For each ordinal α it is given a model for Skala's set theory using the well-known cumulative type hierarchy.

Quite early in the Covid-19 pandemic, a recommendation was issued in Germany to address potential scarcity scenarios in hospital intensive care units. At its core, the recommendation from Germany’s medical professional societies stated that, in the event of overcrowded ICUs, physicians should base the selection of patients who could still be admitted on the likelihood of success for each individual in need (DIVI 2021). The purpose of focusing on the likelihood of success is to use the available resources to help (...) the greatest possible number of people in need effectively. However, legal scholars have repeatedly argued that a lottery-based solution would be far more suitable for such tragic rescue conflicts. This perspective was also adopted by some disability advocates, who fear the risk of discrimination against people with disabilities in scarcity scenarios, as their chances of success are often presumed to be systematically lower than those of people without disabilities. From an ethical standpoint, this raises the legitimate question of the conditions under which a decision-making criterion implies indirect discrimination against a particular group of people. ----- Schon recht früh in der Covid-19-Pandemie wurde in Deutschland eine Empfehlung für mögliche Knappheitsszenarien auf den Intensivstationen der Krankenkenhäuser herausgegeben. Im Kern besagt die Empfehlung der deutschen medizinischen Fachgesellschaften, die Ärzteschaft solle im Falle überfüllter Intensivstationen die Auswahl derjenigen, die in einem solchen Fall nochmal aufgenommen werden können, an der Erfolgsaussicht der einzelnen Bedürftigen festmachen. Der Zweck einer Orientierung an der Erfolgsaussicht besteht darin, mit den vorhandenen Ressourcen einer möglichst großen Anzahl an Bedürftigen erfolgreich helfen zu können. Insbesondere von Juristen wurde jedoch auch immer wieder argumentiert, eine Lotterie-Lösung sei sehr viel geeigneter für derartige tragische Rettungskonflikte. Eine solche Auffassung wurde auch von einigen Behindertenvertreter:innen übernommen, die eine Gefahr der Benachteiligung von Menschen mit Behinderung in Knappheitsszenarien befürchten, denn bei ihnen dürften die Erfolgsaussichten regelhaft schlechter sein als bei Menschen ohne Behinderung. In ethischer Hinsicht wurde hier also die berechtigte Frage aufgeworfen, unter welchen Bedingungen ein Entscheidungskriterium eine indirekte Diskriminierung einer bestimmten Personengruppe impliziert. (shrink)

This paper considers two mysteries having to do with vagueness. The first pertains to existence. An argument is presented for the following conclusion: there are possible cases in which ‘There exists something that is F’ is of indeterminate truth-value and with respect to which it is not assertable that there are borderline-cases of being F. It is contended that we have no conception of vagueness that makes this result intelligible. The second mystery has to do with ordinary vague predicates, such (...) as ‘tall’. An argument is presented for the conclusion that although there are people who are tall to degree 1 —definitely tall, tall without qualification—, no greatest lower bound can be assigned to the set of numbers n such that a man who is n centimeters tall is tall to degree 1. But, since this set is bounded from below, this result seems to contradict a well-known property of the real numbers. (shrink)

In "An Alternative Semantics for Quantified Relevant Logic" (JSL 71 (2006)) we developed a semantics for quantified relevant logic that uses general frames. In this paper, we adapt that model theory to treat quantified modal logics, giving a complete semantics to the quantified extensions, both with and without the Barcan formula, of every proposi- tional modal logic S. If S is canonical our models are based on propositional frames that validate S. We employ frames in which not every set of (...) worlds is an admissible proposition, and an alternative interpretation of the uni- versal quantifier using greatest lower bounds in the lattice of admissible propositions. Our models have a fixed domain of individuals, even in the absence of the Barcan formula. For systems with the Barcan formula it is possible to preserve the usual Tarskian reading of the quantifier, at the expensive of sometimes losing va- lidity of S in the underlying propositional frames. We apply our results to a number of logics, including S4.2, S4M and KW, whose quantified extensions are incomplete for the standard semantics. (shrink)

With more than half of individuals incarcerated having serious mental health concerns, correctional settings offer excellent opportunities for epidemiological, prevention, and intervention research. However, due to unique ethical and structural challenges, these settings create risks and vulnerabilities for participants not typically encountered in research populations. We surveyed 1,224 researchers, Institutional Review Board members, and IRB prisoner representatives to assess their perceptions of risks and vulnerabilities associated with mental health research conducted in correctional settings. Highest ranked risks were related to privacy, (...) stigma, and confidentiality; lowest ranked risks were related to prisoners’ loss of privileges or becoming targets of violence due to having participated in research. Cognitive impairment, mental illness, lack of autonomy, and limited access to services emerged as the greatest sources of vulnerability; being male, being female, being older than age 60, being a minority, and being pregnant were the lowest ranked sources of vulnerability. Researchers with corrections experience perceived lower risks and vulnerabilities than all other groups, raising the question whether these researchers accurately appraise risk and vulnerability based on experience, or if their lower risk and vulnerability perceptions reflect potential bias due to their vested interests. By identifying areas of particular risk and vulnerability, this study provides important information for researchers and research reviewers alike. (shrink)

With the use of a suitable assumption about the structure of the class of experimental filters, it is shown that the sequence of alternating replicas of two filters is their greatest lower bound, as Jauch suggests. A generalization of his suggestion yields the greatest lower bound of a denumerable set of filters. The criteria of admissibility of filters are briefly discussed.

This paper considers two “mysteries” having to do with vagueness. The first pertains to existence. An argument is presented for the following conclusion: there are possible cases in which ‘There exists something that is F’ is of indeterminate truth-value and with respect to which it is not assertable that there are borderline-cases of “being F.” It is contended that we have no conception of vagueness that makes this result intelligible. The second mystery has to do with “ordinary” vague predicates, such (...) as ‘tall’. An argument is presented for the conclusion that although there are people who are “tall to degree 1”—definitely tall, tall without qualification—, no greatest lower bound can be assigned to the set of numbers n such that a man who is n centimeters tall is tall to degree 1. But, since this set is bounded from below, this result seems to contradict a well-known property of the real numbers. (shrink)

There is a vast amount of evidence across countries that the use of health care services (including hospitalizations, physician services, and clinical preventive services) is positively associated with income, education and other markers of socioeconomic position. In some analyses, lower socioeconomic status (SES) is associated with greater physician and hospital use, although it appears that these findings are primarily driven by higher rates of poor health status or medical need in socioeconomically disadvantaged populations. Three general sets of explanations have (...) been investigated to explain SES differences in health care use: (1) financial access or affordability differences (e.g. the poor use fewer services because they have fewer financial means); (2) knowledge, attitudinal and cultural differences in seeking care (e.g. the poor use fewer services because they value and/or understand the benefits of health care less than other people); and (3) health care system factors (e.g. the poor use fewer services because of ways in which the health care system is organized). The empirical evidence from a number of countries suggests that health care system variables, especially non-financial components of access, offer the greatest explanatory power regarding SES differences in utilization. The policy implications of such findings are important, for they suggests that providing universal coverage or offering free health services to the poor is not a panacea for reducing social inequalities in health care utilization. Research across countries also suggests that, although SES differences in the use of health care services may contribute to some portion of observed SES disparities in health status, the contribution here is likely to be small. Social inequalities in health status are driven by myriad factors other than access to and use of personal health services. (shrink)

Introduction. A radical tendency in modern approaches to understanding the mechanisms of the brain is the tendency of some scientists to believe that the brain is a receptor capable of capturing thoughts; the nature of the occurrence of the thoughts themselves, however, is not to be clarified. However, speech expressing thoughts is undoubtedly the result of the work of the brain, so studies of the frequency structure of speech can be the basis for considering the material structure of the brain (...) as a kind of “antenna”. In this approach, the problem of noise protection against the background of the undeniable frequency similarity of speech and music appears to us from somewhat different positions. This study raises the question of how essential the overall height of the musical system is to the perception of music (are there musical systems that are harmful or useful, in terms of their effects on the psyche). This question is also relevant to speech perception.Methodology and sources. The main sources in which the work of the brain and the essence of consciousness are considered from the positions indicated above were for us the work of American and British neurophysiologists and psychiatrists (Sam Parnia, Peter Fenwick). These scientists are studying the phenomena that accompany clinical death, and argue that at these moments the brain functions to the greatest extent as a receiving “antenna”. Assuming that any antenna is to be tuned, we are trying to identify possible ways to “tune” the brain. To do this, we propose to study the frequency characteristics of speech (in the simplest case, when singing vowels in a calm state) for their belonging to a particular musical system, as well as the peculiarities of music perception depending on the musical system (on the height of the note “la”). Varying the frequency characteristics of speech in a particular musical system can be considered, in our opinion, the main way to “tune” the brain. The methodology of the method is based on the use of frequency analysis of sound and the basic provisions of the elementary theory of music.Results and discussion. The main conclusion made by Western psychiatrists is the brain is not an organ of thought, consciousness exists independently from outside, the work of consciousness cannot be explained by the functioning of the brain – it requires a hardware check. If the neural network is an “antenna” that captures thoughts, and its “adjustment” at the physical level can be carried out (and is carried out) through sensory systems (including the hearing organ), the study of the frequency structure of speech will answer a number of important questions, including including related and higher brain functions (insight, creativity). Our experiments (Saint Petersburg Electrotechnical University, FIBS, department of EUT) showed that the influence of the “increased” or “lowered” musical-speech system on brain activity is insignificant. The study revealed the equiprobability of the frequency structure of speech. Since our brain lacks some characteristic set of frequencies – elements of a uniformly temperamental system, it is not necessary to talk about the harmful (or any other noise) effect of the “raised” and “lowered” systems due to deviation from the “internal standard”.Conclusion. In response to the assumptions made by Western experts, we proposed a frequency interpretation of the processes occurring in the brain, which, perhaps, will explain in more detail such phenomena as inspiration, discovery, etc., which occur with minimal activity of consciousness. Despite the limited methods of hardware study of factors that influence the activity of the brain and largely determine its higher functions (for example, creativity), the results of the brain's work in relation to music (both in terms of its creation and in terms of our reaction to it) are quite analyzable, which was shown in this study. The “musicality” of speech is extremely vividly represented in its frequency structure and allows one to reveal, to one degree or another, the features of the brain. (shrink)

Companies that are serious about corporate governance and business ethics are turning their attention to gender diversity at the most senior levels of business . Board gender diversity has been the subject of several studies carried out by international organizations such as Catalyst , the World Economic Forum , and the European Board Diversity Analysis . They all lead to reports confirming the overall relatively low proportion of women on boards and the slow pace at which more women are being (...) appointed. Furthermore, the proportion of women on corporate boards varies much across countries. Based on institutional theory, this study hypothesizes and tests whether this variation can be attributed to differences in cultural settings across countries. Our analysis of the representation of women on boards for 32 countries during 2010 reveals that two cultural characteristics are indeed associated with the observed differences. We use the cultural dimensions proposed by Hofstede to measure this construct. Results show that countries which have the greatest tolerance for inequalities in the distribution of power and those that tend to value the role of men generally exhibit lower representations of women on boards. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The Weight I Just Can’t LoseShelley Lynn MeyersI have always been a “fat person”. According to the medical definition though, I have not always been obese. I have spent most of my life on a journey from chubby to obese, finally ending at my current “overweight” status. After years of struggling with obesity I had gastric bypass surgery, finally losing enough weight to be “normal.” However, regardless of the (...) number on the scale or the BMI category into which I fell, I was still “fat”. I may have lost weight but I did not lose the experience and memories of life as an obese person. I was a fat girl on the inside.My earliest memories of childhood consist of feeling fat and awkward. I was the kid reading a book, watching other little girls practice their cartwheels and boys play tag. I was the kid who also hated gym class, especially the days we practiced tumbling or had to climb ropes. I heard the other kids laugh when I had difficulty doing these things. It’s no surprise that I was last or next to last when we had to choose teams for sports. At least when we played flag football I could play center and use my weight as an asset, blocking players from the other team.Certainly, taunts about my weight and even my own intrusive condemning thoughts were not constant, but they were frequent. Admittedly, I probably berated myself much more often than my peers did. I hated being different. What saddens me to this very day are promises I would make to God if I only I could be “like everyone else”. Oh the things that I would change, or give up for the gift of being a normal size. Even my good qualities, such as academic achievement, became another characteristic that made me stand out when all I wanted to do was hide amongst the crowd. I would have happily traded the high GPA for a lower number on the scale. [End Page E4]Some memories from that era seem to be forever etched into my mind. It has been more than thirty years since I was in the seventh grade, but I remember one particular incident very clearly. I went to my first school dance and was thrilled that I actually slow danced with a boy that I had liked since the fourth grade, Jeff1*. We danced to “How Much I Feel” by Ambrosia. Jeff wore a plaid flannel shirt, and I remember how soft it felt when I put my arms around his neck. The puppy love joy I felt that night was short-lived. At school the next day I read a note written by a female classmate. She wrote about the dance, saying that she had wanted to dance with Jeff, but “he was dancing with that fat pig”. She included my name as well, so there was no mistaking to whom she was referring. I felt nauseous. I decided that happiness was just a set-up for disappointment.Even though I thinned out somewhat during high school, I was still larger than most of my friends and saw myself as fat. I received few actual comments about my weight but I just knew they were thinking it. My best friends were exceptionally thin (one, I would later find out had an eating disorder), which added to my distorted body image. I also was the “friend”, rather than the “girlfriend”, with boys asking me to introduce them to my skinny friends. I was ecstatic when I had a horrible case of the flu and lost a lot of weight due to vomiting and the inability to keep food down. I remember hoping that I could get the flu every couple of months.I read fashion magazines and studied the latest, greatest ways to lose weight. Diet pills, fad soup diets and low calorie frozen dinners were popular and I tried most of them. Sadly, the very methods I tried to “get skinny” likely put me on the path to obesity. Starving myself just led to unhealthy eating, cravings and quite possibly, a metabolism that had no... (shrink)

The main goal of publicly funded biomedical research is to generate social value through the creation and application of knowledge that can improve the well-being of current and future people. Prioritising research with the greatest potential social value is crucial for good stewardship of limited public resources and ensuring ethical involvement of research participants. At the National Institutes of Health (NIH), peer reviewers hold the expertise and responsibility for social value assessment and resulting prioritisation at the project level. However, (...) previous research has shown that peer reviewers place more emphasis on a study’s methods (‘Approach’) than on its potential social value (best approximated by the criterion of ‘Significance’). Lower weighting of Significance may be due to reviewers’ views on the relative importance of social value, their belief that social value is evaluated at other stages of the research priority-setting process or the lack of guidance on how to approach the challenging task of assessing expected social value. The NIH is currently revising its review criteria and how these criteria contribute to overall scores. To elevate the role of social value in priority setting, the agency should support empirical research on how peer reviewers approach the assessment of social value, provide more specific guidance for reviewing social value and experiment with alternative reviewer assignment strategies. These recommendations would help ensure that funding priorities align with the NIH’s mission and the obligation of taxpayer-funded research to contribute to the public good. (shrink)

Professional workplaces that embody an “ideal worker” image that is implicitly white and male set-up persistent biases against the competence and suitability for authority of those who are not white men, forcing them to work harder to prove their competence and fit in. The added labor of coping with these burdens is largely invisible to dominant actors in the workplace who do not experience them. To facilitate change by making such burdens visible for all, we present data from a survey (...) of 1,349 architects, including white, Asian, Black, Latinx, and mixed race/other underrepresented men and women, about their specific behavioral experiences of prove-it-again bias, tightrope bias, problems of fit, exclusion, emotion work, and interruptions. Across all measures, white men architects report significantly lower levels of these burdens than do women of any race and almost all non-white men. Consistent with status expectations and stereotype prototypicality theories, we find intersectional patterns in the relative burdens experienced by women and men of different racial groups. Gender differences in bias experiences are greatest among white, less among Asian, and least among Black architects. Women of color report the highest levels of bias overall. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reading the Bloody "Face of Nature":The Persecution of Religion in Hawthorne's The Marble FaunMartin Kevorkian (bio)Perhaps The Marble Faun is a novel which needs to be seen in a certain light to be fully revealed. Although Hawthorne has always had his admirers and defenders among literary critics, this novel has sometimes been selected for unfavorable comparison"; this 1941 assessment by Dorothy Waples (224) still aptly describes the critical terrain (...) and the challenge of reading Hawthorne's last complete novel. In recent scholarship, Nancy Bentley's The Ethnography of Manners (1995) has been influential in marking The Marble Faun for continued unfavorable comparison. Geoffrey Sanborn (1998), in building a case for the postcolonial intelligence of Herman Melville, uses Bentley's argument about the novel's disregard for the "lower orders of creation" to set up Hawthorne as a representative of the typically blinkered "white male writers" against whose limitations Melville shines (18, 214n33). Hawthorne, especially in The Marble Faun, has become a kind of whipping boy for American literary history.Be that as it may, my concern is not to establish Hawthorne's status as a victim of criticism, but rather to seek a recovery of what may be sacrificed in hasty dismissals of The Marble Faun. The present article proposes that this novel arrives at its greatest insights by a consideration of the dynamics of exclusionary violence as such. Henry James lamented the absence of "real psychology" in the novel, and Ludwig Lewisohn complained about its lack of "acceptable intellectual or moral content" (cited in Waples 1941, 224). Yet the novel's achievement may be seen to meet both these criteria, in part because it delivers an analysis of intellectual history as a history of mimetic sacrifice. In response to Waples's terms of challenge—the need for a certain light that reveals—I suggest that mimetic theory's reading of the Enlightenment allows the novel to disclose more critical historical intelligence than has generally been attributed to it. [End Page 133]This reading will focus on the interaction of three characters: the mysterious Miriam, the mysterious Donatello, and the even more mysterious figure known as the Model. In setting up the action of the narrative, the novel divulges little about the backgrounds of any of these characters but places them in a situation with a readily discernible structure: the relationships between the figures may be defined by the element of pursuit. Donatello follows Miriam wherever she goes. But he is not the only one who does so. The hazy figure of the Model likewise shadows Miriam. The Model's pursuit of Miriam may precede Donatello's, or the two pursuits may be somehow coeval; the novel refuses to specify either pursuit as original, focusing instead on the late-stage escalation of resentment between Donatello and the Model.This mimetic pursuit culminates in the central violent event of the novel: Donatello, claiming authorization from Miriam's glance, hurls the Model from a precipice. I have argued elsewhere that when the protagonists thus decisively act to exclude the shadowy character known as the Model, they enact the foundational move of Enlightenment discourse and the ideal of Platonic dialogue upon which that discourse is based.1 Michel Serres summarizes the Platonic-Enlightenment strategy of communicational purity and clarity:To hold a dialogue is to suppose a third man and to seek to exclude him; a successful communication is the exclusion of the third man. The most profound dialectical problem is not the problem of the Other, who is only a variety—or a variation—of the Same, it is the problem of the third man. We might call this third man the demon, the prosopopeia of noise.(1982, 67)Miriam and Donatello, the united protagonists, indeed demonize the Model in these terms. What I would now add to that equation is the value of the Model's vocational identity: he is a Capuchin monk. Within the communicational framework of my earlier analysis, the most telling details were detected in Hawthorne's emphasis on the Model's "noisy" and "hazy" profile. In hurling the Model from the edge of the precipice and thus silencing his interruptions, Donatello secures for... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Philosophy and Literature 26.1 (2002) 107-124 [Access article in PDF] Shakespeare and Political Philosophy John D. Cox Though Shakespeare has been praised as one of the greatest thinkers who ever lived, he has no standing in the history of Western philosophy, being at best a footnote to the derivative neo-Platonists and skeptics of the late Renaissance. He died in 1616, more than twenty years before Descartes's Discourse on (...) Method heralded the autonomous rationalism of the Enlightenment, and Shakespeare did not achieve a reputation as a deep thinker until the nineteenth century, as a consequence of admiration for his characters. People seemed to think that a reflective and witty prince who could say to his friend, "There are more things in heaven and earth, Horatio, / Than are dreamt of in your philosophy" must be the product of a keenly philosophical intelligence—never mind that Hamlet is referring to the "antique Roman" philosophy he so admires in Horatio, i.e., Stoicism, which by 1599 was little more than an oft-repeated set of moral and social platitudes. 1 To assert that there are more things in heaven and earth than late Renaissance Stoicism is not to assert very much.But other ways of thinking about Shakespeare philosophically are more promising than character analysis. He was indeed a thoughtful playwright, and though he had no university education, he was a voracious and incisive reader, so the influences on his plays and poems include many writers who have some standing in the history of philosophy. More complex than discerning historical philosophical influences on Shakespeare is what might be called the hermeneutical approach, i.e., the interpretation of the plays and poems with particular philosophers and philosophies in mind, regardless of their possible historical influence in the sixteenth century. To survey the range of philosophical influences and hermeneutical approaches is impossible [End Page 107] in a single essay, but a manageable example of Shakespeare's thinking is his political philosophy, where both ways of understanding him can be discerned. The most influential interpreter of Shakespeare's history plays for the second half of the twentieth century, for example, was E. M. W. Tillyard, who purported to excavate the neo-Platonic assumptions of Shakespeare's political culture: order, degree, hierarchy, and obedience. 2 Though questions were increasingly raised concerning Tillyard's assumptions and documentation, the decisive challenge to his authority was issued in the 1980s by New Historicists and Cultural Materialists, whose allegiance was more or less explicitly Marxist, and who therefore interpreted Shakespeare in light of a particular nineteenth-century philosophy. 3 A clearer example of the difference between history and hermeneutics in understanding Shakespeare is hard to imagine.The clarity of the difference, however, does not mean that the two approaches are mutually exclusive. Tillyard construed Shakespeare's emphasis on hierarchical order as an advocacy of divine-right monarchy, and much in the plays of Shakespeare supports this construal. Despite his sympathetic portraits of particular characters, including commoners, remarks in his plays about commoners taken together ("the people") are always slighting and mistrustful—often indeed scornful—and the proportion of upper-class to lower-class characters reflects their perceived social importance, for the former invariably outnumber the latter, even in the comedies, whereas the aristocracy were a tiny fraction of the total population in Shakespeare's England. Shakespeare's portrayal of pre-imperial Rome, in Julius Caesar, Antony and Cleopatra, and Coriolanus, shows little understanding of, and less sympathy with, republican alternatives to one-person rule. Shakespeare was not responsive to Calvin's spirited defense of the "poor common people" against rapacious kings (even, or especially, under godly magistrates), and Shakespeare's plays offer no support to the nascent republicanism of those who took arms against the king of England in the mid-seventeenth century, largely inspired by Calvinism. 4 Shakespeare, in short, was no Milton.This is not to say, however, that he was an uncritically idealizing royalist, as we can see from his first venture into writing about English history: his four early plays on the civil unrest of the fifteenth century. Three of these plays... (shrink)

We show that MAκ implies that each collection of Pc-points of size at most κ which has a Pc-point as an RK upper bound also has a Pc-point as an RK lower bound.

Continuing the earlier research from [T. Bigorajska, H. Kotlarski, Partitioning α-large sets: some lower bounds, Trans. Amer. Math. Soc. 358 4981–5001] we show that for the price of multiplying the number of parts by 3 we may construct partitions all of whose homogeneous sets are much smaller than in [T. Bigorajska, H. Kotlarski, Partitioning α-large sets: some lower bounds, Trans. Amer. Math. Soc. 358 4981–5001]. We also show that the Paris–Harrington independent statement remains unprovable if the number of (...) colors is restricted to 2, in fact, the statement is unprovable in IΣb. Other results concern some lower bounds for partitions of pairs. (shrink)

We define a realizability interpretation of Aczel's Constructive Set Theory CZF into Explicit Mathematics. The final results are that CZF extended by Mahlo principles is realizable in corresponding extensions of T 0 , thus providing relative lower bounds for the proof-theoretic strength of the latter.

For Tarski logics, there are simple criteria that enable one to conclude that two premise sets are equivalent. We shall show that the very same criteria hold for adaptive logics, which is a major advantage in comparison to other approaches to defeasible reasoning forms. A related property of Tarski logics is that the extensions of equivalent premise sets with the same set of formulas are equivalent premise sets. This does not hold for adaptive logics. However a very similar criterion does. (...) We also shall show that every monotonic logic weaker than an adaptive logic is weaker than the lower limit logic of the adaptive logic or identical to it. This highlights the role of the lower limit for settling the adaptive equivalence of extensions of equivalent premise sets. (shrink)

Lower limb major amputations are both life-saving procedures and life-changing events. Individual responses to limb loss are varied and complex, some individuals experience functional, psychological and social dysfunction, many others adjust and function well. Some patients refuse amputation for religious and/or cultural reasons. One of the greatest difficulties for a person undergoing amputation surgery is overcoming the psychological stigma that society associates with the loss of a limb. Persons who have undergone amputations are often viewed as incomplete individuals. (...) The medical and physical consequences of amputation serve as the centerpiece in acute care and are commonly at the forefront of prosthetic rehabilitation. Prosthetic prescription aims to compensate for functional and/or cosmetic losses where possible. The aims of rehabilitation following amputation are to restore acceptable levels of functioning that allow individuals to achieve their goals, to facilitate personal health, and to improve participation in society and quality of life either with or without prosthesis. Our article aims at underscoring some medical, social and religious aspects that can contribute to the wellbeing of patients who suffer a life changing event such as lower limb amputation. (shrink)

In order to achieve flexible and smooth walking, we must accomplish subtasks (e.g., loading response, forward propulsion or swing initiation) within a gait cycle. To evaluate subtasks within a gait cycle, the analysis of muscle synergies may be effective. In the case of walking, extracted sets of muscle synergies characterize muscle patterns that relate to the subtasks within a gait cycle. Although previous studies have reported that the muscle synergies of individuals with disorders reflect impairments, a way to investigate the (...) instability in the activations of muscle synergies themselves has not been proposed. Thus, we investigated the local dynamic stability and orbital stability of activations of muscle synergies across various walking speeds using maximum Lyapunov exponents and maximum Floquet multipliers. We revealed that the local dynamic stability in the activations decreased with accelerated walking speeds. Contrary to the local dynamic stability, the orbital stability of the activations was almost constant across walking speeds. In addition, the increasing rates of maximum Lyapunov exponents were different among the muscle synergies. Therefore, the local dynamic stability in the activations might depend on the requirement of motor output related to the subtasks within a gait cycle. We concluded that the local dynamic stability in the activation of muscle synergies decrease as walking speed accelerates. On the other hand, the orbital stability is sustained across broad walking speeds. (shrink)

The Declaration of Helsinki and the Council of the International Organization of Medical Sciences provide guidance on standards of care and prevention in clinical trials. In the current and increasingly challenging research environment, the ethical status of a trial design depends not only on protection of participants, but also on social value, feasibility, and scientific validity. Using the example of a study assessing efficacy of a vaccine to prevent human papilloma virus in HIV-1 infected adolescent girls in low resource countries (...) without access to the vaccine, we compare several trial designs which rank lower on some criteria and higher on others, giving rise to difficult trade-offs. This case demonstrates the need for developing more nuanced guidance documents to help researchers balance these often conflicting criteria. (shrink)

Radzikowska and Kerre developed L-fuzzy rough set as a fuzzy generalisation of the notion of rough sets. Specifically, they have taken a residuated lattice L as the underlying set of truth degrees. However, in real life, we may encounter situations where truth degrees are not always linear, or where the existence of the least upper bound of two elements is no longer required. Instead, there may be the possibility of having minimal upper bounds, and dually, maximal lower bounds, multilattices (...) have become a suitable algebraic structure for addressing such cases. Our aim is to extend Radzikowska and Kerre's work by replacing a residuated lattice with a multilattice M, thereby obtaining a more flexible structure. We define M-fuzzy rough sets using operators derived from adjoint pairs within the multilattice M. For a tolerance and an equivalence M-fuzzy relation, we define an appropriate M-fuzzy rough set and investigate its properties. (shrink)

This paper gives a characterization of those quasi-normal extensions of the modal system S4 into which intuitionistic propositional logic Int is embeddable by the Gödel translation. It is shown that, as in the normal case, the set of quasi-normal modal companions of Int contains the greatest logic, M*, for which, however, the analog of the Blok-Esakia theorem does not hold. M* is proved to be decidable and Halldén-complete; it has the disjunction property but does not have the finite model (...) property. (shrink)

We examine the set of formula-to-formula valid inferences of Classical Logic, where the premise and the conclusion share at least a propositional variable in common. We review the fact, already proved in the literature, that such a system is identical to the first-degree entailment fragment of R. Epstein's Relatedness Logic, and that it is a non-transitive logic of the sort investigated by S. Frankowski and others. Furthermore, we provide a semantics and a calculus for this logic. The semantics is defined (...) in terms of a \-matrix built on top of a 5-valued extension of the 3-element weak Kleene algebra, whereas the calculus is defined in terms of a Gentzen-style sequent system where the left and right negation rules are subject to linguistic constraints. (shrink)

We consider small-weight Cutting Planes (CP * ) proofs; that is, Cutting Planes (CP) proofs with coefficients up to $\operatorname{Poly}(n)$ . We use the well known lower bounds for monotone complexity to prove an exponential lower bound for the length of CP * proofs, for a family of tautologies based on the clique function. Because Resolution is a special case of small-weight CP, our method also gives a new and simpler exponential lower bound for Resolution. We also (...) prove the following two theorems: (1) Tree-like CP * proofs cannot polynomially simulate non-tree-like CP * proofs. (2) Tree-like (CP * proofs and Bounded-depth-Frege proofs cannot polynomially simulate each other. Our proofs also work for some generalizations of the CP * proof system. In particular, they work for CP * with a deduction rule, and also for any proof system that allows any formula with small communication complexity, and any set of sound rules of inference. (shrink)

In recent years, a proportion of older Germans has been sent to relatively high‐end care homes within lower‐income countries where the care tends to be cheaper and more extensive than that in German care homes. Destination countries are found predominantly within Eastern Europe (e.g. Poland, Hungary, Czech Republic), but to a lesser extent also within South‐East Asia (e.g. Thailand). At the same time, these expatriations have caused much controversy, with some German commentators calling them ‘inhumane’ and ‘shameful’. In this (...) article, I argue that such criticisms are overdrawn. Although sending an older individual to a care home within a lower‐income country can be morally impermissible, I find that there are at least three sets of conditions under which it is not. (shrink)

The algebra of all binary relations on a given set is the most important example of a relation algebra . In this note we will examine the possible isomorphisms within some subclasses of a closely related class ; A is a relation set algebra with base U if its Boolean reduct is a field of sets with unit element 2 U, its universe A contains the identity relation on U and it is closed under the operations −1 and |, where (...) R |S = { : ∈ R, ∈ S for some z} and R−1 = { : ∈ R} for any R, S ⊆ 2 U. The class of all relation set algebras is denoted by Rs. (shrink)

LK is a natural modification of Gentzen sequent calculus for propositional logic with connectives ¬ and $\bigwedge, \bigvee$. Then for every d ≥ 0 and n ≥ 2, there is a set Td n of depth d sequents of total size O which are refutable in LK by depth d + 1 proof of size exp) but such that every depth d refutation must have the size at least exp). The sets Td n express a weaker form of the pigeonhole (...) principle. (shrink)

In this paper I reconsider a standard counterexample to the chance-raising theory of singular causation. Extant versions of this theory are so different that it is difficult to formulate the core thesis that they all share, despite the guiding idea that causes raise the chance of their effects. At one extreme, ‘Humean’ theories – which can be traced to Reichenbach – say that a particular event of type C is the cause of a particular event of type E only if (...) P(E|C & K) > P(E|~C & K) where K is a set of background conditions and where the probabilities are interpreted as relative frequencies. At the other extreme, explicitly non-Humean theories take chance to be a physical, particular, local feature of the world. (shrink)

Where would humanity be now without fire, vaccinations, farming--or wine? A great idea is one that has changed the path of human civilisation. But which is the greatest of them all? John Farndon, author of the bestselling Do You Think You're Clever?, has set out to find the answer. A distinguished panel of experts agreed on a list of 50 ideas, and each chapter of The World's Greatest Idea sees Farndon explore the argument for a different one. The (...) candidates are intriguingly varied: Electricity grids enable us to power our cities, but then sewers allowed those cities to grow. Without the wheel, modern civilisation would be pretty much impossible, but take away Logic and we'd lose the essential structures for rational thought... But then what would be the point of all of this without the idea of romance? The World's Greatest Idea is an enthralling voyage of discovery through the most powerful intellectual, social, scientific and creative brainwaves humans have ever had. They are ranked in the book determined by a public vote on www.theworldsgreatestidea.com But will you agree with the verdict? (shrink)

We consider the first-order finite-difference expression of the commutator between d / dx and x. This is the appropriate setting in which to propose commutators and time operators for a quantum system with an arbitrary potential function and a discrete energy spectrum. The resulting commutators are identified as universal lowering and raising operators. We also find time operators which are finite-difference derivations with respect to the energy. The matrix elements of the commutator in the energy representation are analyzed, and we (...) find consistency with the equality \. We apply the theory to the particle in an infinite well and for the Harmonic oscillator as examples. (shrink)

In quantum logic, introduced by Birkhoff and von Neumann, De Morgan's Laws play an important role in the projection-valued truth value assignment of observational propositions in quantum mechanics. Takeuti's quantum set theory extends this assignment to all the set-theoretical statements on the universe of quantum sets. However, Takeuti's quantum set theory has a problem in that De Morgan's Laws do not hold between universal and existential bounded quantifiers. Here, we solve this problem by introducing a new truth value assignment for (...) bounded quantifiers that satisfies De Morgan's Laws. To justify the new assignment, we prove the Transfer Principle, showing that this assignment of a truth value to every bounded ZFC theorem has a lower bound determined by the commutator, a projection-valued degree of commutativity, of constants in the formula. We study the most general class of truth value assignments and obtain necessary and sufficient conditions for them to satisfy the Transfer Principle, to satisfy De Morgan's Laws, and to satisfy both. For the class of assignments with polynomially definable logical operations, we determine exactly 36 assignments that satisfy the Transfer Principle and exactly 6 assignments that satisfy both the Transfer Principle and De Morgan's Laws. (shrink)

We give an example of a dense o-minimal structure in which there is a definable quotient that cannot be eliminated, even after naming parameters. Equivalently, there is an interpretable set which cannot be put in parametrically definable bijection with any definable set. This gives a negative answer to a question of Eleftheriou, Peterzil, and Ramakrishnan. Additionally, we show that interpretable sets in dense o-minimal structures admit definable topologies which are “tame” in several ways: (a) they are Hausdorff, (b) every point (...) has a neighborhood which is definably homeomorphic to a definable set, (c) definable functions are piecewise continuous, (d) definable subsets have finitely many definably connected components, and (e) the frontier of a definable subset has lower dimension than the subset itself. (shrink)

A dictionary is a set of finite words over some finite alphabet X. The omega-power of a dictionary V is the set of infinite words obtained by infinite concatenation of words in V. Lecomte studied in [Omega-powers and descriptive set theory, JSL 2005] the complexity of the set of dictionaries whose associated omega-powers have a given complexity. In particular, he considered the sets $W({bfSi}^0_{k})$ (respectively, $W({bfPi}^0_{k})$, $W({bfDelta}_1^1)$) of dictionaries $V subseteq 2^star$ whose omega-powers are ${bfSi}^0_{k}$-sets (respectively, ${bfPi}^0_{k}$-sets, Borel sets). In (...) this paper we first establish a new relation between the sets $W({bfSigma}^0_{2})$ and $W({bfDelta}_1^1)$, showing that the set $W({bfDelta}_1^1)$ is ``more complex' than the set $W({bfSigma}^0_{2})$. As an application we improve the lower bound on the complexity of $W({bfDelta}_1^1)$ given by Lecomte. Then we prove that, for every integer $kgeq 2$, (respectively, $kgeq 3$) the set of dictionaries $W({bfPi}^0_{k+1})$ (respectively, $W({bfSi}^0_{k+1})$) is ``more complex' than the set of dictionaries $W({bfPi}^0_{k})$ (respectively, $W({bfSi}^0_{k})$). (shrink)

We prove an exponential lower bound on the size of proofs in the proof system operating with ordered binary decision diagrams introduced by Atserias, Kolaitis and Vardi [2]. In fact, the lower bound applies to semantic derivations operating with sets defined by OBDDs. We do not assume any particular format of proofs or ordering of variables, the hard formulas are in CNF. We utilize (somewhat indirectly) feasible interpolation. We define a proof system combining resolution and the OBDD proof (...) system. (shrink)

Part II of Fichte’s System of Ethics is titled “Deduction of the Reality and Applicability of the Moral Law.” In this chapter, I argue that what motivates Fichte’s new deduction is a concern to avoid what he calls “empty formula philosophy,” that is, a philosophy which fails to explain how willing an object is possible. Fichte sets out to avoid this shortcoming by offering a complex theory of the drives, focusing first on what he calls our “lower capacity of (...) desire.” I argue that the key to understanding this section of the System of Ethics lies in Fichte's attempt to derive the character of our “natural drive” (Naturtrieb) from how we represent the system of “nature“ (Natur) as a whole. At the centre of this derivation we find Fichte drawing upon an organicist model of nature, according to which all the parts of natural systems reciprocally interact for the sake of the whole, and vice versa. While largely overlooked by scholars, I contend that this organicist model gives Fichte the resources to present an original theory of desire as an activity of “forming and being formed” by natural objects, in a way that foreshadows what he later calls our “ethical drive” (sittlicher Trieb) to unite with others, both cooperatively and reciprocally, in rational community. (shrink)

Time and resource constraints, combined with competing priorities, mean that research prioritization is a critical ethical consideration in pandemics and emergencies, given the increased need for relevant research findings to address health needs, and the multiple adverse ways that emergencies can impact capacities to conduct research. At international, national and local levels, careful consideration is needed of which research topics should be prioritized and on what grounds. This needs to take into account the ethically significant considerations that should inform prioritization; (...) existing frameworks to guide prioritization decisions; and the consequences associated with prioritizing or de-prioritizing research. The need to prioritize research that is directly responsive to the pandemic may generate debate about which types of research should be prioritised, and within fields of research, which studies should be continued, paused, or re-oriented. In determining which research proposals may have the greatest likelihood of reducing urgent epidemic health burdens, both the nature and distribution of such burdens are key considerations. Epidemics and pandemics typically disproportionately affect the most disadvantaged and vulnerable people in society, highlighting the necessity of inclusive and responsive approaches, which evaluate not just which research approaches have the greatest potential public health benefit, but also the likelihood that they will help address inequities. Key questions also arise when determining if current studies should be de-escalated or stopped, particularly when this may result in highly compromised results. It is also important to consider what obligations arise for research communities (including funders) to pledge to taking the outcomes of research prioritisation processes into account. The case studies in this chapter prompt consideration of how qualitative research into the impacts of isolation should be prioritised, and whether and how research prioritization measures should be responsive to widespread use of traditional medicine and off-label use of medications. The cases also highlight issues that research teams may face as research priorities are re-evaluated in pandemics, including whether and how to redesign proposed research in response to the logistical challenges posed by the pandemic and evolving pandemic research priorities. (shrink)

The Washington National Cathedral, set on the highest hill in the capital city of the world's greatest economic and military power, is an iconic location for an examination of the intersection of immaterial faith, material power, and human conscious experience. It is a location made even more symbolic due to the fact that surrounding the Cathedral on three sides are three private schools -- an elementary school (Beauvoir) to the east, a boys' school (St. Albans) to the south, and (...) a girls' school (National Cathedral School) to the north. The students at these private schools include children of persons who wield the secular power headquartered in the City below the Cathedral Tower. Every day these students study and compete upon a hill giving them panoramic views over the great monuments and symbols of American power: the Capitol Dome, the Washington Monument, the entire City. And the Cathedral that marks their spot upon this globe is visible from all over the region, high above the City. These students are intelligent and informed, and thus for purposes of a dramatic-oriented form of exploration of interesting issues, provide a persuasive characterization for participants in a dialog of two iconic children, older teenagers, a boy and a girl, students at these schools and worshippers in the Cathedral, to develop an examination of themes of faith, power, and the experience of sentience in the material world, walking within and around the Washington National Cathedral, two of its affiliated schools, and the gardens and forests surrounding. The approach recalls the form of the dialogs of Plato, in which persons of elite educational and cultural status encounter each other within a specific building or location, and proceed to discuss such matters as are provoked to mind by the encounter of those minds in that place. The major character of the piece, Merian Validus, is, among other things, a bell-ringer of the Cathedral, a denizen of its highest tower -- as are in reality a group of the girls of NCS. She is an Esmeralda performing the role of Quasimodo. After reading this, think of that the next time you land at Reagan National Airport and catch your cab, looking right at the Cathedral as you speed north into the City. (shrink)

In this paper, we propose an extension of free pregroups with lower bounds on sets of pregroup elements. Pregroup grammars based on such pregroups provide a kind of an algebraic counterpart to universal quantification over type-variables. In particular, we show how our pregroup extensions can be used for pregroup grammars expressing natural-language coordination and extraction.

We give upper and lower bounds for the strength of ordinal definable determinacy in a small admissible set. The upper bound is roughly a premouse with a measurable cardinal $\kappa$ of Mitchell order $\kappa^{++}$ and $\omega$ successors. The lower bound are models of ZFC with sequences of measurable cardinals, extending the work of Lewis, below a regular limit of measurable cardinals.

The work broadens – to a considerable extent – Z. Pawlak’s original method (1982, 1992) of approximation of sets. The approximation of sets included in a universum U goes on in the contextual approximation space CAS which consists of: 1) a sequence of Pawlak’s approximation spaces (U,Ci), where indexes i from set I are linearly ordered degrees of contexts (I, <), and Ci is the universum partition U, 2) a sequence of binary relations on sets included in U, relations called (...) context relations indexed with degrees of contexts. The introduction of relations of contexts of sets was inspired by the work of W. Ziarnko (1993). Intuitively, set X is the context of set Y to the degree i, when on the basis of knowledge of the elements of set X we can obtain knowledge about the belonging of these elements to set Y to the degree i which is a degree of uncertainty or ambiguity, or inaccuracy. The operations of approximation of sets Ci-, BNi, Ci+, called lower approximation of the degree i, boundary of the degree i, upper approximation of the degree i, are formulated in a way which is analogous with the systems of Pawlak’s approximation, by expanding their formulas accordingly. In the next part of the work, it is shown (in an analogous way to Bryniarski’s work (1989)) that one can define the following operations on contextual rough sets: the union of contextual rough sets, the intersection of contextual rough sets and the complement of contextual rough set. It is proved that the algebra of contextual rough sets is a ditributive lattice with a unit and with a zero. On the basis of the results presented above the problem of defining operations on contextual rough sets by membership relations (Bryniarski 1989) may be formulated analogously to the classical operations on sets. (shrink)

Given a countable model of set theory, we study the structure of its generic multiverse, the collection of its forcing extensions and ground models, ordered by inclusion. Mostowski showed that any finite poset embeds into the generic multiverse while preserving the nonexistence of upper bounds. We obtain several improvements of his result, using what we call the blockchain construction to build generic objects with varying degrees of mutual genericity. The method accommodates certain infinite posets, and we can realize these embeddings (...) via a wide variety of forcing notions, while providing control over lower bounds as well. We also give a generalization to class forcing in the context of second-order set theory, and exhibit some further structure in the generic multiverse, such as the existence of exact pairs. (shrink)