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)

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)

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 for Solomon'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)

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.

Reviewing works by James Alison, Alistair McFadyen, Andrew Sung Park, Ted Peters, and Solomon 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)

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)

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)

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)

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)

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)

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)

When the ancient Greek philosopher, Pythagoras, was asked if he was a wise man, he humbly replied "No, I am only a lover of wisdom." This love of wisdom has been central to the philosophical enterprise for thousands of years, inspiring some of the most dazzling and daring achievements of the human intellect and providing the very basis for how we understand the world. Now, readers eager to acquire a basic familiarity with the history of philosophy but intimidated by the (...) task will find in A Passion for Wisdom: Philosophy Through the Ages, a lively, accessible, and highly enjoyable tour of the world's great ideas. Without simplifying their subject, editors Robert Solomon and Kathleen Higgins tell the story of philosophy's development with great clarity and refreshing wit. The brevity of their study, in fact, allows readers to see more clearly the connections and divergences between philosophers, as well as the way ideas change, reappear, and evolve over time. The authors begin with the most ancient religious beliefs and bring us right up to the feminist and multicultural philosophies of the present. Along the way, major philosophers are highlighted, from Plato and Aquinas to William James and Simone deBeauvoir, and major categories explored, from metaphysics and ethics to politics and logic. We also see the evolution of enduring ideas--how, for example, the value of subjective experience is treated in Augustine, Luther, Descartes, and Kirkegaard, how the idea of dynamic change appears in the work of Heraclitus, Darwin, Hegel, and Nietzsche, and how the recurring dichotomies between faith and reason, belief and skepticism, mysticism and empiricism occupy philosophers from one generation to the next. The authors make clear the many ways philosophers have argued with, borrowed from, and built on each other's ideas throughout the ages. We see Francis Bacon rejecting Aristotelian dogma, the impact of Buddhism on Schopenhauer, and the influence of Hume and Rousseau on the monumental philosophy of Imanuel Kant. The book is enlivened as well by telling anecdotes and sparkling quotations. We're treated to Thomas Hobbes' assessment--"Life is nasty, brutish, and short," Hegel's description of Napoleon as "world history on horseback," Schopenhauer's assertion that Art allows us a "Sabbath from the penal servitude of willing," and many other memorable and provocative observations. Accessible, comprehensive, and delightfully written, A Passion for Wisdom is a splendid introduction to an intellectual tradition that reaches back over three thousand years. More than that, it is a much-needed reminder for the present of the power inherent in humanity's wonder before the world. (shrink)

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)

In lieu of an abstract, here is a brief excerpt of the content:"What Is Philosophy?"The Status of World Philosophy in the ProfessionRobert C. SolomonThe question "What is philosophy?" is both one of the most virtuously self-effacing and one of the most obnoxious that philosophers today tend to ask. It is virtuously self-effacing insofar as it questions, with some misgivings, its own behavior, the worth of the questions it asks, and the significance of the enterprise itself. It is obnoxious when it (...) refuses to question its own behavior but instead takes that same behavior as the exclusive standard to delegitimize any other activity that dares to call itself "philosophy." Thus, for most of this century, Anglo-American and most European philosophers have simply ignored the rich philosophical traditions of Africa, Asia, Latin and Native America, and the rest of the world. Some leading African American and African European philosophers have dismissed "ethnophilosophy" as "not philosophy," presumably to protect their own analytic credentials. Universities as far flung as Singapore, Sierra Leone, and New Delhi have prided themselves on their fidelity to Oxbridge philosophy. It seems that the globalization of free market economics goes with the globalization of one brief moment in philosophy, with similarly devastating effects on local cultures and the rich varieties of human experience.Philosophy might be thought of as made up of two components: critical thinking and passionate vision. But "critical thinking" does not necessarily imply the hermeneutics of suspicion, skepticism, or intellectual paranoia—all too often the trademarks of the bright young professional philosopher. One can be "critical," that is, reflective, while at the same time be committed, even devoted, to an idea or a way of thinking. The emphasis on passionate vision, however, is just as essential, and any philosophy that doesn't include both components just isn't worthy of the name. Without passionate vision, we get that utterly eviscerated focus on forms of argumentation—philosophia minimalia—devoid of "empirical" content (that is to say, content) and, as far as most people are concerned, devoid of any interest. Without critical reflection, we get gullibility and the worst of New Age philosophy, accepting of any kind of nonsense, just because it stirs the passions. But simply to assume that philosophy must be as rigorously self-questioning as modern European and Anglo-American philosophy is a subtle form of ethnic chauvinism. It eliminates from the realm of philosophy not only African ethnophilosophy and Latin and Native American and South Pacific mythology but a good deal of the philosophy of religion, the basis (for better or worse) of the development of Western philosophy over much of the past two thousand years. [End Page 100]I have just withdrawn from a recent dispute, in a respectable and supposedly eclectic philosophy journal, in which my worst fears in this regard were rather bluntly confirmed. I had made the point mentioned above—rather matter-of-factly, I thought—that if (analytic) philosophy dismisses or ignores modes of thinking that are not obviously self-critical and are presented poetically instead of by way of positions to be argued for, then a good deal of the world's philosophy, including a good deal of Western philosophy, would be left out of the arena. The journal's board reacted indignantly, to put it mildly, to the suggestion that anything should count as "philosophy" that was not sufficiently self-critical in just this sense. But what about the millennium or so of religious philosophy in the West? Does anyone believe that thinkers like Anselm, or Alvin Plantiga for that matter, are seriously skeptical of the truth of Christianity, as they go through their admittedly brilliant argumentative routines? For that matter, to what extent is the emphasis on logical form and argument subjected to scrutiny in contemporary analytic philosophy? (As one of the foremost practitioners of that art commented, "Metaphilosophy makes me sick.")Some of the hostility to world philosophy, to be sure, turns on the conflict between philosophy and religion, which may have its origins in ancient and medieval philosophy but emerges full-blown with the Enlightenment and its campaign against "superstition." But many people and a good many cultures do not distinguish between philosophy and religion. If we consider the word "philosophy... (shrink)

INTRODUCTION: REASON AND THE PASSIONS i. Philosophy? This same philosophy is a good horse in the stable, but an arrant jade on a journey. ...

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)

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

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)

• This comes from my general view of the nature of mathematics, that it is humanly based and that it deals with more or less clear conceptions of mathematical structures; for want of a better word, I call that view conceptual structuralism.

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.

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)

Is grief a “negative” emotion? Is it an emotion at all? We often tend to conflate what causes an emotion with the value of the emotion itself. I argue that grief plays an unappreciated positive role in our experience. I also suggest that we too often tend to think of emotions as distinctive feelings and not as processes, but grief is a clear case of an emotional process. I similarly suggest that gratitude is an unappreciated emotion in ethics. But, on (...) a cosmic level, there is some question who the grateful person is grateful to. (shrink)

A notion of finitary inductively presented (f.i.p.) logic is proposed here, which includes all syntactically described logics (formal systems)met in practice. A f.i.p. theory FS0 is set up which is universal for all f.i.p. logics; though formulated as a theory of functions and classes of expressions, FS0 is a conservative extension of PRA. The aims of this work are (i)conceptual, (ii)pedagogical and (iii)practical. The system FS0 serves under (i)and (ii)as a theoretical framework for the formalization of metamathematics. The general approach (...) may be used under (iii)for the computer implementation of logics. In all cases, the work aims to make the details manageable in a natural and direct way. (shrink)

I met Dan Callahan in 1986—when I came to pitch him. Coming from a sleek office setting near Boston, I was intrigued by The Hastings Center's higgledy‐piggledy environment where so many smart people got to work in a relaxed, inviting atmosphere. I had noticed that the Center was producing a great deal of policy work on a wide range of topics but didn't seem to go further than publishing the highly valuable guidance developed under Dan Callahan's leadership. I ended my (...) pitch, “Look, Dan, where Hastings gets bored and wants to go on to the next topic, my group in Boston gets interested.” To my great pleasure, and despite his skepticism, Dan accepted the pitch. Beyond his generous responsiveness to unproven young people, Dan had many other virtues. For one, he was a boundary crosser. (shrink)

What Gödel accomplished in the decade of the 1930s before joining the Institute changed the face of mathematical logic and continues to influence its development. As you gather from my title, I’ll be talking about the most famous of his results in that period, but first I want to indulge in some personal reminiscences. In many ways this is a sentimental journey for me. I was a member of the Institute in 1959-60, a couple of years after receiving my PhD (...) at the University of California in Berkeley, where I had worked with Alfred Tarski, another great logician. The subject of my dissertation was directly concerned with the method of arithmetization that Gödel had used to prove his theorems, and my main concern after that was to study systematic ways of overcoming incompleteness. Mathematical logic was going through a period of prodigious development in the 1950s and 1960s, and Berkeley and Princeton were two meccas for researchers in that field. For me, the prospect of meeting with Gödel and drawing on him for guidance and inspiration was particularly exciting. I didn’t know at the time what it took to get invited. Hassler Whitney commented for an obituary notice in 1978 that “it was hard to appoint a new member in logic at the Institute because Gödel could not prove to himself that a number of candidates shouldn’t be members, with the evidence at hand.” That makes it sound like the problem for Gödel was deciding who not to invite. Anyhow, I ended up being one of the lucky few. (shrink)

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

Scholars and policymakers continue to struggle over the meaning of the word “vulnerable” in the context of research ethics. One major reason for the stymied discussions regarding vulnerable populations is that there is no clear distinction between accounts of research vulnerabilities that exist for certain populations and discussions of research vulnerabilities that require special regulations in the context of research ethics policies. I suggest an analytic process by which to ascertain whether particular vulnerable populations should be contenders for additional regulatory (...) protections. I apply this process to two vulnerable populations: the cognitively vulnerable and the economically vulnerable. I conclude that a subset of the cognitively vulnerable require extra protections while the economically vulnerable should be protected by implementing existing regulations more appropriately and rigorously. Unless or until the informed consent process is more adequately implemented and the distributive justice requirement of the Belmont Report is emphasized and operationalized, the economically disadvantaged will remain particularly vulnerable to the harm of exploitation in research. (shrink)

What clearly emerges from Hegel's writings is that "Geist" refers to some sort of general consciousness, a single "mind" common to all men. The entire sweep of the Phenomenology of Spirit is away from the "disharmonious" conceptions of men as individuals to the "absolute" conception of all men as one. In the Phenomenology, we are first concerned with the inadequacy of conceptions of oneself as an individual in opposition to others and in opposition to God. This opposition is first resolved (...) in ethics, in the conception of oneself as a member of a family, of a community, of Kant's "Kingdom of Ends," as a citizen of the state, and then in religion, in which one conceives of oneself as "part" of God and a religious community. Absolute consciousness is the explicit recognition of one's identity as universal Spirit. The concept of "Geist" is the hallmark of a theory of self identity--a theory in which I am something other than a person. (shrink)

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)

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.

When I was a teenager growing up in Los Angeles in the early 1940s, my dream was to become a mathematical physicist: I was fascinated by the ideas of relativity theory and quantum mechanics, and I read popular expositions which, in those days, besides Einstein’s The Meaning of Relativity, was limited to books by the likes of Arthur S. Eddington and James Jeans. I breezed through the high-school mathematics courses (calculus was not then on offer, and my teachers barely understood (...) it), but did less well in physics, which I should have taken as a reality check. On the philosophical side I read a mixed bag of Bertrand Russell, John Dewey and Alfred Korzybski (the missionary for “General Semantics” in Science and Sanity, a mish-mash of the theory of types, non-. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Some Sources for Hume's Opening Remarks to Treatise LIVJII Graham Solomon 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 GRAHAM SOLOMON 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)

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)