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Arxiv:1812.00226V2 [Math.HO] 11 Feb 2019 2010 EBI’ ELFUDDFCIN N THEIR and FICTIONS WELL-FOUNDED LEIBNIZ’S ..Bso W Prahs5 Approaches Two on Bos 130 1.2
LEIBNIZ’S WELL-FOUNDED FICTIONS AND THEIR INTERPRETATIONS JACQUES BAIR, PIOTR BLASZCZYK, ROBERT ELY, PETER HEINIG, AND MIKHAIL G. KATZ Abstract. Leibniz used the term fiction in conjunction with in- finitesimals. What kind of fictions they were exactly is a subject of scholarly dispute. The position of Bos and Mancosu contrasts with that of Ishiguro and Arthur. Leibniz’s own views, expressed in his published articles and correspondence, led Bos to distinguish between two methods in Leibniz’s work: (A) one exploiting clas- sical ‘exhaustion’ arguments, and (B) one exploiting inassignable infinitesimals together with a law of continuity. Of particular interest is evidence stemming from Leibniz’s work Nouveaux Essais sur l’Entendement Humain as well as from his correspondence with Arnauld, Bignon, Dagincourt, Des Bosses, and Varignon. A careful examination of the evidence leads us to the opposite conclusion from Arthur’s. We analyze a hitherto unnoticed objection of Rolle’s concern- ing the lack of justification for extending axioms and operations in geometry and analysis from the ordinary domain to that of infini- tesimal calculus, and reactions to it by Saurin and Leibniz. A newly released 1705 manuscript by Leibniz (Puisque des per- sonnes. ) currently in the process of digitalisation, sheds light on the nature of Leibnizian inassignable infinitesimals. In a pair of 1695 texts Leibniz made it clear that his incompa- rable magnitudes violate Euclid’s Definition V.4, a.k.a. the Archi- medean property, corroborating the non-Archimedean construal of the Leibnizian calculus. Keywords: Archimedean property; assignable vs inassignable quantity; Euclid’s Definition V.4; infinitesimal; law of continuity; arXiv:1812.00226v2 [math.HO] 11 Feb 2019 law of homogeneity; logical fiction; Nouveaux Essais; pure fiction; quantifier-assisted paraphrase; syncategorematic; transfer princi- ple; Arnauld; Bignon; Des Bosses; Rolle; Saurin; Varignon Contents 1. -
Court of Versailles: the Reign of Louis XIV
Court of Versailles: The Reign of Louis XIV BearMUN 2020 Chair: Tarun Sreedhar Crisis Director: Nicole Ru Table of Contents Welcome Letters 2 France before Louis XIV 4 Religious History in France 4 Rise of Calvinism 4 Religious Violence Takes Hold 5 Henry IV and the Edict of Nantes 6 Louis XIII 7 Louis XIII and Huguenot Uprisings 7 Domestic and Foreign Policy before under Louis XIII 9 The Influence of Cardinal Richelieu 9 Early Days of Louis XIV’s Reign (1643-1661) 12 Anne of Austria & Cardinal Jules Mazarin 12 Foreign Policy 12 Internal Unrest 15 Louis XIV Assumes Control 17 Economy 17 Religion 19 Foreign Policy 20 War of Devolution 20 Franco-Dutch War 21 Internal Politics 22 Arts 24 Construction of the Palace of Versailles 24 Current Situation 25 Questions to Consider 26 Character List 31 BearMUN 2020 1 Delegates, My name is Tarun Sreedhar and as your Chair, it's my pleasure to welcome you to the Court of Versailles! Having a great interest in European and political history, I'm eager to observe how the court balances issues regarding the French economy and foreign policy, all the while maintaining a good relationship with the King regardless of in-court politics. About me: I'm double majoring in Computer Science and Business at Cal, with a minor in Public Policy. I've been involved in MUN in both the high school and college circuits for 6 years now. Besides MUN, I'm also involved in tech startup incubation and consulting both on and off-campus. When I'm free, I'm either binging TV (favorite shows are Game of Thrones, House of Cards, and Peaky Blinders) or rooting for the Lakers. -
Aachen, 13 Absolutism, 12 Académie D'architecture, 100 Académie Des Beaux-Arts, 100 Académie Des Belles-Lettres De Caen, 12
The Information Master: Jean-Baptiste Colbert's Secret State Intelligence System Jacob Soll http://www.press.umich.edu/titleDetailDesc.do?id=243021 The University of Michigan Press, 2009. Index Aachen, 13 152; information management, 143–52; Absolutism, 12 and politics, 142 Académie d’Architecture, 100 Archives, 7, 11; archival pillages, 101–8, Académie des Beaux-Arts, 100 126; de Brienne archive, 103; Colbert Académie des Belles-Lettres de Caen, and archives, 37, 104–12; colonial 123–24 archives, 113–19; Dutch archives, 24; Académie des Inscriptions et Belles- ecclesiastical archives, 103–6; Fouquet’s Lettres, 100, 109, 128 archive, “la Cassette de Fouquet,” 46; Académie des Inscriptions et Médaillons, French parliamentary archives, 43–44, 100 108; French state archives, 28–30, Académie des Sciences, 100, 109 101–8; Fugger family archive, 19; ge- Académie Française, 31 nealogical archives, 182–83; medieval Académie Française de Rome, 100 archives, 14–15; nineteenth- Académie Politique of de Torcy, 156 century centralizing state archives, Accounting, 18, 34, 36, 54–58; and Louis 158–59; openness and archives, 166; XIV, 60–66 and Orientalism, 105–7; permanent Agendas, 6, 18; made for Louis XIV, state archives, 158; Renaissance 51–66; of Seignelay, 89 archives, 16; and royal authority, 162; D’Aguesseau, Henri de, intendant, 91 searchable archives, 158; and secrecy, Alberti, Leon Battista, 54, 57 166; Spanish Archives, 19–21 Amelot de La Houssaye, Abraham- Archivio di Stato di Torino, 163 Nicolas, 54, 57 Archivio Segreto del Vaticano, 22, 28 American Historical Association, 11 Arnoul, Nicolas, intendant, 73–74, 106 Amsterdam, 24–25 Arnoul, Pierre, ‹ls, intendant, 78–79 Ancient Constitution, the, 13, 29, 31, Ars apodemica, 70–72 49 Ars mercatoria, 18, 35 Ann of Austria, Queen of France, 38, 58 Atlantic World, lack of concept of, 115, Antiquarianism, 25–33; and government, 118 269 The Information Master: Jean-Baptiste Colbert's Secret State Intelligence System Jacob Soll http://www.press.umich.edu/titleDetailDesc.do?id=243021 The University of Michigan Press, 2009. -
La Cour De Louis XIV
La Cour de Louis XIV (Période 1640-1720) D’après : Le Siècle de Louis XIV, Anthologie des mémorialistes du siècle de Louis XIV, par ALAIN NIDERST, Robert Laffont, Paris 1997. Les valets de chambre de Louis XIV, par MATHIEU DA VINHA, Perrin, Paris 2004. Louis XIV, par FRANÇOIS BLUCHE, Fayard, Perrin 1986. Ducs et pairs, paieries laïques à l’époque moderne (1519-1790), par CHRISTOPHE LEVANTAL, Mai- sonneuve et Larose 1996. I – Les personnages La cour de Louis XIV a laissé le souvenir impérissable de ses grands personnages. Mais beaucoup d’autres, plus ou moins connus, nobles ou roturiers, participaient à la vie de la cour. Pour les curieux d’Histoire qui se penchent sur cette époque, il a paru intéressant de dresser la liste de ceux qui ont marqué le règne du Roi-Soleil. Les noms ont été pris parmi les plus souvent cités dans les Mémoires des témoins de l’époque, qu’ils soient désignés par leur nom, leur titre ou leur fonction. Ont été explicitées les identités des personnages habituellement désignés à l’époque par leur seul statut, comme "Monseigneur", "Monsieur le Duc", "Monsieur le Grand",.. Pour certaines grandes familles, sont cités des personnages repères : Condé (Monsieur le Prince) : familles de Conti, Longueville, du Maine, Vendôme. Colbert : familles de Beauvillier, Croissy, Desmarets, Seignelay, Torcy ; voir la généalogie de la famille COLBERT en 4e partie. La Vrillère : familles de Châteauneuf, Maurepas, Phélypeaux, Pontchartrain. Louvois : familles de Barbézieux, Courtenvaux, Le Tellier. Mazarin : familles de Conti, La Meilleraye, Nevers. Turenne : famille de Bouillon. II - Les enfants de Louis XIV, légitimes et naturels. -
Introduction
Introduction The Other Voice [Monsieur de Voysenon] told [the soldiers] that in the past he had known me to be a good Catholic, but that he could not say whether or not I had remained that way. At that mo- ment arrived an honorable woman who asked them what they wanted to do with me; they told her, “By God, she is a Huguenot who ought to be drowned.” Charlotte Arbaleste Duplessis-Mornay, Memoirs The judge was talking about the people who had been ar- rested and the sorts of disguises they had used. All of this terrified me. But my fear was far greater when both the priest and the judge turned to me and said, “Here is a little rascal who could easily be a Huguenot.” I was very upset to see myself addressed that way. However, I responded with as much firmness as I could, “I can assure you, sir, that I am as much a Catholic as I am a boy.” Anne Marguerite Petit Du Noyer, Memoirs The cover of this book depicting Protestantism as a woman attacked on all sides reproduces the engraving that appears on the frontispiece of the first volume of Élie Benoist’s History of the Edict of Nantes.1 This illustration serves well Benoist’s purpose in writing his massive work, which was to protest both the injustice of revoking an “irrevocable” edict and the oppressive measures accompanying it. It also says much about the Huguenot experience in general, and the experience of Huguenot women in particular. When Benoist undertook the writing of his work, the association between Protestantism and women was not new. -
Famille Le Tellier
Paris, Île-de-France, Champagne, Bourgogne Louvois (Champagne, Election d’Epernay) : marquisat (1624 pour M. de Conflans d’Armentières) vendu à Claude Pinart de Comblizy (nouvelle érection en marquisat par Lettres de 02/1625, enregistrées aux Parlement & Chambre des Comptes 16/07 & 21/08/1656) puis vendu à Michel Le Tellier, Chancelier de France. Montmirail : ancien fief d’une famille alliée aux Coucy. Famille Le Tellier Autres branches : Barbézieux, d’Estrées, de Montmirail Armes : & marquis de Louvois, «D’azur, à trois lézards d’argent posés en pals, au chef cousu de gueules chargé de trois étoiles d’or» Souvré & Courtenvaux alias : «D’azur, à trois lézards d’argent posés en pal & Le Tellier accostés, au chef de gueules chargé de trois étoiles d’or» Branche des Marquis de Souvré : «Ecartelé : aux 1 & 4, de Le Tellier ; & aux 2 & 3, d’azur, aux cinq cotices d’or (de Souvré)». Branche des Marquis de Souvré et de Louvois : «Ecartelé : aux 1 & 4, de Le Tellier ; aux 2 & 3, de Souvré; sur-le-tout écartelé : a & d, d’azur, à la tour d’or ; b & c, d’argent, au cerf rampant d’azur». Louis Charles César Le Tellier, Duc d’Estrées : «Ecartelé : aux 1 & 4, de Le Tellier ; au 2, contre-écartelé Louis-Charles- François-Louis Auguste-Michel- Le Tellier, Le Tellier, Le Tellier, César Le Tellier Le Tellier Félicité Le Tellier seigneurs marquis marquis d’Estrées & de La Cauchie ; & 3, de Souvré». (1695-1771) (1704-1767) (1783-1844) de Courtanvaux de Louvois de Souvré Nombreuses (~16) familles homonymes (Guyenne, Île-de-France, Soissonnais & Normandie surtout) dont Le Tellier (seigneurs de Triqueville, Tourneville, du Val et Vauclères) : «D'azur, à la tour d'argent, ouverte & maçonnée de sable». -
The Unigenitus of Clement XI
Theological Studies 49 (1988) THE UNIGÉNITOS OF CLEMENT XI: A FRESH LOOK AT THE ISSUES JACQUES M. GRES-GAYER The Catholic University of America HERE is an enigma about Unigenitus, the ill-fated bull issued by Pope TClement XI (1713) against the resurgence of Jansenism. If the Jansenist movement in general has continued to attract scholars, whose recent contributions are changing perspectives,1 the constitution that condemned 101 "Jansenist propositions" extracted from the Réflexions morales was until recently left scrupulously untouched. It seemed taken for granted as an inevitable pivot—either a terminus ad quern, the logical conclusion of a century of theological and political disputes, or a terminus a quo, the origin of a movement of rebellion that eventually developed into a revolution.2 In other words, it was considered more a catalyst or an excuse for a latent social and political conflict than its real cause; hence the interest manifested in its prolegomena or later development rather than in the document itself. It was the document itself, however, the solemn exercise of the papal magisterium, that stimulated what was then perceived as the major crisis in Catholic history. The animosities, the political schemes, and the negotiations which accompanied its preparation, the uproar, the renewed negotiations, and the conflicts which followed its publication, suggest that there was more to this document than a collection of 101 condemned extracts from a spiritual book. But what was Unigenitus all about? In what appears to be a healthy reaction to a quasi-exclusive emphasis on the social and political elements of the conflicts surrounding the bull, major scholars of Jansenism have lately advocated an approach that 1 See the review article by William H. -
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Hermeneutics of the Differential Calculus in Eighteenth- Century Europe
Hermeneutics of the differential calculus in eighteenth- century Europe: from the Analyse des infiniment petits by L’Hôpital (1696) to the Traité élémentaire de calcul différentiel et de calcul intégral by Lacroix (1802)12 Mónica Blanco Abellán Departament de Matemàtica Aplicada III Universitat Politècnica de Catalunya In the history of mathematics it has not been unusual to assume that the communication of mathematical knowledge among countries flowed without constraints, partly because mathematics has often been considered as “universal knowledge”. Schubring,3 however, does not agree with this view and prefers referring to the basic units of communication, which enable the common understanding of knowledge. The basic unit should be constituted by a common language and a common culture, both interacting within a common national or state context. Insofar this interaction occurs within a national educational system, communication is here potentially possible. Consequently Schubring proposes comparative analysis of textbooks as a means to examine the differences between countries with regard to style, meaning and epistemology, since they emerge from a specific educational context. Taking Schubring’s views as starting point, the aim of this paper is to analyze and compare the mathematical development of the differential calculus in France, Germany, Italy and Britain through a number of specific works on the subject, and within their corresponding educational systems. The paper opens with an outline of the institutional framework of mathematical education in these countries. In order to assess the mathematical development of the works to be analyzed, the paper proceeds with a sketch of the epistelomogical aspects of the differential calculus in the eighteenth century. -
Christiaan Huygens's New Method of Printing
Delight of men and gods: Christiaan Huygens's new method of printing Article Published Version Kindel, E. (2009) Delight of men and gods: Christiaan Huygens's new method of printing. Journal of the Printing Historical Society, 14 (new se. pp. 5-40. Available at http://centaur.reading.ac.uk/22131/ It is advisable to refer to the publisher’s version if you intend to cite from the work. See Guidance on citing . Published version at: http://www.printinghistoricalsociety.org.uk/journal_indices/index.html#60 Publisher: The Printing Historical Society All outputs in CentAUR are protected by Intellectual Property Rights law, including copyright law. Copyright and IPR is retained by the creators or other copyright holders. Terms and conditions for use of this material are defined in the End User Agreement . www.reading.ac.uk/centaur CentAUR Central Archive at the University of Reading Reading’s research outputs online Delight of men and gods: Eric Kindel Christiaan Huygens’s new method of printing In 1669 Christiaan Huygens (1629–95), foremost Dutch mathemat ician, physicist and astronomer of his era, was living in Paris. Aged just forty, he was already nearly three years into his appointment to the recently established Académie royale des Sciences. That year, 1669, Huygens devised and tested a ‘new method of printing’ which he recorded in a single page of notes. It involved first scribing onto then etching through a thin metal plate to form a stencil from which copies could be made using a rolling press. It was intended, Huygens said, ‘for printing writing and also for geometrical figures’. -
Sources and Studies in the History of Mathematics and Physical Sciences
Sources and Studies in the History of Mathematics and Physical Sciences Editorial Board J.Z. Buchwald J. Lu¨tzen G.J. Toomer Advisory Board P.J. Davis T. Hawkins A.E. Shapiro D. Whiteside Gert Schubring Conflicts between Generalization, Rigor, and Intuition Number Concepts Underlying the Development of Analysis in 17–19th Century France and Germany With 21 Illustrations Gert Schubring Institut fu¨r Didaktik der Mathematik Universita¨t Bielefeld Universita¨tstraße 25 D-33615 Bielefeld Germany [email protected] Sources and Studies Editor: Jed Buchwald Division of the Humanities and Social Sciences 228-77 California Institute of Technology Pasadena, CA 91125 USA Library of Congress Cataloging-in-Publication Data Schubring, Gert. Conflicts between generalization, rigor, and intuition / Gert Schubring. p. cm. — (Sources and studies in the history of mathematics and physical sciences) Includes bibliographical references and index. ISBN 0-387-22836-5 (acid-free paper) 1. Mathematical analysis—History—18th century. 2. Mathematical analysis—History—19th century. 3. Numbers, Negative—History. 4. Calculus—History. I. Title. II. Series. QA300.S377 2005 515′.09—dc22 2004058918 ISBN-10: 0-387-22836-5 ISBN-13: 978-0387-22836-5 Printed on acid-free paper. © 2005 Springer Science+Business Media, Inc. All rights reserved. This work may not be translated or copied in whole or in part without the written permission of the publisher (Springer Science+Business Media, Inc., 233 Spring St., New York, NY 10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in connection with any form of information storage and retrieval, electronic adaptation, com- puter software, or by similar or dissimilar methodology now known or hereafter developed is for- bidden. -
Berkeley Bibliography
Berkeley Bibliography (1979-2019) Abad, Juan Vázques. “Observaciones sobre la noción de causa en el opusculo sobre el movimiento de Berkeley.” Analisis Filosofico 6 (1986): 35-44. Abelove, H. “George Berkeley’s Attitude to John Wesley: the Evidence of a Lost Letter.” Harvard Theological Review 70 (1977): 175-76. Ablondi, Fred. “Berkeley, Archetypes, and Errors.” Southern Journal of Philosophy 43 (2005): 493- 504. _____. “Absolute Beginners: Learning Philosophy by Learning Descartes and Berkeley.” Metascience 19 (2010): 385-89. _____. “On the Ghosts of Departed Quantities.” Metascience 21 (2012): 681-83. _____. “Hutcheson, Perception, and the Sceptic’s Challenge.” British Journal for the History of Philosophy 20 (2012): 269-81. Ackel, Helen. Über den Prozess der menschlichen Erkenntnis bei John Locke und George Berkeley. München und Ravensburg: Grin, 2008. Adamczykowa, Izabella. “The Role of the Subject in the Cognitive Process after George Berkeley: Passive for Active Subject?” Annales Universitatis Mariae Curie Sklodowska, Sectio 1 Philosophia-Sociologia 6 (1981): 43-57. Adar, Einat. “From Irish Philosophy to Irish Theatre: The Blind (Wo)Man Made to See.” Estudios Irlandeses 12 (2017): 1-11. Addyman, David and Feldman, Matthew. “Samuel Beckett, Wilhelm Windelband, and the Interwar ‘Philosophy Notes’.” Modernism/Modernity 18 (2011): 755-70. Agassi, Joseph. “The Future of Berkeley’s Instrumentalism.” International Studies in Philosophy 7 (1975), 167-78. Aichele, Alexander. “Ich Denke Was, Was Du Nicht Denkst, Und Das Ist Rot. John Locke Und George Berkeley Über Abstrakte Ideen Und Kants Logischer Abstraktionismus.” Kant- Studien 103 (2012): 25-46. Airaksinen, Timo. “Berkeley and the Justification of Beliefs [Abstract].” Berkeley Newsletter 8 (1985), 9.