DOCSLIB.ORG

Objectiones Qvintae Y Disqvisitio Metaphysica De Pierre Gassendi

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Objectiones Qvintae Y Disqvisitio Metaphysica De Pierre Gassendi OBJECTIONES QVINTAE Y DISQVISITIO METAPHYSICA DE PIERRE GASSENDI . TESIS DOCTORAL. REALIZADA POR JESÚS DEL VALLE CORTÉS. DIRIGIDA POR EL CATEDRÁTICO DOCTOR DON MARCELINO RODRÍGUEZ DONÍS. A la memoria de Fernando del Valle Vázquez, de su hijo agradecido. Y a Silvia Aguirrezábal Guerrero. LIBRO PRIMERO. EXHORDIVM. A MODO DE INTRODUCCIÓN. ería necesario un largo estudio para establecer con detalle las condiciones en las cuales fueron compuestas, en primer lugar, las S Quintas Objeciones de Pierre Gassendi, Prepósito de la Iglesia de Digne y agudísimo Filósofo, designadas de esta manera en un Índice redactado por Mersenne, y después las Instancias 1, fechadas el 15 de marzo de 1642, pero que seguramente comenzaron a difundirse durante el invierno anterior . Son palabras de Bernard Rochot 2 y con ellas comenzaba la introducción de su traducción francesa de la Petri Gassendi Disquisitio metaphysica . Esta tesis no es sino el cumplimiento de este anhelo de Rochot, que ha ya mucho convertimos en propio, si bien hemos ampliado los límites de la empresa, toda vez que este trabajo no se contenta con plasmar los acontecimientos que dieron lugar a la aparición de ambos escritos, sino que incluye el análisis pormenorizado de ellos, e incluso el de las escuetas réplicas de Descartes a las Instancias . Es la primera vez que se recorre el ciclo completo de los argumentos de la querella, hasta su cierre con la Carta a Clerselier . Eran años de carrera cuando estudiábamos, bajo la tutela del Doctor D. Marcelino Rodríguez Donís, las Meditationes de prima philosophia , con sus siete Objeciones y Respuestas y, de entre ellas, las agrias Objectiones quintae sobresalían, a nuestro juicio, muy por encima de las demás, a pesar de que uno de los siete objetores fuese el ínclito Thomas Hobbes 3. La Respuesta de Descartes a las Objeciones de Gassendi también rezumaba gran copia de ajenjo. Sin lugar a dudas, ante nuestras pupilas, se presentaba una discusión que parece haber trascendido más por el continente que por el contenido. ¿Continente o contenido? Nos sorprende que tanto exegetas como filósofos posteriores a ellos quedasen encandilados por la rugosa cáscara de la nuez de la discusión y, empero, no aplicasen toda su industria en partirla. Es en su interior, en la cerebriforme semilla de esa nuez, donde se encuentra lo que verdaderamente aporta la querella a un filósofo y es que, como ya avanzó Rochot, no hay ningún estudio profundo acerca de ella ni, particularmente, de la Disquisitio metaphysica . Posiblemente esta empresa no haya sido acometida antes por no estar traducida la Disquisitio más que al francés, y además tardíamente (en 1962). Aunque el investigador ha de beber directamente de la fuente en su idioma original, de haber sido trasladada esta obra a otras lenguas modernas, el interés por ella habría sido mayor y hubiese tenido más trascendencia. Existe una excelente traducción española, realizada 1 Entiéndase la Disquisitio metaphysica . 2 Bernard Rochot (1900-1971) era licenciado en filosofía y, en 1940, se doctoró en la Sorbona con una tesis acerca de Gassendi y el epicureísmo. Por su traducción de las Exercitationes paradoxicae adversus aristoteleos de Pierre Gassendi (Vrin, París 1959) obtuvo en 1960 el Prix Langlois de la Académie Française , ganando la suma de 50.000 francos franceses de la época. El Prix Langlois se instituyó en 1868 y se otorga a la mejor traducción al francés de una obra griega o latina, aunque también se admiten traducciones de otras lenguas. Rochot realizó muchos trabajos sobre Marin Mersenne, Galileo y Descartes y fue miembro de la Société Française de Philosophie , del Centre Internacional de Synthèse , del Centre Alexandre Koyré y del Centre National de la Recherche Scientifique . Era un gran traductor y sus traslaciones francesas de las Exercitationes y de la Disquisitio metaphysica son realmente excelentes. También es destacable su labor investigadora y exegética en el campo filosófico; era un especialista en la filosofía del siglo XVII. Se harán muchas alusiones a Rochot en esta tesis. Aunque en ocasiones disintamos con él, su labor nos parece encomiable y sus referencias bibliográficas nos han facilitado mucho el trabajo. Sea éste un modesto homenaje. 3 Concretamente de las Terceras objeciones . 7 por el Doctor Vidal Isidro Peña García 4, de las Meditationes de prima philosophia , en la que se incluyen las siete Objeciones y Respuestas , mas no contiene la contestación de Gassendi a las Respuestas de Descartes, por ser éste el contenido de una obra aparte: la Disquisitio metaphysica . Hubo réplica cartesiana a la Disquisitio metaphysica , aunque sucinta: se encuentra en la Carta del Señor Descartes al Señor Clerselier , fechada el 12 de enero de 1646, que sí fue traducida a nuestra lengua en el volumen de las Meditaciones metafísicas del Doctor Peña y que apareció por primera vez en la edición de 1647 de las Meditationes, trasladada al francés por el Duque de Luynes y Claude Clerselier 5, con el placet de Descartes. La elección del autor que iba a ser estudiado en esta tesis, Pierre Gassendi, vino dada, en parte, por la impronta antes referida, pero no fue ésta la única razón: Gassendi fue uno de los filósofos más importantes del siglo XVII. Además de ser muy prolífico en sus escritos, su erudición científica, histórica, filológica y filosófica era extraordinaria; sería muy difícil encontrar a alguien de su época con tan vasto conocimiento, incluido Descartes. A pesar de la importancia de nuestro autor, apenas hay tesis doctorales o estudios profundos acerca de él, siendo incluso entre los franceses casi un completo desconocido. Henri Berr defendió en 1898 su tesis acerca del escepticismo de Gassendi 6. Bernard Rochot hizo lo propio en 1940 con una tesis sobre el atomismo y el epicureísmo gassendianos7. El trabajo más completo lo realizó Olivier René Bloch: La philosophie de Gassendi. Nominalisme, Matérialisme et Métaphysique 8. Los dos primeros tratan de aspectos muy particulares de Gassendi, mientras que el tercero es más amplio, tanto en número de páginas como en contenidos. Sin embargo, el trabajo de Bloch no está centrado en la querella de nuestro autor con Descartes ni en la Disquisitio metaphysica . ¿Por qué es Gassendi casi un desconocido? Creemos que hay cuatro razones principales para ello: La primera de ellas es que Gassendi no escribió ninguna obra que supusiese un antes y un después en el terreno filosófico. Se dice de él que era más un historiador de la filosofía que un filósofo, y su enorme erudición alimenta este aserto. Su gran conocimiento de la filosofía anterior hace que sus referencias a otros autores sean constantes en sus obras. No obstante, sería más justo decir de él que no logró un lugar en el Olimpo de los filósofos por no postular algo completamente novedoso, de importancia capital o paradigmático. La segunda, quizás, sea que no creó un sistema filosófico propiamente dicho. Sin embargo, esto es a la vez defecto y virtud: defecto porque los filósofos más recordados y estudiados suelen ser los que establecieron sistemas integrales, como Descartes, Kant, Hegel, etc. Pero los sistemas suelen adolecer de coherencia cuando tratan bajo un mismo prisma todos los asuntos que se presentan al entendimiento humano, y por ello, a menudo, utilizan grandes dosis de aglomerante que, las más de las veces, no son sino excusas para conciliar lo irreconciliable. No haber creado un sistema filosófico, pues, es 4 Meditaciones metafísicas con objeciones y respuestas . Alfaguara, Madrid 1977; reeditada por KRK ediciones, Oviedo 2005. 5 En dicha edición, la Carta se encuentra en las pp. 593-606. 6 La tesis, en latín, tenía por título An jure inter scepticos Gassendus numeratus fuerit , siendo traducida al francés por Bernard Rochot bajo el título Du Scepticisme de Gassendi , Éditions Albin Michel, París, 1960. 7 Publicada como Les travaux de Gassendi sur Épicure et sur l´atomisme , Librairie philosophique J. Vrin. París, 1944. 8 Impresor Martinus Nijhoff. La Haya, 1971. 8 virtud, ya que supone una huida de esas reconciliaciones artificiales 9. Es más, el pensamiento gassendiano era sumamente ecléctico, manteniendo, según fuese el asunto y el período de su vida, posiciones escépticas, fideístas, atomistas, etc. La tercera causa del olvido sobre Gassendi, posiblemente, sea que su obra no ha sido traducida sino en una ínfima parte. Gran culpa de esto, creemos, es de la Abrégé de la philosophie de M. Gassendi , realizada por François Bernier 10 , publicándose la primera parte en Lyon, 1674, y terminándose en 1678. Por un lado, la Abrégé , si es que puede llamarse así a una extensa obra en siete tomos, dio a conocer al mundo los contenidos de los escritos de nuestro autor. Bernier no es parco en detalles. Su exposición es exhaustiva y a poco se convierte en una traducción francesa de la Petri Gassendi opera omnia ; por el otro, al tener ya en un idioma moderno el pensamiento de Gassendi, pocos debieron tener la intención de leer sus gruesos volúmenes latinos. La cuarta y última razón, a nuestro juicio, es que, aunque Descartes no logró hacer triunfar sus postulados filosóficos en vida, es cierto que, un siglo después de su deceso, el sistema cartesiano llegó a ser preeminente y ampliamente conocido. Gassendi es más recordado por las Objectiones quintae a las Meditationes de prima philosophia que por cualquier otro escrito suyo. De esta manera, al ser identificado como el opositor más beligerante para con la doctrina cartesiana, su figura no podía más que descender cuanto más se alzaba la de Descartes. Dado el amplísimo abanico de obras que escribió Gassendi, conviene dar una explicación de por qué elegimos la Disquisitio metaphysica como centro de esta tesis: Hemos dicho que Gassendi es recordado, sobre todo, por oponerse a la metafísica cartesiana en sus Objectiones quintae . Pero este escrito no fue sino el comienzo de la querella pública que se dio entre ambos sabios.
Load more

Recommended publications
  • Pascal's and Huygens's Game-Theoretic Foundations For
    Pascal's and Huygens's game-theoretic foundations for probability Glenn Shafer Rutgers University [email protected] The Game-Theoretic Probability and Finance Project Working Paper #53 First posted December 28, 2018. Last revised December 28, 2018. Project web site: http://www.probabilityandfinance.com Abstract Blaise Pascal and Christiaan Huygens developed game-theoretic foundations for the calculus of chances | foundations that replaced appeals to frequency with arguments based on a game's temporal structure. Pascal argued for equal division when chances are equal. Huygens extended the argument by considering strategies for a player who can make any bet with any opponent so long as its terms are equal. These game-theoretic foundations were disregarded by Pascal's and Huy- gens's 18th century successors, who found the already established foundation of equally frequent cases more conceptually relevant and mathematically fruit- ful. But the game-theoretic foundations can be developed in ways that merit attention in the 21st century. 1 The calculus of chances before Pascal and Fermat 1 1.1 Counting chances . .2 1.2 Fixing stakes and bets . .3 2 The division problem 5 2.1 Pascal's solution of the division problem . .6 2.2 Published antecedents . .7 2.3 Unpublished antecedents . .8 3 Pascal's game-theoretic foundation 9 3.1 Enter the Chevalier de M´er´e. .9 3.2 Carrying its demonstration in itself . 11 4 Huygens's game-theoretic foundation 12 4.1 What did Huygens learn in Paris? . 13 4.2 Only games of pure chance? . 15 4.3 Using algebra . 16 5 Back to frequency 18 5.1 Montmort .
    [Show full text]
  • A Tale of the Cycloid in Four Acts
    A Tale of the Cycloid In Four Acts Carlo Margio Figure 1: A point on a wheel tracing a cycloid, from a work by Pascal in 16589. Introduction In the words of Mersenne, a cycloid is “the curve traced in space by a point on a carriage wheel as it revolves, moving forward on the street surface.” 1 This deceptively simple curve has a large number of remarkable and unique properties from an integral ratio of its length to the radius of the generating circle, and an integral ratio of its enclosed area to the area of the generating circle, as can be proven using geometry or basic calculus, to the advanced and unique tautochrone and brachistochrone properties, that are best shown using the calculus of variations. Thrown in to this assortment, a cycloid is the only curve that is its own involute. Study of the cycloid can reinforce the curriculum concepts of curve parameterisation, length of a curve, and the area under a parametric curve. Being mechanically generated, the cycloid also lends itself to practical demonstrations that help visualise these abstract concepts. The history of the curve is as enthralling as the mathematics, and involves many of the great European mathematicians of the seventeenth century (See Appendix I “Mathematicians and Timeline”). Introducing the cycloid through the persons involved in its discovery, and the struggles they underwent to get credit for their insights, not only gives sequence and order to the cycloid’s properties and shows which properties required advances in mathematics, but it also gives a human face to the mathematicians involved and makes them seem less remote, despite their, at times, seemingly superhuman discoveries.
    [Show full text]
  • Cycloid Article(Final04)
    The Helen of Geometry John Martin The seventeenth century is one of the most exciting periods in the history of mathematics. The first half of the century saw the invention of analytic geometry and the discovery of new methods for finding tangents, areas, and volumes. These results set the stage for the development of the calculus during the second half. One curve played a central role in this drama and was used by nearly every mathematician of the time as an example for demonstrating new techniques. That curve was the cycloid. The cycloid is the curve traced out by a point on the circumference of a circle, called the generating circle, which rolls along a straight line without slipping (see Figure 1). It has been called it the “Helen of Geometry,” not just because of its many beautiful properties but also for the conflicts it engendered. Figure 1. The cycloid. This article recounts the history of the cycloid, showing how it inspired a generation of great mathematicians to create some outstanding mathematics. This is also a story of how pride, pettiness, and jealousy led to bitter disagreements among those men. Early history Since the wheel was invented around 3000 B.C., it seems that the cycloid might have been discovered at an early date. There is no evidence that this was the case. The earliest mention of a curve generated by a -1-(Final) point on a moving circle appears in 1501, when Charles de Bouvelles [7] used such a curve in his mechanical solution to the problem of squaring the circle.
    [Show full text]
  • Marin Mersenne As Mathematical Intelligencer
    Hist. Sci., li (2013) SMall SkIllS, BIG NETwORkS: MaRIN MERSENNE aS MaTHEMaTICal INTEllIGENCER Justin Grosslight Independent Scholar Writing in August 1634, the French polymath Nicolas-Claude Fabri de Peiresc reflected upon Marin Mersenne’s endeavours. Mersenne, Peiresc asserted, had forced himself into “frontiers that are a little more in fashion of the times than these prolix treaties of the schools that so few men handle outside of the colleges”.1 Peiresc was quite prescient to realize the novel claims that Mersenne was promoting. From the middle of the 1620s until his death in 1648, Mersenne encouraged discussion on a number of new mathematical concepts, ideas that lacked a secure home within the Aristotelian university curriculum.2 By mathematics, I am referring to mixed mathematics, the application of arithmetic and geometry often to physical proc- esses, and related topics in natural philosophy: examples include Galilean mechan- ics, the question of whether a void exists in nature, and analysis of conic sections and their spatial counterparts.3 For Peiresc and others, Mersenne was an exemplar of new, heterodox ideas: though he was a member of the religious Minim order, he was respected widely as a mathematician, he lived a gregarious life in cosmopoli- tan Paris, and he was an intimate friend of the famed French mathematician rené Descartes as well as a correspondent with the Italian Galileo Galilei and the Dutch Christiaan huygens.4 But while Mersenne is still remembered as a mathematician and correspondent of famous mathematicians, Peiresc’s description of Mersenne as trend-conscious or even a trendsetter has been effectively forgotten.
    [Show full text]
  • Figurate Numbers and Sums of Numerical Powers: Fermat, Pascal, Bernoulli
    Figurate numbers and sums of numerical powers: Fermat, Pascal, Bernoulli David Pengelley In the year 1636, one of the greatest mathematicians of the early seventeenth century, the Frenchman Pierre de Fermat (1601—1665), wrote to his correspondent Gilles Personne de Roberval1 (1602—1675) that he could solve “what is perhaps the most beautiful problem of all arithmetic” [4], and stated that he could do this using the following theorem on the figurate numbers derived from natural progressions, as he first stated in a letter to another correspondent, Marin Mersenne2 (1588—1648) in Paris: 11111111 Pierre de Fermat, from Letter to Mersenne. September/October, 1636, and again to Roberval, November 4, 1636 The last number multiplied by the next larger number is double the collateral triangle; the last number multiplied by the triangle of the next larger is three times the collateral pyramid; the last number multiplied by the pyramid of the next larger is four times the collateral triangulo-triangle; and so on indefinitely in this same manner [4], [15, p. 230f], [8, vol. II, pp. 70, 84—85]. 11111111 Fermat, most famous for his last theorem,3 worked on many problems, some of which had ancient origins. Fermat had a law degree and spent most of his life as a government offi cial in Toulouse. There are many indications that he did mathematics partly as a diversion from his professional duties, solely for personal gratification. That was not unusual in his day, since a mathematical profession comparable to today’sdid not exist. Very few scholars in Europe made a living through their research accomplishments.
    [Show full text]
  • Circular Reasoning: Who First Proved That $ C/D $ Is a Constant?
    CIRCULAR REASONING: WHO FIRST PROVED THAT C=d IS A CONSTANT? DAVID RICHESON Abstract. We answer the question: who first proved that C=d is a con- stant? We argue that Archimedes proved that the ratio of the circumfer- ence of a circle to its diameter is a constant independent of the circle and that the circumference constant equals the area constant (C=d = A=r2). He stated neither result explicitly, but both are implied by his work. His proof required the addition of two axioms beyond those in Euclid's Elements; this was the first step toward a rigorous theory of arc length. We also discuss how Archimedes's work coexisted with the 2000-year belief|championed by scholars from Aristotle to Descartes|that it is impossible to find the ratio of a curved line to a straight line. For a long time I was too embarrassed to ask the question in the title. The expression C = πd, which gives the relationship between the circumference and the diameter of a circle, is one of the few formulas known to almost all children and adults, regardless of how long they have been out of school. But who first proved it? I was sure that merely asking the question would tarnish my reputation as a mathematician and as a student of the history of mathematics. Surely the answer is well-known and easy to find. But I could not locate it|at least none of the standard reference books discussed the matter. When I finally summoned the courage to ask others I received two types of replies: either \It is obvious; all circles are similar" or \I don't know." The first of these is intriguing and has some merit; it may be why the invariance of C=d was discovered in so many different cultures.
    [Show full text]
  • History of Mathematics 17Th Century Developments
    History of Mathematics 17th century developments Peter Gibson November 5, 2019 Overview and historical context The 17th century was marked by imperial expansion and rivalry. The Russian empire expanded to encompass vast territories, governed by the Romanov imperial family (which ruled from 1584-1917). In particular, Peter the Great (r. 1682-1725) consolidated both territory and political power. In western Europe there was rivalry between the French Bourbon kings and the Hapsburg rulers of Spain and Austria. The Dutch Republic broke away from Spanish control at the end of the Thirty Years War (1618-1648). There was an expansion of naval power among European states, accompanying increased overseas trade and colonisation of the Americas. The slave trade flourshed during this time. P. Gibson Math 4400 2 / 19 An estimate 12M tons of sugar was transported to Europe in the century 1690-1790, during which time an estimated 12M African slaves were forced into labour in European colonies. Politically, the prevailing model was one of absolutist, dynastic monarchy, as typified by Louis XIV (r. 1643-1715) in France or Peter the Great in Russia. (The situation in England was an exception, with the civil war having resulted in power sharing between the monarchy and the nobility.) The balance of power shifted away from Spain and Portugal, toward Britain and France. Overall, mercantalism was the dominant economic model, involving extraction of wealth from colonial territory in the Americas and elsewhere, and transportation of goods to Europe. P. Gibson Math 4400 3 / 19 Overall, mercantalism was the dominant economic model, involving extraction of wealth from colonial territory in the Americas and elsewhere, and transportation of goods to Europe.
    [Show full text]
  • 2009 Math History (Open) 1 E Is None of These 1) a Sizable Portion of Our
    2009 Math History (Open) E is none of these 1) A sizable portion of our current knowledge of ancient Egyptian mathematics stems from this text. In its 14th problem the volume of a frustum acting as a base for a pyramid is calculated. What is the name of this ancient Egyptian manuscript? A) Reisner Papyrus B) Rhind Papyrus C) Moscow Papyrus D) Berlin Papyrus 2) This Indian mathematician and priest from around 800 BC presented an approximation for √2 correct to five decimal places in his Sulbasutra. In addition, his Sulbasutra also contained geometric solutions to linear equations of one unknown, an early version of the Pythagorean Theorem, and an approximation of π accurate enough for constructing circular shapes on altars. Quadratic equations of the forms ax2 = c and ax2 + bx = c were also found in his writings. A) Baudhayana B) Katyayana C) Apastamba D) Aryabhata I 3) Born around 624 BC, this Greek mathematician, philosopher, scientist, and engineer, regarded as the first of the Seven Sages, or wise men of Ancient Greece, founded abstract geometry. He is credited for theorems such as “If two straight lines intersect, the opposite angles formed are equal”, and “Any angle inscribed in a semicircle is a right angle”. The latter theorem is named after him. It is also said that he defined the constellation Ursa Minor, which greatly helped navigators. A) Thales of Miletus B) Anaximander C) Archimedes D) Zeno of Elea 4) Although Gauss provided the first rigorous proof for the Fundamental Theorem of Arithmetic, stating that “All natural numbers can be formed by multiplying a unique set of prime numbers unless they are prime themselves”; this Greek mathematician essentially proved it a millennium and a half earlier.
    [Show full text]
  • Isaac Barrow English Version
    ISAAC BARROW (October, 1630 – May 4, 1677) by HEINZ KLAUS STRICK, Germany Unlike many of his ancestors and close relatives, THOMAS BARROW – after a dispute with his father – did not embark on an academic career, but worked his way up in London to become linen merchant to the court of King CHARLES I of England. His first marriage produced a son; his wife died when the boy with the first name ISAAC was four years old. The child was given to the grandfather, who spoiled the boy beyond measure. His father, who remarried after two years, soon enrolled ISAAC at Charterhouse School, an elite boarding school founded in 1611 which still exists today, and paid double the school fees – in the expectation that the boy would then receive special support. This was not the case, however, and ISAAC soon acquired a reputation as a bully. So the father tried another boarding school, the Felsted School in Essex, founded in 1564, which JOHN WALLIS had also attended. At this school, education and the strict observance of rules were very important. Now, at last, the boy's talent became apparent; he made good progress in the core subjects of Greek, Latin, Hebrew and logic. As a result of the bloody clashes between the Catholic population and the Protestant settlers in Ireland (the Irish Rebellion), his father lost his fortune and could no longer pay the school fees. But ISAAC did not have to leave the school, as the headmaster of the Felsted School had recognized his talent and was willing to support him further.
    [Show full text]
  • Awareness and Cavalieri's Principle
    ALGEBRAIC FORMULAS, GEOMETRIC AWARENESS AND CAVALIERI’S PRINCIPLE JÉRÔME PROULX, DAVID PIMM It seems appropriate in a new journal of mathematics deployed, geometry has vanished (despite the etymological education [For the Learning of Mathematics] that there origins of the word itself). should be an attempt to tackle a perennial problem [the We argue that offering and focusing upon formulas in this loss of geometry] with new terms. (Tahta, 1980, p. 9) context transports the mathematical work from the geomet- ric realm of area and volume to that of substitution of One of the fundamental tensions at work in both learning numerical values into formulas – a quite different mathe- and teaching mathematics is that between fluency and matical arena of potential technique, fluency and skill. (One understanding. [1] Formulas are frequently offered as an of us, for instance, remembers classroom work involving aid to fluency, as a concise and manipulable summary of an ‘changing the subject of the formula’ – algebraic tasks that invariance, an indifference to change and to the contingent. were quite independent of the meaning and referents of the Formulas contain a tacit ‘always’ (with ‘under suitable con- particular formula in question and, indeed, whose unavowed ditions’, sometimes said sotto voce). One unfortunate result purpose was precisely such semantic suppression.) Signifi- can be students at various levels seeing mathematics as cantly, however, this arena has nothing to do with the being ‘all about formulas’. More than twenty-five years ago, geometric notions of area and volume themselves: when stu- Hart (1981) observed: dents work with area or volume formulas, they are not mathematics teaching is often seen as an initiation into working on understanding concepts of area or volume, they the rules and procedures which, though very powerful are working within a particular sub-domain of algebra, (and therefore attractive to teachers), are often seen by namely substitution.
    [Show full text]
  • Naming Infinity: a True Story of Religious Mysticism And
    Naming Infinity Naming Infinity A True Story of Religious Mysticism and Mathematical Creativity Loren Graham and Jean-Michel Kantor The Belknap Press of Harvard University Press Cambridge, Massachusetts London, En gland 2009 Copyright © 2009 by the President and Fellows of Harvard College All rights reserved Printed in the United States of America Library of Congress Cataloging-in-Publication Data Graham, Loren R. Naming infinity : a true story of religious mysticism and mathematical creativity / Loren Graham and Jean-Michel Kantor. â p. cm. Includes bibliographical references and index. ISBN 978-0-674-03293-4 (alk. paper) 1. Mathematics—Russia (Federation)—Religious aspects. 2. Mysticism—Russia (Federation) 3. Mathematics—Russia (Federation)—Philosophy. 4. Mathematics—France—Religious aspects. 5. Mathematics—France—Philosophy. 6. Set theory. I. Kantor, Jean-Michel. II. Title. QA27.R8G73 2009 510.947′0904—dc22â 2008041334 CONTENTS Introduction 1 1. Storming a Monastery 7 2. A Crisis in Mathematics 19 3. The French Trio: Borel, Lebesgue, Baire 33 4. The Russian Trio: Egorov, Luzin, Florensky 66 5. Russian Mathematics and Mysticism 91 6. The Legendary Lusitania 101 7. Fates of the Russian Trio 125 8. Lusitania and After 162 9. The Human in Mathematics, Then and Now 188 Appendix: Luzin’s Personal Archives 205 Notes 212 Acknowledgments 228 Index 231 ILLUSTRATIONS Framed photos of Dmitri Egorov and Pavel Florensky. Photographed by Loren Graham in the basement of the Church of St. Tatiana the Martyr, 2004. 4 Monastery of St. Pantaleimon, Mt. Athos, Greece. 8 Larger and larger circles with segment approaching straight line, as suggested by Nicholas of Cusa. 25 Cantor ternary set.
    [Show full text]
  • The Origins of Mathematical Societies and Journals
    University of Tennessee, Knoxville TRACE: Tennessee Research and Creative Exchange Masters Theses Graduate School 5-2010 The Origins of Mathematical Societies and Journals Eric S. Savage University of Tennessee - Knoxville, [email protected] Follow this and additional works at: https://trace.tennessee.edu/utk_gradthes Part of the History of Science, Technology, and Medicine Commons, and the Other Mathematics Commons Recommended Citation Savage, Eric S., "The Origins of Mathematical Societies and Journals. " Master's Thesis, University of Tennessee, 2010. https://trace.tennessee.edu/utk_gradthes/658 This Thesis is brought to you for free and open access by the Graduate School at TRACE: Tennessee Research and Creative Exchange. It has been accepted for inclusion in Masters Theses by an authorized administrator of TRACE: Tennessee Research and Creative Exchange. For more information, please contact [email protected]. To the Graduate Council: I am submitting herewith a thesis written by Eric S. Savage entitled "The Origins of Mathematical Societies and Journals." I have examined the final electronic copy of this thesis for form and content and recommend that it be accepted in partial fulfillment of the requirements for the degree of Master of Science, with a major in Mathematics. William R. Wade, Major Professor We have read this thesis and recommend its acceptance: Charles Collins, Philip Schaefer, Mary Sue Younger Accepted for the Council: Carolyn R. Hodges Vice Provost and Dean of the Graduate School (Original signatures are on file with official studentecor r ds.) To the Graduate Council: I am submitting herewith a thesis written by Eric S. Savage entitled “The Origins of Mathematical Societies and Journals” I have examined the final electronic copy of this thesis for form and content and recommend that it be accepted in partial fulfillment of the requirements for the degree of Master of Science, with a major in Mathematics.
    [Show full text]