DE MOTU AND THE ANALYST The New Synthese Historical Library Texts and Studies in the History of Philosophy VOLUME 41 Series Editor: NORMAN KRETZMANN, Cornell University Associate Editors: DANIEL ELLIOT GARBER, University of Chicago SIMO KNUUTTILA, University of Helsinki RICHARD SORABJI, University of London Editorial Consultants: JAN A. AERTSEN, Free University, Amsterdam ROGER ARIEW, Virginia Polytechnic Institute E. JENNIFER ASHWORTH, University of Waterloo MICHAEL AYERS, Wadham College, Oxford GAiL FINE, Cornell University R. J. HANKINSON, University of Texas JAAKKO HINTIKKA, Boston University, Finnish Academy PAUL HOFFMAN, Massachusetts Institute of Technology DAVID KONSTAN, Brown University RICHARD H. KRAUT, University of Illinois, Chicago ALAIN DE LmERA, Ecole Pratique des Hautes Etudes, Sorbonne DAVID FATE NORTON, McGill University LUCA OBERTELLO, Universita degli Studi di Genova ELEONORE STUMP, Virginia Polytechnic Institute ALLEN WOOD, Cornell University The titles published in this series are listed at the end of this volume. GEORGE BERKELEY DE MOTU AND THEANALYST A Modem Edition, with Introductions and Commentary Edited and translated by DOUGLAS M. JESSEPH North Carolina State University, Raleigh, U.S.A. SPRINGER-SCIENCE+BUSINESS MEDIA, B.V. Library of Congress Cataloging-in-Publication Data Berkeley, George, 1685-1753. [De motul De motu, and, the analyst I by George Berkeley; a modern edition with introductions and commentary by Douglas M. Josseph. p. cm. -- (The New synthese historical library ; v. 41) Inc 1udes index. ISBN 978-94-010-5144-6 ISBN 978-94-011-2592-5 (eBook) DOI 10.1007/978-94-011-2592-5 1. Science--Philosophy. 2. Mathematics--Philosophy. 1. Jesseph, Douglas M. II. Berkeley, George, 1685-1753. Analyst. 1992. III. Title. IV. Series. 0175.B4674 1992 501--dc20 91-37667 ISBN 978-94-010-5144-6 Printed on acid-free paper AlI Rights Reserved © 1992 Springer Science+Business Media Dordrecht Originally published by Kluwer Academic Publishers in 1992 Softcover reprint of the hardcover 1st edition 1992 No part of the material protected by this copyright notice may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording or by any information storage and retrieval system, without written permission from the copyright owner. For Doreen Table of Contents Preface ......................... ix Abbreviations ..................... xi DE MOTU EDITOR'S INTRODUCTION. 3 1. MOTION AND THE MECHANICAL PHILOSOPHY 4 1.1 Aristotelian and Scholastic Background. 5 1.2 Descartes, Galileo, and the Inertial Concept of Motion 9 1.3 Leibniz and the Physics of Forces . 15 1.4 Newtonian Mechanics . 19 2. DISPUTED POINTS IN THE MECHANICAL PHILOSOPHY 24 2.1 The Vis Viva Controversy 25 2.2 The Force of Percussion . .. 27 2.3 The Nature of Gravitation . .. 30 3. THE PLACE OF DE MOTU IN BERKELEY'S PHILOSOPHY 33 4. A NOTE ON THE TEXT AND TRANSLATION 37 5. BIBLIOGRAPHY . .. 37 TEXT . .. 45 TRANSLATION . .. 73 Vlll CONTENTS THE ANALYST EDITOR'S INTRODUCTION. 111 1. THE MATHEMATICAL BACKGROUND. 112 1.1 The Classical Standard of Rigor. 112 1.2 Infinitesimal Calculus . 116 1.3 The Newtonian Calculus of Fluxions. 123 2. THE THEOLOGICAL BACKGROUND 128 3. BERKELEY'S CASE AGAINST THE CALCULUS 132 4. OUTLINE ANALYSIS . 141 4.1 Introduction . 142 4.2 The Object of the Calculus . 142 4.3 Principles and Demonstrations of the Modern Analysis . 143 4.4 The Compensation of Errors Thesis . 143 4.5 Alternative Interpretations of the Calculus Rejected 144 4.6 Conclusion and Queries. 145 5. RESPONSES TO THE ANALYST. 145 6. A NOTE ON THE TEXT. 148 7. BIBLIOGRAPHY . 148 TEXT . .. 159 INDEXES. .. 223 Preface Berkeley's philosophy has been much studied and discussed over the years, and a growing number of scholars have come to the realization that scientific and mathematical writings are an essential part of his philosophical enterprise. The aim of this volume is to present Berkeley's two most important scientific texts in a form which meets contemporary standards of scholarship while rendering them accessible to the modern reader. Although editions of both are contained in the fourth volume of the Works, these lack adequate introductions and do not provide com­ plete and corrected texts. The present edition contains a complete and critically established text of both De Motu and The Analyst, in addi­ tion to a new translation of De Motu. The introductions and notes are designed to provide the background necessary for a full understanding of Berkeley's account of science and mathematics. Although these two texts are very different, they are united by a shared a concern with the work of Newton and Leibniz. Berkeley's De Motu deals extensively with Newton's Principia and Leibniz's Specimen Dynamicum, while The Analyst critiques both Leibnizian and Newto­ nian mathematics. Berkeley is commonly thought of as a successor to Locke or Malebranche, but as these works show he is also a successor to Newton and Leibniz. Another obvious similarity between these two texts is their predom­ inantly critical stance: both are essentially critiques of the scientific and mathematical theories of the early eighteenth century, with compara­ tively little emphasis on a positive account of Berkeley's views. A full account of Berkeley's science and mathematics is a task for another time and place, but any proper understanding of his philosophical conception of these subjects must begin with De Motu and The Analyst. x PREFACE I am happy to acknowledge the support of the National Endowment for the Humanities for two grants: a travel grant in 1989 which helped send me to the British Library, and a summer fellowship in 1991. The British Library, the Special Collections Division of the Regenstein Li­ braryat the University of Chicago, and the Bodleian Library all deserve thanks for providing access to primary sources. The Clapp Library of Wellesley College provided an excellent microfilm of The Analyst, while the Special Collections Division of Regenstein allowed me to use their copy of De Motu. With their permission I have reproduced the title pages from both works. Thanks are due to the proprietors and regu­ lar patrons of the Museum Tavern in Bloomsbury, most especially to John Henderson and Brian Rooney. Good beer and good conversation in the evenings made two research trips to the British Library more pleasant than I had reason to expect. Dan Garber and Ken Winkler provided advice, assistance, and encouragement which I greatfully ac­ knowledge; correspondence with Lisa Downing was helpful in sorting out my thoughts on De Motu. By far my greatest debt is to my wife, Doreen, whose patience, good nature, and assistance were invaluable. Abbreviations AG Leibniz, G. W. 1989. G. W. Leibniz: Philosophical Essays. Ed. and trans. Roger Ariew and Daniel Garber. Indianapolis, IN and Cambridge, MA: Hackett Publishing Company. AT Descartes, Rene. [1897-1909] 1964-1976. Oeuvres de Descartes. Ed. C. Adam and P. Tannery. Paris: VrinjC.N.R.S. 12 vols. CSM Descartes, Rene. 1984. The Philosophical Writings of Descartes. Ed. John Cottingham, Robert Stoothofi', and Dugald Murdoch. 2 vols. Cambridge: Cambidge University Press. GM Leibniz, G. W. [1849-55] 1962. G. W. Leibniz: Mathematische Schriften. Ed. C. 1. Gerhardt. 7 vols. Hildesheim: Olms. Papers Newton, Isaac. 1967-1981. The Mathematical Papers of Isaac New­ ton. Ed. D. T. Whiteside and M. A. Hoskins. 8 vols. Cambridge: Cambridge University Press. Principia Newton, Isaac. [1729] 1934. Sir Isaac Newton's Mathematical Prin­ ciples of Natural Philosophy and his System of the World. 2 vols. Trans. Andrew Motte; rev. Florian Cajori. Berkeley and Los An­ geles: University of California Press. Works Berkeley, George. 1948-57. The Works of George Berkeley, Bishop of Cloyne. Ed. A. A. Luce and T. E. Jessop. 9 vols. (Edinburgh and London: Thomas Nelson). Quotations from Aristotle come from The Complete Works of Aristotle: The Revised Oxford Translation. Ed. Jonathan Barnes. 2 vols. Prince­ ton: NJ, Princeton University Press, 1984. Citations include the Bekker page numbers for the Greek followed by volume and page numbers for the Revised Oxford Translation. De Motu Editor's Introduction In 1720 the Royal Academy of Sciences in Paris announced a prize es­ say competition on two topics, the first being the nature, principle, and cause of the communication of motion. Berkeley was in Europe at the time, acting as tutor to George Ashe, son of the Bishop of Clogher. Joseph Stock's biography reports that "On his way homeward [Berke­ ley] drew up at Lyons a curious tract De motu, which he sent to the royal academy of sciences at Paris, the subject being proposed by that assembly."(Stock [1776] 1989, 19) This was the first prize offered by the Academy, and it was awarded to Jean-Pierre Crousaz, professor at Lausanne. The decision seems to have been somewhat controversial, be­ cause the indifferent effort of Crousaz won out against competiton from several more competent entries, including one from Jean Bernoulli.! No record of Berkeley's entry survives in the archives of the Academy of Sciences, and we cannot be certain whether it was ever submitted.2 De­ spite the apparent failure of the essay to win favor in Paris, Berkeley thought highly enough of it to publish De Motu in London in 1721, but again it failed to arouse interest in scientific and philosophical circles. 1 Bertrand ([1869] 1969, 184-5) reports that "Les concurrents devaient trai­ ter du principe, de la nature et de la communication du mouvement. Jean Bernoulli concourut; l' Academie, sans comprendre la portee de son excellent memoire, couronna Ie discours superficiel et insignificant d'un M. de Crousas. L'injustice etait flagrante, ou plut6t la meprise." 2 Claudine Pouret, documentaliste in the ar~hives of the Academie des sci­ ences, reports in a letter of 24 January, 1990 "Je n'ai trouve aucune trace de ce memoire." The earliest manuscripts of prize essay submissions date from 1760 and the first register of submissions dates from 1745, so it is impossible to tell whether Berkeley actually submitted his work.