PHILOSOPHERS AT WAR PHILOSOPHERS AT WAR THE QUARREL BETWEEN NEWTON AND LEIBNIZ A. RUPERT HALL Imperial College of Science and Technology CAMBRIDGE UNIVERSITY PRESS CAMBRIDGE LONDON NEW YORK NEW ROCHELLE MELBOURNE SYDNEY PUBLISHED BY THE PRESS SYNDICATE OF THE UNIVERSITY OF CAMBRIDGE The Pitt Building, Trumpington Street, Cambridge, United Kingdom CAMBRIDGE UNIVERSITY PRESS The Edinburgh Building, Cambridge CB2 2RU, UK 40 West 20th Street, New York NY 10011-4211, USA 477 Williamstown Road, Port Melbourne, VIC 3207, Australia Ruiz de Alarcon 13,28014 Madrid, Spain Dock House, The Waterfront, Cape Town 8001, South Africa http://www.cambridge.org © Cambridge University Press 1980 This book is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 1980 First paperback edition 2002 A catalogue record for this book is available from the British Library Library of Congress Cataloguing in Publication data Hall, Alfred Rupert, 1920- Philosphers at war. Includes index. 1. Calculus - History. 2. Newton, Isaac, Sir, 1642-1727. 3. Leibniz, Gottfried Wilhelm, Freiherr von, 1646-1716. I. Title. QA303.H16 515'.09 79-15724 ISBN 0 521227321 hardback ISBN 0 521 52489 X paperback TO DTW Apres tout ces Anglais ont leur merite N. Remond to Leibniz 2 September 1714 Contents Preface page ix Chronological outline xi 1 Introduction 1 2 Beginnings in Cambridge 10 3 Newton states his claim: 1685 24 4 Leibniz encounters Newton: 1672-1676 44 5 The emergence of the calculus: 1677-1699 70 6 The outbreak: 1693-1700 110 7 Open warfare: 1700 -1710 129 8 The philosophical debate 146 9 Thrust and parry: 1710 -1713 168 10 The dogs of war: 1713-1715 202 11 War beyond death: 1715-1722 232 Appendix: Newton's "Account of the Book entituled Commercium Epistolicum" 261 Notes 315 Index 332 vn PREFACE N TELLING THIS STORY of the bitter quarrel between two of the greatest men in the history of thought, the most notorious I of all priority disputes, I have not attempted to enter into the vtechnical details of the evolution of the differential and integral calculus and have tried rather to trespass as little as may be into the province of the professional historian of mathematics. My in- terest has been in the course of the quarrel, rather than in the tech- nical nature of its subject, in mathematicians rather than in mathe- matics. So far as I am aware, there is no earlier history of the calculus dispute of any size, though it is discussed in general histories of mathematics and in biographies of the participants, nor has there been any reissue of the Commercium Epistolicum since that edited by J-B. Biot and F. Lefort in 1856 (Paris: Mallet-Bachelier); a Spanish version of its documents was published by J. Babini in 1972 (Gotifredo Guillermo Leibniz, Isaac Newton. El cdlcula infinites- imal. Origen. Polemica, Buenos Aires) and an Italian one by G. Cantelli in 1958 (La disputa Leibniz-Newton sulVanalysi, Turin and Florence: P. Boringhieri). Older works such as F. Cajori's History of the Conceptions of Limits and Fluxions in Great Britain from Newton to Woodhouse (Chicago and London: Open Court Publishing Co., 1919) and J. M. Child's Early Mathematical Manuscripts of Leibniz (London: Open Court, 1920) are very out of date. As a guide to the sources and to modern studies, the reader may consult the works listed in the Notes, pursuing particularly the many addi- tional references given in the books of J. E. Hofmann and D. T. Whiteside (especially The Mathematical Papers of Isaac Newton, Vol. VIII, to appear shortly), including other writings by these schol- ars. A number of contributions are noted in the Short Titles pre- ceding the Notes section at the end of this book. The reader should also refer to P. and R. Wallis, Newton and Newtoniana 1672-1975, a bibliography (Folkestone, Eng.: Dawson, 1977), where IX PREFACE modern publications on the origins of the calculus are listed in the section devoted to "Fluxions." In quoting from letters and drafts originally composed in En- glish I have often lightly modified the orthography, because it is pointless to trouble the reader with the idiosyncrasies, invariably inconsistent among themselves, that are to be found in the printed sources I have used. Most translations from other languages are my own. I am necessarily greatly indebted to the historians of mathe- matics, as will appear later. Among living colleagues I am particu- larly indebted to Laura Tilling, who patiently explored the calcu- lus dispute in our joint work on The Correspondence of Isaac Newton, to Adolf Prag, who read and improved the whole manu- script, and to Tom Whiteside for counsel and a generous sharing of information, as in so many previous years, notably by allowing me to read part of the manuscript of the eighth volume of his Mathematical Papers of Isaac Newton. I thank my wife for forbear- ance, encouragement, and constructive criticism, and both Mar- jorie Downs and Celia Richards for producing the typescript. At the end of the book I have reprinted from the Philosophical Transactions of 1715 Newton's anonymous "Account of the Book entituled Commercium Epistolicum" the only narrative of the whole affair to come from the pen of either contestant. A. R. H. x CHRONOLOGICAL OUTLINE 1661 Newton goes up to Cambridge; Leibniz enters the Uni- versity of Leipzig. 1664-6 Newton's anni mirabiles: Cambridge and Lincolnshire. 1666 Leibniz composes On the combinatory Art; Newton (Oc- tober) his second tract on fluxions. 1669 Newton's On Analysis imparted to Barrow and Collins. 1670 Leibniz opens correspondence with the Royal Society. 1671 Newton writes On the Method of Series and Fluxions. His telescope sent to London. 1672 Leibniz moves from Mainz to Paris, forms acquaintance with Huygens. Newton's optical letters published. 1673 Leibniz's first visit to London (January-March); return- ing to Paris, his mathematical skill develops rapidly. 1675 (October) Leibniz conceives the first idea of his differen- tial calculus. 1676 Qune) Newton writes his First Letter to Leibniz; followed (October) by his Second Letter. (October) Leibniz briefly returns to London on his way to Hanover. 1677 (June) Leibniz receives the Second Letter and in reply out- lines the differential method to Newton. 1682 Leibniz publishes his arithmetical quadrature of the cir- cle. xi CHRONOLOGICAL OUTLINE 1684 Leibniz publishes a brief outline of the differential calcu- lus. 1687 Newton in the Principia describes calculation by "mo- ments," mentioning the Second Letter and Leibniz's reply to it. 1691 Newton writes "On the Quadrature of Curves." 1695-9 Newton's calculus letters published, with amplifications, in Wallis's Works. 1697 Johann Bernoulli issues the brachistochrone challenge problem, solved anonymously by Newton. 1699 Fatio de Duillier asserts the priority and superiority of fluxions. 1704 Newton publishes (with Op ticks) "On the Quadrature of Curves" and "On the Enumeration of Lines of the Third Order." 1705 Leibniz reviews Opticks and the mathematical essays. 1710 Leibniz in Theodicee attacks Newtonian attraction theory; John Keill accuses Leibniz of plagiarism. 1711 Leibniz unsuccessfully demands redress from the Royal Society. Jones publishes Newton's mathematical essays. 1712 Newton prepares the Commercium Epistolicum, issued in February 1713. 1713 Second edition of Principia published. (Summer) Leibniz prepares and circulates the Charta Volans, endorsing Ber- noulli's opinion that Newton had plagiarized Leibniz's calculus. Bernoulli publishes mathematical criticisms of the Principia. Keill takes up the systematic defense of Newton. 1715 Conti and others fail to reconcile Newton and Leibniz. xn CHRONOLOGICAL OUTLINE Newton publishes (anonymously) his "Account" of the Commercium Epistolicum (spring). Leibniz's first letter critical of the Newtonian philosophy is addressed to Samuel Clarke. 1716 (November) Death of Leibniz. The dispute continues be- tween Bernoulli, Keill, and others. 1720 Publication of Des Maizeaux's Collection, and of the first French edition of Opticks. 1721 (August) Death of Keill. 1722 Publication of the second edition of the Commercium Ep- istolicum, with the "Account" and harsher comments upon Leibniz. 1727 (20 March) Death of Newton. Xlll 1 INTRODUCTION BECAME interested in the theme of this book while editing Newton's correspondence during the years of his controversy I with Leibniz and Leibniz's supporters. Although the outline of its story has often been told, the great richness of materials bearing upon it that has appeared during recent years made a more detailed study seem worthwhile, and more than one scholar has asked that it should be made. Moreover, a historian of today can approach the calculus dispute with a more detached perspective than his Victorian predecessors could do. He will not be shocked to discover that even Leibniz and Newton could display human faults. Again, the historian who (like myself) has no intention of investigating in technical detail the origins, development, and ap- plications of calculus methods in mathematics can safely rely on modern work devoted to precisely these questions. Although he will not overlook his debt to the pioneers, notably C. I. Gerhardt, he must be particularly grateful for the interpretations and espe- cially the documentation provided by J. E. Hofmann, H. W. Turnbull, and D. T. Whiteside, not to mention other equally reli- able scholars who have examined the lesser mathematicians con- temporary with Leibniz, James Gregory, and Newton.1 What hap- pened, mathematically speaking, in the 1660s and 1670s is no longer in doubt - as it certainly was to many a century ago and perhaps to some more recently still - and therefore consideration of the quarrel between the two great rivals need be clouded by no hesitation as to the actual historical facts upon which the quarrel turned.