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Cantor on Infinity in Nature, Number, and the Divine Mind
Cantor on Infinity in Nature, Number, and the Divine Mind Anne Newstead Abstract. The mathematician Georg Cantor strongly believed in the existence of actually infinite numbers and sets. Cantor’s “actualism” went against the Aristote- lian tradition in metaphysics and mathematics. Under the pressures to defend his theory, his metaphysics changed from Spinozistic monism to Leibnizian volunta- rist dualism. The factor motivating this change was two-fold: the desire to avoid antinomies associated with the notion of a universal collection and the desire to avoid the heresy of necessitarian pantheism. We document the changes in Can- tor’s thought with reference to his main philosophical-mathematical treatise, the Grundlagen (1883) as well as with reference to his article, “Über die verschiedenen Standpunkte in bezug auf das aktuelle Unendliche” (“Concerning Various Perspec- tives on the Actual Infinite”) (1885). I. he Philosophical Reception of Cantor’s Ideas. Georg Cantor’s dis- covery of transfinite numbers was revolutionary. Bertrand Russell Tdescribed it thus: The mathematical theory of infinity may almost be said to begin with Cantor. The infinitesimal Calculus, though it cannot wholly dispense with infinity, has as few dealings with it as possible, and contrives to hide it away before facing the world Cantor has abandoned this cowardly policy, and has brought the skeleton out of its cupboard. He has been emboldened on this course by denying that it is a skeleton. Indeed, like many other skeletons, it was wholly dependent on its cupboard, and vanished in the light of day.1 1Bertrand Russell, The Principles of Mathematics (London: Routledge, 1992 [1903]), 304. -
Hans-Ludwig Wußing
Wußing, Hans-Ludwig akademischer Titel: Prof. Dr. rer. nat. habil. Prof. in Leipzig: 1968-69 Professor mit LA für Geschichte der Mathematik und Naturwissenschaften. 1969-92 o. Professor für Geschichte der Naturwissenschaften. Fakultät: 1952-55 Mathematisch-Naturwissenschaftliche Fakultät – Mathematisches Institut. 1955-57 Arbeiter- und Bauern-Fakultät. 1957-69 Medizinische Fakultät - Karl-Sudhoff-Inst. für Geschichte der Medizin u. der Naturwissenschaften. 1969-92 Bereich Medizin - Karl-Sudhoff-Institut für Geschichte der Medizin u. der Naturwissenschaften. Lehr- und Geschichte der Naturwissenschaften. Geschichte der Mathematik. Forschungsgebiete: weitere Vornamen: Lebensdaten: geboren am 15.10.1927 in Waldheim/Sachsen. gestorben am 26.04.2011 in Leipzig Vater: Hans Wußing (Kfm. Angestellter) Mutter: Lucie Wußing geb. Altmann (Hausfrau) Konfession: ohne Lebenslauf: 1934-1937 Bürgerschule Waldheim. 1937-1943 Oberschule Waldheim. 9/43-11/43 Einberufung als Luftwaffenhelfer in Leipzig.. 11/43-4/45 Einberufung zur Wehrmacht als Kanonier und Kriegsteilnahme. 4/45-12/45 Britische Kriegsgefangenschaft in Belgien. 12/45-4/46 Landwirtschaftlicher Hilfsarbeiter in Mentrup Kr. Osnabrück. 4/46-07/47 Oberschule Waldheim mit Abschluss Abitur. 1947-1952 Studium der Mathematik und Physik an der Philosophischen Fakultät der Universität Leipzig. 1.09.1952 Staatsexamen für Lehrer an der Oberstufe der Deutschen Demokratischen Schule im Hauptfach Mathematik und Nebenfach Physik. 1.09.1952 Aufnahme in die planmäßige wiss. Aspirantur im Fach Mathematik an der Universität Leipzig. 1952-1955 plm. wiss. Aspirant am Mathematischen Institut der Karl-Marx-Universität Leipzig. 1955-1957 Lektor an der Arbeiter-und Bauern-Fakultät (ABF) der Karl-Marx-Universität Leipzig. 1957-1959 Wiss. Ass. am Karl-Sudhoff-Institut für Geschichte der Medizin und der Naturwissenschaften. -
The Sixth Award of the Kenneth O May Medal and Prize
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Available online at www.sciencedirect.com Historia Mathematica 37 (2010) 4–7 www.elsevier.com/locate/yhmat News and Notices The sixth award of the Kenneth O. May Medal and Prize Karen Hunger Parshall Department of History & Mathematics, University of Virginia, Kerchof Hall, Charlottesville, VA 22904-4137, USA On the 31 July, 2009, in Budapest, at the quadrennial International Congress for the History of Science and Technology, the sixth Kenneth O. May Prizes and Medals were awarded by the International Commission for the History of Mathematics to Ivor Grattan-Guinness and Radha Charan Gupta. In the absence of the ICHM Chair, Karen Parshall, Craig Fraser, the ICHM Vice Chair, read the following citation: In 1989, the International Commission for the History of Mathematics awarded, for the first time, the Kenneth O. May Prize in the History of Mathematics. This award honors the memory of Kenneth O. May, mathematician and historian of mathematics, who was instrumental in creating a unified international community of historians of mathematics through his tireless efforts in founding in 1971 the International Commission for the His- tory of Mathematics and in 1974 the ICHM’s journal, Historia Mathematica. The Kenneth O. May Prize has been awarded every four years since 1989 to the historian or historians of mathematics whose work best exemplifies the high scholarly standards and intellectual con- tributions to the field that May worked so hard to achieve. To date, the following distin- guished historians of mathematics have been recognized for their work through receipt of the Kenneth O. -
The History of Arabic Sciences: a Selected Bibliography
THE HISTORY OF ARABIC SCIENCES: A SELECTED BIBLIOGRAPHY Mohamed ABATTOUY Fez University Max Planck Institut für Wissenschaftsgeschichte, Berlin A first version of this bibliography was presented to the Group Frühe Neuzeit (Max Planck Institute for History of Science, Berlin) in April 1996. I revised and expanded it during a stay of research in MPIWG during the summer 1996 and in Fez (november 1996). During the Workshop Experience and Knowledge Structures in Arabic and Latin Sciences, held in the Max Planck Institute for the History of Science in Berlin on December 16-17, 1996, a limited number of copies of the present Bibliography was already distributed. Finally, I express my gratitude to Paul Weinig (Berlin) for valuable advice and for proofreading. PREFACE The principal sources for the history of Arabic and Islamic sciences are of course original works written mainly in Arabic between the VIIIth and the XVIth centuries, for the most part. A great part of this scientific material is still in original manuscripts, but many texts had been edited since the XIXth century, and in many cases translated to European languages. In the case of sciences as astronomy and mechanics, instruments and mechanical devices still extant and preserved in museums throughout the world bring important informations. A total of several thousands of mathematical, astronomical, physical, alchemical, biologico-medical manuscripts survived. They are written mainly in Arabic, but some are in Persian and Turkish. The main libraries in which they are preserved are those in the Arabic World: Cairo, Damascus, Tunis, Algiers, Rabat ... as well as in private collections. Beside this material in the Arabic countries, the Deutsche Staatsbibliothek in Berlin, the Biblioteca del Escorial near Madrid, the British Museum and the Bodleian Library in England, the Bibliothèque Nationale in Paris, the Süleymaniye and Topkapi Libraries in Istanbul, the National Libraries in Iran, India, Pakistan.. -
Elizabeth F. Lewis Phd Thesis
PETER GUTHRIE TAIT NEW INSIGHTS INTO ASPECTS OF HIS LIFE AND WORK; AND ASSOCIATED TOPICS IN THE HISTORY OF MATHEMATICS Elizabeth Faith Lewis A Thesis Submitted for the Degree of PhD at the University of St Andrews 2015 Full metadata for this item is available in St Andrews Research Repository at: http://research-repository.st-andrews.ac.uk/ Please use this identifier to cite or link to this item: http://hdl.handle.net/10023/6330 This item is protected by original copyright PETER GUTHRIE TAIT NEW INSIGHTS INTO ASPECTS OF HIS LIFE AND WORK; AND ASSOCIATED TOPICS IN THE HISTORY OF MATHEMATICS ELIZABETH FAITH LEWIS This thesis is submitted in partial fulfilment for the degree of Ph.D. at the University of St Andrews. 2014 1. Candidate's declarations: I, Elizabeth Faith Lewis, hereby certify that this thesis, which is approximately 59,000 words in length, has been written by me, and that it is the record of work carried out by me, or principally by myself in collaboration with others as acknowledged, and that it has not been submitted in any previous application for a higher degree. I was admitted as a research student in September 2010 and as a candidate for the degree of Ph.D. in September 2010; the higher study for which this is a record was carried out in the University of St Andrews between 2010 and 2014. Signature of candidate ...................................... Date .................... 2. Supervisor's declaration: I hereby certify that the candidate has fulfilled the conditions of the Resolution and Regulations appropriate for the degree of Ph.D. -
Archives De L'académie Internationale D'histoire Des Sciences
Fonds de l’Académie internationale d’histoire des sciences Inventaire des archives de l'Académie internationale d'histoire des sciences Producteur : Académie internationale d'histoire des sciences Historique / Présentation de l’Académie : L'Académie internationale d'histoire des sciences est une association régie par la loi de 1901. L’Académie internationale d’histoire des sciences est une institution qui a pris en 1932 la succession du Comité international d’histoire des sciences fondé à Oslo le 17 août 1928. Elle est associée à la Division d’histoire des sciences et des techniques de l’Union internationale d’histoire et de philosophie des sciences pour la représentation et l’organisation de l’histoire des sciences sur le plan international. CAPHÉS - 2017 Page 1 Fonds de l’Académie internationale d’histoire des sciences Les membres effectifs et correspondants sont choisis sur base de leur œuvre scientifique. L’Académie comprend aussi des membres d'honneur élus parmi les personnalités qui ont contribué au progrès de l’histoire des sciences. L’Académie est dirigée par un Conseil d’administration ainsi constitué : un président, trois vice-présidents, un trésorier, un archiviste, et un secrétaire aux réseaux élus par l’Assemblée générale pour une durée de quatre ans, un secrétaire perpétuel élu pour une durée de sept ans, ainsi que par les anciens présidents et anciens secrétaires perpétuels, siégeant ex officio. L’Assemblée générale ordinaire, composée de tous les membres actifs, se réunit tous les quatre ans lors de la tenue des Congrès internationaux d’histoire des sciences organisés par la Division d’histoire des sciences et des techniques de l’Union internationale d’histoire et de philosophie des sciences. -
Mathematics People, Volume 52, Number 11
Mathematics People Bos Awarded 2005 May Prize Heinrich and Liu Receive 2005 The International Commission for the History of Mathe- CMS Awards matics (ICHM) has awarded the 2005 Kenneth O. May Prize and Medal to HENK BOS of the University of Utrecht. The The Canadian Mathematical Society (CMS) has awarded the May Prize honors outstanding contributions to the history 2005 Adrien Pouliot Award to KATHERINE HEINRICH of the Uni- of mathematics. According to the prize citation, Bos’s versity of Regina, Saskatchewan, and the 2005 G. de B. studies of the work of Descartes and his contemporaries Robinson Prize to YU-RU LIU of the University of Waterloo. and predecessors are “an exploration of what counted as The Adrien Pouliot Award is given to individuals or good mathematics in a particular period…Henk Bos has, teams of individuals who have made significant and sus- through his deep and insightful research, fundamentally tained contributions to mathematics education in Canada. shaped present-day understanding of the mathematics of Heinrich originated the Canadian Mathematics Education the seventeenth century…Bos gives to this seventeenth- Forum in 1995 as a venue for people interested in math- century material the kind of careful attention it was given ematics education at all levels to meet and discuss issues by the experts when it was new.” His other writings, in- of common interest and has been involved in the promo- cluding a collection of essays on the history of mathematics, tion of mathematics and mathematics education through- have “effectively extended Bos’s audience beyond the com- out her career. -
View This Volume's Front and Back Matter
Titles in This Series Volume 8 Kare n Hunger Parshall and David £. Rowe The emergenc e o f th e America n mathematica l researc h community , 1876-1900: J . J. Sylvester, Felix Klein, and E. H. Moore 1994 7 Hen k J. M. Bos Lectures in the history of mathematic s 1993 6 Smilk a Zdravkovska and Peter L. Duren, Editors Golden years of Moscow mathematic s 1993 5 Georg e W. Mackey The scop e an d histor y o f commutativ e an d noncommutativ e harmoni c analysis 1992 4 Charle s W. McArthur Operations analysis in the U.S. Army Eighth Air Force in World War II 1990 3 Pete r L. Duren, editor, et al. A century of mathematics in America, part III 1989 2 Pete r L. Duren, editor, et al. A century of mathematics in America, part II 1989 1 Pete r L. Duren, editor, et al. A century of mathematics in America, part I 1988 This page intentionally left blank https://doi.org/10.1090/hmath/008 History of Mathematics Volume 8 The Emergence o f the American Mathematical Research Community, 1876-1900: J . J. Sylvester, Felix Klein, and E. H. Moor e Karen Hunger Parshall David E. Rowe American Mathematical Societ y London Mathematical Societ y 1991 Mathematics Subject Classification. Primary 01A55 , 01A72, 01A73; Secondary 01A60 , 01A74, 01A80. Photographs o n th e cove r ar e (clockwis e fro m right ) th e Gottinge n Mathematisch e Ges - selschafft, Feli x Klein, J. J. Sylvester, and E. H. Moore. -
Visions of Scientific Imagination
Visions of Scientific Imagination J E F F W E B E R R A R E B O O K S C A T A L O G U E – 1 7 4 Visions of Scientific Imagination Catalogue 174 2013 THIS IS THE FIRST OF A MULTI-PART CATALOGUE on the sciences. Special among recent purchases are: Boyer’s copy of Bouguer’s Optics [118]. Lewis Carroll’s Game of Logic [159]. Cavendish’s work on electricity was J.J. Thomson’s copy [168] Computing history is present with Boole [116] (“From the author” and Cooley & Tukey’s paper on FFT [195]. Ralph Rutherford’s copy of Darwin’s Origin [228]. Einstein papers [268-277]. Faraday autograph letter [288]. Item [47] offers three late nineteenth century manuscript Persian astronomical calendars. So much more astronomical is found throughout…. www.WeberRareBooks.com On the site are more than 10,000 antiquarian books in the fields of science, medicine, Americana, classics, books on books and fore-edge paintings. The books in current catalogues are not listed on-line until mail-order clients have priority. ALL RECENT CATALOGUES ARE FOUND AT THE ABOVE WEB-SITE. Our inventory is available for viewing by appointment. Terms are as usual. Shipping extra. RECENT CATALOGUES: 168: Harry Friedman Library; Neurology (281 items) 169: The Path to Knowledge; Scientific Literature (488 items) 170: Surgeon’s Knife & Blade (272 items) 171: For the Love of Books (197 items) 172: Medicine Cabinet (197 items) 173: The Dance of Books (219 items) COVER: Chladni #178 Jeff Weber George W. Fitting, Senior Cataloguer - Ida L. -
Una Fundamentaci´On De La Historia De Las Matem´Aticas
UNA FUNDAMENTACION´ DE LA HISTORIA DE LAS MATEMATICAS´ UNA FUNDAMENTACION´ DE LA HISTORIA DE LAS MATEMATICAS´ Jesus Hernando P´erezAlc´azar OSCAR´ ARMANDO IBARRA RUSSI Rector ALEJANDRO ALVAREZ´ GALLEGO Vicerrector Acad´emico MARIO BALLESTEROS MEJ´IA Vicerrector Administrativo y Financiero NOHORA PATRICIA MORENO GARC´IA Vicerrectora de Gesti´onUniversitaria c Universidad Pedag´ogicaNacional c Jes´us Hernando P´erez Alc´azar Profesor investigador Universidad Sergio Arboleda ISBN: Primera edici´on,2007 Preparaci´oneditorial Universidad Pedag´ogicaNacional Fondo Editorial LUIS EDUARDO VASQUEZ´ SALAMANCA Coordinador Impresi´on Bogot´a,Colombia, 2007 Dedicado a: La memoria de mi padre, el educador matem´atico Jos´e Ignacio P´erez, Mi madre Aura Mar´ıaAlc´azar. Contenido Agradecimientos IV Presentaci´on V Prefacio VIII 1. Principios orientadores para la fundamentaci´onde la historia de la matem´aticas 1 1.1. (P1) Principio de Durkheim o de la divisi´onsocial trabajo . 1 1.2. (P2) Principio ´eticoy legal o de las tensiones entre permitido versus prohibido y conveniente versus inconveniente . 2 1.3. (P3) Principio acad´emico o de la dial´ecticaimaginarios versus teor´ıas 4 1.4. (P4) Principio de historicidad . 8 1.5. (P5) Principio de Chomsky o de la tensi´onentre finito e infinito . 10 1.6. (P6) Principio anfibi´oticoo de la tensi´onentre ser y no ser . 14 2. Ejemplos iniciales de documentos historiogr´aficos 19 2.1. Un art´ıculode divulgaci´on. 19 2.2. Un trabajo hist´orico-filos´ofico . 24 2.3. Historia de la historia . 27 2.4. (P7) Principio de Struik o de la dignificaci´onde la especie humana 30 2.4. -
Lightning Spring 04
L EHMAN ○○○○○○○○○○○○○○○○○○ ○○○○○ L I G H T N I N G ○○○○○○○○○○○○○ Spring 2004 New Entrance Celebrates Wisdom of the Ages inside… M BIOLOGY LAB GIVES STUDENTS A ‘DISTINCT ADVANTAGE’ ............... 2 ANTHROPOLOGY MAJOR LEARNS ‘EVERY STEP HAS A MEANING’ ....... 3 LEHMAN TO EXPAND FOCUS ON ENVIRONMENTAL ISSUES ............ 4 HELPING LEHMAN STUDENTS Green Jason ‘LET IN THE LIGHT’ ......................... 5 The plaza and walkway provide the first east-west Lehman’s Seventh corridor for the campus and a place for students to enjoy A FAMILIAR FACE a quiet moment between classes. Distinguished Professor Named GREETS STRAPHANGERS ................... 6 Dr. Joseph W. Dauben, COURSE OFFERS A LENS INTO uhammad Ali never met French phi- a leading scholar of the THE IMMIGRANT EXPERIENCE .......... 7 Mlosopher Rene Descartes, who lived history of mathematics three-and-a-half centuries ago. And Neil and a member of the LEHMAN FOUNDATION HONORS Armstrong only knows Galileo from his studies Lehman faculty since DISTINGUISHED FACULTY ............ 8-9 of science and history. But time is bridged in 1972, has been named Lehman College’s new main entrance at Gate Distinguished Pro- ALUMNI NEWS ........................ 10-11 Five on Goulden Avenue, which opened last fessor of History by the fall and features a new walkway and plaza with DEVELOPMENT NEWS .............. 12-15 Cozby J. CUNY Board of a striking work of public art. Trustees. He joins six Criss-crossing stones on the pavement of Joseph W. Dauben Making It on Broadway other current Lehman both the walkway and plaza invite students faculty in holding the prestigious title, which and visitors alike to linger and consider the is reserved for a select group of scholars and quotations, symbols, and other thoughts artists who have attained the highest levels of inscribed on the stones. -
KUIL, Vol. 26, 2003, 429-474 the HISTORY of CHINESE
KUIL, vol. 26, 2003, 429-474 THE HISTORY OF CHINESE MATHEMATICS: THE PAST 25 YEARS ANDREA EBERHARD-BRÉARD REHSEIS (CNRS), France • Ph. D. Program in History • The Graduate Center, CUNY JOSEPH W. DAUBEN Ph. D. Program in History • The Graduate Center, CUNY XU YIBAO Ph.D. Program in History • The Graduate Center, CUNY RESUMEN ABSTRACT El presente artículo presenta los más This paper presents the major accom- importantes logros de la investigacián plishments of research over the past quar- sobre historia de las matemáticas chinas en ter century in the field of Chinese mathe- el ŭltimo cuarto del siglo XX. Comienza matics and its history. We begin with a con una breve panordmica sobre el estado brief overview of the progress of our de conocimientos y las principales figuras knowledge of that history, and the major que realizaron las prirneras contribuciones figures who contributed the fundamental fundamentales antes de 1975 para después early works prior to 1975, and then exam- examinar más detenidamente las aporta- ine more carefully the achievements of the ciones Ilevadas a cabo durante el ŭltimo past quarter century, beginning with a cuarto de siglo: autores europeos, publica- general overview of the subject before ciones en inglés y, finalmente, la extraor- surveying in more detail the contributions dinaria produccián en chino, en su mayor made in the past twenty-five years, first parte tras la Revolución Cultural. by Europeans, then by scholars publishing in English, after which this survey turns to examine the extraordinary production of scholarship written in Chinese, most of it since the end of the Cultural Revolution.