1.1. From the Publisher.

The selections contained in these volumes from the papers and letters of Leibniz are intended to serve the student in two ways: first, by providing a more adequate and balanced conception of the full range and penetration of Leibniz's creative intellectual powers; second, by inviting a fresher approach to his intellectual growth and a clearer perception of the internal strains in his thinking, through a chronological arrangement. Much confusion has arisen in the past through a neglect of the development of Leibniz's ideas, and Couturat's impressive plea, in his edition of the Opuscules et fragments (p. xii), for such an arrangement is valid even for incomplete editions. The beginning student will do well, however, to read the maturer writings of Parts II, III, and IV first, leaving Part I, from a period too largely neglected by Leibniz criticism, for a later study of the still obscure sources and motives of his thought. The Introduction aims primarily to provide cultural orientation and an exposition of the structure and the underlying assumptions of the philosophical system rather than a critical evaluation. I hope that together with the notes and the Index, it will provide those aids to the understanding which the originality of Leibniz's scientific, ethical, and metaphysical efforts deserve.

1.2. From the Preface.

The selections contained in these volumes from the papers and letters of Leibniz are intended to serve the student in two ways: first, by providing a more adequate and balanced conception of the full range and penetration of Leibniz's creative intellectual powers; second, by inviting a fresher approach to his intellectual growth and a clearer perception of the internal strains in his thinking, through a chronological arrangement. Much confusion has arisen in the past through a neglect of the development of Leibniz's ideas, and Couturat's impressive plea, in his edition of the Opuscules et fragments, for such an arrangement is valid even for incomplete editions.

The beginning student will do well, however, to read the maturer writings of Parts II, III, and IV first, leaving Part I, from a period too largely neglected by Leibniz criticism, for a later study of the still obscure sources and motives of his thought.

The Introduction aims primarily to provide cultural orientation and an exposition of the structure and the underlying assumptions of the philosophical system rather than a critical evaluation. I hope that together with the notes and the Index, it will provide those aids to the understanding which the originality of Leibniz's scientific, ethical, and metaphysical efforts deserve.

My indebtedness to all who have in some measure aided me in the preparation of the translations and interpretations is so extensive as to forbid detailed acknowledgment. Professor Paul Schrecker, whose knowledge of the thought forms and relations of Leibniz, and indeed, of seventeenth century thought in general, is unsurpassed, has read and corrected a large number of the translations, particularly in Volume I, and should be credited with setting norms for accuracy and adequacy.

Professor Elizabeth DeLacey has exercised extensive editorial supervision, caught many defects, and suggested changes which have consistently improved the work.

Beyond the extensive work of these, there are many others who deserve my gratitude for help rendered. A fellowship of the Rosenwald Foundation in 1938 and a grant from an anonymous source in 1951 enabled me to begin a detailed study of Leibniz, to make use of the Hanover manuscripts, and to confer with European scholars.

The editors of the Prussian Academy edition, and the directors of the Hanover Landesbibliothek, gave generous advice and opportunities for study. Professor Helmut Kuhn, now of the University of Munich, checked the translations. For detailed answers to many questions I am indebted to more friends and colleagues than I can conveniently name.

Publication was subsidised in part by a grant from the Research Committee of the University Center in Georgia, generously enlarged by Emory University. More important even than this, however, has been the climate of study provided by Emory University and its administration during troubled years of war and of uncertain peace.

To acknowledge with gratitude the social co-operation required in such work is a pleasure which does not, however, remove the uneasy recognition that the responsibility for errors and other blights on the usefulness of these translations, being the fruits of solitary decision, must be borne by the translator and editor himself.

All parentheses in the text are Leibniz's own, though some of his parentheses have been removed. All editorial interpolations are in brackets. Leibniz's own underscoring has been retained except when he used it to indicate direct quotation. The keys used throughout in references to the editions of Leibniz and related works may be identified in the Bibliography.

1.3. Review by: L J Russell.
Philosophy 33 (124) (1958), 60-65.

Professor Loemker is capable of the most elementary howlers through neglect of French or Latin grammar. He can group phrases wrongly. He is not always clear about his tenses, and verbs which in Latin have to be in the subjunctive he sometimes makes subjunctive in English when they should be indicative. French requires the definite article more frequently than English: in many cases Professor Loemker keeps it in his translation. There are passages of "translator's English" - sentences no-one would dream of writing if he were expressing his own thoughts; and passages where long English sentences tag along breathless, at the heels of the originals.

Yet, in spite of all this, there are in these 900 odd pages of translation many pages of successful writing, where Professor Loemker threads his way delicately through cumbrous sentences, breaking them up into easy English. At his best he is very good: and as there is no translation of anything like comparable range in English, the only thing one can do is to be thankful for what is good, while using the book with circumspection. It is a safe rule, when one comes across anything that looks queer, to assume that the translator has turned traitor, and to check with the original.

The papers cover the whole range of Leibniz's philosophic thought from 1666 to 1716, arranged as far as possible in chronological order, and including writings on logic, the foundations of the calculus, principles of dynamics, ethics, law, theology, so far as they are of philosophical importance. There are naturally papers missing one would have liked to see included. He has (wisely) omitted any selections from the New Essays and the Theodicy, and I would willingly have seen the Monadology and the other writings contained in Latta's translation omitted, and also the Discourse on Metaphysics and the selections from the Clarke correspondence (now available elsewhere) in order to find room for other things. I should have wanted to include, e.g. the important Pacidius Philalethi of 1676, and more extracts from those printed by Jagodinsky, and a number of fragments and letters of special interest. We ought to have had the letter to the Marquis de l'Hospital 12/22 July 1695 (G.M. II, 294) which contains the first use of the word "monad" as applied to his substances, contrary to what Loemker says (Vol. II n. 198). I drew attention to this in 1921, but apart from Iwanicki, so far as I know, scholars continue to say that the first use of the word was in September 1696, and many like Loemker repeat from Stein's Leibniz und Spinoza (a bad book) that Leibniz took the word from Van Helmont, who visited him in Hanover in 1696. My own theory is that he took the word from the most obvious source for a mathematician - Euclid. Nieuwentiit had in 1694 published a book attacking the foundations of the calculus, and both de l'Hospital and Leibniz had replied to him. In Leibniz's reply in the Acta Eruditorum (July 1695) one of his fundamental points depended on Euclid's definition of the ratio between two finite quantities, and Leibniz gave the reference (Euclid, Bk. V, Def. V). I think it very likely that he verified his reference, in one of the various editions of Euclid common in those days, with the Greek text and a Latin translation on the same page. The definitions in Book V don't contain the word "μ o ν α' ζ", but Book VII, which deals with the theory of quantity, is full of it, and as Leibniz was replying to a criticism of his theory of quantity, it is plausible to suppose that he glanced through Book VII to see if there was any ammunition for his guns. But whether this is how the word occurred to him does not matter very much; he was writing to a mathematician, commending his Système Nouveau (which he had just begun to expound in the Journal des Savants, June 1695) to mathematicians rather than to philosophers, and mathematical concepts would readily come to mind. The MSS. give only an extract of the letter; and its last sentence runs: "The central point in my doctrine lies in the consideration of what is properly a real unity, Monas." The extract (printed by Gerhardt in 1850) is short, but however widely neglected, it is full of interest.

...

1.4. Review by: Martha Kneale.
The Philosophical Review 66 (4) (1957), 574-576.

These two volumes, reproduced from typescript, give the fullest selection of Leibniz's work yet translated into English and are thus of great importance. The only selection at all comparable is Duncan's, and Professor Loemker offers us much more than Duncan, more early work and more that is purely logical or concerned with the philosophy of science.

The pieces are arranged in chronological order and the selection has been well made. All Leibniz's interests, except the purely historical, are represented at all periods in a balanced way. Many of the pieces have not been translated into English before, and one (II, 32), which is of considerable interest, has not previously been published. At the same time the most important of the works generally used in teaching Leibniz, the Discourse, the New System, the Monadology and the Correspondence with Clarke (including Clarke's letters), are also included. One addition which might have been made is the Introduction to the Nouveaux essais, which gives a fuller account of the doctrine of unconscious perceptions than anything included here.

An enterprise such as this must, however, be judged above all on the accuracy of the translation, for presumably the volumes are intended largely for those who are not able to use the original. The translation should, therefore, be absolutely reliable and, unfortunately, Professor Loemker's is not quite this. Not but that he is a perfectly good guide for whole pages and papers; but careful examination shows that when the language, especially Latin, presents difficulties, he is apt to make a dash at the sentence without much regard for grammar and syntax. This has sometimes serious consequences for the sense. I take a few examples from Volume I. Attention to gender should have shown Professor Loemker that the sentence on page 195, "Everything would be its own form, a part of the concept implied in itself" cannot translate "Idem erit forma sui ipsius, seu pars conceptus sui, quod implicat." "Implicat" here must have the common seventeenth-century sense, "implies a contradiction." It is surprising that Professor Loemker has missed this here since he shows in other places that he is familiar with the usage. On page 363, "Exempli causa id quod majorem partem ducati Hungarici facit" is translated "(with an added special quality) such as greater ductility or coming from Hungary." This is of no philosophical importance, but there is a more serious example in the same paper, which is a logical one and difficult. "Si quae sunt quarum requisita assignare difficile est, iis interim ascribemus numerum aliquem primitivum" is translated, "If it is hard to decide which constituents belong to which, we can assign them some prime number temporarily." This has an ambiguity from which the Latin is entirely free.

...

2.1. Summary.

This is a reprint of the first edition [1956], except for some improvements in the texts of the translations. The whole consists of 71 articles and letters by Leibniz, some given only in part, translated and edited by Leroy E Loemker, intended to provide the student with a balanced conception of the full range of Leibniz's work and to give a clearer idea of Leibniz's intellectual growth.

2.2. From the Preface.

The appearance of a corrected edition of these Leibniz translations provides an opportunity to thank many who have suggested improvements in the text, and in particular Professor L J Russell of Birmingham and Professor G H R Parkinson of Reading for their numerous corrections.

2.3. Review by: Mario Dal Pra.
Rivista Critica di Storia della Filosofia 29 (3) (1974), 357-359.

The second edition of what is probably the most extensive and comprehensive Leibniz anthology currently in existence in English (the first edition was published in 1956 by Chicago University Press) deserves to be brought to our readers' attention not only for its widespread popularisation but also for its success among Leibniz scholars themselves. It is certainly a work without an equivalent in Italian, especially because of the extensive space it devotes to the translation of so many of Leibniz's writings. Consulting these requires typically resorting to many different editions, some more or less critically reliable, while awaiting the completion of the monumental edition of the Sämtliche Schriften und Briefe begun by the German Academy of Sciences in 1923.

Leibniz's writings are arranged here in chronological order; the first part of the anthology concerns the years in Mainz and Paris and includes the decade 1666-1676 (it contains, among other things, selected passages from the Dissertatio de arte combinatoria, the Demonstrationes catholicae and the studies on physics and on the nature of the body, as well as the Parisian notes and includes a letter to Thomasius from 1669, one to Hobbes from 1670, one to Oldenburg from 1675). The second part is dedicated to the period in Hanover and to the trip to Italy and goes from 1676 to 1687 (important, among other things, in addition to the passages from the very well-known Meditationes de cognitione veritate atque ideis and the celebrated Discourse on metaphysics, those from two dialogues on religion from 1678 and from the writings on the general characteristic, on logical calculus, on geometria situs, as well as the letters to Malebranche and the correspondence with Arnauld). The third part refers to the period in Hanover until the death of Ernest Augustus, that is, to the years from 1690 to 1698 (here are reported the prefaces to the Codex juris gentium diplomaticus and to the Mantissa codicis juris gentium, as well as the critical thoughts on the general part of Descartes' principles, the important Specimen dynamicum, the no less relevant Tentamen analogicum on the search for the causes of '96, and the study on logical calculus, not to mention the correspondence with Huygens and the letters to Gabriel Wagner on the value of logic and to Des Billettes on the main concepts of metaphysics). The fourth period goes from 1698 to 1716 and concerns Leibniz's stay in Hanover under George Louis until his death (here we find, in addition to the passages taken from the Monadology and the writings on the controversy between Leibniz and Clarke, also the correspondence with Bernouilli, that with Des Bosses and an interesting series of other writings on logic, mathematics, physics, metaphysics and the theory of justice). Each of the writings from which passages are presented is introduced by brief considerations that indicate their dating, historical circumstances and philosophical significance; notes accompany the texts, both to clarify certain terms and to compare the doctrines contained in them with passages from other Leibnizian texts.

...

2.4. Review by: Lauri Routila.
Studia Leibnitiana 6 (2) (1974), 281-282.

This is the second, revised edition of the book first published in 1956, which has since become a staple of Leibniz scholarship. It goes without saying that such a comprehensive selection of Leibnizian texts can satisfy a wide range of expectations and needs, but the value of this volume does not lie solely in its size.

First, the translations are exceptionally good; they are both adequate and elegant, and one must greatly admire Loemker's ability to consistently find in English the formulation that leaves open various interpretations. Loemker's translations are therefore not reflections of a supposedly closed, single possible interpretation. Furthermore, most translations are based on several texts; the most important readings are noted in the footnotes. Occasionally, a few minor details may slightly bother the critical reader, for example, when 'explication' is rendered as 'definition' or 'premier principe' as 'highest principle' (pp. 307, 327). However unimportant such deviations from the original may be with regard to Leibniz's substantive conclusion, they can easily disrupt the precise philosophical meaning of his argument.

The second merit of the volume lies in the sensible organisation of the extensive material; this allows insight into the enduring core of Leibniz's philosophical ideas and simultaneously illustrates their maturation process. The volume is divided into four chronologically ordered parts, the sections of which are consecutively numbered. Often, a section contains several essays, letters, or fragments that are related both thematically and chronologically. Each section is followed by an informative historical preface and a section of notes. Modern specialist literature is cited only sparingly, but there are many references to the other texts in the volume. Unfortunately, the reader has to do a lot of flipping through the extensive volume to follow these internal references, as they refer to the section numbers: looking things up would be easier if the column heading included the number of the respective section.

Loemker's 70-page introduction, "Leibniz as Philosopher," provides reliable information not only about the spirit of the age and Leibniz's life, but also about his thought. Loemker seeks to understand Leibniz's philosophical theories as a synthesis of three guiding ideas (universal harmony, individuality, and force) and to describe them using a terminology whose focus is determined by "mathematical function," "representation," and "conatus." The most interesting part of this introduction, in my opinion, is the investigation into the "transcendental" presuppositions of Leibniz's theories. The connections between Leibniz's metaphysical and mathematical ideas, as suggested by Loemker, deserve particular attention. The book includes a comprehensive subject and name index.

3.1. From the Foreword.

The present study would never have seen the light of day had it not been for the encouragement and advice of the late M Alexandre Koyré, director of studies at the Ecole Pratique des Hautes Études de la Sorbonne. His lectures on the history of science have enabled us to make a careful study of the fundamental questions discussed during the course on the seventeenth century and to experience the benefit of a collective research worthy of higher education. By reason of our own individual work in the course, our study was first of all directed to a more technical subject, namely, the problem of impact as investigated by Huygens and Mariotte. It was during our fruitless search for documents relating to Mariotte's experiments that we came across two Leibnizian manuscripts in the archives of the Académie, and that discovery caused us to change our plans. We have no regrets for having done so.

The manuscripts in question are two copies, dating from the year 1692, of texts dealing with mechanics. Examination of internal and external evidence, identification of the copyist, investigation of the circumstances of, and the motives for, making the copies led us to a careful study of an imperfectly known story, namely, the difficulties encountered by Leibniz in the French intellectual circle. A patient, detailed study enabled us to discover elucidation of the more general and extended theses on the internal coherence of the thought of Leibniz. The result confirms a general view, to which many minds are nowadays tempted to limit the benefit of detailed study. It has been our one ambition to show through our work that such a hasty conclusion is not justified. Grand syntheses and general ideas are precious and indispensable. Nevertheless, they have no firm substance without profound and lively knowledge which is acquired patiently by contact with the great men of the past. The tact, mistakes and inadequacies of Leibniz make him most human and bring him close to us; the depth of his analysis and his tenacious application in following to the end the  lines traced by metaphysical principles make him even greater, and force us to realise the difficulties he had to overcome, which difficulties were related not only to his period and to his environment, but which are perhaps eternal.

Everything that restores life and saves us from eternal abstract discussion of ideas is of great value. If we have been able to provide some slight proof thereof, then our thanks on that account are due to the lectures of M Alexandre Koyré .

We have to thank M Joseph Ehrenfield Hoffmann who saved us much time in seeking the first manuscript by providing an immediate reference. Special thanks are due to M André Robinet for information kindly placed at our disposal. The appearance of M Robinet's thesis on Malebranche and Leibniz was a very great help when we were finally assembling the necessary facts for the account in our first chapter, which aims at being exhaustive.

3.2. Review by: Joseph Ehrenfried Hofmann.
Mathematical Reviews MR0354274 (50 #6756).

The author edits the Essay de dynamique (first printed from a poor copy in Hanover in A Foucher de Careil [Oeuvres de Leibniz, Paris, 1859; pp. 470-483]) and the Règle générale de la composition des mouvements (printed in a modified version in J des Scavans 7 and 14, IX, 1693) based on the very careful transcript of the lost manuscript by G-F des Billettes, which he rediscovered in the archives of the Académie des Sciences. This is preceded by a meticulously detailed introduction (94 pp.) that deals with all the details of the history of science and the textual history. The excellent index of persons and subjects is particularly noteworthy. Appendix I contains, on facing pages, both the text of the copy made by Gilles Filleau des Billettes in 1962 (found by the author in 1956 in the archives of the Académie des Sciences) and its English translation.

3.3. Review by: E J Aiton.
Isis 66 (1) (1975), 129-130.

Pierre Costabel's perceptive study Leibniz et la dynamique was the outcome of his discovery in 1956 in the archives of the Academie des Sciences in Paris of copies of two Leibnizian manuscripts in the hand of Gilles Filleau des Billettes, an antiquarian whom Leibniz had met in Paris. These documents illuminate not only the development of Leibniz' dynamics but also the obstacles that Leibniz encountered in seeking to promote his ideas in France. The present volume is a carefully prepared translation of this important contribution to the history of dynamics in the seventeenth century.

The two documents are, first, a copy of the Essay de dynamique sent by Leibniz to Pelisson in January 1692 and published in the nineteenth century by A Foucher de Careil and, second, a copy of a draft of the memoir Règle générale de la composition des mouvemens, published by Leibniz in 1693 in the Journal des Sçavans. The texts of the copies made by des Billettes are given in two appendices. That of the Essay de dynamique is accompanied by a translation, while the other is given only in the French version but parallel with the printed text of the article in the Journal des Sçavans for comparison.

Following the controversy on the measure of force with Catalan and Malebranche, it was necessary for Leibniz to educate opinion, if he wished to prepare the way for the acceptance of his projected work on dynamics. The Essay de dynamique was written for this purpose. A copy was sent to Pelisson early in January 1692 with the request that it be communicated to Malebranche (in the hope that he might show it favour) and submitted to the judgment of the members of the Académie des Sciences. As described by Leibniz in the letter to Pelisson, the Essay was a development of the ideas defended during the controversy but reduced to the bare essentials and presented in a popular form.

Here Leibniz no longer says that the conservation of force, which he points out is equivalent to the impossibility of mechanical perpetual motion, may readily be conceded, but he states the conservation of force as an axiom. This innovation is seen by Costabel as just one indication of the depth of Leibniz' reflection on the metaphysics underlying the construction of a mathematical structure. In the Essay de dynamique, the categories of the Theoria motus abstracti are retained, so that, while mechanical perpetual motion is impossible, there is a physical perpetual motion; the physical method is that of nature while the mechanical method is that of art. It is in the Essay that Leibniz first uses the expression force vive (translated as "kinetic force"), though he had already in 1686 distinguished between potentia viva and potentia mortua.

Leibniz does not seem to have been well served by Pelisson. For it was only after some delay that Pelisson had Leibniz' essay read in the Académie, and it seems improbable that he arranged for a copy to be sent to Malebranche. The reading in the Académie evidently had little effect, for there is no mention of Leibniz' essay in the minutes of subsequent meetings.

Leibniz' article on the composition of motions was designed as a further attempt to promote his ideas on dynamics, following the failure of the Essay de dynamique to influence the members of the Académie. While the problem of the composition of motions might seem to be purely one of kinematics, in the mind of Leibniz it was essentially connected with dynamics and therefore suitable for his purpose. Leibniz took as his starting point the geometrical problem of Tschirnhaus on the construction of tangents to curves defined by means of threads wrapped around "foci," which could be either points or closed curves. Costabel describes the elegant solutions of Fatio de Duillier, Huygens, and l'Hôpital, based on kinematical considerations, before showing how Leibniz' concept of the realism of force led him to see the problem as one of dynamics.

3.4. Review by: Carolyn Iltis.
The British Journal for the History of Science 10 (2) (1977), 176-
177.

by Pierre Costabel's Leibniz et la dynamique, which first appeared in French in 1960 is now made more readily available to English readers through the translation of Dr R E W Maddison, Librarian of the Royal Astronomical Society. The work reproduces two texts of Leibniz written in 1692, the manuscripts of which were discovered by Costabel inserted together among un-classified papers in the archives of the Académie des Sciences, Paris. The first memoir, the Essay de dynamique, is a copy of a manuscript published by A Foucher de Careil in 1859 in volume I of the Oeuvres de Leibniz. The second is a variation of a text entitled, Règle générale de la composition des mouvemens which appeared in the Journal des sçavans for 7 September 1693. Although published elsewhere the two texts are of interest to students of Leibniz's dynamics and mathematics, and Pierre Costabel's detailed and valuable discussion places them in historical perspective.

The Essay de dynamique is a logically coherent exposition of the concept of 'force' (mv2) as an absolute real entity existing 'intact at every moment' and distinct from the Cartesian 'quantity of motion' which measures successive time-dependent motion. In contrast to earlier papers Leibniz presents his ideas in the form of definitions, axioms, postulates, and propositions. Costabel delineates the increase in sophistication in Leibniz's treatment of the semantic problems in the definition of 'force' in the 1692 Essay over his earlier discussions with Abbé Catalan and his 1690 De causa gravitatis (Acta eruditorum, May 1690). The structure of Leibniz's argument, that mechanical perpetual motion could result if Descartes' quantity of motion m|v| was conserved, is treated in detail. The appearance of the Essay in the files of the Académie des Sciences was the result of an abortive attempt by Leibniz to place it in the hands of Malebranche via the intermediaries Pelisson and Des Billettes.

Costabel stresses the intimate link between the Essay de dynamique and the accompanying Règle générale de la composition des mouvemens, by showing that Leibniz saw the problem of the motions acting simultaneously on a moving body as a problem in dynamics, treating the moving body not as a geometric point but as a material point endowed with mass. The motion of the centre of gravity as a fundamental property of bodies, essential to an understanding of motion, was used by Leibniz in formulating his general rule. Costabel skilfully discusses the logical problems inherent in Leibniz's proof, and his debt to Huygens and Fatio de Duillier.

The value of this book as a history of the development of Leibniz's dynamics during the crucial period 1686-1692 is weakened by a curious failure on the part of Costabel to discuss or even mention the controversy between Leibniz and Denis Papin during the years 1689-91. The Essay de dynamique was a recasting of arguments laid out in the 1690 De causa gravitatis, first developed as a reply to Papin's 1689 De gravitatis causa et proprietatibus observationes (Acta eruditorum, April 1689). In both this exchange and the 1692 Essay the central issue was the possibility that mechanical perpetual motion could result from the conservation of Descartes' quantity of motion m|v|. The primary example of perpetual motion (proposition 4), and the substance of propositions 8 and 9 in the Essay had appeared in the 1690 reply to Papin. The response of Papin a few months later (Acta eruditorum, January 1691) challenged Leibniz's perpetual motion argument by questioning the possibility of transferring all of the 'power' from one of the bodies in the example to the other. This forced Leibniz to write another paper (Acta eruditorum, September 1691) defining (unsatisfactorily) the mechanisms of transfer. The Essay de dynamique reproduced by Costabel was sent to Pelisson on 8 January 1692. It is clearly a result of Leibniz's attempts to clarify and present in a coherent form the issues and arguments raised in his intellectual struggles with Papin.

That Costabel should make no mention of the influence of the Papin controversy on the content of one of his two 'texts of 1692' leaves an important omission in his otherwise competent and thorough analysis of a brief but crucial period in the development of Lebnizian dynamics.

3.5. Review by: Herbert Goldstein.
American Scientist 62 (4) (1974), 500.

Unlike his archrival, Leibniz never wrote a comprehensive treatise expounding his system of mechanics. His formulation must be assembled from a succession of short essays, notes, and letters in which he propounded again and again the key ideas for his system. The Reverend Father Pierre Costabel, an eminent Leibniz scholar, some twenty years ago discovered copies of two of these brief pieces in the archives of the Academie Royale des Sciences in Paris and published them in the original French in 1960, accompanied by an extensive and detailed discussion of their nature and significance. This lengthy introductory essay is presented now in English translation, along with the text of one of the documents ("Essay de Dynamique") in both French and English and excerpts of the second (in French). Although both papers had been published before in somewhat different form, Costabel has presented them here in a more accessible and carefully edited form, and more important, he has clarified their significance in the contexts of Leibniz's ideas about mechanics and of contemporary concepts of mechanics.

Leibniz saw himself as rooting out a false Cartesian notion that implied what we would now call conservation of momentum (in magnitude, not vectorially) and replacing it with an idea that we recognise as taking the first steps toward the principle of conservation of energy. He conceived of the conservation of the "force" of a moving body as measured by what in modern terms would be its initial kinetic energy. The "Essay de Dynamique" was a careful reformulation of arguments he had presented before (and was to present again), intended primarily as propaganda to convince the eminent Cartesians of the Academie. In this intention he was completely unsuccessful; manuscript copies of his "Essay" were circulated in 1692 among the Academicians but failed to make them reconsider their orthodox Cartesianism. The second text discussed by Costabel refers to a problem in analytic geometry that had been tackled by a number of the leading mathematicians of the period including Christiaan Huygens. Leibniz's contribution was to see that the problem concerned the composition of several velocity vectors (to use modern terms), and could be resolved by making use of the notion of centre of gravity. In his brief report, Leibniz seizes the occasion to champion his concepts of mechanics in contrast to those of Descartes.

To a modern scientist brought up on the magnificent structure and calculational successes of Newtonian mechanics, the dynamics of Leibniz makes a poor showing. Leibniz's formulation of the calculus and his nascent notions of conservation of energy were among the factors that caused leadership in the development of analytical mechanics to pass to the Continent in the eighteenth century. But these contributions are barely glimpsed here, and to modern eyes Leibniz's own efforts seem sterile and stumbling. As Costabel and others have made clear, however, the main impetus behind the researches of Leibniz was philosophical. The very term dynamics seems to have been coined by Leibniz for metaphysical, not to say theological, reasons. It even appears that Leibniz owed many of his main ideas of mechanics, at least in genesis, to Christiaan Huygens, who emerges here as a wise and perceptive scientist. What Leibniz did, what was apparently his chief interest, was to expand them as key elements in his philosophical approach. Although we have been taught by recent historians of science not to take too literally Newton's disclaimer of involvement in metaphysics, one cannot help feeling that his conscious attempt to disregard metaphysics and concentrate on what we might call "problem solving" remains one of the fundamental reasons for the immediate fruitfulness of Newton's system of mechanics.

Costabel views with microscopic detail two episodes in the development of Leibniz's dynamics. But the overall picture is often obscured by the mass of minutiae and lengthy reasoning about particular points. It is symptomatic that the book has only one passing mention of Newton, even though the Principia had appeared five years before the events discussed here. For a more general view of the Leibnizian dynamics, one is well advised to turn, for example, to the relevant chapter in Westfall's recent book Force in Newton's Physics. Another limitation of Costabel's book is the translation which is stiff and clumsy.

4.1. From the Publisher.

Although Leibniz's writing forms an enormous corpus, no single work stands as a canonical expression of his whole philosophy. In addition, the wide range of Leibniz's work - letters, published papers, and fragments on a variety of philosophical, religious, mathematical, and scientific questions over a fifty-year period - heightens the challenge of preparing an edition of his writings in English translation from the French and Latin.

4.2. Leibniz: Life and Works.

Gottfried Wilhelm Leibniz was born on 1 July 1646, in Leipzig. His father, Friedrich, a scholar and a Professor of Moral Philosophy at the University of Leipzig, died in September 1652, when Leibniz was only six years old. But despite his father's early death, the younger Leibniz was later to recall how his father had instilled in him a love of learning. Learning was, indeed, to become an important part of his life. Leibniz began school when he was seven years old. Even so, he later describes himself as self-taught. Leibniz seems to have taught himself Latin at age seven or eight, in order to read editions of Livy and Calvisius that fell into his hands; as a result, he was allowed admission into his late father's extensive library. There he read widely, but concentrated especially in the Church Fathers and in the Latin classics. Leibniz attended university from age fourteen to age twenty-one, first at the University of Leipzig (1661-1666) and then at the University of Altdorf (1666-1667), graduating with degrees in law and in philosophy. He was quickly recognised as a young man of great promise and talent and was invited to join the faculty at the University of Altdorf. He chose instead to go into public service. Under the patronage of Baron Johann Christian von Boineburg, Leibniz entered the service of the Elector of Mainz and occupied a number of positions in Mainz and nearby Nuremburg. There he stayed until he was sent to Paris in spring 1672 on diplomatic business, a trip that deeply affected his intellectual development.

The intellectual world of the late seventeenth century was very exciting indeed. The century began still very much under the influence of the Aristotelian philosophy that had dominated European thought since the 13th century, when the bulk of the Aristotelian corpus was rediscovered and translated from Greek and Arabic into Latin. But much had happened by the time Leibniz went to school. A new philosophy had emerged from figures like Galileo and his students, Torricelli and Cavalieri, from Descartes and his numerous camp, from Gassendi, Pascal, Hobbes, and from countless others. Not without a fight and not without hesitations, the substantial forms and primary matter of the schoolmen had given away to a new world, the mechanist world of geometrical bodies or atoms in motion. Together with this new world had come new mathematical tools for dealing with the new geometrical bodies. But this new world view raised new problems as well, including, among others, problems of necessity, contingency, and freedom in a world governed by laws of motion, problems connected with the place of the soul and its immortality, and problems concerning God and his creation, sustenance, and ends.

Leibniz knew little of the new philosophy before 1672. He was originally brought up in an older tradition of Aristotelian Scholasticism, supplemented with liberal doses of Renaissance humanism. He reports much later in life that he was converted to the new mechanism at age fifteen, in 1661 or 1662, presumably, and reports having given up Aristotle for the new philosophy. But even so, he later confesses that the knowledge he had of the moderns was quite slim at that time, and despite his enthusiasm, the considerable amount of work he did in what he took to be the new philosophy was the work of an amateur.

When in Paris from 1672 to 1676, Leibniz made his entrance into the learned world and did his best to seek out the intellectual luminaries that made Paris an important centre of learning. Most important, he came to know Christiaan Huygens, under whose tutelage Leibniz was introduced to the moderns. Leibniz quickly progressed, and in those years he laid the foundations for his calculus, his physics, and the central core of what was to become his philosophy.

Before Leibniz returned to Germany in December 1676, he stopped in England and in Holland, where he met Spinoza. Both Boineburg and the Elector of Mainz had died while he was in Paris. Leibniz returned to the court of Hanover as a counsellor. Though he often travelled and took on responsibilities elsewhere, Hanover was to be his main home for the rest of his life. Leibniz took on a wide variety of tasks, both for the court at Hanover and for his numerous other employers. He served as a mining engineer, unsuccessfully supervising the draining of the silver mines in the Harz mountains, as the head librarian over a vast collection of books and manuscripts, as an advisor and diplomat, and as a court historian. In this later capacity, Leibniz wrote a geological history of the region of Lower Saxony, the Protogaea, that proved to be an important work in the history of geology when it was finally published in 1749, many years after his death. In this connection he also published a number of volumes of the historical documents he found in the archives he combed, looking for material for his history, and he undertook some of the earliest research into European languages, their origins, and their evolution.

But all the while, through a succession of employers at Hanover and elsewhere, Leibniz continued to develop the philosophical system he had started in Paris and before, in a series of essays, letters, and two books. In metaphysics, the unpublished "Discourse on Metaphysics," composed in 1686 but anticipated in earlier writings, developed themes discussed in the letters to Arnauld written in that and the following years. Themes from the "Discourse" also appear, somewhat transformed, in the "New System of Nature," which Leibniz published in 1695 - the first public exposition of his metaphysical system - and again in the unpublished essay "On the Ultimate Origination of Things" of 1697 and again in the important essay "On Nature Itself," published in 1698. These themes appear further transformed in the late summaries of his doctrines, the unpublished "Principles of Nature and Grace" and "Monadology." Behind the metaphysics of these essays is Leibniz's program for logic and a universal language, developed most conspicuously in a remarkable series of papers from the late 1670s and 1680s, in which he explicates the concept of truth which he draws upon in the celebrated characterisation of the individual he gives in section 8 of the "Discourse." Leibniz was also deeply involved with the study of physics. The most extensive account of his physics is found in his Dynamics (1689-1691), in which he sets out the basic laws of motion and force. This work was never published, but Leibniz was persuaded to publish an essay based on it. The essay "A Specimen of Dynamics" appeared in 1695; it contained a discussion of the metaphysical foundations of his physics. In the course of articulating and defending his own view, Leibniz differentiated his conception of physics from that of the Cartesians and the Newtonians and related his view to that of the schoolmen; to those ends he maintained an extensive circle of correspondents, including Huygens, De Volder, Des Bosses, and Clarke. Theology was a constant theme; it became central in the Theodicy of 1710, one of two philosophical books Leibniz wrote. His other philosophical book was the New Essays on Human Understanding, finished in 1704 but never published. The New Essays were meant as a response to Locke's Essay Concerning Human Understanding, but Locke's death in 1704 caused Leibniz to withhold publication. In general, Leibniz was an avid reader, reading and reacting to the thought of his contemporaries. In addition to the New Essays and other writings on Locke, Leibniz left detailed essays and notes on Hobbes and Spinoza, Descartes and Malebranche, Newton and even the very young George Berkeley, to name but a select few of those who caught Leibniz's attention.

It is natural enough to try to find order in this apparent chaos, to try to identify the Leibnizian doctrine of one thing or another, or to try to find the single key to Leibniz's thought, the premise from which everything follows neatly. No doubt this can be done, to some extent, and an orderly Leibnizian philosophy can be reconstructed from the somewhat disorderly notes Leibniz left. But it is also important to be sensitive to the sometimes subtle, sometimes not so subtle changes as Leibniz develops a doctrine, first trying one thing, then another, looking at the world of his philosophy from different points of view. It is also important to appreciate not only the philosophical premises Leibniz uses, but also the different historical strands he attempts to weave together. Late in life Leibniz told one correspondent, Nicolas Remond, that he had always tried "to uncover and reunite the truth buried and scattered through the opinions of the different sects of philosophers." Leibniz continued: "I have found that most sects are correct in the better part of what they put forward, though not so much in what they deny. ..." In this way Leibniz hoped to unite Catholicism and Protestantism, Hobbesian materialism with Cartesian dualism, and the mechanism of the moderns with the substantial forms of the schoolmen.

Leibniz died in his bed in Hanover on November 14, 1716. The last of his many employers, Georg Ludwig, had been in London since succeeding to the throne of England as George I some two years earlier. But Leibniz was not welcome there. The official reason was that Leibniz was to stay in Hanover until the history of the House of Hanover was close to complete. But there was also great hostility at court to the then elderly counsellor. Important too must have been the protracted debate between Leibniz and Newton over the priority of the discovery of the calculus, which had been going on for some years and had taken on decidedly nationalistic overtones. When Leibniz died in Hanover, what was left of the court failed to attend his otherwise proper funeral. But though his immediate fellows may not have appreciated him, he had already become extremely well known and respected by the time of his death. He never founded a school of thought, as Descartes before him had, but even after his death, his works continued to be published and his views discussed.

4.3. From the Preface.

Principle of Selection and Rationale for the Volume.

Preparing an edition of Leibniz's writings in English translation is a delicate business. There is nothing in Leibniz's enormous corpus that corresponds to Descartes's Meditations, Spinoza's Ethics, or Locke's Essay, no single work that stands as a canonical expression of its author's whole philosophy. Although works like the "Discourse on Metaphysics" and the "Monadology" are obviously essential to any good collection of Leibniz's writings, neither of these nor any other single work is, by itself, an adequate exposition of Leibniz's complex thought. Unlike his more systematic contemporaries, Leibniz seems to have chosen as his form the occasional essay, the essay or letter written about a specific problem, usually against a specific antagonist, and often with a specific audience in mind. Even Leibniz's two mature philosophical books, the New Essays and the Theodicy, read this way, as collections of smaller essays and comments, only loosely bound together, almost as an afterthought. The problem of coming to grips with Leibniz's thought is greater still when we take account of the range of his work, notes, letters, published papers, and fragments, on a variety of philosophical, theological, mathematical, and scientific questions, written over a period of more than fifty years. In addition, there is the problem of the original-language texts. While there are some good editions of individual works, there is no critical edition of the Leibnizian corpus available even now; the scholars at work on the so-called Academy Edition, in progress for over sixty years, are still in the process of completing the definitive edition of what most scholars consider Leibniz's juvenilia. The problems facing editors of a selection of Leibniz's works are immense, and the choices are difficult; the editors must be aware of the needs of students and scholars and, most of all, the need to present a fair and balanced view of Leibniz's philosophy, all within a very limited volume.

Our goals in this book are to collect, translate, and annotate a selection of Leibniz's philosophical works that, as a whole, will give an accurate picture of Leibniz's mature philosophical thought. Part I of the collection consists of a selection of essays, papers, and letters that together provide materials for the study of Leibniz's main doctrines. We have sought to include the "standard" texts, the "Discourse on Metaphysics," "Monadology," "New System of Nature," etc., which are essential to an understanding of Leibniz. But we have also included a selection of lesser-known pieces from Leibniz's mature thought the late 1670s on that deal with Leibniz's program for logic, his various accounts of contingency and freedom, and his account of body. In this part of the collection, we arrange the pieces in the order of their composition (as much as possible dating is sometimes problematic) to remind the reader that chronological considerations can sometimes be helpful in sorting out a philosopher's thought.

However, it is difficult to understand and appreciate Leibniz's thought when it is detached from its historical context. Hence, in Part II of the collection, we present a selection of Leibniz's writings about other philosophers. The figures we have chosen to emphasise are the ones most often discussed in connection with Leibniz: Hobbes, Descartes, Spinoza, Malebranche, Locke, and Berkeley. In addition, we have included some of Leibniz's philosophical writings on Newton, both for the light they shed on Leibniz's own philosophy and to emphasise the extent to which Leibniz was involved in the scientific debates of his day. We hope that the writings in this section will allow the reader to see how Leibniz saw his contemporaries. The case can be made, we think, that Leibniz's thought can only be understood fully in the context of the contrasts he draws between his thought and that of others.

Many of the pieces included are new (and, we hope, better) translations of familiar material already available in English. In addition, we are including as much important but currently neglected material as we can, translations of never-before-translated essays and letters that deserve to be known better, and translations of significant pieces that are either currently unavailable in English or available only in unsatisfactory translations. Our main source of original language texts is C I Gerhardt's nineteenth-century editions of Leibniz's writings; with all their shortcomings, they are, unfortunately, the best and most comprehensive collections of Leibniz's writings currently available. We have supplemented Gerhardt's texts with other editions, including the earlier collections of Dutens, Erdmann, and Foucher de Careil, more recent collections of manuscripts omitted by Gerhardt, such as the editions of Couturat and Grua, and recent editions based on manuscripts unavailable to Gerhardt, such as Lestienne's edition of the Discourse and Rodis-Lewis's edition of the Correspondence with Arnauld. We have also consulted the previews of Academy Edition volumes yet to come out - what they call the Vorausedition - for the best current information concerning texts and dating, when available.

In translating the texts, we have aimed for a balance between accuracy and literal translation, keeping in mind the needs of the student reader. Our translations are supplemented by (i) brief headnotes, setting the context for individual selections; (ii) explanatory historical and philosophical footnotes (including cross-references to Leibniz's other essays and to the work of his contemporaries and predecessors necessary to understand specific portions of text); and (iii) textual and linguistic endnotes (indicated by asterisks in the text). We include bibliographies of editions and translations of Leibniz's writings, secondary sources on Leibniz, and principal secondary sources, as well as brief biographies of Leibniz's contemporaries.

We would both like to acknowledge the anonymous readers who reviewed our translations at various stages in the preparation of this book. While it was not always easy to face up to the inaccuracies in our translations or the infelicities in our style, their careful work improved the volume immeasurably. (Any imperfections that remain are, of course, their responsibility.) We would also like to recognise the numerous scholars who made helpful suggestions about the selections we chose for the volume, and the many students and colleagues who used earlier versions of the translations and shared their comments with us. And finally, we would like to thank our families for all their support; they put up with a great deal.

4.4. Review by: Nicholas Jolley.
Philosophy in Review 11 (1) (1991), 10-12.

In recent years the search for a good selection of Leibniz's writings that is suitable for undergraduate courses has been a rather frustrating one. Despite its value for scholars, Loemker's edition is far too daunting and expensive for most teaching purposes; other editions have tended to be either out of date or, what is worse, out of print. No doubt Leibniz himself is partly to blame for this state of affairs; if only he had written one indisputable philosophical masterpiece, such as Descartes's Meditations or Spinoza's Ethics, his philosophy would be much more readily available. Fortunately, Ariew and Garber have helped to remedy this situation; they have added a worthwhile selection of Leibniz texts to the growing Hackett library of philosophical classics.

In conception this is an interesting and somewhat unusual volume. Ariew and Garber include many of the 'basic works' such as the Discourse on Metaphysics and the Monadology, but they do not confine themselves to these; they also devote a large portion of their volume to Leibniz's writings about his contemporaries. In this section Leibniz's famous letters to Clarke rub shoulders with lesser-known criticisms of Malebranche, Locke, Berkeley, and others. This part of the book is valuable not just because it helps to round out the historical context but also because it reminds the reader that, more than most philosophers, Leibniz needed the stimulus of disagreement with other thinkers in order to commit his ideas to paper. Not that Leibniz is merely negative in his reactions; certainly he did not see himself in this light. Often he is seeking to forge a new synthesis out of philosophical views with which he has at least partial sympathy.

Under the heading 'Basic Works' Ariew and Garber include some major texts that have not often found their way into English anthologies. The selections from the De Volder and Des Bosses correspondences, for instance, show Leibniz grappling with the thorny problems posed by his doctrine of monads. These exchanges are in many ways more illuminating than such curt, summary presentations of his later metaphysics as the Monadology and the Principles of Nature and of Grace. Readers who are fascinated by Leibniz's attempts to define the status of bodies within an idealist framework will find that Ariew and Garber are sometimes more helpful than even Loemker; unlike Loemker, for instance, they reproduce the remarkable letter in which Leibniz explains that he is not seeking to eliminate body, but only to reduce it (181). However, though they are generous with unfamiliar material, Ariew and Garber sometimes give relatively short measure to such classic texts as the Leibniz-Arnauld correspondence. Many readers have thought that when Leibniz told Arnauld that in every true proposition, the concept of the predicate is contained in the concept of the subject, he was stating a doctrine which was at the root of the whole correspondence. Surprisingly, Ariew and Garber do not print the letter in which these words occur. It is true that similar statements are found elsewhere in the volume, but that is not quite the same thing. From a pedagogical perspective, the omission of key parts of the Leibniz-Arnauld correspondence is regrettable.

Ariew's and Garber's translations are generally fluent, but in terms of accuracy they leave something to be desired. The severest test is of course posed by those texts which have not previously been translated into English, at least in full, and here, unfortunately, errors are rather easier to spot than they should be. Leibniz's polemical writings against Locke and Newton furnish some instructive examples. In the Anti-Barbarus Physicus Leibniz bemoans Locke's adoption of the Newtonian theory of gravitation by contrasting it with his earlier commitment to mechanism: 'Johannes Lockius in prima editione Tentamenti de intellectu statuit, ut dignum erat, ... ut nullum corpus moveretur nisi impulsu corporis tangentis ...' Garber and Ariew translate: 'John Locke, in the first edition of his Essay Concerning Human Understanding, judged that it is appropriate that no body is moved except through the impulse of a body touching it ...' (317). If this were what Leibniz wanted to say, he would have used the subjunctive instead of the indicative 'erat'. The correct translation is: 'John Locke, in the first edition of his Essay Concerning [Human] Understanding, asserted, as was correct, that no body is moved except through the impulse of a body touching it...'. In another piece where Locke is again the target, Ariew and Garber make a more serious error. Leibniz tells Lady Masham: 'Il est vray que l'illustre Mons. Locke a soutenu dans son excellent Essay... que Dieu pourroit donner à la matière la force de penser, parce qu'il peut faire ce qui passe tout ce que nous pouvons concevoir.' In Ariew's and Garber's hands this becomes: 'It is true that the illustrious Locke maintained in his excellent Essay that God can give matter the power of thinking because he can make everything we can conceive happen' (290). But the last clause of course means something quite different: 'because he can do what surpasses everything we can conceive.' (Perhaps Ariew and Garber were thinking of the English expression 'bring to pass'.) It is understandable, if unfortunate, that Ariew and Garber should make mistakes in translating works for the first time. But it is surprising that they should introduce errors into a classic text such as the Discourse on Metaphysics of which several good translations already exist. In a section of this work defending 'the utility of final causes in physics', Leibniz inveighs against 'quelques esprits forts pretendus' who say that we see because it happens that we have eyes and not that eyes were made for seeing. According to Ariew and Garber, Leibniz is talking here about 'certain extremely pretentious minds' (52). Neither Loemker nor Lucas and Grint made this mistake; they correctly saw that Leibniz's target is 'certain would-be free-thinkers'.

This is a useful volume, but it needs to be treated with some caution. Since it is likely to be widely adopted, one must hope that Hackett will bring out a new edition in which such errors are corrected. It will then be much more useful.

4.5. Review by: Emily Grosholz.
Mathematical Reviews MR1091250 (92d:01079).

This collection of the philosophical essays of G W Leibniz was compiled by two philosophers, Roger Ariew and Daniel Garber, who understand and value the history of philosophy and the sciences in the seventeenth century. They are also accomplished Latinists, offering works for the most part previously published in scholarly editions but not available in English translation, as well as strikingly fresh translations of well-known texts. Leibniz scholars will appreciate the new perspectives engendered by their versions of, for example, the "Discourse on Metaphysics" and the "Monadology".

The intelligence of an anthology lies in its principle of selection. Ariew and Garber have chosen significant and often overlooked or underrated essays from every one of the major editions, from Gerhardt to the Academy edition. Their way of arranging the texts is inventive and lucid. The first two-thirds of the volume are devoted to "Basic works", set forth in chronological order. In addition to standbys like "Preface to a universal characteristic", "A specimen of dynamics", and "Principles of nature and grace, based on reason", this section includes a healthy sampling of Leibniz' correspondence with well-known and lesser-known interolocutors, as befits a philosophical profile of one of history's great letter-writers. The last third includes Leibniz' opinions and criticisms of his contemporaries: Descartes, Malebranche, Hobbes, Spinoza, Locke, Berkeley and Newton. The bibliographical material is accurate and as full as need be, and the index is helpful. Brief biographies of Leibniz' contemporaries, his intellectual context, are provided at the end of the book. This volume should serve well for graduate and some undergraduate courses treating Leibniz' role in the history of philosophy, logic, mathematics and physics.

5.1. From the Publisher.

Discourse on Metaphysics and Other Essays contains complete translations of the two essays that constitute the best introductions to Leibniz's complex thought: Discourse on Metaphysics of 1686 and Monadology of 1714. These are supplemented with two essays of special interest to the student of modern philosophy, On the Ultimate Origination of Things of 1697 and the Preface to his New Essays of 1703-1705.

The translations are taken from Leibniz, Philosophical Essays, edited and translated by Roger Ariew and Daniel Garber (Hackett, 1989).

5.2. Summary.

The main items in this brief collection of philosophical essays by Leibniz are the Discourse on metaphysics, On the ultimate origination of things, and The principles of philosophy, or, The monadology, all of which are also contained in a larger collection prepared by the same editors/translators [G W Leitniz, Philosophical essays, Hackett, Indianapolis, IN, 1989]. In addition there are a brief outline of Leibniz' life and works, a selected bibliography (of works of Leibniz, secondary works, and translations and other texts referred to in the notes), Leibniz' preface to the New essays, and "brief" (telegraphic) biographies of some contemporaries of Leibniz.

5.3. Review by: Joella Yoder.
Isis 85 (1) (1994), 119.

Daniel Garber and Roger Ariew's edition of Discourse on Metaphysics and Other Essays is obviously intended to be used as a supplementary textbook, providing English translations of some key essays for students unable to read the originals. The "other essays" in the set are "On the Ultimate Origination of Things," the preface to the unpublished rejoinder to John Locke called New Essays on the Understanding, and "Monadology." The translators provide a condensed (four pages) biography of Leibniz that has enough hints to pique the curious, a short bibliography that not surprisingly concentrates on English-language studies, and a set of brief biographies of some of the people mentioned in the book. The background to the texts themselves is confined to a couple of sentences before each selection, presumably leaving the details to the instructor. The footnotes include short definitions of such terms as empirics, some variant readings, and lines from earlier drafts. The translations are duplicated from the Philosophical Essays (1989) produced by the same translators and press. This book's large-sized print and stapled binding attest to the hope that it will be well worn from use. May it be so.

6.1. From the Introduction.

In November of 1715, Gottfried Wilhelm Leibniz, the elderly librarian, historian, and counsellor to the House of Hanover in Lower Saxony, wrote a letter to Caroline, Princess of Wales, cautioning her about the odd cosmological-theological views of Sir Isaac Newton and his followers. This would seem an unusual event in international relations except that Leibniz had a long-standing relationship with Caroline, who was married to Georg August. The latter was Prince of Wales, Elector Prince of Hanover, and son of Leibniz's employer, Georg Ludwig, Elector of Hanover who, from 1714 on, was George I, King of Great Britain and Ireland. Caroline became Queen Consort in 1727 when Georg August ascended to the throne of England as George II; she was the third of three royal women who had befriended Leibniz. The whole court of Hanover had moved to London in 1714. However, Leibniz was not welcome there. Georg Ludwig had refused his request to join the royal family in England. The official reason was that he was to stay in Hanover until the history of the House of Hanover, which he was commissioned to write, was closer to completion. By 1714 there was great hostility at the court to the then elderly counsellor. He was often a subject of ridicule, treated as an old fossil, with his enormous black wig and once fashionable ornate clothes. The court may have been unhappy with his failure to finish the history of the House of Hanover, but it was also surely embarrassed by the protracted debate between him and Newton over the discovery of the calculus, which had taken on decidedly nationalistic overtones.

Admittedly, the debate about the priority of the invention of the calculus was not the only controversy of the final period of Leibniz's life, but it was certainly the most bitter. The first public blow in the dispute was probably delivered by Fatio de Dullier, who wrote an article in 1697 attributing the discovery to Newton and attacking Leibniz. The feud simmered, and in 1711 Leibniz complained to the Royal Society about an accusation by John Keill, another Newtonian, that Leibniz had stolen Newton's calculus. In 1712 the Society declared that Leibniz did not know anything of differential calculus before Newton revealed it to him in a letter of 1672; that Newton invented the calculus in 1669, fifteen years before Leibniz published his version of it in the Acta Eruditorum of Leipzig; and that, consequently, Keill had not slandered Leibniz. The Society made its findings public in its Commercium Epistolicum de Analysi promota (mostly composed by Newton, as we now understand). The episode obviously had many repercussions up to Leibniz's death four years later. Perhaps the only charitable thing one could say about it is that it provides a glimpse into the workings of the Royal Society at the start of the eighteenth century and illustrates its domination by Newton and the Newtonians.

Newton (1642-1727) was, of course, the foremost mathematician and natural philosopher of the late seventeenth century. He attended Trinity College, Cambridge, was elected Fellow in 1667, and succeeded Isaac Barrow as Lucasian Professor of Mathematics in 1669. Newton's great work, Philosophiae naturalis principia mathematica (The Mathematical Principles of Natural Philosophy, referred to as the Principia), published in 1687 (2nd ed. 1713; 3rd ed. 1726), was a revision and expansion of several treatises he previously composed but did not publish. He was elected President of the Royal Society in 1703 and knighted in 1705, the year after the publication of Optics. During his life he engaged in several bitter priority disputes about scientific and mathematical discoveries - for example, with Robert Hooke in 1686-1688 over the inverse square law and, of course, with Leibniz over the calculus. His influence in the history of science is unequalled.

When Leibniz wrote to Caroline cautioning her about Newton's views, he surely did not expect to elicit a reply from Newton. But by the end of the month, on November 26, 1715, he had received a letter written by Samuel Clarke on behalf of Newton. This resulted in a series of four more letters by Leibniz and four more replies by Clarke, the exchange being cut short by Leibniz's death on November 14, 1716. There is always a lingering question of authorship in Clarke's letters: were they really Clarke's or were they composed by Newton? Clarke was obviously Newton's stand-in, but was he also merely a mouthpiece? Enzio Vailati, the author of a recent commentary on the Leibniz-Clarke correspondence, reviews the arguments both pro and con:

First, the documentary evidence about Newton's role in the correspondence is scant at best. There are neither drafts of Clarke's letters to Leibniz by Newton nor letters between Clarke and Newton that might help in assessing the latter's role in the correspondence. Since Clarke was Newton's parish priest at St James, Picadilly, they were neighbours, which rendered epistolary exchanges unlikely. We know that Newton played some indirect role in the correspondence. There is a copy in Newton's hand of the postscript on atoms and void to Clarke's fourth letter, and almost certainly Clarke consulted some of his papers in drafting the physical arguments that make up much of the notes in his fifth letter; but whether Newton played a direct role, and if so what its extent and depth were, is unclear at best.

The author goes on to state that Clarke's views coincided with Newton's and that Newton's influence on Clarke was great, but that "all the philosophical positions and most of the arguments Clarke aired in the correspondence had appeared in his 1705-1706 Boyle Lectures, in previous epistolary exchanges with Collins (1707-1708) and Butler (1714-1715), and in philosophical sermons." All of that is surely right, and Vailati's emphasis in re-establishing Clarke as a philosopher who should be studied seriously is certainly welcome. Still, there is no doubt that Clarke was Newton's agent and that he would not have written anything that he knew was not in keeping with Newton's views. The relationship between Clarke and Newton was too close to think of Clarke as independent. That was also how Caroline saw it. In the letter she wrote to Leibniz on 10 January 1716, enclosed with Clarke's Second Replies, she said:

I enclose a reply to your paper; I considered very carefully the replies made on both sides. I do not know whether the bias I have for your merit makes me partial, but I find all his replies are rather words than what could be called replies. You are right about the author of the reply; they are not written without the advice of Sir Newton, whom I should like to be reconciled with you. I do not know if you will consent, but the Abbé Conti and myself have made ourselves mediators; it would be a great pity if two such great men as you and he were to be estranged by misunderstandings.

Ironically, Leibniz had previously asked about the possibility of translating the Theodicy into English and Caroline had written to him on 14 November 1715, saying: "I have talked today with the Bishop of Lincoln about the translation of your Theodicy; he assures me that there is no one capable of doing it except Dr Clarke, whose books I sent you by Oeynhausen. He is a close friend of Sir Newton." But less than two weeks later, in the letter in which she enclosed Clarke's First Reply, Caroline said:

I hope you received the books I sent you. Send me, please, your opinion on Dr Clarke's works, which I think have considerable merit, although not comparable to your 'Theodicy'. ... We are thinking seriously of getting your 'Theodicy' translated; but we are looking for a good translator. Dr Clarke is too opposed to your opinions to do it; he would certainly be the most suitable person of all, but he is too much of Sir Isaac Newton's opinion and I am myself engaged in a dispute with him.

Caroline's opinion of Clarke was clearly correct: he was an excellent translator of philosophy and science but he was too much of the Newtonian.

Samuel Clarke (1675-1729) was educated at Gonville and Caius College, Cambridge, receiving his B.A. in 1695. It was said that he was one of the first to master Newton's Principia. In 1697 he translated into Latin the Traité de physique of the Cartesian Jacques Rohault, adding extensive footnotes "correcting" Descartes by incorporating Newtonian principles. It became the standard physics textbook in English schools and thereby the conduit through which Newtonian principles were taught - it was itself translated into English, footnotes and all, by John Clarke (1682-1757) in 1723. Samuel Clarke also published several theological works and sermons and was involved in various theological disputes (including the one with Henry Dodwell over the immortality of the soul mentioned in the correspondence). He gave the Boyle lectures in 1704 and 1705. In 1706 he translated Newton's Optics into Latin. But perhaps he is best known now for his correspondence with Leibniz, in which he and Leibniz had a wide-ranging discussion of the nature of God, human souls, free will and indifference of choice, space and time, the vacuum, miracles, and matter and force.

These philosophical topics have always been important, but they took on an even greater significance in the seventeenth century, when philosophers had to reconsider their fundamental doctrines in the light of the scientific revolution that was taking place. New scientific and philosophical doctrines had emerged, posing a challenge to the Aristotelian (or scholastic) philosophy, which had dominated European thought ever since the thirteenth century when the majority of the Aristotelian corpus was rediscovered, translated from Greek and Arabic into Latin, and made compatible with Christian doctrine. The substantial forms and primary matter of the scholastics were giving way to a new mechanistic world of geometrical bodies, corpuscles, or atoms in motion. Old problems that seemed to have been resolved within a scholastic framework were raised again with new urgency. Leibniz, of course, was a major contributor to this intellectual movement, which defined the modern world.

Leibniz (1646-1716) attended the universities of Leipzig (1661-1666) and Altdorf (1666-1667), graduating with degrees in law and philosophy. Invited to join the faculty at Altdorf, he chose instead to enter the service of the Elector of Mainz. In 1672 he was sent on diplomatic business to Paris. While in Paris, he read and copied René Descartes's manuscripts and sought out proponents of the new philosophy, including Antoine Arnauld and Nicholas Malebranche; his own later work was often precipitated by the correspondence he maintained with them. He travelled to London and met members of the Royal Society (Henry Oldenburg and Robert Boyle, among others, though not Newton). Leibniz returned to Germany, in 1676, in the service of the court of Hanover, where he resided until his death. His literary output was massive, but he did not publish much of what he wrote. Among his unpublished manuscripts were such important works as "Discourse on Metaphysics" (1686), Dynamics (1689-1691), and "Monadology" (1714). In 1705 he finished his New Essays on Human Understanding, a book-length commentary on John Locke's Essay but did not issue the work. He usually wrote essays, small treatises, and letters to learned correspondents. With the rise of intellectual journals in the second half of the seventeenth century, he had a ready means of disseminating his thought. He did publish several significant philosophical articles: "New System of Nature" (Journal des Scavants, 1695), "Specimen of Dynamics" (Acta Eruditorum, 1695), and "On Nature Itself" (Acta Eruditorum, 1698). Ultimately, he published a book-length volume, Theodicy (1710), though it is a rather loosely structured work, consisting largely of responses to Pierre Bayle's scepticism. Leibniz maintained an extensive circle of correspondents.

The correspondence with Clarke took place during Leibniz's last few years; as such, the doctrines it contains resemble those of the Theodicy and "Monadology." In the exchange Leibniz is especially concerned to defend the principle of sufficient reason as the basis for contingent truths, as opposed to the principle of contradiction, which he asserts is the foundation for necessary truths. He also defends a number of his characteristic theses: small perceptions which we do not consciously perceive, pre-established harmony between the soul and the body, and especially the identity of indiscernibles. According to Leibniz, the thesis of the identity of indiscernibles would "put an end to such doctrines as the empty tablets of the soul, a soul without thought, a substance without action, void space, atoms, and even particles in matter not actually divided, complete uniformity in a part of time, place, or matter and a thousand other fictions of philosophers which arise from their incomplete notions" - doctrines which he disputed with Newton and Clarke.

6.2. Review by: James S Mcdonald.
The Review of Metaphysics 55 (4) (2002), 867-868.

The correspondence between G W Leibniz and Samuel Clarke on the implications of Sir Isaac Newton's physics to natural theology was the last battle that Leibniz fought with the Newtonians. That battle, not so famous as the one over the invention of calculus, ended abruptly with the death of Leibniz in November 1716; however, Clarke soon after translated the correspondence into English and published it in 1717. It became one of a relatively tiny number of Leibniz's writings to be published before the nineteenth century. Thus, besides being a meaningful clash of the rationalist and empiricist traditions, the correspondence between Leibniz and Clarke was one of the few primary sources that eighteenth-century philosophers had of the mature thought of one of Europe's most celebrated thinkers. Furthermore, it was relevant to the philosophy of that day. Immanuel Kant, for instance, used the correspondence to launch his own formulation of space and considered his theory a resolution of the controversy.

This new edition by Roger Ariew is a simple, moderately edited version of Clarke's original translation. Ariew changes the original by modernising and Americanising the English and tweaking Clarke's translation of Leibniz from French. In places, Clarke's original translation tends to over simplify the subtle differences between relevant terms in Leibniz's philosophy. For instance, Clarke translated percevoir and appercevoir both as "perceive" when the two terms are quite different for Leibniz. Unfortunately perhaps, Ariew chooses to translate appercevoir as "consciously perceive," which is still too ambiguous.

6.3. Review by: Peter Loptson.
Philosophy in Review 20 (5) (2000), 363-365.

The Leibniz-Clarke correspondence, carried out at the end of Leibniz's life - interrupted, in fact, by his death in 1716 - is a splendid philosophical exchange. It is of rich value for the student of Leibniz's views, for the philosophical public face of Newtonianism, for Enlightenment intellectual culture, and for the perennial exploration of fundamental themes in philosophy of religion. It is a very accessible read, and it is very attractively presented in this new edition prepared by Roger Ariew.

The only flaws in Ariew's introductory material are relatively minor. He has trouble getting the name and title data straight for Leibniz's royal employers. It is 'George Augustus' (English) or 'Georg August' (German), not, as Ariew names him, 'Georg Augustus'; similarly, either Ernest Augustus' or 'Ernst August', not 'Ernst Augustus'. Also, Georg August, subsequently King George II of Great Britain, was Electoral Prince (not 'Elector Prince') of Hanover. And the three women of elevated status who befriended Leibniz were all of royal, not noble, rank. All of these errors occur on the very first page (vii) of Ariew's introductory essay. They are minor, trivial, and it is perhaps pedantic to note them. But they do not start Ariew's book off well, and they are matters the seventeenth- and eighteenth-century intellectual historian should get right, particularly since this is so supremely aristocratic a period.

Thereafter, all goes excellently well. The texts consist of Leibniz's five letters and Clarke's replies to each, followed by selections from previously published writings of Leibniz and Newton on the themes of the correspondence. Clarke had published the whole set together (with his own translations from French and Latin) in 1717. Ariew makes modest modernisations in Clarke's edition.

Clarke is, of course, Newton's bulldog - to adapt the phrase so famously used a century and a half later for Huxley in relation to Darwin. He - Clarke - is quite good. Sharp, obviously very intelligent, a keen polemicist, the thorough, painstaking Anglo-Saxon confronting the extravagant continental. Clarke is also a bully; Leibniz twenty-nine years his senior is badgered without mercy. Leibniz of course tries to respond in kind; he is occasionally brilliant. One wonders what degree of more genuine understanding of the interconnected system of the genius he stalks Clarke may have had.

Both Clarke and Leibniz represent world-views for which it is difficult now to feel more than selective sympathetic engagement. One reads as an interested outsider, it is a marvellous exchange, with delightful mutually uncomprehending riposte. Common sense versus scientific realism, both against an unwavering theistic backdrop.

On Leibniz's mature metaphysical views, his side of the correspondence is helpful and revealing. Leibniz straightforwardly enunciates and commits himself to positions the world then and since has seen as extravagant if not bizarre. Among them are the doctrine of the pre-established harmony. In one place he answers a question the inquirer will find seldom clearly addressed elsewhere. 'It is true that there is no production of new simple substances' (57) must imply that you and I and all other simple monads have been in the world since its first creation. (Since the creation and annihilation of monads are for Leibniz miracles whenever they occur, monadology as such might have allowed God's perfection to bring later monads into the scheme of things.)

Leibniz's transparency also makes it difficult to accept the once orthodox and now rightly contested view that he was a metaphysical idealist. These spirited adumbrations, at the very end of his life, affirm a body realism as clearly as could be asked for.

The broad contours of the fundamental view of the world conveyed in this correspondence are dualist. This is true on both sides: Clarke and Leibniz both affirm the reality of minds and bodies, and their deep difference of kind.

There are otherwise of course enormous contrasts and oppositions of view between the two. In the case of Leibniz what stands out for this reviewer is a strong sense that, as with Spinoza, the centre of gravity in the system and what motivates it is to be found in the philosophy of Descartes. The fundamental conception (for both Spinoza and Leibniz) is that something at the core in Descartes is profoundly right and sound; and the primary impetus is to get the details straight, and correct Cartesian crudities, but in a deeply Cartesian way. Leibniz sets the fundamental Cartesian picture out clearly and succinctly in 124 (fifth letter): 'All the natural forces of bodies are subject to mechanical laws, and all the natural powers of spirits are subject to moral laws. The former follow the order of efficient causes, and the latter follow the order of final causes. The former operate without liberty, like a watch; the latter operate with liberty, though they exactly agree with that machine which another cause, free and superior, has adapted to them beforehand' (64). Similarly Cartesian is Leibniz's vehement repudiation of action at a distance, and non-corpuscular forces, as occult. This of course is one of the most significant sites of clash with Newton.

Some of the most interesting features of contrast and dispute are theological. Leibniz repeatedly asserts that if God had to choose between entirely equivalent alternatives, since he is perfectly rational he could not act at all; and Clarke repeatedly denies this. Leibniz repeatedly asserts that divine perfection implies creating the most possible reality; and Clarke repeatedly denies this. Each offers what they take to be compelling proof of their view, Clarke accusing Leibniz of question-begging and Leibniz accusing Clarke of accepting unintelligible or wholly unmotivated conceptions of agency.

Throughout Clarke represents scientifically-informed common sense. Indeed, he is a scientific and common sense realist, sharply aware of contrasts between the nature of things and the evidence for it. (Clarke is also a clear, fully explicit, advocate of a sense data theory of perception.) Leibniz speaks for the convergence of what is real, or possible, and what is observable or testable. He is the proto-operationalist; and the seeker of most comprehensive theoretical account.

This volume would be an ideal choice for any course in the history of philosophy in the post-Renaissance period. Because it is so short it would work well in a general survey; or in a detailed course on Leibniz, or in Enlightenment intellectual history. It would also serve effectively in a course in philosophy of religion; or a general introductory philosophy course. The positions present themselves as clear, contrasting, and at least locally persuasive - you tend to assent to whomever of the two you are reading (given their assumptions). It is fun, lively; and importantly philosophical. Highly recommended.

7.1. From the Publisher.

This volume is a critical edition of the eight-year correspondence (1698-1706) between Gottfried Wilhelm Leibniz and Burcher de Volder, professor of philosophy and mathematics at Leiden University.

Containing the surviving correspondence between Leibniz and De Volder, the volume also presents a generous selection from the letters between Leibniz and his friend Johann Bernoulli, through whose intercession the correspondence began. Bernoulli acted as intermediary throughout, and the often candid discussions between Leibniz and Bernoulli provide illuminating background to the correspondence proper. Each of the selections appears both in the original Latin and in English translation.

7.2. Review by: Wiep van Bunge.
Notre Dame Philosophical Reviews (19 July 2013).

Reconstructing the philosophical development of Gottfried Wilhelm Leibniz is a notoriously difficult enterprise. Over the past few years alone, such experts as Catherine Wilson, Christia Mercer and Daniel Garber have come to widely varying conclusions, and it was only in 2009 that Rosa Maria Antognazza succeeded in providing a comprehensive intellectual bibliography of the man. It is not difficult to see why this should be, for Leibniz's scholarly output remains astounding: he contributed not only to all the philosophical disciplines of his day, but also, famously, to mathematics, physics, geology, biology, medicine and psychology, as well as to theology, jurisprudence, linguistics and history. In addition, he played a crucial role in the early histories of calculation machines and European sinology. The Leibniz Nachlass is reported to consist of nearly 200,000 pages, including 15,000 letters exchanged with some 1,100 correspondents.

More often than not, Leibniz's correspondents were also at a loss about how to keep track of his creative genius, not least because of his curious publication policies. A regular contributor to such journals as the Journal des Sçavans, the Acta Eruditorum and the Histoire des ouvrages des savants, many of his ideas yet remained hidden in his massive private correspondence. Nearly all of his major texts were published posthumously, including his Nouveaux Essais, which only saw the light of day in 1765. Clearly, the editing of Leibniz's papers presents a daunting scholarly challenge, which in 1985 was taken up by the Leibniz Archive in Hanover in cooperation with editorial centres in Münster, Potsdam and Berlin. It is supervised by the Göttingen and the Berlin-Brandenburg Academies of Sciences, and to date, the Leibniz Archive has managed to add 33 volumes to the mere 19 published from 1901 to 1985. In due course, the Akademie Ausgabe will come to replace the nineteenth-century edition of C I Gerhardt.

The Leibniz Nachlass will be published in eight separate series, three of which will contain his correspondence. At present, the philosophical correspondence from 1695 to 1700 is being prepared by Martin Schneider and Stephan Meier-Oeser. It will be presented as Volume II, iii of the Akademie edition, but a Vorausedition is available on line already. So Paul Lodge's edition of Leibniz's correspondence with Burchard de Volder is more than welcome, as is his translation into English (Leibniz and de Volder corresponded, of course, in Latin). Lodge was in a unique position to prepare this edition, having edited Leibniz and his Correspondents (2004) and having studied the correspondence between Leibniz and De Volder "for more years than I care to remember" (p. xi). In particular the detailed annotation, as well as the highly perceptive Introduction accompanying the 67 letters, turns this fourth instalment of The Yale Leibniz Series into something of a gem. It should be added that over half of the letters collected in this volume were written by or addressed to Johann Bernoulli, who acted as a mediator between Leibniz and De Volder. Unfortunately, most of the letters exchanged between Bernoulli and de Volder are lost, and understandably only a small selection of the huge correspondence between Leibniz and Bernoulli is presented here. As far as the correspondence between Leibniz and De Volder is concerned, all the material of philosophical relevance has been included.

Parts of Leibniz's letters to De Volder have been translated into English before, but this is the first translation ever of De Volder's letters. This should come as no surprise, for few experts of early modern philosophy have ever read a single line written by this Leiden professor, despite the fact that he was widely considered one of the leading authorities on natural philosophy during his lifetime. Being a professor, he was not really expected to publish much besides the occasional oratio and the habitual series of disputationes. Born and raised in Amsterdam in a Mennonite family, he took his doctorate in medicine in 1664 at Leiden University. Six years later Leiden gave him a chair in philosophy, and in 1682 added a chair in mathematics. Trained as a Cartesian, he continued to uphold Descartes's natural philosophy until well into the 1690s. Jean Le Clerc's Éloge de feu, however, written in 1709 shortly after De Volder's death, had it that by the end of his life De Volder had abandoned Cartesianism in favour of the experimental approach flourishing across the Channel. A s early as 1675, following a visit to the Royal Society, De Volder had managed to install a physics laboratory at the university in order to illustrate his lectures experimentally.

To Leibniz, De Volder must have been an extremely interesting correspondent. Holding a crucial position at one of the finest universities in Europe, this possibly wavering adherent to Cartesianism would have made a wonderful ally at a time of great confusion in natural philosophy. Half a century earlier, Descartes had managed to make many friends both at Utrecht and Leiden, and this had turned the academic infrastructure of the Dutch Republic into a major asset in the further proliferation of "Cartesianism". So, in what looks like an attempt to emulate Descartes's example, Leibniz first addressed De Volder by the very end of 1698, when Descartes's philosophy was rapidly losing much of its former credibility. In 1687, Isaac Newton had sent De Volder a presentation copy of the Principia mathematica, but De Volder, who was purported to be one of the few scholars on the Continent able to grasp the mathematics involved, remained unconvinced. As is well-known, it was only following the publication of the second edition of the Principia in 1713 that "Newtonianism" would start to conquer Europe, and in doing so it would redefine the relationship between natural philosophy and metaphysics for most of the eighteenth century. Leibniz for his part had been working on his own alternative to Cartesianism, and in the course of his correspondence with De Volder, he gradually proposed his own views on substance, after having criticised Descartes's conception of matter as extended substance.

Despite his willingness to defend Cartesianism (e.g.,, against Huet's Censura of 1694) over the years De Volder appears to have grown increasingly sceptical of Descartes's ability to explain "the cause of motion in bodies". The correspondence with Leibniz testified to his willingness to at least consider alternative approaches to the concept of substance, involving some notion of activity. Typically, however, De Volder kept insisting on an a priori demonstration of the active nature of corporeal substance, which Leibniz refused to deliver. In view of Le Clerc's statement about De Volder's mature abandonment of Cartesianism, De Volder remained remarkably loyal to Descartes's methodology as well as to his definition of extended substance. Le Clerc, it should be added, was one of the first Continental scholars embracing Locke's "way of ideas" as well as Newton's Principia. As a consequence, we are left wondering whether De Volder's "disenchantment" with Cartesianism should not, perhaps, be interpreted as the product of the ambiguous heritage of Descartes himself, for the relationship between the rather sketchy metaphysics that Descartes concocted as a young man and his more mature work in the natural sciences is often rather loose. This much is clear, however: at no stage of the correspondence, which was terminated by De Volder in 1706, was the Leiden academic willing to accept Leibniz's dismissal of the reality of a corporeal substance.

As noted above, the origins of Leibniz's mature views on substance have elicited widely varying interpretations. This edition will not settle the debate, but in his long Introduction Lodge makes a valiant effort to spell out the significance of this correspondence, in which he discerns five distinctive phases. The first, consisting of the exchange between Leibniz and Bernoulli during the summer and autumn of 1698, anticipates many of the topics subsequently discussed between Leibniz and De Volder. In fact, Leibniz initiates the enquiry into the Cartesian definition of matter by pointing to its inability to account for the elasticity of material objects. In the next phase, Leibniz and De Volder discuss the measure of motive force, and after a prolonged and sometimes confusing exchange, De Volder appears to be willing to accept Leibniz's laws for measuring force. By the spring of 1700 the debate moved from Leibniz's dynamics to issues of metaphysics and epistemology. According to Lodge, this more technical episode of the correspondence mainly served Leibniz as a test: was De Volder up to his standards? Apparently the Leiden professor passed the test, but during the third phase, it looks as if the tables are turned: taking Leibniz up on his repeated claim that Descartes' notion of substance fails to accommodate its intrinsic activity, De Volder keeps asking in vain for an a priori demonstration by Leibniz that every substance is active. Leibniz was unable to supply such a demonstration, but instead went on to criticise De Volder's Cartesian concept of substance, after which Leibniz's own metaphysics takes centre stage. It has always been this particular moment that has drawn the attention of Leibniz scholars bent on tracing the emergence of his mature metaphysics, for La Monadologie would of course only appear in 1714, two years before the German philosopher passed away.
Leibniz, however, failed to win De Volder over to his position. During the fifth and final stage of their encounter, De Volder grew increasingly impatient with Leibniz's ontology, which allowed only for the existence of mindlike "monads". In January 1706, he terminated the correspondence.
In view of the many, mutual misunderstandings (e.g., on the nature of extension and the "entelechies" Leibniz introduced), beautifully elucidated by Lodge, it is indeed remarkable that De Volder did not do so much earlier. In a sense, this correspondence reads like the history of a massive failure, but this hardly diminishes its relevance, providing as it does a highly instructive insight into a fascinating episode from the heyday of Continental rationalism. Paul Lodge proves to be its ideal editor and translator.
7.3. Review by: Volker Peckhaus.
Mathematical Reviews MR3113323.

The volume under review provides a bilingual edition of the correspondence between Gottfried Wilhelm Leibniz and Burchard de Volder, a correspondence initially mediated by Leibniz's friend Johann Bernoulli. In sum, the editor publishes 67 letters of the correspondences between Leibniz and Bernoulli, Leibniz and de Volder, and Bernoulli and de Volder, written between 15 July 1698 and 19 January 1706.

The editor distinguishes five phases of these correspondences. The topics debated concern natural philosophy, in particular dynamics. They include the measure of motive force, in relation to the contemporary vis viva debate and Leibniz's controversy with Papin. Leibniz fails to solve de Volder's challenge for him when demanding an a priori demonstration for Leibniz's account of substantial activity. De Volder's notion of substance is discussed, the Cartesian thesis "that the material world is an entirely passive substance where nature is wholly constituted by the attribute of extension" (p. lx) and Leibniz's opposition towards the idea of a merely extended material world.

This volume of The Yale Leibniz follows the highest editorial standards. The correspondence between Leibniz and de Volder has recently been published in Volume II, of the Akademie edition (2013). Contrary to this edition, the volume under review does not aim at completeness in chronological order, but at a coherent and comprehensive selection of related texts, giving both the Latin original and a useful English translation. The editor of this volume provides an extensive introduction (101 pp.), with an analysis of the topics discussed and with further information on their historical and philosophical contexts. The appendix contains a catalogue of the Leibniz-de Volder-Bernoulli correspondence, notes and indices of names and subjects.

7.4. Review by: Nicholas Jolley.
Renaissance Quarterly 66 (3) (2013), 1056-1057.

In recent years few Leibniz texts have attracted more attention from scholars than his correspondence with De Volder, but we have had to wait until now for a satisfactory edition. The present volume, edited by Paul Lodge, is the latest contribution to the remarkable Yale series, which is helping to transform Anglo-American scholarship on Leibniz. Like other editors in the series, Lodge prints the original texts and English translations on facing pages; he has also gone back to the manuscripts and corrected Gerhardt's transcriptions where necessary. In one respect Lodge has gone beyond the call of editorial duty: he includes excerpts from the letters of the Swiss mathematician, Johann Bernoulli. It was Bernoulli who acted as an intellectual matchmaker between Leibniz and De Volder; he served to encourage the correspondence and he followed its progress with active interest.

Leibniz's letters to De Volder are best known for their exposition of the theory of monads, but this theory occupies only a relatively small part of the exchange. De Volder was a Dutch professor of mathematics and philosophy who had become disenchanted with Cartesian physics and metaphysics; he sought help from Leibniz with such issues as the measurement of force and the origin of motion in the universe. De Volder was particularly keen for Leibniz to provide him with an a priori demonstration of the activity of substance. Yet all he really received from Leibniz was an indirect proof in the form of an argument by elimination: either the scholastic theory of influx or Malebranche's occasionalism or Leibniz's own doctrine of the pre-established harmony according to which substances are sources of activity. It is no wonder that De Volder expressed disappointment with Leibniz's replies in a letter that Bernoulli indiscreetly, and perhaps improperly, forwarded to Leibniz himself. It is clear, too, that De Volder took fright when Leibniz began to expound the theory of monads; De Volder confessed to finding it obscure and he may indeed have found it incredible. As a result of his frustration with Leibniz's explanations De Volder effectively terminated the correspondence in 1706.

The failure of the correspondence to satisfy De Volder is one of the themes that Lodge emphasises in his long and substantial introduction. Lodge is a thoroughly authoritative guide to the content of the correspondence; he is equally at home in discussing technical issues in physics concerning the measurement of force and the current scholarly disputes over the interpretation of Leibniz's theory of monads. If there is a criticism to be made, it is that Lodge does not adequately address the phenomenalist interpretation of bodies for which the correspondence provides some support. There are passages in which Leibniz seems to anticipate a Berkeleian analysis of bodies as harmonised sets of the contents of perceptual states. Thus Leibniz tells De Volder that "matter and motion are ... the phenomena of perceivers, the reality of which is located in the harmony of perceivers with themselves at (different) times and with other perceivers" (307).

Lodge is to be congratulated not just on his textual work and his authoritative introduction, but also on undertaking the huge task of translating the correspondence in its entirety. Lodge's translations achieve a high standard of accuracy; the only mistake I noted was the occasional rendering of volo and its cognates as "want" in contexts where "hold" is the correct translation. Although they are generally accurate, the translations are sometimes a little stiff and prone to archaism. Thus De Volder is made to exclaim to Bernoulli: "Would that it had pleased the illustrious gentleman to enrich the Republic of Letters with his thoughts on these matters" (23). This kind of optative construction sounds awkward in modern English. It also seems strange to translate vale as "goodbye" at the end of a letter; since vale expresses a concern for a person's health, "with best wishes" would be more appropriate.

But it would be churlish to end on a note of criticism in the face of all that Lodge has accomplished. The volume indeed is a splendid and worthy addition to a major scholarly project; it will enable Anglo-American commentators to write with much greater authority about a series of texts that have come to occupy a central place in Leibniz scholarship.

7.5. Review by: Stephen Puryea.
https://philpapers.org/archive/PURTLV.pdf

In 1698 a young Johann Bernoulli, then professor of mathematics at the University of Groningen, paid a visit to the city of Leiden, whereupon he had the good fortune to meet the prominent natural philosopher Burcher De Volder. Among the topics they discussed during their frequent meetings over lunch and at the homes of other professors from the local university was a controversy that had been brewing by then for several years. The dispute, now known as the vis viva controversy, began with the appearance of Leibniz's "Brevis Demonstratio Erroris memorabilis Cartesii" in the March 1686 issue of Acta Eruditorum. In this brief essay, Leibniz challenged the view of Descartes and his followers that a body's "motive force" (vis motrix), that is, the force which moves it, equals its "quantity of motion" and thus varies as the product of the body's size or bulk and its speed (roughly, mv). By way of a clever counterexample, Leibniz purported to show that a body's motive force does not always track its quantity of motion but instead tracks the quantity of the effect its force is capable of producing, a quantity which was known to vary as the product of the body's bulk and the square of its speed (roughly, mv²). He thereby sparked a lively series of exchanges between himself and the Cartesians Abbé Catelan and Denis Papin, who stood fast in defending the received view.

De Volder, it turned out, harboured some sympathy for the Cartesian view, as indeed Bernoulli himself once had. But Bernoulli had since been convinced by his friend Leibniz to switch sides. Accordingly, when he learned of De Volder's Cartesian sympathies during his visit to Leiden, Bernoulli offered to share with him the relevant excerpts of his correspondence with Leibniz in the hopes that the arguments which won him over to Leibniz's point of view might also persuade De Volder. Unfortunately for Bernoulli, the task of persuading De Volder proved more difficult than perhaps he had initially hoped, and by the end of that year he decided it might be best to put De Volder directly in touch with the great philosopher. In turn, he enticed Leibniz to participate with the suggestion that such a correspondence might bear great fruit:

Since he [i.e., De Volder] has admitted to me that he has long since abandoned the principles of Cartesianism as inadequate and mostly false, there is no doubt that once he properly understood your philosophy and imbibed it, he would propagate it diligently and impress it upon his students (of which he always has an extraordinary number) in such a way that perhaps it might soon have dominion over the Cartesian and Aristotelian philosophies, as if reconciling the ancients and the moderns. I ask you again and again whether you are willing to consider the world of philosophy worthy of this. I beg you to consider us and posterity, and erect a memorial to your name. After all, do you think you are inferior to Descartes? (25-27)

Shortly thereafter, in December of 1698, Leibniz addressed himself directly to De Volder and the two began a wide-ranging correspondence, mediated throughout by Bernoulli, that would last some seven years and become one of our richest sources of insight into Leibniz's mature philosophy.

Paul Lodge's excellent new contribution to the Yale Leibniz series collects together the entirety of the Leibniz-De Volder correspondence, totalling some thirty-three letters, together with a generous selection of relevant excerpts from Leibniz's concurrent correspondence with Bernoulli, which Lodge has helpfully interspersed throughout. As with previous volumes in the series, the texts appear in the original language, in this case Latin, together with an English translation on opposing pages. Lodge's transcriptions reflect his careful study of all the available manuscripts and represent a significant improvement over the existing versions in GP II (Leibniz-De Volder) and GM III (Leibniz-Bernoulli). Rounding out the volume are a long introduction (79 pp.), itself a valuable contribution to Leibniz scholarship, together with extensive notes on the texts, a bibliography, and indexes for names and subjects.

Lodge plausibly suggests that these intertwining correspondences may be divided into five phases. The first (Letters 1-7) comprises a series of letters exchanged between Leibniz and Bernoulli in the months leading up to the beginning of the correspondence with De Volder. In these letters Bernoulli relates De Volder's concerns about Leibniz's view and Leibniz offers some initial reactions. The second phase (Letters 8-34) then sees De Volder enter the fray as he debates the proper measure of motive force with both Leibniz and Bernoulli. This phase, the longest of the five, draws to a close shortly after De Volder appears to concede in Letter 33 (5 April 1700) that Leibniz's measure is indeed the correct one, though ironically De Volder relates that it was an argument of Bernoulli's rather than one of Leibniz's that finally convinced him.

In March of 1694, Leibniz had published another brief essay in Acta Eruditorum, "De primae philosophiae Emendatione, et de Notione Substantiae". De Volder had read this essay and was particularly intrigued by Leibniz's contention that substances are essentially active. If it were possible to produce an a priori proof of this thesis, De Volder thought, this would be a remarkable result; for as he related to Bernoulli, such a proof would be in his eyes a "most fruitful source of truth" and a key to resolving not only his worries but also "those difficulties that have burdened every natural philosopher up until now" (21). In many of his letters to Leibniz, therefore, De Volder pressed the philosopher for such a proof, though to little avail. At one point Leibniz did offer what he described as a "first attempt at a proof" (161), which he sent more than anything as a gesture intended to show De Volder that his requests were not being ignored. In essence, the proof was this: The changes a substance undergoes must be caused; but they cannot be caused by other substances, since such an influence is inexplicable; nor can they be caused by God, since that would be an unreasonable hypothesis; hence, each substance must be intrinsically active. Judging from his response, De Volder was not impressed. From his perspective, Leibniz's entirely reasonable dismissal of occasionalism rested on a posteriori considerations, whereas he was seeking an a priori demonstration of the intrinsic activity of substance "from the notion of substance itself" (169). In his next letter, De Volder continued to press Leibniz for the a priori demonstration. Meanwhile, Leibniz was well aware that he was not in possession of any such demonstration, and indeed he confided as much to Bernoulli (161). But for whatever reason, he hesitated to admit this to De Volder, and so the dance continued.

In his reply to the request for a demonstration from the notion of substance itself, Leibniz observed that "we must first establish a notion of substance and agree upon it" (181). Instead of using this as an opportunity to advance and defend his own definition of substance, however, Leibniz decided to turn the tables on De Volder and ask for his definition instead. In his next letter, De Volder was happy to oblige. In keeping with a familiar tradition, he maintained that substance is that which can be conceived separately, or equivalently, that which exists through itself, i.e., independently of all other created things (187-189); and in good Cartesian fashion, he suggested extension as an example of something which satisfied this definition. This raised Leibniz's hackles and set the agenda for the third phase of the correspondence (Letters 35-47), as he pressed several lines of criticism in an unsuccessful bid to liberate De Volder from these opinions.

In the fourth phase of the correspondence (Letters 48-58), De Volder managed to turn the tables back on Leibniz. To this point Leibniz had largely avoided discussion of his own metaphysical system, perhaps for fear that it would be judged too radical. But this would change in the fall of 1702, when De Volder received from Leibniz a copy of his "Réponse aux réflexions contenues dans la seconde edition du Dictionnaire critique de M Bayle". De Volder took this opportunity to shift the focus of discussion to Leibniz's views on substance, force, body, and other allied topics. Over the remainder of the fourth phase, De Volder continued to press Leibniz for clarifications of his view, and Leibniz did his best to explain and defend his views. In this, however, he met with limited success, and eventually the philosopher's patience began to wear thin. Though his tone had been consistently polite up to this point, it took a turn for the worse in his letter to De Volder of 21 January 1704 (Letter 55), as we can see from this excerpt:

You speak as if you do not understand what I mean when I say that derivative forces are mere modifications, and that the active cannot be a modification of the passive. So do you not understand what modification means, or active, or passive? In the meantime, finding I know not what obscurity in my argument, you have touched on what I said so cursorily that you even attribute to me things that I did not say or, rather, the opposite of what is said. You maintain that I deny that derivative forces are active But in fact, I am so far from denying that they are active that from the fact that they are active and, nonetheless, modifications, I conclude that there is some primitive active thing of which they are modifications. (287)

After not hearing from De Volder for several months, Leibniz wrote to Bernoulli in May of 1704 (Letter 57): "Perhaps Mr De Volder has taken some offense at some of the things I may have said too freely because he seems to have been writing without paying enough attention and to have shown himself to be insufficiently teachable. This has made me fear that we may be debating in vain" (293-295). After some prompting from Bernoulli, De Volder did eventually reply to Leibniz. But Leibniz was right to suspect that De Volder had taken offense; for De Volder replied thus to Bernoulli: "You ask why I have been silent so long. It is because I was unsure whether I should reply to the illustrious Leibniz at all. For his last letter contains some things that convince me that he does not like to be contradicted, as is the way with great men. I would not want to do anything that might displease him, especially since I do not expect very great fruit from this debate of ours" (299). With renewed politeness, Leibniz and De Volder continued to correspond for another twenty months, this being the fifth and final phase of the correspondence (Letters 59-67). But the discussion progressed little and De Volder eventually lost the will to continue.

Lodge's edition of this correspondence will no doubt prove immensely valuable to Leibniz scholars and indeed anyone with an interest in this episode in the histories of philosophy and science. Among its many merits, I would like to call special attention to three. First, though in this respect it will one day be superseded by future volumes in the Akademie series, it is now the most accurate available edition of the Leibniz-De Volder correspondence and the directly relevant portions of the Leibniz-Bernoulli correspondence. Second, this volume goes a long way toward making these valuable correspondences more accessible. Up till now, only a selection of Leibniz's letters to De Volder and one of his letters to Bernoulli, and indeed none of De Volder's or Bernoulli's replies to Leibniz, had appeared in English. Thanks to Lodge's skill and hard work, Anglophones who are not expert Latinists will now have access to the full range of this material. Finally, the excerpts from the Leibniz-Bernoulli correspondence included in this volume are tremendously helpful for following and understanding the main debate. The decision to include them was a wise one. For all these reasons and more, Lodge should be applauded for producing this superb resource.

8.1. Abstract.

This book offers a general introduction to the geometrical studies of Gottfried Wilhelm Leibniz and his mathematical epistemology. In particular, it focuses on his theory of parallel lines and his attempts to prove the famous Parallel Postulate. Furthermore it explains the role that Leibniz's work played in the development of non-Euclidean geometry. The first part is an overview of his epistemology of geometry and a few of his geometrical findings, which puts them in the context of the 17th-century studies on the foundations of geometry. It also provides a detailed mathematical and philosophical commentary on his writings on the theory of parallels, and discusses how they were received in the 18th century as well as their relevance for the non-Euclidean revolution in mathematics. The second part offers a collection of Leibniz's essays on the theory of parallels and an English translation of them. While a few of these papers have already been published (in Latin) in the standard Leibniz editions, most of them are transcribed from Leibniz's manuscripts written in Hannover, and published here for the first time. The book provides new material on the history of non-Euclidean geometry, stressing the previously neglected role of Leibniz in these developments.

8.2. From the Preface.

In this book, I provide an edition of Leibniz' writings on the theory of parallels, which include several attempts to prove the Parallel Postulate. A few of these papers were published by Leibniz himself in his lifetime, while others were only printed in modern editions of his mathematical works. The most important essays, however, were still unpublished, and I have transcribed them from the Leibnizian manuscripts in the Niedersächsische Landesbibliothek in Hannover. Given the enormous amount of Leibnizian papers preserved in the Leibniz-Archiv, I cannot claim to have found all the relevant material, and to have a complete picture of Leibniz' endeavours in this direction we have to wait for the publication of the related volumes by the Academy Edition of Leibniz' Werke; since however the scholars at the Leibniz-Archiv have just begun the first surveys of Leibniz' geometrical writings after 1676, it is likely that a full edition will require many years. In any case, I am confident that the present collection of papers on the theory of parallels is comprehensive enough to give a quite good idea of Leibniz' work in this field.

Most of the texts presented here are sections and paragraphs of longer essays on the foundations of geometry, while a few others are self-contained notes and remarks on the Parallel Postulate that Leibniz penned from time to time. Given the highly fragmentary character of these drafts and private notes, their meaning and significance may easily be missed and reading them requires a careful study of Leibniz' intellectual development and environment. To this end, I introduce them with an essay commenting the most relevant passages and outcomes, while dealing with the history of the attempts to prove the Parallel Postulate at the time of Leibniz, the main epistemological tenets of Leibniz' philosophy of geometry, and the historical reception of Leibniz' ideas on the subject. On the one hand, my introductory essay is strictly related to my previous book Geometry and Monadology, published in this Birkhäuser series in 2007; and while the latter book dealt with Leibniz' philosophy of space and metaphysical foundations of geometry, the present essay complements those researches expounding Leibniz' geometrical epistemology (albeit from a very specific perspective). On the other hand, this volume may also be read in connection with my commented editions of Saccheri and Lambert on the theory of parallel lines (both published by Birkhäuser), and the three books together offer a comprehensive account of the prehistory of non-Euclidean geometry in the eighteenth century.

I would like to thank the Leibniz-Archiv and the Niedersächsische Landesbibliothek for allowing me to read, transcribe and publish Leibniz' manuscripts on the theory of parallels. My deepest gratitude goes to Siegmund Probst, whose help in finding and deciphering Leibniz' papers was invaluable for the present edition.

I began to work on Leibniz' theory of parallels in 2009, while I was Alexander von Humboldt Fellow at the Technische Universität Berlin. I would like to thank the Alexander von Humboldt Stiftung for financial support, and my generous host in Berlin, Eberhard Knobloch, who also carefully read and commented on the first draft of this book. His suggestions and advice saved me from several mistakes and considerably enhanced the final version. I am also very grateful to Richard Arthur, Gideon Freudenthal, Mattia Mantovani, and Victor Pambuccian, whose illuminating remarks on further drafts of the volume were crucial to my understanding of several passages.

My studies were presented and discussed in a few seminars from 2010 onwards, in Paris, Hannover, Pisa, Urbino, Leipzig, Ghent, and Princeton, and I am grateful to all the participants who helped me in understanding Leibniz' mathematics and epistemology; in particular, I mention here Herbert Breger, Daniel Garber, Tal Glezer, Pierluigi Graziani, Jürgen Jost, Massimo Mugnai, Enrico Pasini, Francesco Piro, and David Rabouin, whose comments and remarks substantially improved the present study.

Finally, I would like to thank Fred Sengmueller and James Garahan for a linguistic revision of the manuscript, David Merry for having helped me with the translation of Leibniz' texts, and Chiara Fabbrizi for the general editing.

This book is dedicated to my mother Laura, whose unfailing care made everything possible.

8.3. Review by: Victor V Pambuccian.
Mathematical Reviews MR3468016.

In a departure from standard histories of non-Euclidean geometry, which list the attempts at proofs of the Parallel Postulate while finding little value in them - the most comprehensive anthology of them being [J-C Pont, L'aventure des parallèles, 1986] - Vincenzo De Risi has set out to take seriously three figures involved in such attempts and to devote a book-length study to each of them. The figures are Saccheri, Leibniz, and Lambert, and this is the second part of that trilogy, following his study of G G Saccheri [Euclid vindicated from every blemish, edited and annotated by Vincenzo De Risi, translated from the Latin by G B Halsted and L Allegri, 2014].

The choice of Leibniz may appear, at first, to be an unusual one, for he never published anything on the Parallel Postulate. On the other hand, the biggest roadblock on the path to an adequate solution of the problems raised by the Parallel Postulate lay in the foggy notions of axiom and of the geometric project itself. It is in this sense that Leibniz's thought, for which no less than Gödel had only words of praise, on the issues deserves attention.

In his concern to make the geometry of Euclid amenable to his logicist programme, to do away with diagrammatic reasoning, and to make proofs correspond to his own standards of rigour, Leibniz came up with (i) an analysis situs, based on the concept of distance, in which the Pasch axiom is stated (in an essay from 1679); (ii) a theory of definition, that was meant to lead, by a conceptual analysis of the notions occurring in geometry, to dispensing with the axioms (as they would become provable once their concepts were rigorously defined); (iii) in connection with a special type of definitions, the essential ones, a symbolism to express them in, a characteristica geometrica; (iv) a new understanding of geometry as the science of space, which is a narrative regarding situations (i.e., relations between objects); (v) the spatium absolutum, "the ground of the possibility of all the other geometrical figures" (p. 44).

Given the fact that Leibniz didn't publish anything on this subject and that some of the fragments dealing with the Parallel Postulate were published only in 1858 and then didn't have much of an impact, these fragments have played no role in the history of the attempts to prove the Parallel Postulate or the birth of non-Euclidean geometry. He himself had to admit in 1712, after more than thirty years had passed from his first attempt to prove the Parallel Postulate, that he had "attempted much, but proved nothing" (p. 4).

This very well-written book is organised into six chapters. The first one describes the state of knowledge on parallel lines in Leibniz's time, the second one dwells on his epistemology (dealing with (i)-(v) and much more), the fourth one analyses in great detail each of Leibniz's attempts to prove the Parallel Postulate, the fifth one is devoted to the reception and legacy of Leibniz's attempts, and the sixth one presents the original Latin and the English translation of all fragments dealing with parallel lines in Leibniz's Nachlass.

9.1. From the Publisher.

Leibniz published the Dissertation on Combinatorial Art in 1666. This book contains the seeds of Leibniz's mature thought, as well as many of the mathematical ideas that he would go on to further develop after the invention of the calculus. It is in the Dissertation, for instance, that we find the project for the construction of a logical calculus clearly expressed for the first time. The idea of encoding terms and propositions by means of numbers, later developed by Kurt Gödel, also appears in this work. In this text, furthermore, Leibniz conceives the possibility of constituting a universal language or universal characteristic, a project that he would pursue for the rest of his life. Mugnai, van Ruler, and Wilson present the first full English translation of the Dissertation, complete with a critical introduction and a comprehensive commentary.

9.2. From the Preface.

History is bound to cherish the youthful work of a later genius, especially if its themes anticipate those of masterpieces to come. In the case of Leibniz's Dissertatio de arte combinatoria (1666), however, scholarship has been curiously reserved in dealing with this particular travail de jeunesse. Although studies by such eminent Leibniz specialists as Louis Couturat (1868-1914), Karl Dürr (1875-1928), and Eberhard Knobloch have added much to the interpretation of Leibniz's first publication in print, a critical edition of the Dissertatio has thus far been wanting, no doubt due to its arduous phrasing, its wide-ranging subject matter, as well as its complex overall theme.

All of these factors make Leibniz's De arte combinatoria (henceforth DAC) a text that is not easy to edit. Working on the present edition, moreover, the editors came across many further obscurities complicating an annotated rendition of the work. Its mix of languages and subject matters is only a minor hurdle in comparison to the strenuous way in which Leibniz at times gives expression to the ideas contained in it, which, for instance, may include descriptions in Latin of complex mathematical operations. Another problem encountered was to find the many texts by authors cited in the DAC, a difficulty that was enhanced by Leibniz's recurrent habit of quoting authors indirectly - and on occasion incorrectly.

The wealth of materials in De arte combinatoria and the dense argumentation it contains did not impede Martin Wilson to work on an English translation of the text over a period of many years, until he finally suggested to prepare it for publication in the wake of the appearance of Arnold Geulincx's Ethics in 2006, a project on which he and Han van Ruler had been working together. Finding numerous puzzling details in Leibniz's text and a multitude of references unaccounted for in the extant secondary literature, it would take Martin Wilson and Han van Ruler some further years of textual and bibliographical investigations to come up with a reasonably reliable translation. At this point, Massimo Mugnai joined Martin and Han and the project began to take the shape of an edition aiming not only to satisfy the requirements of the inner circle of Leibniz's scholars but a larger spectrum of readers interested in Leibniz's philosophy and the origins of the combinatorial calculus in general. This implied not only the obvious task of preparing an intelligible translation of the DAC, but even that of explaining the many difficult passages of the text. As a corollary to this task, it became indispensable to find all writings and authors mentioned by Leibniz, some of them very obscure or almost unknown, and to equip the text with a rich apparatus of footnotes.

Thus, the annotated translation that lies before you is the product of a collective enterprise in which Martin Wilson has been the principal translator of Leibniz's text. Massimo Mugnai and Han van Ruler have revised and edited the translation to produce the text as it now stands, and jointly contributed to its annotation. Han has taken care of the largest part of the footnotes, whereas Massimo, besides preparing the Latin version of the DAC here included, has provided the main text with an Introduction, aiming to situate in its historical context this early work of Leibniz and to present the main results contained in it.

In the process of the collaborative work on the project, Martin Wilson was sadly found missing for a period, due to a stroke he suffered on 1 March, 2011. Though quickly regaining most of his colourful personality, Martin has not been able to fully recover. The editors would like to express their gratitude to Astley Nursing Home in Worcestershire, England, for the care they have given Martin ever since, as well as to Barry Sweeting, who has been acting as Martin's representative and became a good friend.

The editors are also grateful to Matthias Armgardt, Albrecht Heeffer, Franco Montanari, Jan Papy, Horst Pfefferl, Wolfgang Schlosser, and Andrew Weeks for their helpful comments on some questions of detail. Richard Arthur, Vincenzo De Risi, Enrico Giusti, Enrico Pasini, and Monica Ugaglia have read a first draft of the Introduction, finding mistakes and kindly suggesting amendments. A special word of thanks is due to Mariano Giaquinta and Eberhard Knobloch for their generous advice on many technical questions.

Working on the annotation of the DAC during years in which there has been a stupendous increase in the number of electronic sources available online, Han van Ruler was nonetheless pleased to be helped by the cooperative staff of a huge number of libraries still important for their treasures - Leiden University Library, the Herzog August Bibliothek Wolfenbüttel, the British Library, and the Bibliothèque Nationale de France in particular. Besides expressing his debt to the staff of these and many other libraries, he also wishes to thank Atsuko Fukuoka, Iqbal Faridi, and Peter Guttner, as well as Patrick Masereel and Vincent de Keijzer for their hospitality in Wolfenbüttel, London, and Paris over the years.

Finally, the editors are grateful to Maria Rosa Antognazza and Paolo Mancosu for their constant encouragement and to Peter Momtchiloff of Oxford University Press, whose confidence and dedication have given an enormous spurt to the realisation of this long-term project.

9.3. Extract from the Introduction.

Leibniz was twenty years old when the Dissertation on Combinatorial Art (henceforth DAC) was first published. As he would later write: "the booklet was composed when the author was still young, in the year 1665, and was edited at Leipzig in the year 1666". The work expanded the text of a dissertation he had defended earlier that same year at the Leipzig Faculty of Philosophy, aiming for a university position. This first embryonic form of the Dissertation was entitled Disputatio Arithmetica de complexionibus ('Arithmetical Disputation on Complexions') and contained the first part of the 1666 work, from Cum Deo ("With God's Help") through to the end of section 8 of the first problem.

At the time, Leibniz was not particularly well trained in mathematics, as he was to admit later on the occasion of a re-edition of the DAC. When, indeed, the DAC was published again without the author's permission by the Frankfurt book dealer Cröker in 1690, this provoked a reaction on Leibniz's part, who wrote a short notice in the Acta Eruditorum. As he writes there, the booklet was "not sufficiently polished" and no longer agreed with the ideas he held "at present" (1691). Moreover, the book left something to be desired:

... some problems concerning numbers could have been solved in a far better way and the solutions are susceptible of more accurate proofs. At the time, indeed, [the author] had only a vague idea of higher mathematics and thus, unaware of the discoveries of others and not sufficiently acquainted with mathematical analysis, he was able to produce something of his own on the basis of a hasty reflection ...

Despite this, however, Leibniz also notes that "the booklet" contains "many new meditations" that he does not regret, concerning the "art of discovery" (ars inveniendi) and the "excellent" idea of an alphabet of human thoughts.

The 'art of discovery' and the alphabet of human thoughts are two issues strongly connected with one another. They both pertain to the discipline of logic, for which Leibniz manifested a genuine interest from an early age onwards. According to an autobiographical passage included in a text probably written in the year 1682, Leibniz, when he was "not yet twelve", was filling "sheets of paper with wonderful meditations about logic, attempting to overcome the subtleties of the scholastics." In the same vein, in a text composed during the years 1683-1685, he writes:

As a boy I learned logic, and having already developed the habit of digging more deeply into the reasons for what I was taught, I raised the following question with my teachers. Seeing that there are categories for the simple terms by which concepts are ordered, why should there not also be categories for complex terms, by which truths may be ordered? I was then unaware that geometricians do this very thing when they demonstrate and order propositions according to their dependence upon each other. It seemed to me however that this could be achieved universally if we first had the true categories for simple terms and if, to obtain these, we set up something new in the nature of an alphabet of thoughts, or a catalogue of the highest genera or of those we assume to be highest, such as a, b, c, d, e, f, out of whose combination inferior concepts may be formed.

Later on, the idea of building an 'alphabet of thoughts' evolved into a very complex project, which remained a central topic among Leibniz's philosophical interests until the end of his life: the composition of a 'universal characteristic', or 'characteristic art' (ars characteristica).

...

9.4. Review by: Athanase Papadopoulos.
Mathematical Reviews MR4229141.

This is the first complete English edition of Leibniz's Dissertatio de arte combinatoria (Dissertation on combinatorial art), a work often referred to in simplified form as De arte combinatoria (On combinatorial art). It is one of Leibniz' early contributions (he was not yet 20 years old when he wrote it). It constitutes a dissertation which he submitted to the faculty of philosophy at the University of Leipzig for a position there, published with a slight revision, in 1666. At that time, Leibniz had not formally begun his studies of mathematics. It was only later, during his stay in Paris (1672@-1676), and his meeting with Huygens there, that Leibniz became truly involved in mathematics. Despite his young age at the time that he wrote the De arte combinatoria, Leibniz had a serious knowledge of logic and metaphysics, and the idea of a universal language based on mathematics already was for him a subject of thorough investigation. Indeed, since his younger years, Leibniz had been preoccupied with the development of something he referred to later on as a "rational language", or "universal language", or "universal art", or "characteristica universalis"; in any case, it was the idea of a universal language, suitable for a "meta-science" encoding all the concepts of knowledge, in which mathematics and logic would play a prominent role. This being said, the Dissertatio de arte combinatoria also contains a certain number of mathematical results, in particular on combinatorics (permutations, permutations with certain conditions, symmetrical arrangements, with applications), but also on algebra and number theory, and one can also find there ideas on the applications of these problems to logic and to the theory that in modern terms we call formal languages. The main part of the dissertation is properly philosophical; it is concerned with the analysis of thought and contains reflections on the "mathesis universalis", an important theme at that time and one that Leibniz was to work on later, related to the development of a unifying and very general science built on the model of mathematics.

The present edition of the De arte combinatoria includes an introduction of about 50 pages that gives an overview of the work and that situates it in Leibniz's later works. The text of the translation is accompanied by extensive footnotes.

For the benefit of non-Latin-speaking readers, this edition is an invaluable addition to the works of Leibniz translated into English. One should remember that only a small number of Leibniz's works have been translated into the vernacular (and Leibniz is not the only preeminent philosopher or scientist to whom this applies).

9.5. Review by: Eberhard Knobloch.
Studia Leibnitiana 51 (2) (2019), 272-274.

From autumn 1665, Leibniz worked on the longest of his early writings, which was published in Leipzig in 1666 under the baroque-length title Dissertatio de arte combinatoria, in qua ex arithmeticae fundamentis complicationum ac transpositionum doctrina novis praeceptis exstruitur; et usus ambarum per universum scientiarum orbem ostenditur; nova etiam artis meditandi, seu logicae inventionis semina sparguntur. Praefixa est synopsis totius tractatus, et additamenti loco demonstratio existentiae Dei, ad mathematicam certitudinem exacta. That is to say, A treatise on the art of combinatorial mathematics, in which the doctrine of combinations and permutations is established from the foundations of arithmetic through new rules, and the application of both to the entire field of science is shown; new seeds of the art of reflection or the logic of discovery are also sown. An overview of the entire treatise precedes it, and in lieu of an addendum, a mathematically rigorous proof of God's existence is presented. In 1690, an unauthorised reprint appeared in Frankfurt am Main, prompting Leibniz to comment on it in the Acta Eruditorum of 1691. Despite some shortcomings, it was and remained an important work for the author, already addressing several key ideas of his later, mature philosophy and science.

This bilingual, first Latin-English edition is therefore most welcome. The volume begins with an exceptionally knowledgeable and comprehensive 56-page introduction, consisting of sixteen sections: The Project for the Characteristic Art; Lullism in the 17th Century: The Art of Memory and First Steps Towards the Creation of an Encyclopaedia; The Project for the Creation of a Universal Language; Atomism and Perichoresis (the continuous relationship of everything to everything else by similarity or dissimilarity); Themes from the Dissertatio in Leibniz's Mature Philosophy; The First Two Problems and Their Solutions; The Application to Traditional Syllogistic; Individual Sentences and Some Syllogistic Rules; Classification of Syllogistic Modes; Useful and Useless, Valid and Invalid Modes, General Method of Finding Counterexamples; Influence of Wirth (Hospinianus), de la Ramée, and Thomasius; Use of Numbers for Encoding Concepts and Sentences; Finding All Possible Subjects and Predicates; The number of all valid syllogistic arguments with a given proposition as conclusion; some problems concerning permutations, the head of a set of permutations; atomism and mereology.

In this way, the three authors explain the cultural background against which Leibniz conceived the Dissertatio, clarify the structure of the work, give, where necessary, a modern formulation of the problems (e.g., p. 19), or reconstruct Leibniz's line of reasoning (e.g., p. 33). A few particularly important aspects should be highlighted.

Leibniz attempts to combine the atomistic perspective with an anti-materialist metaphysics. Among the essential themes he developed are the concept of blind thinking; the distinction between eternally true propositions and those based not on essence but on existence; a detailed and systematic treatment of the theory of the syllogism: he is probably the first to have made the finding of counterexamples a project.

Equally fundamental are his use of numbers to encode concepts, the plan for a universal language, to which he repeatedly returned, particularly in his extensive correspondence, and the plan to develop a logic of invention, an ars inveniendi, as he already emphasises in the title of the work. The discussion of combinations and permutations with a given head (caput), that is, a subset of elements that remain unchanged under different combinations or permutations, is original.

The Latin text on the left is matched on the right, in a reader-friendly manner, by a reliable and easily readable English translation. There, too, are the 304 footnotes included, which - referring to the English text - comment on the rich content, explain Latin expressions, and provide corrections where necessary.

An extensive bibliography and an index of names conclude this highly recommended volume.

10.1. From the Publisher.

Published in association with the British Society for the History of Philosophy

The aim of this series is to encourage and facilitate the study of all aspects of the history of philosophy, including the rediscovery of neglected elements and the exploration of new approaches to the subject. Texts are selected on the basis of their philosophical and historical significance and with a view to promoting the understanding of currently under-represented authors, philosophical traditions, and historical periods. They include new editions and translations of important yet less well-known works which are not widely available to an Anglophone readership. The series is sponsored by the British Society for the History of Philosophy (BSHP) and is managed by an editorial team elected by the Society. It reflects the Society's main mission and its strong commitment to broadening the canon.

In General Inquiries on the Analysis of Notions and Truths, Leibniz articulates for the first time his favourite solution to the problem of contingency and displays the main features of his logical calculus. Leibniz composed the work in 1686, the same year in which he began to correspond with Arnauld and wrote the Discourse on Metaphysics. General Inquiries supplements these contemporary entries in Leibniz's philosophical oeuvre and demonstrates the intimate connection that links Leibniz's philosophy with the attempt to create a new kind of logic.

This edition presents the text and translation of the General Inquiries along with an introduction and commentary. Given the composite structure of the text, where logic and metaphysics strongly intertwine, Mugnai's introduction falls into two sections, respectively dedicated to logic and metaphysics. The first section ('Logic') begins with a preliminary account of Leibniz's project for a universal characteristic and focuses on the relationships between rational grammar and logic, and discusses the general structure and the main ingredients of Leibniz's logical calculus. The second section ('Metaphysics') is centred on the problem of contingency, which occupied Leibniz until the end of his life. Mugnai provides an account of the problem, and details Leibniz's proposed solution, based on the concept of infinite analysis.

10.2. Extract from the Introduction.

Leibniz composed the General Inquiries on the Analysis of Notions and Truths [Generales inquisitiones de analysi notionum et veritatum] ('GI henceforth) during the year 1686, the same year in which he began to correspond with Arnauld and wrote the Discourse on Metaphysics. The correspondence with the philosopher and theologian Antoine Arnauld (1612-1694) constitutes one of the main sources for the study of Leibniz's philosophy, and the same holds for the Discourse, which offers a first systematic account of notions like those of complete concept of an individual, pre-established harmony between soul and body, and substantial form (something very similar to the 'monad' of Leibniz's mature philosophy).

The GI is a necessary supplement to the correspondence with Arnauld and the Discourse in so far as it develops a central topic of Leibniz's metaphysics and shows the intimate connection that links Leibniz's philosophy with the attempt to create a new kind of logic. It is in the GI, indeed, that Leibniz articulates for the first time his favourite solution to the problem of contingency, and it is in the GI that he displays the main features of his logical calculus.

At first glance, the GI gives the impression of a 'compact and coherent work: it begins with a fairly long introduction where several topics are discussed (philosophy of logic, metaphysics, and grammar), and then a list of paragraphs of various lengths follows, marked with numbers from 1 to 200. To the sequence of paragraphs, however, there is no corresponding systematic and coherent development of a logical calculus. It is only towards the end of the essay that Leibniz proposes a set of principles from which the theorems previously proved can be derived; and he attains this result without explicitly discussing the relationship of his final outcome with the other principles previously proposed: these simply survive in the body of the text as evidence of the steps that have evolved to produce the final outcome.

On at least two occasions he revives his old project of employing numbers to express propositions but then, after a while, he abandons this issue and abruptly begins to develop a different topic. As George Parkinson remarked, the GI is a difficult work 'in which Leibniz often seems to be groping his way. This, however, does not undermine the extraordinary value of the GI, which is very rewarding for everyone interested in logic, philosophy of logic, and metaphysics (besides Leibniz's thought). As Marko Malink and Anubav Vasudevan point out, the GI:

... does not take the form of a methodical presentation of an antecedently worked-out system of logic, but rather comprises a meandering series of investigations covering a wide range of topics. As a result, it can be difficult to discern the underlying currents of thought that shape the treatise amidst the varying terminology and conceptual frameworks adopted by Leibniz at different stages of its development.

Given this composite structure of the GI, in what follows I devote two sections to introduce each of the two main topics of this work: logic and metaphysics.

Section 2 ('Logic') begins with a preparatory account of Leibniz's project for a universal characteristic and focuses on the relationships between rational grammar and logic. Then, I will discuss the general structure and the main ingredients of Leibniz's logical calculus as presented in the GI.

Section 3 ('Metaphysics') is centred on the problem of contingency, which caused a lot of trouble for Leibniz from the beginning of his correspondence with Arnauld until the end of his life. I attempt to explain, first, the nature of this problem and then to show how Leibniz reckoned he had solved it: in the GI, indeed, we find, even though it is expressed in a tentative way, the core of his solution based on infinite analysis.

...

10.3. Review by: Volker Peckhaus.
Mathematical Reviews MR4517231.

This volume presents a new bilingual (Latin-English) translation of G W Leibniz's Generales inquisitiones de analysi notionum et veritatum (General inquiries on the analysis of notions and truths). This manuscript, written in 1686 but not published until 1903, contains the most comprehensive elaboration of Leibniz's logic. The translation is based on the definitive Berlin Academy edition (with some formal revisions concerning marginal notes and use-mention notation), carefully considering earlier translations.

The editor's introduction gives the context of this manuscript and highlights some important points. The editor discusses the role of rational grammar within Leibniz's program of a universal characteristic, elements of a relational logic, the connections between extensions and intensions of concepts related to their possible coincidence, the containment relation and substitutivity. Leibniz quantified judgments using indefinite letters to indicate particularity. The editor also considers one of the most interesting achievements of this text to be "the attempt to develop a logical calculus for both terms and propositions based on the logic of terms" (p. 22).

The main problem in the metaphysical passages is the relation between contingency and necessity, related to the problem of whether analytically true concepts can be contingent. The editor discusses Leibniz's two proposals for a solution, the first based on so-called "divine decrees", the second based on infinite analysis.

The editor adds a commentary for certain passages of the text, and indices. Overall this is an important edition that provides access to one of the most important texts in the history of modern logic.

10.4. Review by: Ricardo Barroso Batista.
Revista Portuguesa de Filosofia 78 (1/2) (2022), 599-602.

Fortunately for all scholars of Modern Philosophy, the British Society for the History of Philosophy (BSHP), in partnership with Oxford University Press, has published a bilingual edition of Leibniz's treatise "General Questions on the Analysis of Concepts and Truths" [Generales inquisitiones de analysi notionum et veritatum] ("QG"). Not only is this the first time this treatise has been published in a bilingual edition (Latin-English), but it is also the first time it has been fully annotated and accompanied by a critical analysis of its content. In this BSHP edition, unlike others from this association, the roles of editor, translator, commentator, and critic are all shared by the same person: Massimo Mugnai, an author who has published important studies on Leibnizian philosophy in recent years.

This treatise was written by Leibniz during the year 1686, curiously, the same year in which he began his correspondence with Arnauld and in which he wrote the Discourse on Metaphysics.

The original manuscript of the Quantum General, which has already been digitised, reveals the difficulty of its writing. It shows the use of different inks and pen nibs, several marginal notes, and many erasures - all clear evidence that Leibniz revised the text many times. Some paragraphs were even crossed out and completely rewritten in the margins. All this demonstrates that Leibniz pondered at length the content of the Quantum General, which is his most complete and explicit work dedicated to the project of constructing a new logic.
...
Without a doubt, this work, brought to light thanks to M Mugnai and the British Society for the History of Philosophy, was one of the most significant milestones in 2021, not only for all those who closely follow Leibnizian studies, but also for everyone else interested in the history of Modern Philosophy and the history of Philosophy in general.