M O DERN STUDIES IN PHILOSOPHY LEIBNIZ A Collection of Critical Essays EDITED BY HARRY G. FRANKFURT UNIVERSITY OF NOTRE DAME PRESS NOTRE DAME LONDON Wyaraida Community Col lag* library 4600 Magnol)« Avanua Rlvaratta, California 92906 University of Notre Dame Press edition 1976 Printed by special arrangement with Doubleday & Company, Inc. Anchor Books edition: 1972 Doubleday & Company, Inc. Garden City, N.Y. Copyright © 1972 by Harry G. Frankfurt Manufactured in the United States of America Library of Congress Cataloging in Publication Data Frankfurt, Harry G 1929- comp. Leibniz: a collection of critical essays. Reprint of the 1st ed. published by Anchor Books, Garden City, N.Y., in series: Modern studies in philosophy. Bibliography: p. CONTENTS: Broad, C.D. Leibniz’s predicate-in-notion principle and some of its alleged consequences.—Couturat, L. On Leibniz’s metaphysics.— Friedrich, C.J. Philosophical reflections of Leibniz on law, politics, and the state, [etc.] 1. Leibniz, Gottfried Wilhelm, Freiherr von, 1646-1716—Addresses, essays, lectures. [B2598.F67 1976] 193 764 1 843 ISBN 0-26 8-0125 8-X ISBN 0-268-01259-8 pbk. PREFACE This anthology brings together both new writing on Leibniz and older work that might otherwise escape the student’s notice or that he might have difficulty finding. I have not included excerpts from any books devoted pri­ marily to Leibniz, although it has meant omitting some excellent material. Such books will readily come to the attention of anyone who looks up Leibniz’s name in the card catalogue of a good library. Five of the fourteen essays collected here—those by E. M. Curley, Ian Hacking, Jaakko Hintikka, Hidé Ishiguro, and Martha Kneale—were written especially for this vol­ ume, although Hintikka’s piece has already been published in Ajatus, vol. XXI (1969). A sixth essay, by Louis Couturat, has never before appeared in English. I am grateful to E. M. Curley, Maurice Mandelbaum, Amelie Rorty, and Margaret Wilson for their kindnesses to me in connection with the preparation of this book. Harry G. Frankfurt CONTENTS Preface v c. D. broad, Leibniz's Predicate-in-Notion Principle and Some of its Alleged Consequences 1 louis couTURAT, On Leibniz’s Metaphysics 19 carl j. Friedrich, Philosophical Reflections of Leibniz on Law, Politics, and the State 47 e. M. curley, The Root of Contingency 69 Montgomery Furth, Monadology 99 Ian hacking, Individual Substance 137 jAAKKO HiNTiKKA, Leibniz on Plenitude, Relations, and the “Reign of Law” 15$ hide iSHiGURO, Leibniz’s Theory of the Ideality of Relations 191 Martha KNEALE, Leibniz and Spinoza on Activity 215 Alexandre KOYRE, Leibniz and Newton 239 Arthur o. love j OY, Plenitude and Sufficient Reason in Leibniz and Spinoza 281 \ Benson mates, Leibniz on Possible Worlds 335 viii Contents Bertrand russell, Recent Work on the Philosophy of Leibniz 365 Margaret D. Wilson, On Leibniz’s Explication of “Necessary Truth" 401 Bibliography 421 LEIBNIZ LEIBNIZ’S Predicate-in-Notion Principle AND SOME OF ITS ALLEGED CONSEQUENCES C. D. BROAD Historical. What I call the Predicate-in-Notion Principle was, as far as I know, first explicitly formulated and recog­ nized by Leibniz as a basic principle in his philosophy in the Discourse on Metaphysics, which he wrote towards the end of 1685. It was further elucidated and defended in the Correspondence with Arnauld, which was occasioned by Leibniz submitting a synopsis of the Discourse for Arnauld’s inspection and criticism. Both the Discourse and the Correspondence with Arnauld remained unpublished until the middle of the XIXth century. My account of the Predicate-in-Notion Principle will be derived from those two closely interrelated sources. Formulations of the Principle. Leibniz formulates the Principle in several slightly different ways. I think it is difficult to be certain as to which is the Principle itself and which of them he would have regarded as immedi­ ate inferences from it or obvious applications of it. I think we may take the following as the Principle itself: In every true affirmative proposition, whether it be necessary or contingent, universal or singular, the notion of the predi- From Theoria, vol. XV (1949). Reprinted by permission of the author and the editor of Theoria. 2 C. D. Broad cate is contained either explicitly or implicitly in that of the object. If it is contained explicitly the proposition is analytic; if only implicitly, it is synthetic. Leibniz says that this seems to him to be self-evident when he con­ siders what is meant by a proposition being true. We must notice also, however, the following two as­ sertions which occur in close connection with the one I have just quoted, (i) Every substance has a notion so com­ plete that anyone who fully understood it could infer from it all the predicates, down to the minutest detail, which will ever belong to that substance. I think that Leibniz regarded this as an immediate consequence of applying the Predicate-in-Notion Principle to the special case of true affirmative propositions about individuals. We might call this the Principle of Pre-determinate Individual His­ tory. (ii) For every contingent fact there is a reason why the fact is just so and not otherwise, but such reasons in­ cline without necessitating. This is what Leibniz calls the Principle of Sufficient Reason. He says that it is equivalent to the principle that there is a proof a priori, even in the case of contingent true propositions, which would show that the connection between subject and predicate is founded upon the natures of those terms. Alleged Consequences of the Principle. I will now state Leibniz's opinions about the logical relations of the Principle to certain other propositions. These may be di­ vided into negative and positive. 1. He held, and he argued strongly against Amauld, that the Principle does not en­ tail that all facts are logically necessary, and does not ex­ clude free-will. As we know, Leibniz held that there are contingent facts, and he held that human voluntary de­ cisions are in some sense free. 2. In Section 9 of the Dis­ course he explicitly states that the following propositions follow from the Principle, (i) That no two substances are exactly alike in all their predicates, (ii) That a substance cannot begin except by being created, nor cease except by being annihilated by God. (iii) That a substance cannot Leibniz’s Predicate-in-Notion Principle 3 be divided into two, and that two or more substances can­ not be compounded into one. (iv) That each substance is like a complete world, and mirrors the whole universe from its own point of view. In Section 14 he adds the fol­ lowing further consequences, (v) Each substance is in­ dependent of everything else except God, and no created substance acts upon or is acted upon by any other, (vi) If a person were able to cognize distinctly all that is hap­ pening in or appearing to him at the present moment, he could foresee all that will happen in him or appear to him forever. He reiterates many of these statements in his let­ ters to Arnauld. Comments and CRmciSMS. I hope that I have now said enough to give a rough general idea of what Leibniz meant by the Predicate-in-Notion Principle and what he believed to be its logical relations to certain other important propo­ sitions. I shall devote the rest of the lecture to comments and criticisms. 1. The complete notion of a species. Leibniz says that it is important to distinguish between the complete notion of a species, e. g., the circle, and the complete notion of an individual, e. g., Adam. We will begin with species. The first example that I will take is the circle. There is an unlimited number of geometrical properties which belong to all circles and to nothing but circles. I think that Leibniz would say that the complete notion of the circle consists of all these properties. Now one and only one of these would commonly be said to be what the word ‘circle’ means, viz., the property of being a plane curve all of whose points are equidistant from a certain fixed point. I think that Leibniz would call this property ‘the essence of the circle’ and would say that it constitutes ‘the real definition’, as opposed to various pos­ sible ‘nominal definitions’ of the word ‘circle’. Now, in the case of the circle, I think that he would