in nature-the existence of laws `out there' – they are adopting a theological world view. P. C. W. Davies. (shrink)

The strong law of large numbers and considerations concerning additional information strongly suggest that Beauty upon awakening has probability 1/3 to be in a heads-awakening but should still believe the probability that the coin landed heads in the Sunday toss to be 1/2. The problem is that she is in a heads-awakening if and only if the coin landed heads. So, how can she rationally assign different probabilities or credences to propositions she knows imply each other? This is (...) the problem I address in this article. I suggest that ‘p whenever q and vice versa’ may be consistent with p and q having different probabilities if one of them refers to a sample space containing ordinary possible worlds and the other to a sample space containing centred possible worlds, because such spaces may fail to combine into one composite probability space and, as a consequence, ‘whenever’ may not be well defined; such is the main contribution of this article. 1The Sleeping Beauty Game2Groisman’s and Peter Lewis’s Approaches3Discussing Beauty’s Credences4The Principle of Equivalence's Failure5Making Sense of the Principle of Equivalence's Failure6Elga’s and Lewis’s Approaches7ConclusionAppendix. (shrink)

Quantum mechanics and probability theory share one peculiarity. Both have well established mathematical formalisms, yet both are subject to controversy about the meaning and interpretation of their basic concepts. Since probability plays a fundamental role in QM, the conceptual problems of one theory can affect the other. We first classify the interpretations of probability into three major classes: inferential probability, ensemble probability, and propensity. Class is the basis of inductive logic; deals with the frequencies of events in repeatable experiments; describes (...) a form of causality that is weaker than determinism. An important, but neglected, paper by P. Humphreys demonstrated that propensity must differ mathematically, as well as conceptually, from probability, but he did not develop a theory of propensity. Such a theory is developed in this paper. Propensity theory shares many, but not all, of the axioms of probability theory. As a consequence, propensity supports the Law of Large Numbers from probability theory, but does not support Bayes theorem. Although there are particular problems within QM to which any of the classes of probability may be applied, it is argued that the intrinsic quantum probabilities are most naturally interpreted as quantum propensities. This does not alter the familiar statistical interpretation of QM. But the interpretation of quantum states as representing knowledge is untenable. Examples show that a density matrix fails to represent knowledge. (shrink)

Objectives: The mental health legislation of most developed countries includes either a dangerousness criterion or an obligatory dangerousness criterion (ODC). A dangerousness criterion holds that mentally ill people may be given treatment without consent if they are deemed to be a risk to themselves or others. An ODC holds that mentally ill people may be given treatment without consent only if they are deemed to be a risk to themselves or others. This paper argues that the dangerousness criterion is unnecessary, (...) unethical and, in the case of the ODC, potentially harmful to mentally ill people and to the rest of the community. Methods: We examine the history of the dangerousness criterion, and provide reasoned argument and empirical evidence in support of our position. Results: Dangerousness criteria are not required to balance the perceived loss of autonomy arising from mental health legislation. Dangerousness criteria unfairly discriminate against the mentally ill, as they represent an unreasonable barrier to treatment without consent, and they spread the burden of risk that any mentally ill person might become violent across large numbers of mentally ill people who will never become violent. Mental health legislation that includes an ODC is associated with a longer duration of untreated psychosis, and probably contributes to a poorer prognosis and an increase risk of suicide and violence in patients in their first episode of psychosis. Conclusions: Dangerousness criteria should be removed from mental health legislation and be replaced by criteria that focus on a patient’s capacity to refuse treatment. (shrink)

We present a new method of constructing Condorcet domains from pairs of Condorcet domains of smaller sizes (concatenation + shuffle scheme). The concatenation + shuffle scheme provides maximal, connected, copious, peak-pit domains whenever the original domains have these properties. It allows to construct maximal peak-pit Condorcet domains that are larger than those obtained by the Fishburn’s alternating scheme for all $$n\ge 13$$ n ≥ 13 alternatives. For a large number n of alternatives, we get a lower bound $$2.1045^{n}$$ 2. (...) 1045 n for the cardinality of the largest peak-pit Condorcet domain and a lower bound $$2.1890^{n}$$ 2. 1890 n for the cardinality of the largest Condorcet domain, improving Fishburn’s result. We also show that all Arrow’s single-peaked domains can be constructed by concatenation + shuffle scheme starting from the trivial domain. (shrink)

Instances of the law of large numbers are used to model many different physical systems. In this paper, I argue for a particular interpretation, of those instances of that law, which appeals to typicality. As I argue, the content of that law, when used to model physical systems, is that the probability of an event typically—rather than probably—approximates the frequency with which that event occurs.

For large-scale optimization, CMA-ES has the disadvantages of high complexity and premature stagnation. An improved CMA-ES algorithm called GI-ES was proposed in this paper. For the problem of high complexity, the method in this paper replaces the calculation of a covariance matrix with the modeling of expected fitting degrees for a given covariance matrix. At the same time, to solve the problem of premature stagnation, this paper replaces the historical information of elite individuals with the historical information of all (...) individuals. The information can be seen as approximate gradients. The parameters of the next generation of individuals are generated based on the approximate gradients. The experimental results were tested using CEC 2010 and CEC2013 LSGO benchmark test suite, and the experimental results verified the effectiveness of the algorithm on a number of different tasks. (shrink)

The Italian law of December 2010 establishes new criteria and parameters for the evaluation of faculty members. The parameters are represented by the number of articles published in journals listed in the main international data banks, the total number of citations and the h index. Candidates with qualifications at least in two out of three parameters may access the national competitions for associate or full professor and apply for an academic appointment. This system developed with the aim to fight nepotism (...) and promote meritocracy, progressively led to the deterioration of the Italian university system. Since promotion in academia is strictly dependent on publications the faculty members found the solution to get over this system by organizing themselves into large consortia or small groups with the purpose of sharing authorship in scientific publications. In this way parameter thresholds may be easily reached and even surpassed. An Italian adagio says: “Fatta la Legge, Trovato l’Inganno”; “Every law has its Loophole”. However, there is no science without ethics and researchers must stay away from any kind of compromise. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:102 HISTORY OF PHILOSOPHY and removal of the social self, through the devaluation of values and de-culturation, to the objectivizatlonof the ego, the state of oneness and unity with all. The remaining sections of the book give an analysis of Rumi, the universal man of the Eas~, and an analysis of Goethe, the universal man of the West. The Rumi chapter contains impressive translations of RumPs poems and the (...) Goethe study offers a very pertinent critique of K. R. Eissler's psychoanalytic interpretation of the great man. Added is a case history of a young man who lived in two cultures, and after many errors and meanderings obtained full integration. The final section offers an application of the transcultural state to health, social change and leadership. A most rewarding and challenging work, marred only by an incredible number of typographical errors and a sometimes uneven English due to misunderstandings of the Dutch printers. Hg~RY WALTESBRANN Washington, D. C. Natural Law and Modern Society. Essays by John Cogley, Robert M. Hutchins, John Courtney Murray, SJ., Scott Buchanan, Philip Selznick, Harvey Wheeler, and Robert Gordis. (Cleveland and New York: The World Publishing Company, 1966. Pp. 285. Meridian Books. $1.75.) This group of essays has been discussed from time to time at the Center for the Study of Democratic Institutions in Santa Barbara, California. The essays provide an excellent survey of the various contexts in which the idea of natural law is functioning today: in jurisprudence, political theory, sciences, religions, and philosophies of culture. Though the emphasis is on "modem society," there is a large amount of history in this collection, going back to the ancients, and one of the most valuable features of the analysis is the evidence here offered that "natural law" has meant and still means many different things, and that this flexibility of meaning gives the idea an enduring vitality and relevance. This is the particular theme of Scott Buchanan's "Natural Law and Teleology", which chapter reviews almost the whole history of philosophy to show how the content of natural law has varied for teleological reasons. Since it is impossible to review this whole story, it seems simplest and least distorting to quote a series of passages from the essays so that the reader can estimate the range of subject-matter and the kind of observations in the volume : The natural lawyer who lacks a sense of history, a factual sense, is as seriously deficient as the one who has been victimmed by the historical setting of his own time. Social scientists are concerned with digging up and evaluating exactly the kind of factual material the conscientious natural lawyer needs (Cogley, pp. 24, 26). We are free, with the deference that is due previous laborers in the vineyard, to work out the ~pplication of the principles of natural law to the conditions of our own time. The ends of uman life are heldto be unchanging; the search for the best way of achieving them is continuous and adapted to changing conditions and new knowledge. The search for a revival of natural law--not necessarily, or even principally pitched in Thomistic terms but projected more generally on a ~us gent~um, pluralistic basis--may well be the dominant theme of American legal philosophy over the second half of the century (Hutchins, pp. 34, 37, 46). Plato saw an epitome of the legal and political crisis of the city-state in the trial and death of Socrates.... The sophists are operators in opinion and power.... Plato sets out to find the truth in science and the good of the state.... There is no doctrinal answer to the quest.... The Dialogues practice what they preach, a relentless dialectical exposure of ideas masquerading in dogmas and opinions.... The endless mutual persuasions in any community could result in good laws if the formal processes of government provided insights for the citizens and magistrates alike.... Neither Plato nor Aristotle commonly uses the phrase 'natural law'.... For the Stoics what Plato had described as the "community of ideas," which was only the notion of the interpenetration of BOOK REVIEWS 103 mutual implication of ideas, became the Logos, the perhaps infinite total of... (shrink)

In the past few years an increasing number of colleges and universities have added courses in biomedical ethics to their curricula. To some extent, these additions serve to satisfy student demands for "relevance. " But it is also true that such changes reflect a deepening desire on the part of the academic community to deal effectively with a host of problems which must be solved if we are to have a health-care delivery system which is efficient, humane, and just. To (...) a large degree, these problems are the unique result of both rapidly changing moral values and dramatic advances in biomedical technology. The past decade has witnessed sudden and conspicuous controversy over the morality and legality of new practices relating to abortion, therapy for the mentally ill, experimentation using human subjects, forms of genetic interven tion, suicide, and euthanasia. Malpractice suits abound and astronomical fees for malpractice insurance threaten the very possibility of medical and health-care practice. Without the backing of a clear moral consensus, the law is frequently forced into resolving these conflicts only to see the moral issues involved still hotly debated and the validity of existing law further questioned. In the case of abortion, for example, the laws have changed radically, and the widely pub licized recent conviction of Dr. Edelin in Boston has done little to foster a moral consensus or even render the exact status of the law beyond reasonable question. (shrink)

If all the fundamental constants x of physics were expressed in one set of units (e.g., mks) and then used as pure numbers in one overall histogram, what shape would that histogram have? Based on some invariances that the law should reasonably obey, we show that it should have either an x−1 or an x−2 dependence. Empirical evidence consisting of the presently known constants is consistent with an x−1 law. This is independent of the system of units chosen for (...) the constants. The existence of the law suggests that the fundamental constants may have been independently and randomly chosen, at creation, from it, and hence that at the next “big bang” randomly a different set will be produced. Also, because of the law, the number 1.0 has an interesting cosmological property: it is the theoretical median of all the fundamental constants. Finally, as a practical matter, the law predicts that current methods of evaluating the fundamental constants are biased toward overly large numbers. A correction term is given for each of three kinds of noise. (shrink)

As a concrete basis for thought, we first share the experience of a correspondence analysis applied to a morphosyntactically tagged corpus. The automatic tagging has been partially checked and shows errors. Knowing how factorial analysis works, and having identified the noisiest tags, we adjust the data to be submitted to the analysis so that it is both reliable and clear, making sense for the interpretation of the results to be drawn.This experiment calls for a three-fold discussion. Firstly, about the evaluation (...) of such a process: indeed, by bypassing (rather than correcting) errors (noise), we shift the analysis framework, which no longer allows an evaluation based on the usual comparison of results and improvement measurement. Next, we justify how tweaking the data can still be a sound scientific approach, when the process is methodical and transparent. Then we consider whether corpus size matters, in relationship with the law of large numbers: statistics neutralize the noise of random fluctuations, but not that of repetitive bias.Thus, we argue for “taming” noise: that is, knowing your corpus and your tools, so as to be able to design quality analyses while managing the residual noise, and freeing yourself from a prior and probably illusory requirement for data perfection. (shrink)

In his [1937, 1938], Paul Dirac proposed his “Large Number Hypothesis” (LNH), as a speculative law, based upon what we will call the “Large Number Coincidences” (LNC’s), which are essentially “coincidences” in the ratios of about six large dimensionless numbers in physics. Dirac’s LNH postulates that these numerical coincidences reflect a deeper set of law-like relations, pointing to a revolutionary theory of cosmology. This led to substantial work, including the development of Dirac’s later [1969/74] cosmology, and (...) other alternative cosmologies, such as the Brans-Dicke modification of GTR, and to extensive empirical tests. We may refer to the generic hypothesis of “Large Number Relations” (LNR’s), as the proposal that there are lawlike relations of some kind between the dimensionless numbers, not necessarily those proposed in Dirac’s early LNH. Such relations would have a profound effect on our concepts of physics, but they remain shrouded in mystery. Although Dirac’s specific proposals for LNR theories have been largely rejected, the subject retains interest, especially among cosmologists seeking to test possible variations in fundamental constants, and to explain dark energy or the cosmological constant. In the first two sections here we briefly summarize the basic concepts of LNR’s. We then introduce an alternative LNR theory, using a systematic formalism to express variable transformations between conventional measurement variables and the true variables of the theory. We demonstrate some consistency results and review the evidence for changes in the gravitational constant G. The theory adopted in the strongest tests of Ġ/G, by the Lunar Laser Ranging (LLR) experiments, assumes: Ġ/G = 3(dr/dt)/r – 2(dP/dt)/P – (dm/dt)/m, as a fundamental relationship. Experimental measurements show the RHS to be close to zero, so it is inferred that significant changes in G are ruled out. However when the relation is derived in our alternative theory it gives: Ġ/G = 3(dr/dt)/r – 2(dP/dt)/P – (dm/dt)/m – (dR/dt)/R. The extra final term (which is the Hubble constant) is not taken into account in conventional derivations. This means the LLR experiments are consistent with our LNR theory (and others), and they do not really test for a changing value of G at all. This failure to transform predictions of LNR theories correctly is a serious conceptual flaw in current experiment and theory. (shrink)

In this work we deal with a general class of spatially distributed periodic SIS epidemic models with two time scales. We let susceptible and infected individuals migrate between patches with periodic time dependent migration rates. The existence of two time scales in the system allows to describe certain features of the asymptotic behavior of its solutions with the help of a less dimensional, aggregated, system. We derive global reproduction numbers governing the general spatially distributed nonautonomous system through the aggregated (...) system. We apply this result when the mass action law and the frequency dependent transmission law are considered. Comparing these global reproductive numbers to their non spatially distributed counterparts yields the following: adequate periodic migration rates allow global persistence or eradication of epidemics where locally, in absence of migrations, the contrary is expected. (shrink)

This paper begins an axiomatic development of naive set theoryin a paraconsistent logic. Results divide into two sorts. There is classical recapture, where the main theorems of ordinal and Peano arithmetic are proved, showing that naive set theory can provide a foundation for standard mathematics. Then there are major extensions, including proofs of the famous paradoxes and the axiom of choice (in the form of the well-ordering principle). At the end I indicate how later developments of cardinal numbers will (...) lead to Cantor’s theorem, the existence of large cardinals, and a counterexample to the continuum hypothesis. (shrink)

Today, large language models are very powerful, informational and analytical tools that significantly accelerate most of the existing methods and methodologies for processing informational processes. Scientific information is of particular importance in this capacity, which gradually involves the power of large language models. This interaction of science and qualitative new opportunities for working with information lead us to new, unique scientific discoveries, their great quantitative diversity. There is an acceleration of scientific research, a reduction in the time spent (...) on its implementation – the freed up time can be spent both on solving new scientific problems and on scientific creativity, which, although it may not necessarily lead to a specific solution to a particular scientific problem, but is able to demonstrate the beauty of science in various disciplinary areas. As a result, the interaction of large language models and scientific information is at the same time a research for solutions to scientific problems, scientific problems, and scientific creativity. Solving scientific problems requires the ability to efficiently process big data, which cannot be done without an effective method – one of the significant methods was the Transformer architecture, introduced in 2017 and comprehensively integrated into the GPT‑3 model, which, as of September 2020, was the largest and most advanced language model in the world. Therefore, GPT‑3 can be called the basis of most scientific developments carried out in the context of using large language models. The interaction of science and large language models has become a factor in the emergence of a large number of questions, among which are: «Is the result of data analysis new knowledge?», «What are the prospects for scientific creativity in the era of big computing?». Currently, these issues are extremely important, because they allow us to develop the foundations for effective human‑computer interaction. Therefore, this study analyzes the issues presented. (shrink)

With the publication of the Carnegie Foundation’s 2007 report on legal education, law schools are focused again on curriculum reform. The Carnegie report highlighted a number of important issues, one of which is the need to improve the teaching of lawyering skills. This article takes up one subset of the skills package of lawyers – transactional law skills – and suggests that health law courses provide an excellent forum for exploring and teaching such skills.With their reliance on the case method, (...) law schools historically have done little to introduce students to transactional thinking, practice, or skills. Yet today, transactional work is a significant component of most attorneys’ practices. A common misperception is that transactional law only means “doing deals” while at a large law firm. (shrink)

. We demonstrate that a comprehensive nonstandard set theory can be developed in the standard $\displaystyle{\in}$ -language. As an illustration, a nonstandard ${\sf Law of Large Numbers}$ is obtained.