Before examining de Moivre's contributions to the science of mathematics, this article reviews the source materials, consisting of the printed works and the correspondence of de Moivre, and constructs his biography from them. The analytical part examines de Moivre's contributions and achievements in the study of equations, series, and the calculus of probability. De Moivre contributed to the continuing development from Viète to Abel and Galois of the theory of solving equations by means of constructing particular (...) equations, the roots of which can be written in the form $$\sqrt[n]{{a + \sqrt b }} + \sqrt[n]{{a - \sqrt b }}$$. He also discovered the reciprocal equations. In the course of this work de Moivre discovered an expression equivalent to (cos α+i sin α) n =cos n α+i sin n α and, following Cotes, he succeeded in expressing the nth roots of unity in trigonometric form. In the theory of series, de Moivre developed a polynomial theorem encom-passing Newton's binomial theorem and, in particular, a theorem of recurrent series useful in the calculus of probability. The demands of the calculus of probability led de Moivre to an approximation for the binomial coefficients $$\left( {_m^n } \right)$$ for large values of n. The interaction between de Moivre and James Stirling, particularly in regard to the asymptotic series for log (n!), is treated at length. This work supplied the foundation for de Moivre's limit theorem for the binomial distribution. The calculus of probability, which occupied him from 1708 onward, became in time ever more the center of de Moivre's inquiries. Proceeding from contemporary collections of gambling exercises, de Moivre, by introducing an explicit measure of probability for the so-called Laplace experiments, found the beginnings of a theory of probability. De Moivre expanded the classic application of probability calculus to games of chance by addressing himself to the problem of annuities and by adopting Halley's work with its conception of “Probability of life”. De Moivre was the first to publish a mathematically formulated law for the decrements of life derived from mortality tables. (shrink)

In 1708 Pierre Rémond de Montmort published Essay d’analyse sur les jeux de hazard, an analysis of contemporary games of chance using probability theory. Three years later Abraham de Moivre published De Mensura Sortis in which various probability problems were solved. Montmort felt that De Moivre had plagiarized his work. In 1718 De Moivre expanded his work under the title The Doctrine of Chances. Montmort remained unhappy with this new work. Both the Essay d’analyse and The (...) Doctrine of Chances contain allegorical engravings that describe in pictures the nature and importance of their respective author’s work. (shrink)

Milton Friedman's famous methodological essay contains, along with much else, some strands that look as though they were taken from the “empirical-scientific” fabric described by Karl Popper. Think, for example, of Friedman's conviction that the way to test a hypothesis is to compare its implications with experience. Or of his more or less explicit espousal of the view that while no amount of facts can ever prove a hypothesis true, a single “fact” may refute it. Or of his assertion that (...) hypotheses are to be accepted only as provisionally true, and then only after repeated efforts to refute them have failed. The appearance of these Popperian ideas is not surprising. (shrink)

This volume brings together a collection of essays on the history and philosophy of probability and statistics by one of the eminent scholars in these subjects. Written over the last fifteen years, they fall into three broad categories. The first deals with the use of symmetry arguments in inductive probability, in particular, their use in deriving rules of succession. The second group deals with four outstanding individuals who made lasting contributions to probability and statistics in very different ways: Frank Ramsey, (...) R. A. Fisher, Alan Turing, and Abraham de Moivre. The last group of essays deals with the problem of 'predicting the unpredictable' - making predictions when the range of possible outcomes is unknown in advance. The essays weave together the history and philosophy of these subjects and document the fascination that they have exercised for more than three centuries. (shrink)

This article develops a new and expanded interpretation of the typology exclusivism, inclusivism, pluralism. The proposal refines the categories of what was originally a Christian typology in order to provide a truly cross-cultural and interreligious framework to better understand and compare the most common views of religious diversity found not only in Christianity, but also in Buddhism and other religions. Although building upon Schmidt-Leukel's logical reinterpretation of the typology, the article substantially modifies his framework and understands the typology, not as (...) a comprehensive classification of possible attitudes toward other religions, but rather as an open-ended framework to clarify the nature of the most common theologies of religions that exist in reality. The new interpretation provides a more precise definition of inclusivism that does not conflate inclusivism with the affirmation of a singular maximum, thus distinguishing between absolutistic and non-absolutistic forms of inclusivism. The new interpretation introduces an intermediate position between inclusivism and pluralism called pluralistic inclusivism. The article challenges David Ray Griffin's concept of generic pluralism and proposes a new understanding of pluralism indebted to Raimundo Panikkar. (shrink)

INTRODUCTION WERNER ABRAHAM, LACI MARÁCZ, SJAAK DE MEY & WIM SCHERPENISSE University of Groningen The Groningen Conference on Topic, ...

: This essay attempts to clarify the position of Nāgārjuna in the history of Buddhist philosophy by comparing the concept of emptiness in the Pāli Nikāyas and the Mūlamadhyamakakārikā. It is argued that the identity of samsāra with nirvāna, the emptiness of svabhāva of all dharmas, and the equating of emptiness and dependent arising are not revolutionary innovations of Nāgārjuna or the second turning of the wheel of Dharma, but orthodox philosophical moves entailed by the teachings of early Buddhism.

This essay attempts to clarify the position of Nāgārjuna in the history of Buddhist philosophy by comparing the concept of emptiness in the Pāli Nikāyas and the Mūlamadhyamakakārikā. It is argued that the identity of samsāra with nirvāna, the emptiness of svabhāva of all dharmas, and the equating of emptiness and dependent arising are not revolutionary innovations of Nāgārjuna or the second turning of the wheel of Dharma, but orthodox philosophical moves entailed by the teachings of early Buddhism.

This article develops a new and expanded interpretation of the typology exclusivism, inclusivism, pluralism. The proposal refines the categories of what was originally a Christian typology in order to provide a truly cross-cultural and interreligious framework to better understand and compare the most common views of religious diversity found not only in Christianity, but also in Buddhism and other religions. Although building upon Schmidt-Leukel's logical reinterpretation of the typology, the article substantially modifies his framework and understands the typology, not as (...) a comprehensive classification of possible attitudes toward other religions, but rather as an open-ended framework to clarify the nature of the most common theologies of religions that exist in reality. The new interpretation provides a more precise definition of inclusivism that does not conflate inclusivism with the affirmation of a singular maximum, thus distinguishing between absolutistic and non-absolutistic forms of inclusivism. The new interpretation introduces an intermediate position between inclusivism and pluralism called pluralistic inclusivism. The article challenges David Ray Griffin's concept of generic pluralism and proposes a new understanding of pluralism indebted to Raimundo Panikkar. (shrink)

El budismo. Peter Harvey. Cambridge University Press, Madrid 1998. 468 pp. Ptas 2,995. ISBN 84-8323-014-3.

This essay attempts to clarify the position of Nāgārjuna in the history of Buddhist philosophy by comparing the concept of emptiness in the Pāli Nikāyas and the Mūlamadhyamakakārikā. It is argued that the identity of samsāra with nirvāna, the emptiness of svabhāva of all dharmas, and the equating of emptiness and dependent arising are not revolutionary innovations of Nāgārjuna or the second turning of the wheel of Dharma, but orthodox philosophical moves entailed by the teachings of early Buddhism.

In lieu of an abstract, here is a brief excerpt of the content:Raimon Panikkar (1918-2010):Life and LegacyJ. Abraham Vélez de CeaThe interreligious theologian, intercultural philosopher, and pluralist mystic Raimon Panikkar died in Tavertet, Barcelona, on 26 August 2010. He was ninety-one. A pioneer of interreligious dialogue and comparative theology, Panikkar claimed to be at the same time yet without contradiction a Christian, a Buddhist, a Hindu, and a secular man.Panikkar's multiple religious belonging was not a matter of choice and (...) shallow eclecticism but rather a matter of personal experience and profound spiritual growth. His distinction between eclecticism and syncretism might be helpful to understand the complex nature of his religious identity. Eclecticism "is an uncritical mixture of religious traditions and an agreement among them obtained by chopping off all possible discrepancies in favor of an amorphous common denominator." On the contrary, syncretism "is allowing for a possible assimilation of elements by virtue of which these elements cease to be foreign bodies so that organic growth within each tradition is possible, and the mutual fecundation of religious traditions becomes a genuine option."1Another point I would like to clarify is that Panikkar's multiple religious belonging was not a question of being primarily Christian and secondarily something else, as if truth could be quantified. Panikkar objected to this "modern" way of thinking. I remember a conversation with him about this issue in which he compared these attempts to quantify religious identity to those who try to understand the Trinity as being either one or three. He said that if you begin counting you miss the point, and then he added in a defiant tone: "I am 100 percent Christian, 100 percent Hindu, 100 percent Buddhist, and 100 percent secular." When I insisted and told him that for many people multiple religious belonging is just not possible, Panikkar replied: "Well, it is my experience; I cannot help it."Panikkar's multiple religious belonging was often misunderstood and cost him the distrust of both Christians and Hindus. For instance, in 1966, Panikkar applied for a chair in Hindu philosophy at the prestigious Banaras Hindu University. Though [End Page 215] everybody agreed he was by far the most competent candidate, he was not offered the position because for many conservative Hindus Panikkar was not Hindu enough.Similarly, many conservative Catholics today would say that Panikkar went too far with his distinction between Christ and the historical Jesus; for them Panikkar was not Christian enough. However, this would be unfair. As I understand Panikkar, he was not trying to undermine any Christian claim. Quite the contrary, he was challenging what he perceived as a tribal Christology and a reduction of Christianity to a two-thousand-year-old sect. Time will tell, like it did with great thinkers such as Nāgārjuna (ca. 150-250), Śaṅ-kara (788-820), Thomas Aquinas (1225-1274), and Meister Eckhart (ca. 1260-1327), who were also criticized at first by their respective traditions. Perhaps Panikkar was simply ahead of his time, and what today seems controversial to some will become the norm in the future; it would not be the first time.Panikkar was an embodiment of interreligious dialogue, and his theology was the result of such dialogue. He was born in Barcelona on 3 November 1918. His mother was a Catholic from Catalonia, and his father was a Hindu from Kerala, India. After studying philosophy and natural sciences in Barcelona, Madrid, and Bonn, he joined the recently created Opus Dei in 1940. It should be clarified that in the aftermath of the Spanish civil war and compared to the pre-Vatican II National Catholicism of Franco's regime, Opus Dei was a progressive Catholic organization for laypeople interested in sanctifying their professional work.Panikkar was ordained a Catholic priest in 1946 and became the chaplain of a student dormitory in Madrid (Colegio Mayor la Moncloa). That very year he earned his first doctorate, in philosophy, with a dissertation titled El concepto de naturaleza: Análisis histórico y metafísico de un concepto (Complutense University of Madrid, 1946, published in 1951). He was offered a position at the Complutense University but decided to continue with his pastoral work in Madrid, Barcelona... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:A New Direction for Comparative Studies of Buddhists and Christians:Evidence from Nāgārjuna and John of the CrossAbraham Vélez de CeaIs Nāgārjuna's emptiness a means to point out the inadequacy of logic and concepts to express the nature of the Ultimate Reality? Similarly, are John of the Cross's concepts of nothingness and emptiness examples of the apophatic path to God? In sum, is emptiness in Nāgārjuna and John of the (...) Cross comparable to the Christian via negativa and the apophatic path to God?If you answered yes to any of these questions, I believe you might be interested in reading this article carefully. You are not alone; in fact most if not all previous discussions of Nāgārjuna and John of the Cross in the field of Buddhist-Christian studies have assumed an affirmative answer to the former questions. The comparisons of D.T. Suzuki, Thomas Merton, and the Kyoto school between the Christian God and Buddhist emptiness, as well as the comparisons of members of the Masao Abe–John Cobb group, have greatly contributed to this apophatic interpretation of emptiness. The enormous contributions of D. T. Suzuki, Thomas Merton, the Kyoto school, and the Abe-Cobb group to the field of Buddhist-Christian studies cannot be sufficiently praised and appreciated. However, the future of Buddhist-Christian studies and Buddhist-Christian dialogue requires a new comparative direction, a shift from comparative theory to comparative praxis, from doctrinal comparisons to more ethical and spiritually relevant comparisons.This new direction provides Buddhist-Christian studies with a more practical orientation necessary for the urgent needs of our planet as well as for the needs of a growing number of members of different religions with pluralist attitudes. By pluralist attitudes, I do not mean a relativistic standpoint, but rather an attitude of intellectual humbleness and dialogical openness toward other religions. That humble and dialogical openness seeks neither to proselytize nor to create a new religion. Rather, the objective is to build bridges of understanding and solidarity among religious communities and to be personally enriched by the contributions of all religions.In order to justify the need for this new and more practically oriented comparative [End Page 139] direction, it is imperative to review previous scholarship in the field of Buddhist-Christian studies. A comprehensive analysis of all past scholarship would be too ambitious a goal for the purpose of this article. Thus, in the first part of this article I limit myself to reviewing those questionable hermeneutical tendencies that I have identified in former Buddhist-Christian discussions of John of the Cross and Nāgārjuna. In the second part, I continue the justification of this new direction for Buddhist-Christian studies by providing a specific example, namely, a comparison of the instrumental ethical function of emptiness in Nāgārjuna and John of the Cross.Hermeneutical Tendencies in Previous Buddhist-Christian Studies of John of the Cross and NāgārjunaHermeneutical Tendencies in Comparisons of John of the Cross and BuddhismIn the case of John of the Cross, I have identified three questionable hermeneutical tendencies. The first one is to exaggerate the similarity between John of the Cross and Buddhism. Take, for example, what Thomas Merton—whose pioneering work on Buddhist-Christian dialogue deserves careful study—said in 1968: "Frankly, I would say that Zen is nothing but John of the Cross without the Christian vocabulary" (quoted in Nugent 1996: 53). This comparison suggests that the teachings of Zen and John of the Cross are virtually identical, neglecting important differences between them.Similarly, Christopher Nugent compares John's experience of one's own true self to the experience of Buddha-nature, and describes satori as a fusion of all and nothing, and the coincidence of opposites. For Nugent, John of the Cross is not only a Zen master, but also "more Taoist than dualist" (1996: 62–64). These comparisons of John of the Cross to Zen and Taoism concepts fail to bring justice to his ideas. John of the Cross cannot be categorized a nondualist because he maintains a clear distinction between God and creatures. Similarly, from an ethical... (shrink)

Abraham Isaac Hakohen Kook (1865-1935) served as the Ashkenazic Chief Rabbi of Erets Israel during the period of the British mandate. Rav Kook was a polymath, equally talented as a Talmudic legalist and rationalist philosopher, on the one hand, and as a mystic and poet, on the other. Today, we would say that he was both "left and right hemisphere." The present collection brings together in English translation Rav Kook's contributions to the field of Jewish history, though perhaps "historiosophy" (...) would be the better word. Rav Kook joins the ranks of those great Jewish thinkers who preceded him in interpretation of history: Maharal of Prague, Moses Hayyim Luzzatto and Zadok Hakohen of Lublin. If Rav Kook's philosophy were to be summed up in a single word, it would be: Kelaliyut or universality. Whereas most of us are held captive by individual events, Rav Kook has a great gift for the overview of history. He brings this gift to bear in his ability to provide perspective on the modern rebirth of Israel against the backdrop of mankind's ongoing spiritual evolution. In the latter regard, his vision has sometimes been compared to that of Teilhard de Chardin and Sri Aurobido, or more recently Ken Wilber. Contained in this collection are Rav Kook's eulogy for Herzl and Rav Kook's remarks at the opening of Hebrew University in Jerusalem. The essays are placed in historic context and provided with copious scholarly endnotes. (shrink)

In this article the authors reflect on regulations which have been developed to protect research subjects and data in research which uses human subjects. They suggest that regulations related to informed consent and privacy protection are burdensome in research which uses human subjects. They argue that a new category of research risk must be established which informs research subjects of the level of risk that they will be exposed to by participating in the research.

Cuauhtémoc HERNÁNDEZ MARTÍNEZ Editorial Universidad de Guanajuato, 2019, 213 pp. Guanajuato, ISBN : 978-607-441-688-6 ISBN : 978-607-441-689-3.

El presente manuscrito presenta un ensayo sobre una de las cuestiones de relevancia en la actualidad educativa, las trayectorias de los estudiantes vulnerables. A través de los siguientes puntos se presentará un aspecto vertebral en dichas trayectorias, los diferentes elementos del centro escolar y como afectan a los estudiantes, en concreto, a su implicación y como esta se ve alterada a lo largo de su trayectoria.

Tomas Abraham inicia una pesquisa filosofica y no se detiene ante las impugnaciones que dictan el buen gusto y la conveniencia (la que esconde las contradicciones para simular seriedad y rigor intelectual). Nada lo detiene. Observa, analiza, compulsa. Sus preguntas no interrogan esas zonas del discurso para las cuales se han inventado ya benevolas excusas, sino las otras, las peligrosas.Desde 1989, reflexiona Abraham, el factor economico es la clave que permite descifrar los anhelos y las frustraciones de la (...) sociedad. Por que? Porque el factor economico no se reduce a la economia, no se limita a la produccion y a la distribucion de riquezas sino que acusa la visible emergencia de nuevas formas de vida. El factor economico revela el diagrama de las mutaciones culturales. En este ensayo filosofico en el que coexisten una cantidad asombrosa de estilos y tonos, el autor analiza y discute la empresa como nuevo monumento cultural, la demonizacion del estado, las batallas etico-politicas entre intelectuales y economistas culturales, la tarea de los expertos en calidad de vida y su funcion en una nueva sociedad terapeutica. De las historias de vida de los archimillonarios al encuadre historico de la ideologia empresarial, de la puesta en sorna (con el mayor respeto) de la literatura de autoayuda a la meditacion sobre la moral y el dolor en los campos de exterminio, La empresa de vivir, como los libros anteriores del autor, traza una linea osada y firme e incorpora al pensamiento argentino una nueva manera de hacer las cosas. Una nueva manera capaz de abrir discusiones aparentemente concluidas o censuradas, de expandir los efectos de un conflicto intelectual hacia areas desprestigiadas oignoradas, de inaugurar una pasion para abolir la ironia autoindulgente y los entredichos ufan. (shrink)