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This study aims to investigate the Pauline concept of ministry as delineated in 2 Corinthians 4:1–15 and its correlation with the prevalence of the religious celebrity syndrome within the Nigerian Church, with the objective of offering insights into addressing this phenomenon. In contemporary Nigerian Christianity, there has been a noticeable emergence of religious celebrities in Christian ministry who prioritise personal fame, material gain and sensationalism over the sincere and honest proclamation of the gospel of Jesus Christ. This trend raises concerns (...) about the deviation from the biblical model of ministry, as exemplified by the apostle Paul, and its implications for the spiritual health of the church and its impact on society. Through a critical exegesis of 2 Corinthians 4:1–15, this study delves into Paul’s understanding of ministry, focussing on themes such as integrity, humility, suffering, selfless sacrifice and the exaltation of Christ. Additionally, qualitative research methods, including interviews, surveys and case studies, were employed to examine the extent and effects of religious celebrity syndrome in the Nigerian Church. The analysis of 2 Corinthians 4:1–15 underscores Paul’s emphasis on the sacrificial nature of Christian ministry, wherein servants of God are called to embody humility and prioritise the proclamation of the gospel above personal gain or acclaim. Concurrently, the qualitative research reveals the pervasive influence of the religious celebrity syndrome in the Nigerian Church, leading to spiritual shallowness, moral compromise and a distorted view of Christianity and Christian ministry in particular within the church and the larger society. Based on the findings, it is recommended that the Nigerian Church reaffirm its commitment to the Pauline model of ministry by promoting humility, integrity and a Christ-centred focus among its leaders and congregants.Contribution: This study highlights the importance of aligning contemporary ministry practices in the Nigerian Church with the principles elucidated by Paul in 2 Corinthians 4:1–15. By embracing humility, integrity and a fervent devotion to Christ, the Church can effectively combat the religious celebrity syndrome within its fold and reclaim its role as a catalyst for societal change. (shrink)

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Divorce amongst married couples is a disturbing phenomenon amongst the Yoruba people of southern Nigeria. Unfortunately, the church in Yoruba land, which has focused much of its teachings on financial prosperity, has started facing the consequences of these lopsided teachings. Using a phenomenological approach, this study argues that the lack of sexual satisfaction, poverty, activities of fake pastors, infidelity and lies from any of the partners are the major causes of increasing divorce rates amongst Yoruba Christians. Existing literature has not (...) adequately addressed the issue of divorce amongst Yoruba Christians. This study explores the growing divorce rates from the lens of Yoruba Christians and how it impacts on the family, children and the church at large. As part of this recommendation, church leadership should start organising marriage seminars for married couples where they are taught a nonviolent approach to conflict resolution in the family.Contribution: This study indicates that the activities of some churches and their leaders indirectly support divorce, and the consequence is mostly felt by the children. This study argues that divorce is not supported by the church in Yoruba land. The study implicated practical theology. (shrink)

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This article examines the reason behind the charge to secrecy imposed by Jesus on the leper in Mark 1:40–45, in the context of African experience, the implications of the meaning conveyed and the challenges posed on the church and the gospel enterprise in Africa. The ministry of Jesus could have been a platform for conflicts, self-glorification, hero worship and exploitation. Jesus resisted the temptation in those directions. The charge to silence in African context reveals the virtue of silence which is (...) subsumed in integrity, modesty and character. It calls the attention of the followers of Jesus to the worthiness of emulating such a lifestyle as a pattern for service to God and humanity. The textual and historical exegetical methodology is adopted in this research. (shrink)

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This article examined the warning against evil companions in Proverbs 1:8-19 and the role of the church in addressing the involvement of Tiv youths in crime in Benue State and its implications for actions. Wicked people were zealous in seducing others into the paths of destruction. Would young people shun temporal and eternal ruin? This was the reason forSolomon's instruction in Proverbs 1:8-19. He admonished his son with the caption 'hear,' which presented the son with a choice. However, (...)Solomon implored the child to refuse to take any step in destructive paths of evildoers. The persuasive nature of the pericope was important in addressing the growing crime rate amongst Tiv youths in Benue State. Most youths in Tiv communities were being enticed into joining criminal gangs, secret cults and rituals in order to make quick wealth. Unfortunately, the number of youths in these immoral acts such as YahooYahoo amongst Tiv youths kept on increasing in the midst of the growing number of churches in most Tiv societies. Rhetoric analysis was used as the methodology. As part of recommendations, parents should instruct, discipline and stop their children from engaging in acts that lead to death. The youths should also avoid evil companions to avoid falling into trouble.CONTRIBUTION: Youths are the leaders of tomorrow, which makes admonition to youths a necessity for the growth of the Tiv Society. Proverbs 1:8-19 provides roadmaps that Tiv leaders and the church could adopt in preserving morality among Tiv youths. (shrink)

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This article examined the warning against evil companions in Proverbs 1:8–19 and the role of the church in addressing the involvement of Tiv youths in crime in Benue State and its implications for actions. Wicked people were zealous in seducing others into the paths of destruction. Would young people shun temporal and eternal ruin? This was the reason forSolomon’s instruction in Proverbs 1:8–19. He admonished his son with the caption ‘hear,’ which presented the son with a choice. However, (...)Solomon implored the child to refuse to take any step in destructive paths of evildoers. The persuasive nature of the pericope was important in addressing the growing crime rate amongst Tiv youths in Benue State. Most youths in Tiv communities were being enticed into joining criminal gangs, secret cults and rituals in order to make quick wealth. Unfortunately, the number of youths in these immoral acts such as YahooYahoo amongst Tiv youths kept on increasing in the midst of the growing number of churches in most Tiv societies. Rhetoric analysis was used as the methodology. As part of recommendations, parents should instruct, discipline and stop their children from engaging in acts that lead to death. The youths should also avoid evil companions to avoid falling into trouble. Contribution: Youths are the leaders of tomorrow, which makes admonition to youths a necessity for the growth of the Tiv Society. Proverbs 1:8–19 provides roadmaps that Tiv leaders and the church could adopt in preserving morality among Tiv youths. (shrink)

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The technique of the normal ordering of non-commuting operators is an important tool in the solution of problems involving creation and annihilation operators in quantum physics, such as in many-body theory or quantum optics. We point out the inconsistencies in previous definitions of the two standard normal ordering procedures for such operators, and show how consistent definitions may be made.

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Reviewing works by James Alison, Alistair McFadyen, Andrew Sung Park, Ted Peters, andSolomon Schimmel, the author suggests that the status and function of the discourse/doctrine of sin highlight tensions between theology and ethics in ways that suggest the character, limits, and promise of religious ethics. This literature commends attention to sin-talk because it helps religious ethicists to render more adequately the dynamics of human agency, sociality, and culture and because it raises questions about the nature and task of (...) theology, faith, and morality. Yet these volumes also indicate that religious ethics should pay more attention to particular sins. (shrink)

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Treatment informed consent aims to preserve the autonomy of patients in the clinician – patient relationship so as to ensure valid consent. An acceptable method of evaluating understanding of consent information is by assessing the extent of recall by patients of the pieces information believed to have been passed across. When concerns are not satisfactorily addressed from the patients’ perspective, recall of consent information may be low. This study is a questionnaire – based cross – sectional interview of consecutive adult (...) surgical patients who could give their respective medical histories and who were booked for elective major surgical procedures over a period of 7 months in a tertiary health institution in southeastern Nigeria. Four to five days after a formal consent session, during ward admission, extent of recall of information on the nature of the disease condition or diagnosis, the nature of the planned procedure and the risks involved in the planned procedure were assessed and analyzed on the background of how satisfying the consent sessions were from individual patient’s perspective. Generally, the recall of nature of disease condition and nature of planned procedure is better than recall of risks involved in the planned procedure. More specifically however, recall in these 3 domains is significantly better among the patients that affirmed that their concerns were satisfactorily addressed. The findings from this study support that no effort should be spared in ensuring that the consent information are satisfying to the patients from the patients’ viewpoint. (shrink)

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Feferman, S. and G. Jäger, Systems of explicit mathematics with non-constructive μ-operator. Part I, Annals of Pure and Applied Logic 65 243-263. This paper is mainly concerned with the proof-theoretic analysis of systems of explicit mathematics with a non-constructive minimum operator. We start off from a basic theory BON of operators and numbers and add some principles of set and formula induction on the natural numbers as well as axioms for μ. The principal results then state: BON plus set induction (...) is proof-theoretically equivalent to Peano arithmetic PA; BON plus formula induction is proof-theoretically equivalent to the system<0 of second-order arithmetic. (shrink)

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I want to tell you something about the personal and scientific relationship between Alfred Tarski and Kurt Gödel, more or less chronologically. This is part of a work in progress with Anita Feferman on a biography of Alfred Tarski, and in line with most of the things we do, we’ve talked a great deal about the subject together.

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Though the papers in this volume for the most part address the question, “What is Christian about Christian Bioethics”, this paper addresses instead a closely related question, “How would a Christian approach to bioethics differ from the kind of secular academic bioethics that has emerged as such an important field in the contemporary university?” While it is generally assumed that a secular bioethics rooted in moral philosophy will be more culturally authoritative than an approach to bioethics grounded in the contingent (...) particularities of a religious tradition, I will give reasons for rejecting this assumption. By examining the history of the recent revival of academic bioethics as well as the state of the contemporary moral philosophy on which it is based I will suggest that secular bioethics suffers from many of the same liabilities as a carefully articulated Christian bioethics. At the end of the paper I will turn briefly to examine the question of how, in light of this discussion, a Christian bioethics might best be pursued. (shrink)

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I would like to defend a conception of life that many of us in philosophy practice but few of us preach, and with it a set of virtues that have often been ignored in ethics. In short, I would like to defend what philosopher Sam Keen, among many others, has called the passionate life. It is neither exotic nor unfamiliar. It is a life defined by emotions, by impassioned engagement and belief, by one or more quests, grand projects, embracing affections. (...) It is also sometimes characterized in terms of frenzy, vaulting ambition, essentially insatiable goals, impossible affections. I want to contrast this conception of life with ordinary morality and “being a good person,” although for obvious reasons I do not want to say that one must give up the latter in pursuing the former. This is a mistake that Nietzsche often suggests with his “immor-alist” posturing and warrior metaphors, but I am convinced—on a solid textual basis—that he intended no such result. Nor do I want to dogmatically assert any superiority of a passionate, engaged life over a life that is more calm and routine. On the other hand, I do want to raise the question whether mere proper living, obedience to the law, utilitarian “rational choice” calculations, respect for others' rights and for contracts, and a bit of self-righteousness is all there is to a good life, even if one “fills in” the nonmoral spaces with permissible pleasures and accomplishments. Even a greatly enriched version of Kant, in other words, such as that recently defended by Barbara Herman, unfairly denigrates a kind of life that many of us deem desirable. (shrink)

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Although the topic of emotions was long ignored in British and American analytic philosophy and psychology, it remained a rich and exciting subject in Continental Philosophy. Kierkegaard and Nietzsche celebrated the passionate life. In phenomenology Martin Heidegger, Max Scheler, Emmanuel Levinas, Jean‐Paul Sartre, Maurice Merleau‐Ponty, Gabriel Marcel, and Paul Ricoeur all made major contributions. Heidegger pursued a highly original thesis concerning the vital role of moods in human life, notably angst and boredom. Jean‐Paul Sartre added the tantalizing thesis that our (...) emotions are strategies to help us cope with the difficulties in life. Max Scheler gave us the stunning expression, “the emotional a priori,” the idea that emotions are basic structures of human existence. In this essay, I want to expand on the contributions of the classic phenomenologists and existentialists and do more of what they were doing by way of an “original” project of phenomenological investigation. (This follows publication of the first two volumes of a three‐part study of the emotions, Not Passion's Slave and In Defense of Sentimentality, both published by Oxford University Press.). (shrink)

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Machine generated contents note: Preface; Introduction; Part I. Global Health, Definitions and Descriptions: 1. What is global health? Solly Benatar and Ross Upshur; 2. The state of global health in a radically unequal world: patterns and prospects Ron Labonte and Ted Schrecker; 3. Addressing the societal determinants of health: the key global health ethics imperative of our times Anne-Emmanuelle Birn; 4. Gender and global health: inequality and differences Lesley Doyal and Sarah Payne; 5. Heath systems and health Martin McKee; Part (...) II. Global Health Ethics, Responsibilities and Justice: Some Central Issues: 6. Is there a need for global health ethics? For and against David Hunter and Angus Dawson; 7. Justice, infectious disease and globalisation Michael Selgelid; 8. International health inequalities and global justice: toward a middle ground Norman Daniels; 9. The human right to health Jonathan Wolff; 10. Responsibility for global health? Allen Buchanan and Matt DeCamp; 11. Global health ethics: the rationale for mutual caring Solly Benatar, Abdallah Daar and Peter Singer; Part III. Analyzing Some Reasons for Poor Health: 12. Trade and health: the ethics of global rights, regulation and redistribution Meri Koivusalo; 13. Debt, structural adjustment and health Jeff Rudin and David Sanders; 14. The international arms trade and global health Salahaddin Mahmudi-Azer; 15. Allocating resources in humanitarian medicine Samia Hurst, Nathalie Mezger and Alex Mauron; 16. International aid and global health Anthony Zwi; 17. Climate change and health: risks and inequities Sharon Friel, Colin Butler and Anthony McMichael; 18. Animals, the environment and global health David Benatar; 19. The global crisis and global health Stephen Gill and Isabella Bakker; Part IV. Shaping the Future: 20. Health impact fund: how to make new medicines accessible to all Thomas Pogge; 21. Biotechnology and global health Hassan Masun, Justin Chakma and Abdallah Daar; 22. Food security and global health Lynn McIntyre and Krista Rondeau; 23. International taxation Gillian Brock; 24. Global health research: changing the agenda Tikki Pang; 25. Justice and research in developing countries Alex John London; 26. Values in global health governance Kearsley Stewart, Gerald T. Keusch and Arthur Kleinman; 27. Poverty, distance and two dimensions of ethics Jonathan Glover; 28. Teaching global health ethics James Dwyer; 29. Towards a new common sense: the need for new paradigms of global health Isabella Bakker and Stephen Gill; Index. (shrink)

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I had the pleasure of renewing my acquaintance with Per Lindström at the meeting of the Seventh Scandinavian Logic Symposium, held in Uppsala in August 1996. There at lunch one day, Per said he had long been curious about the development of some of the ideas in my paper [1960] on the arithmetization of metamathematics. In particular, I had used the construction of a non-standard definition !* of the set of axioms of P (Peano Arithmetic) to show that P + (...) {¬ Con!} is interpretable in P, where ! is a standard definition of the axioms of P and Con! expresses the consistency of P via that presentation. Per pointed out that there is a simple “two-line” proof of this interpretability result which does not require the use of such formulas as !*, and he wondered whether I had been aware of that. In fact, his proof had never occurred to me, and if it had at the time, it is possible I would never have been led to the use of non-natural definitions. Per regarded this as a happy accident, since subsequent work by him and others on interpretability made essential use of such definitions. In our conversation, I enlarged a bit on the background to my work on arithmetization, and when I was invited to contribute to this special issue of Theoria dedicated to Lindström, it seemed a natural choice to use the occasion to fill out the story. One caveat, though: the following is drawn largely from memory, not always reliable, supplemented by consultation of the 1960 paper and the 1957 dissertation from which it was drawn. (shrink)

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What is Hell? Here is one answer: five straight days of conversation with a garrulous, narcissistic, rather depraved lawyer. This is the text, in fact the entire content, of Camus's brilliant quasi-religious novel, The Fall. The book has been read as a meditation on the "deadly" sin of pride, introducing a host of ethical and theological questions. I interpret the book as the story of a virtuous, contented, vulnerable man who is struck down by his own mistaken self-reflection and then (...) forced to re-establish his superiority by way of the resentment that replaces his pride. (shrink)

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Seder ha-teshuvah -- Marpe la-nefesh -- Teshuvah me-ḥayim.

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I will talk here about three problems that have bothered me for a number of years, during which time I have experimented with a variety of solutions and encouraged others to work on them. I have raised each of them separately both in full and in passing in various contexts, but thought it would be worthwhile on this occasion to bring them to your attention side by side. In this talk I will explain the problems, together with some things that (...) have been tried in the past and some new ideas for their solution. (shrink)

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In lieu of an abstract, here is a brief excerpt of the content:Robert C.Solomon IN DEFENSE OF SENTIMENTALITY "A sentimentalist is simply one who desires to have the luxury of an emotion without paying for it." —Oscar Wilde, De Profundis. 66TA That's Wrong with Sentimentality?"1 That tide of Mark JefV V ferson's 1983 Mindessay already indicates a great deal notonly about the gist of his article but about a century-old prejudice that has been devastating to ethics and literature (...) alike. According to that prejudice, it goes without saying that there is something wrong with it, even if it is difficult to put one's finger on it. To be called "sentimental" is to be ridiculed, or dismissed. Sentimentality is a weakness, it suggests hypocrisy. Or, perhaps it is the fact that sentimental people are so... so embarrassing. (How awkward it is talking or sitting next to someone weeping or gushing, when one is dry-eyed and somber.) Or, perhaps it is the well-confirmed fact that sentimentalists have such poor taste, and sentimental literature is, above all, literature that is cheap, superficial, and manipulative—in other words, verbal kitsch. Such mawkish literature jerks tears from otherwise sensible readers, and sentimentalists are those who actually enjoy that humiliating experience. Perhaps that is why Oscar Wilde thought that sentimentalists were really cynics ("Sentimentality is merely the bank holiday of cynicism").2 Or, perhaps what bothers us is what bothered Michael Tanner, that sentimental people indulge themselves in their feelings instead of doing what should be done.3 It is often said that the problem is that sentimentality and sentimental literature alike give us a false view of the world, distort our thinking and substitute a "saccharine" portrait of the world in place ofwhat we all know to be the horrible realities. Moreover, as Jefferson more than merely suggests, the "simple-minded sympathies " ofsentimentality might actually promote fascism and racism. Mary Midgley similarly suggests that sentimentality leads to brutality.4 But Philosophy and Literature, © 1990, 14: 304-323 Robert C. Solomon305 even where sentimentality is a harmless diversion—a Daphne du Maurier novel on a sad Saturday afternoon—it seems to be all but agreed that sentimentality is no virtue even ifit is not, like cruelty and hypocrisy, intrinsically vicious. Something is wrong with sentimentality; the only question is, what is it that is wrong? In this essay, I will argue that there is nothing wrong with sentimentality. Of course, like any quasi-ethical category, it admits of unwarranted excesses and hypocritical abuses, and is prone to various pathological distortions. But the prejudice against sentimentality, I want to argue, is ill-founded and in fact is an extension ofthat all-too-familiar contempt for the passions in Western literature and philosophy. Our disdain for sentimentality is the rationalist's discomfort with any display of emotion, warranted as well as unwarranted, appropriate as well as inappropriate. It is as ifthe very word, "sentimentality," has been loaded with the connotations of "too much"—too much feeling and too litde common sense and rationality, as if these were opposed instead of mutually supportive. It is as if sentimentality and its sentiments are never warranted and always inappropriate. The word has come to be used as the name of a deficiency or a weakness if not, as some critics have written, a malaise. But I take sentimentality to be nothing more nor less than the "appeal to tender feelings," and though one can manipulate and abuse such feelings (including one's own), and though they can on occasion be misdirected or excessive, there is nothing wrong with them as such and hence nothing (in that respect) wrong with literature that provokes us, that "moves" us, to abstract affection or weeping. Sentimentality implies no deficiency in one's rational faculties and does not imply any inappropriateness, unwillingness, or lack of readiness to act. Sentimentality does not involve any distortion of the world and it does not impede but rather prepares and motivates us to react in "the real world." It is not an escape from reality or responsibility, but, quite to the contrary, provides the precondition for ethical engagement rather than an obstacle to it. Historically, I want to trace the fate of sentimentality to... (shrink)

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I have been arguing, for almost thirty years now, that emotions have been unduly neglected in philosophy. Back in the seventies, it was an argument that attracted little sympathy. I have also been arguing that emotions are a ripe for philosophical analysis, a view that, as evidenced by the Manchester 2001 conference and a large number of excellent publications, has now become mainstream. My own analysis of emotion, first published in 1973, challenged the sharp divide between emotions and rationality, insisted (...) that we reject the established notion that the emotions are involuntary, and argued, in a brief slogan, that ‘emotions are judgments.’ Since then, although the specific term ‘judgment’ has come under considerable fire and my voluntarist thesis continues to attract incredulousness the general approach I took to emotions has been widely accepted in both philosophy and the social sciences. When Paul Griffiths took on what he misleadingly characterized as ‘propositional attitude’ theories of emotion as the enemy of all that was true and scientifically worthy, I knew that we had made it. Such ferocious abuse is surely a sign that we had shifted, in Kuhnian terms, from being revolutionary to becoming the ‘normal’ paradigm. The current counter-revolution of affect programmes and neuro-reductionism says a lot about who we are and how far we have come. (Progress in philosophy is moved more by this drama of one outrageous thesis after another—once called ‘dialectic’—than by cautious, careful argument.). (shrink)

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This paper is divided into two parts. Part I provides a resumé of the evolution of the notion of predicativity. Part II describes our own work on the subject.Part I§1. Conceptions of sets.Statements about sets lie at the heart of most modern attempts to systematize all (or, at least, all known) mathematics. Technical and philosophical discussions concerning such systematizations and the underlying conceptions have thus occupied a considerable portion of the literature on the foundations of mathematics.

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In lieu of an abstract, here is a brief excerpt of the content:Some Sources for Hume's Opening Remarks to Treatise LIVJII GrahamSolomon Hume opens Book I, Part IV, Section III of the Treatise with these remarks: Several moralists have recommended it as an excellent method ofbecoming acquainted with our own hearts, and knowing our progress in virtue, to recollect our dreams in a morning, and examine them with the same rigour, that we wou'd our most serious and deliberate (...) actions. Our character is the same throughout, say they, and appears best where artifice, fear, and policy have no place, and men can neither be hypocrites with themselves nor others. The generosity, or baseness of our temper, our meekness or cruelty, our courage or pusilanimity, influence the fictions of the imagination with the most unbounded liberty, and discover themselves in the mostglaring colours. Who were these moralists? One looks in vain in the work of Malebranche, Locke, Shaftesbury and Hutcheson for such a recommendation. Did anyone make that recommendation? One moralist who did was "John Shadow," in a letter to Joseph Addison published in The Spectator, no. 586, 27 August 1714. Addison introduces Shadow's letter with the remark that it "is built upon a thought that is new, and very well carried on; for which Reasons I shall give it to the Publick without Alteration, Addition, or Amendment." I quote at length, for easy comparison with Hume: Sir, It was a good Piece of Advice which Pythagoras gave to his Scholars. That every Night before they slept they should examine what theyhad been a doing that Day, and so discover what Actions were worthy of Pursuit to Morrow, and what little Vices were to be prevented from slipping unawares into a Habit. If I might second the Philosopher's Advice, it should be mine, That in a morning before my Scholar rose, he should consider what he had been about that Night, and with the Volume XVI Number 1 57 GRAHAMSOLOMON same Strictness, as if the Condition, he has believed himself to be in, was real. Such a Scrutiny into the Actions ofhis Fancy must be of considerable Advantage, for this Reason, Because the Circumstances which a Man imagines himself in during Sleep, are generally such as entirely favour his Inclinations good or bad, and give him imaginary Opportunities of pursuingthem to the utmost; so thathis Temper will lye fairly open to his View, while he considers howitis moved when free from those Constraints which the Accidents ofreal Life put it under. Dreams are certainly the Result of our waking Thoughts, and our daily Hopes and Fears are what give the mind such nimble Relishes of Pleasure, and such severe Touches ofPain, in its Midnight Rambles. AMan that murders his Enemy, or deserts his Friend in a Dream, had need to guard his Temper against Revenge and Ingratitude, and take heed that he be not tempted to do a vile thing in Pursuit of false, or the Neglect of true Honour... I think it has been observed in the Course of your Papers, how much one's Happiness or Misery may depend upon the Imagination: ofwhich Truth those strange Workings ofFancy in Sleep are no inconsiderable Instances; so that not only the Advantage a Man has ofmaking Discoveries ofhimself, but a Regard to his own Ease or Disquiet, may induce him to accept ofmy Advice... Shadow has been identified as the poet John Byrom by various of the later editors of The Spectator? Of these, D. F. Bond footnotes Byrom's reference to Pythagoras, noting the publication in English of André Dacier's The Life ofPythagoras, with his Symbolism and Golden Verses; together with the Life ofHierocles, and his Commentaries upon the Verses. Bond notes Hierodes' comments on the following Verses: Never suffer Sleep to close thy Eye-lids, after thy going to Bed, Till thou hast examin'd by thy Reason all thy Actions of the Day Wherein have I done amiss? What have I done? What have I omitted that I ought to have done? If in this Examination, thou find that thou hast done amiss, reprimand thy self severely for it: And if thou has done any Good, rejoice. Dacier cites Porphyry and Marcus Aurelius... (shrink)

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The final two volumes, numbers IV and V, of the Oxford University Press edition of the Collected Works of Kurt Gödel [3]-[7] appeared in 2003, thus completing a project that started over twenty years earlier. What I mainly want to do here is trace, from the vantage point of my personal involvement, the at some times halting and at other times intense development of the Gödel editorial project from the first initiatives following Gödel’s death in 1978 to its completion last (...) year. It may be useful to scholars mounting similar editorial projects for other significant figures in our field to learn how and why various decisions were made and how the work was carried out, though of course much is particular to who and what we were dealing with. My hope here is also to give the reader who is not already familiar with the Gödel Works a sense of what has been gained in the process, and to encourage dipping in according to interest. Given the absolute importance of Gödel for mathematical logic, students should also be pointed to these important source materials to experience first hand the exercise of his genius and the varied ways of his thought and to see how scholarly and critical studies help to expand their significance. Though indeed much has been gained in our work there is still much that can and should be done; besides some indications below, for that the reader is referred to [2]. (shrink)

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The point of departure for this panel is a somewhat controversial paper that I published in the American Mathematical Monthly under the title “Does mathematics need new axioms?” [4]. The paper itself was based on a lecture that I gave in 1997 to a joint session of the American Mathematical Society and the Mathematical Association of America, and it was thus written for a general mathematical audience. Basically, it was intended as an assessment of Gödel’s program for new axioms that (...) he had advanced most prominently in his 1947 paper for the Monthly, entitled “What is Cantor’s continuum problem?” [7]. My paper aimed to be an assessment of that program in the light of research in mathematical logic in the intervening years, beginning in the 1960s, but especially in more recent years. (shrink)

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In the first part of this article, Feferman outlines his ‘conceptual structuralism’ and emphasizes broad similarities between Parsons’s and his own structuralist perspective on mathematics. However, Feferman also notices differences and makes two critical claims about any structuralism that focuses on the “ur-structures” of natural and real numbers: it does not account for the manifold use of other important structures in modern mathematics and, correspondingly, it does not explain the ubiquity of “individual [natural or real] numbers” in that use. In (...) the second part, Feferman presents a summary of his reasons for the skepticism he has towards contemporary metamathematical investigations of set theory. That skepticism led him to reject the Continuum Problem as a definite mathematical one. He contrasts that attitude sharply to Parsons’s “great sympathy for the current explorations of higher set theory.”. (shrink)

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Paradigme universale -- Pornind de la un zâmbet -- Jocul -- Timpul -- Întâlnirea extremelor.

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What is predicativity? While the term suggests that there is a single idea involved, what the history will show is that there are a number of ideas of predicativity which may lead to different logical analyses, and I shall uncover these only gradually. A central question will then be what, if anything, unifies them. Though early discussions are often muddy on the concepts and their employment, in a number of important respects they set the stage for the further developments, and (...) so I shall give them special attention. NB. Ahistorically, modern logical and set-theoretical notation will be used throughout, as long as it does not conflict with original intentions. (shrink)

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Abstract:Should the responsibilities of business managers be understood independently of the social circumstances and “market forces” that surround them, or (in accord with empiricism and the social sciences) are agents and their choices shaped by their circumstances, free only insofar as they act in accordance with antecedently established dispositions, their “character”? Virtue ethics, of which I consider myself a proponent, shares with empiricism this emphasis on character as well as an affinity with the social sciences. But recent criticisms of both (...) empiricist and virtue ethical accounts of character deny even this apparent compromise between agency and environment. Here is an account of character that emphasizes dynamic interaction both in the formation and in the interplay between personal agency and responsibility on the one hand and social pressures and the environment on the other. (shrink)

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The purpose of this article is to explain why I believe that the Continuum Hypothesis (CH) is not a definite mathematical problem. My reason for that is that the concept of arbitrary set essential to its formulation is vague or underdetermined and there is no way to sharpen it without violating what it is supposed to be about. In addition, there is considerable circumstantial evidence to support the view that CH is not definite.

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“There's glory for you!”“I don't know what you mean by ‘glory,’ ” Alice said.Humpty Dumpty smiled contemptuously. “Of course, you dont—till I tell you. I meant ‘there's a nice knock-down argument.’”“But ‘glory’ doesn't mean a ‘nice knock-down argument,” Alice objected.“When I use a word,” Humpty Dumpty said, in rather a scornful tone, “it means just what I choose it to mean—neither more nor less.”“The question is,” said Alice, “whether you can make words mean so many different things.”“The question is,” said (...) Humpty Dumpty, “which is to be master, that's all.”When applied bioethics confronts the topic of futility, the question of who is to be master turns out to be central. Indeed, much of the literature on futility has focused on exactly this question: who gets to define the terms of the debate? Who gets to decide that treatment is “futile” and therefore allowably withheld or withdrawn? (shrink)

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In addition to this being the centenary of Kurt Gödel’s birth, January marked 75 years since the publication (1931) of his stunning incompleteness theorems. Though widely known in one form or another by practicing mathematicians, and generally thought to say something fundamental about the limits and potentialities of mathematical knowledge, the actual importance of these results for mathematics is little understood. Nor is this an isolated example among famous results. For example, not long ago, Philip Davis wrote me about what (...) he calls The Paradox of Irrelevance: “There are many math problems that have achieved the cachet of tremendous significance, e.g. Fermat, 4 color, Kepler’s packing, Gödel, etc. Of Fermat, I have read: ‘the most famous math problem of all time.’ Of Gödel, I have read: ‘the most mathematically significant achievement of the 20th century.’ … Yet, these problems have engaged the attention of relatively few research mathematicians—even in pure math.” What accounts for this disconnect between fame and relevance? Before going into the question for Gödel’s theorems, it should be distinguished in one respect from the other examples mentioned, which in any case form quite a mixed bag. Namely, each of the Fermat, 4 color, and Kepler’s packing problems posed a stand-out challenge following extended efforts to settle them; meeting the challenge in each case required new ideas or approaches and intense work, obviously of different degrees. By contrast, Gödel’s theorems were simply unexpected, and their proofs, though requiring novel techniques, were not difficult on the scale of things. Setting that aside, my view of Gödel’s incompleteness theorems is that their relevance to mathematical logic (and its offspring in the theory of computation) is paramount; further, their philosophical relevance is significant, but in just what way is far from settled; and finally, their mathematical relevance outside of logic is very much unsubstantiated but is the object of ongoing, tantalizing efforts.. (shrink)

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The work of Tversky, Kahneman and others suggests that people often make use of cognitive heuristics such as availability, salience and representativeness in their reasoning and decision making. Through use of a historical example--the recent plate tectonics revolution in geology--I argue that such heuristics play a crucial role in scientific decision making also. I suggest how these heuristics are to be considered, along with noncognitive factors (such as motivation and social structures) when drawing historical and epistemological conclusions. The normative perspective (...) is community-wide, contextual, and instrumental. (shrink)

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Trust in the practice of rational deliberation is widespread and largely unquestioned. This paper uses recent work from business contexts to challenge the view that rational deliberation in a group improves decisions. Pressure to reach consensus can, in fact, lead to phenomena such as groupthink and to suppression of relevant data. Aggregation of individual decisions, rather than deliberation to a consensus, surprisingly, can produce better decisions than those of either group deliberation or individual expert judgment. I argue that dissent is (...) epistemically valuable, not because of the discussion it can provoke (Mill's and Longino's view about the benefit of dissent), but because dissenting positions often are associated with particular data or insights that would be lost in consensus formation. Social epistemologists can usefully pay attention to various methods of aggregation of individual opinion for their effectiveness at realizing epistemic goals. (shrink)

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