Gottfried Wilhelm Leibniz

Library of Congress

[b. Leipzig (Germany), July 1, 1646, d. Hanover (Germany), November 14, 1716]

Leibniz is best known for having invented the calculus independently from Newton; much of the notation and vocabulary used today comes from Leibniz, who had a flair for both symbolism and language. He also took the first steps in symbolic logic. The calculating machine Leibniz invented was the first to multiply as well as add and subtract. In physics he contributed to developing the idea of kinetic energy.

Gottfried Wilhelm von Leibniz (1646-1716) was a German mathematician and philosopher. Known as a statesman to the general public of his own times and as a mathematician to his scholarly contemporaries, he was subsequently thought of primarily as a philosopher.

Gottfried Wilhelm von Leibniz was born in Leipzig on June 23, 1646. His father, who was professor of moral philosophy at the University of Leipzig, died in the boy's sixth year. As a result, his early education was somewhat haphazard, but through his own industry he was ready for the university at the age of 15. He pursued the course in law in preparation for a political career and also studied theology, mathematics, and the new natural philosophy of the Enlightenment, receiving his bachelor's degree in 1663.

After 3 years of further study at Leipzig, Leibniz transferred to the University of Altdorf, where he received his doctorate in law in 1667. He declined the offer of a professorship there and accepted instead a position in the service of the elector of Mainz.

Early Travels

At this time Louis XIV's aggressive activities were a serious threat to the German states, and in a pamphlet published in 1670 Leibniz proposed a defensive coalition of the northern European Protestant countries. At the same time, to give the German principalities, recently weakened by the Thirty Years War, a respite for economic recovery, he conceived a plan whereby Louis might gain Holland's valuable possessions in Asia by way of a "holy war" against non-Christian Egypt. Leibniz was invited to Paris to present his plan; although it was not adopted, his 4-year stay in the French capital, with visits to London in 1673 and 1676, was crucial for his intellectual development.

Before coming to Paris, Leibniz had devised a calculating machine based on the principles of an earlier one invented by Blaise Pascal but capable of performing much more complicated mathematical operations. His demonstrations of this machine before the Académie Royale des Sciences and the Royal Society of London aroused much interest and led to fruitful relations with members of these groups and to his election to membership in the Royal Society shortly after his first London visit.

Especially important as a stimulus to Leibniz's interest in mathematics was his contact in Paris with the Dutch mathematician Christiaan Huygens, which resulted in Leibniz's developing both the integral and the differential calculus during the years of his residence there.

In the Service of Brunswick

In 1676 Leibniz transferred his services to the house of Brunswick and moved to Hanover, which became his home and the seat of his activities for the remaining years of his life. He was sent on important diplomatic missions, with freedom to seek out leading scholars wherever he went; he received many honors, as well as a generous stipend, and had ample leisure for pursuing his own interests. Charged with the writing of a history of Brunswick from earliest times, he had access not only to the resources of the ducal library but also to the historical repositories of Germany and Italy.

In the history itself (which at his death he had completed to the year 1005) Leibniz brought geological data to bear for the first time on historical interpretation and made use of original documents in a thoroughly modern way. To his historical research was due also his dedication to the solving of political conflict by enlightened compromise. In a pamphlet of 1672 he had proposed an alliance of all the European powers against Turkey; now he sought a reunification of all Christians, not in war but in peace. Through correspondence with the French prelate Jacques Bossuet, he tried, by adducing historical evidence, to establish the reasonableness of Christian unity; but in this he was no more successful than in his earlier grandly conceived attempts at mediation of differences.

In 1678 Leibniz founded the Acta eruditorum, a journal for the publication of scholarly papers which gained wide circulation in Europe and in which, over the next 35 years, most of his own published writings appeared. In 1700 he was elected a member of the French Académie Royale. In the same year, upon his recommendation, the Akademie der Wissenschaften was founded at Berlin. He drew up its statutes, following the pattern of the French Académie and the Royal Society of London, and was its first president, retaining that position for the rest of his life. It was also through his influence that similar academies were established at Dresden, St. Petersburg, and Vienna.

Leibniz's disposition to moderation and tolerance fitted him well for his role as diplomat and for his position of leadership among European scholars. His enormous correspondence reflects the warmth and loyalty of many friends and supporters, among whom were a number of women. The philosopher-diplomat must have had an appeal for the new "learned woman" of his time. In several instances prominent women smoothed the way for Leibniz's contact with people who might otherwise have been difficult to access, helped him to promote interest in the founding of academies of science, and were responsible for his putting some aspects of his philosophy into simplified form for the general reader.

The last years of Leibniz's life were clouded by the controversy with Isaac Newton over the invention of the calculus, now considered to have been a case of independent discovery by two highly gifted minds. The unfortunate taking of sides and exchanges of accusations, the dragging on of the affair, kept alive for more than 10 years by bursts of partisanship on one side and then the other, the "findings" of a biased investigating commission, which exonerated Newton and failed to remove the charge of plagiarism against Leibniz, had serious and far-reaching effects on the development of science. The cutting off of free communication of ideas between the English scientists and those of the Continent was ironically to the detriment of the former: Leibniz's notation was more efficient than Newton's (it has since been generally adopted) and facilitated the great strides in mathematical physics made on the Continent during the next hundred years, in which the participation of English scientists was negligible.

For Leibniz himself, who had always been a proponent of free interchange among scholars, the whole procedure was a crushing offense. The final blow was the Duke of Brunswick's refusal to include him (as a controversial figure) in his entourage when, in 1714, he became England's George I.

When Leibniz died at Hanover 2 years later, on Nov. 14, 1716, his popularity with his own countrymen had waned with his declining court favor. His only worthy eulogy was composed on the first anniversary of his death by the French academician Bernard de Fontenelle; it was read before the meeting of Leibniz's colleagues in Paris and recorded in their archives.

Contribution to Philosophy

His voluminous notebooks indicate that during the years at Hanover Leibniz's thought was increasingly dominated by the development of a comprehensive cosmic philosophy. He composed no complete exposition of his philosophical theories, but to any of his correspondents who inquired about them he freely expounded phases of his "new system," and on three important occasions he took issue with exponents of differing views in extended polemical essays which brought out the essentials of his own philosophy.

In his Théodicé, written in reply to an attack upon his views in Pierre Bayle's Dictionnaire historique et critique (1699), Leibniz defines God as "infinite possibility" and the world (actuality) as "compossibility" in that it contains the greatest number of stimultaneous possibilities; it is therefore the best of all possible worlds. In defining "substance," he proceeds from the traditional postulate that all predicates are contained in their subjects, to the designation as substances of all words which can be used only as subjects.

In a criticism of John Locke's Essay on Human Understanding (1690) Leibniz refuted Locke's major premise that the senses are the source of all understanding by adding "except the understanding itself," distinguishing three levels of understanding: the self-conscious, the conscious, and the unconscious or subconscious. And in an essay known as the "Monadology," he more specifically defines the ultimate elements of the universe as individual precipient centers of possibility or force, which he calls "monads." Each unit perceives the universe from its own point of view and interprets what it perceives according to its own level of understanding, but there is no interaction or intercommunication among the units and therefore no operation of cause and effect.

In the famous exchange of letters (1715-1716) with Samuel Clarke, Leibniz describes space and time as merely systems of relationship or order, calling Newton's treatment of them as absolute entities a reversion to medieval notions.

Such ideas as these, characteristic of Leibniz's application of logic to the problems of metaphysics, found little response among the philosophers of his time, who were more receptive to the patterns of Locke's empiricism. But when Leibniz's Nouveaux essais sur l'entendement humain was finally published in 1765, Locke's influence was receding, and Leibniz's work became a major factor in the formation of the transcendental philosophy of Immanuel Kant.

Antecedents of Mathematical Logic

A striking aspect of Leibniz's thought was the recurring notion of a universal symbolic language. In 1666 he published an article entitled Dissertatio de arte combinatoria, with subtitle "General Method in Which All Truths of the Reason Are Reduced to a Kind of Calculation." This early work establishes the theme of the gigantic project which was Leibniz's lifelong goal. The project involved bringing together all knowledge in a single compendium, with each division of the arts and sciences reduced to its primary propositions and related to other subjects in such a way that any portion or desired fact could be extracted at will, and from which the whole body of human knowledge could be reconstructed. It would provide a tool for learning without a teacher and would point up areas in which further investigation was needed.

The most remarkable feature of the plan was the lingua characteristica, a system of symbols representing logical ideas which would constitute a universal language of reasoning and would facilitate thought in the same way that mathematical symbols facilitate calculation. In the Chinese ideogram, which represents a concept rather than a sound, Leibniz saw a possible model for his "alphabet of thoughts."

Although he was unable to bring to fruition either his grand design for an encyclopedia of knowledge or the symbolic language into which it was to be translated, Leibniz's ideas were embodied in the mathematical logic developed by George Boole and Giuseppe Peano in the 19th century and by Alfred North Whitehead and Bertrand Russell in the 20th, and these ideas foreshadowed modern cybernetics and computer theory.

His Influence

Leibniz's originality of mind left its mark on each of the many areas in which he was active. His detailed memoranda, covering the more than 40 years of his political career, constitute in themselves a major source for the history of this period. His contributions in the field of mathematics had forceful impact on the work of his contemporaries and immediate successors. His innovative ideas in political theory and philosophy, on the other hand, were not congenial to the thought of his times; in the 19th and 20th centuries, however, many of his theories have given rise to important developments in these and related fields, ranging from Freudian psychology to Einsteinian physics, and he is now recognized as one of the most fertile and profound intellects of the age of the Enlightenment.

Further Reading

Generous selections from Leibniz's writings are in Leibniz: Selections, translated by Philip P. Wiener (1951), and Gottfried Wilhelm von Leibniz: Philosophical Papers and Letters, translated with an introduction by Leroy E. Loemker (2 vols., 1969). There is no full-scale modern biography in English. John T. Merz, Leibniz, a 19th-century German biography, is available in an English translation (1948). For a general estimate of Leibniz and his work, Ruth L. Saw, Leibniz (1954), is useful, and Cornelius A. van Peursen, Leibniz (trans. 1969), is a perceptive short study. Bertrand Russell, A Critical Exposition of the Philosophy of Leibniz (1900; 2d ed. 1951), is a comprehensive interpretation. Still worth consulting is Herbert W. Carr, Leibniz (1929). For a more complete discussion of Leibniz in relation to his times than the histories of science and mathematics afford, Rudolf Meyer, Leibniz and the 17th Century Revolution (trans. 1952), is recommended.

Additional Sources

Aiton, E. J., Leibniz: a biography, Bristol; Boston: A. Hilger, 1985.

(1646-1716) German rationalist philosopher and mathematician. Born in Leipzig at the end of the Thirty Years War, Leibniz took a degree in law. He entered on a political and diplomatic career in 1666. This took him to the principal courts of Europe, from Paris to St Petersburg. There he met the learned men of the day. He was made a Fellow of the Royal Society. He and Newton arrived at the calculus independently. He held a debate by correspondence with Samuel Clarke on Newton's notion of space. His learned work was not isolated from his public; he wrote the Theodicy for the Queen of Prussia and the Monodology for Eugene of Savoy. He founded the Berlin Academy of Science. In Hanover he was in charge of the ducal library, from which his scientific and philosophical works have been abstracted with difficulty. (He turned down an offer to take charge of the Vatican Library.)

Leibniz was a practical rather than a theoretical political philosopher. Europe of his time was suffering the ravages of the Thirty Years War. The French had to be restrained in the interests of a united Europe if the Turks were to be constrained and ejected from their march westward. Standing in the way of unity were the religious divisions. Leibniz saw it as his task to bring about a reconciliation between the contending factions. To this end he wrote numerous treatises and letters on the subjects of contention—nature and grace, transubstantiation, and so forth. In these he tried to find a rational basis for discussion and, hopefully, for agreement. It can be argued that the whole of Leibniz's philosophy is designed to the same end, starting with the notion of the combinatory arts and proceeding to the notion of pre-established harmony, though the idea that these abstruse metaphysical notions would somehow mend the rift in Christendom is a testimony to Leibniz's optimism rather than a blueprint for religious and political harmony.

— Cyril Barrett

For more information on Freiherr (baron) Gottfried Wilhelm von Leibniz, visit Britannica.com.

Leibniz, Gottfried Wilhelm (1646-1716). Philosopher, whose work covers most fields of human knowledge and thought. Born in Leipzig, he went to France in 1672 on an unsuccessful diplomatic mission; having made intellectual contacts in Paris, he used French for many of his principal writings (Essais de théodicée, 1710, an answer to Bayle; Principes de la nature et de la grâce, 1714; Principes de la philosophie (Monadologie), 1714). Fontenelle pronounced his funeral éloge, but his great metaphysical system had a limited impact in 18th-c. France and his disciples were caricatured in Voltaire's Candide.

— Peter France

Leibniz, Gottfried Wilhelm von (Leipzig, 1646-1716, Hanover), philosopher, mathematician, and polymath, entered the service of the Electoral Archbishop of Mainz. In 1672 he visited Paris in order to persuade Louis XIV to campaign against the Turks in Egypt and so to divert him from plans of conquest in west Germany. After visiting London in 1673 and 1676, Leibniz was appointed librarian in Hanover to the Duke of Brunswick-Lüneburg, a position which he occupied for the remainder of his life.

Leibniz's many activities included diplomatic missions and the foundation in 1700 of the Sozietät der Wissenschaften (later Preußische Akademie der Wissenschaften, see Akademien), of which he was the first president. He invented the infinitesimal calculus independently of Newton and almost simultaneously. He participated in plans for reuniting the religious denominations of Western Christendom. His publications, which were in Latin or French, refer chiefly to mathematics, to history, and (in anonymous or pseudonymous tracts) to politics. Leibniz's principal published philosophical work is the Essais de Théodicée sur la Bonté de Dieu, la liberté de l'homme et l'origine du mal (1710). In this treatise he outlined an optimistic philosophy which explained evil in the world as necessary. The argument is briefly as follows. God alone is perfection. The world, God's creation, not being God, cannot be perfect. God in his goodness could not make any world but the least imperfect, so that this world is the best of the possible worlds (‘le meilleur des mondes possibles’), a conclusion which half a century later was mocked by Voltaire in Candide (1759). See also Theodizee.

Leibniz also advanced a theory on the composition of the universe, set out in his Monadologie for the benefit of Prince Eugene (see Eugen, Prinz), and published in German in 1720. The world is made up of monads (Monaden), and these simple entities group themselves into more complex monads to make up all that is animate and inanimate. This theory has been seen as an imaginative anticipation of later physics. Faced with the problem of spirit and matter, free will and deterministic (or mechanical) causation, Leibniz offers as solution the concept of a pre-established harmony (prästabilierte Harmonie), which he illustrates by the example of two clocks which keep perfect time. Their simultaneity can be accounted for by one of three assumptions: (1) they are connected mechanically; (2) someone is concealed in one clock moving the hands to keep time with the other; (3) both clocks have been made by so skilful a clockmaker that they perpetually keep the same time. The third solution (with God as clockmaker) is the right one. Leibniz, who had not only one of the greatest but also one of the most inquisitive minds, was never able in his ceaseless inquiries on the most diverse matters to take the time to set forth a coherent system. There exist the two treatises and a number of disconnected essays, a vast quantity of letters on scientific subjects, numerous unpublished papers and jottings, and it is virtually impossible, because of inherent contradictions, to arrive at a co-ordinated systematic conspectus. For this reason Leibniz's views have met with more divergent interpretation than those of most philosophers.

In spite of his intellectual stature, Leibniz had little direct influence in Germany. Christian Wolff of Halle University expounded systematically ideas which he derived from Leibniz, but he himself admitted that there was much in Leibniz's thought that he could not understand.

Die philosophischen Schriften (7 vols.), ed. C. I. Gerhardt, appeared 1875-90 (repr. 1960-1); Briefwechsel mit Christian Wolf, ed. C. I. Gerhardt, in 1860 (repr. 1963); Kleine Schriften zur Metaphysik, ed. H. H. Holz, in 1965, and Politische Schriften (2 vols.), ed. H. H. Holz, 1966-7. The historisch-kritische Ausgabe by the Deutsche Akademie der Wissenschaften (until 1945 Preußische Akademie), Sämtliche Schriften und Briefe (c.40 vols.) appeared 1923 ff.

Leibniz, Gottfried Wilhelm (1646-1716) German philosopher, mathematician, and polymath. Leibniz was born in Leipzig, where he attended university from the age of fifteen, and submitted a thesis for the degree of doctor of law at the age of twenty. In 1667 he entered the service of the Elector of Mainz, where he remained until 1672, engaged largely in political writing. He travelled to Paris in 1672, partly to try to persuade Louis XIV to expel the Turks from Egypt (thereby diverting his attention from Germany; the plan did not succeed). He visited England in 1673, and again in 1676, at which time he had completed his discovery of the differential calculus. In this year he travelled to Amsterdam and met Spinoza, and became librarian to the Duke of Brunswick at Hanover, a post he held until his death. Between 1680 and 1697 he was working on his own system of philosophy. Leibniz was the greatest polymath of modern philosophers, making contributions to mathematics, jurisprudence, and history, as well as philosophy. He corresponded extensively with all the major learned men of the time, and was the founder of the Academy of Berlin.

Leibniz's mature philosophical system is both intricate and strange, resting on a small number of highly general principles. The foundation of his thought is the conviction that to each individual there corresponds a complete notion, knowable only to God, from which is deducible all the properties possessed by the individual at each moment in its history. It is contingent that God actualizes the individual that meets such a concept, but his doing so is explicable by the principle of sufficient reason, whereby God had to actualize just that possibility in order for this to be the best of all possible worlds (the thesis subsequently lampooned by Voltaire in Candide). This deducibility of each of an individual's properties from its complete concept is due to there being an ontological correlate of the complete concept, or in other words a modification of the substance of an individual corresponding to each truth about it. In turn this connects with Leibniz's belief that relations, including causal relations between separate individuals, are only phenomena bene fundata, or constructions that the mind places upon what are at bottom monadic, non-relational facts. However, Leibniz was entirely hostile to 17th-century atomism, so that eventually the individuals of his mature system are the monads: non-physical individual unities, each ‘windowless’, or independent of other things, and each evolving in a way that is entirely dependent upon their intrinsic natures, but each capable of perceptions that in turn ‘express’ the nature of external reality. It is arguable that at this point Leibniz reverts to an Aristotelian conception of nature as essentially striving to actualize its potential. Naturally it is not easy in such a system to make room for space (which Leibniz considered to be relational), corporeal substance, matter (which again he thought of as a phenomenon bene fundatum), or free will. Along with those of Descartes and Spinoza, that of Leibniz's is the third of the great rationalist systems of the 17th century, and in many respects the most unusual. Leibniz's major works, none of which contains a finally developed account of his system, are Discourse of Metaphysics (1685); The New System (1695); Theodicy (1710); and Monadology (c. 1713). His correspondence with Arnauld, Jean Bernoulli, Burcher de Volder, Bartholemew des Bosses, and Clarke have been published in separate volumes, as has his controversy with Bayle, and the Nouveaux Essais which contain his reaction to Locke's Essay.

Leibnitz, Gottfried Wilhelm, Baron von (both: gôt'frēt vĭl'hĕlm bärôn' fan līp'nĭts) , 1646–1716, German philosopher and mathematician, b. Leipzig. Although known primarily as a philosopher, Leibniz's scholarship embraced the physical sciences, history, law, diplomacy, and logic. The recognition of his work in logic came quite late; manuscripts published in the 20th cent. mark him as the founder of symbolic logic.

Life

After studying at Leipzig, his native city, and at Jena, he became a doctor of law at Altdorf (1666). Constantly occupied with practical political concerns, Leibniz never accepted an academic position. He was (1666–73) in the diplomatic service of the elector of Mainz, who employed him on several political projects; one of these was a plan to persuade King Louis XIV of France to attack Egypt and thereby to divert his attention from Germany. While in Paris (1672–76) he came into contact with some of the foremost minds of Europe.

About that time he developed, independently of Newton, the infinitesimal calculus. Leibniz's calculus was published in 1684, three years before Newton's, and his system of notation was universally adopted. From 1676 he was employed by the duke of Brunswick-Lüneburg (later the elector of Hanover), whom he served as privy councillor, librarian, and historian. This association brought him close to the elector of Brandenburg (soon to be king of Prussia), who was persuaded by Leibniz to establish a scientific academy at Berlin. In 1700 he became its first president.

Important Philosophical Works

Most of Leibniz's philosophical writings are occasional pieces, addressed to various people. The two published in his lifetime were Essais de Théodicée sur la bonté de Dieu, la liberté de l'homme, et l'origine du mal (1710) and Monadology (1714). It was largely these works that influenced Christian von Wolff, whose popularization of the Leibnizian system became the standard academic philosophy in 18th-century Germany.

Leibniz's major philosophical work, Nouveaux Essais sur l'entendement humain (1704), contains the views of Leibniz on points raised in Locke's Essay Concerning Human Understanding. Because of Locke's death, however, it was not published until 1765. The publication of Nouveaux Essais in 1765 was important because it revealed for the first time the “true Leibniz” as opposed to the popularized version of Wolff, and it had a decisive effect on Immanuel Kant and the whole German Enlightenment.

Philosophy

Leibniz's philosophy is a consistent rationalism. The universe forms one context in which each occurrence can be seen in relation to every other. Since the universe is the result of a divine plan, Leibniz calls it the best of all possible worlds; for this he was satirized by Voltaire in Candide. Leibniz's assertion, however, does not imply an unqualified optimism, since evil is a necessary ingredient in even the best of all possible worlds. The ultimate constituents of the universe, in his view, are monads or simple substances, each of which represents the universe from a different point of view. Being simple, monads are immaterial and thus cannot act. Apparent interaction is explained in terms of the principle of preestablished harmony.

The principle of continuity as expressed in the phrase “nature makes no leaps” is another part of Leibniz's rationalism. The monads are arranged in an infinitely ascending scale, based on the distinctness with which each represents the universe. All monads have perception (consciousness), but only rational monads have apperception (self-consciousness). A basic distinction in Leibniz's logic is that made between “truths of reason,” or necessary propositions, whose principle is the law of noncontradiction, and “truths of fact,” or contingent propositions, based on the principle of sufficient reason. The principle has its root in the divine intellect, and its most important expression is his law of causality.

With the decline of interest in metaphysics in contemporary philosophy, recent studies have tended to emphasize Leibniz's significance in mathematics and logic. However, Leibniz's metaphysics have not been neglected but rather reinterpreted in light of his mathematical and logical works.

Bibliography

See Liebniz's political writings, ed. and tr. by P. Riley (1972); G. H. Parkinson, Logic and Reality in Leibniz's Metaphysics (1965); H. Ishiguro, Leibniz's Philosophy of Logic and Language (1972); G. M. Ross Leibniz (1984); S. Brown Leibniz (1985).

Leibniz, Gottfried Wilhelm (1646–1716), German philosopher, mathematician, physicist, historian, and diplomat. Gottfried Wilhelm Freiherr von Leibniz was born at the end of the Thirty Years' War in Leipzig, a Protestant university town in Germany, where his father was a professor. His father died when Leibniz was only six, but he inherited his library and his respect for intellectual pursuits and from an early age read widely in the Latin classics, history, Christian theology, and logic. His precocious eclecticism foreshadowed the course of his later life. The sixty thousand handwritten pages that he left behind at his death (now mostly housed in the Leibniz Archives in Hanover, Germany) cover an awesome range of topics, his mastery of each one of which is stamped by the erudition of a scholar and the originality of genius. His legacy includes the invention of the infinitesimal calculus and its application to mechanics via the study of differential equations and transcendental curves; a metaphysics that reconciles mechanistic science with the inviolable integrity of human awareness; a theory of knowledge based on analysis as a search for conditions of intelligibility and guided by a prescient appreciation of formal languages; a moral theory born of his experience as a diplomat that underwrites religious and cultural tolerance and decries tyranny; and a history of the House of Hanover, exemplary in its scholarly procedures, that deepens our understanding of the Middle Ages.

After an early academic post at the University of Altdorf, Leibniz decided in favor of the practical life as an advisor to princes: in 1667 he was called to the Catholic court of the Bishop Elector in Mainz, which led to his four wonderful years in Paris, 1672–1676; thereafter he served the dukes (then electors) of Hanover until his death, service punctuated by frequent voyages in Europe, the longest of which was a sojourn in Italy from 1687 to 1690. The sojourn in Paris changed his life, for there he met the Dutch physicist Christiaan Huygens (1629–1695), who introduced him to Descartes's geometry and the new algebra, and also made the acquaintance of Nicolas de Malebranche (1638–1715) and Antoine Arnauld (1612–1694). It is fair to say that between 1672 and 1676, Leibniz recapitulated the history of Western mathematics, for he came to Paris knowing only Euclid and left with the invention of the infinitesimal calculus, including the essential notational innovations of dx for the differential and ∫ for the integral, to his credit. The inaugural publication of his differential and integral calculus appeared in the journal Acta Eruditorum: "Nova Methodus pro Maximis et Minimis" (A new method for maxima and minima) in October 1684, and "De Geometria Recondita et Analysi Indivisibilium atque Infinitorum" (On a deeply hidden geometry and the analysis of indivisibles and infinites) in June 1686. Leibniz's discovery of the calculus in the 1670s occurred independently of Isaac Newton's (1642–1727) activity, though his later application of the theory of differential equations to planetary motion seems to have been directly inspired by Newton's Principia (1687). Johann (1667–1748) and Jakob (1654–1705) Bernoulli used Leibniz's ideas and notation to work out important problems in analysis and mechanics, which led in turn to the work of Leonhard Euler (1707–1783), Jean Le Rond d'Alembert (1717–1783), and Joseph-Louis Lagrange (1736–1813) in the eighteenth century.

In the same year, 1686, Leibniz composed his Discours de métaphysique (Discourse on metaphysics) and began his correspondence with the French Jansenist philosopher Antoine Arnauld, two works that display the metaphysical position of his middle years with special clarity. The Discourse on Metaphysics argues that we should make God's creation of the world our model in the employment of an ars inveniendi, though since we are finite, we must rest content with employing highly reductive formal languages ("characteristics") to investigate intelligible but infinite or infinitesimal things. Its scientific reflections are developed in the unpublished Dynamica (Dynamics) of 1689–1691, and "Specimen dynamicum" (A specimen of dynamics) published in 1695. The jurisprudential and political works written during Leibniz's maturity also urge that we take God's rational and charitable freedom as the model for our moral decisions, legal system, and the comportment of princes and parliaments. Voltaire could never have satirized Leibniz's philosophical views as naïve in his novel Candide (1759) if he had read and taken to heart the essay "Mars Christianissimus" (1683; Most Christian war god), where Leibniz attacks the aggression and autocracy of Louis XIV, then king of France, with the eloquent fury of a seasoned diplomat whose dearest wish was to see Europe reunited as a pacific confederacy. Leibniz was also one of a handful of seventeenth-century European intellectuals to entertain seriously the learning of China and to argue that Europe might profit from cultural exchange with the great Eastern empire. His later metaphysics, oriented more toward theology than science or politics, is summarized in short unpublished works written in 1714, "Principes de la nature et de la grâce, fondés en raison" (Principles of nature and grace, founded on reason) and "Monadologia" (Monadology), as well as the explicitly theological work of 1710, Essais de Théodicée (Essays on theodicy). Leibniz died quietly in Hanover in 1716, but his thought has enjoyed an animated afterlife ever since.

Bibliography

Primary Sources

Leibniz, G. W. Philosophical Essays. Translated and edited by Roger Ariew and Daniel Garber. Indianapolis, 1989.

——. Political Writings. Translated and edited by Patrick Riley. Cambridge, U.K., 1988.

Secondary Sources

Sleigh, R. C., Jr. Leibniz and Arnauld: A Commentary on Their Correspondence. New Haven and London, 1990.

Wilson, Catherine. Leibniz's Metaphysics: A Historical and Comparative Study. Princeton, 1989.

—EMILY R. GROSHOLZ

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