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Leibniz, Gottfried Wilhelm


(b. Leipzig, Germany, 23 June 1646, d. Hanover, Germany, 14 November 1716),

mathematics, philosophy, metaphysics. For the original article on Leibniz see DSB, vol. 8.

Since the original DSB article, a more nuanced and complex picture of G. W. Leibniz’s scientific work has emerged. This is in part due to the hard work of Leibniz’s editors at the German Academy of Sciences, who continue to uncover rich new material (as of 2007, they have succeeded in bringing before the public well under half of Leibniz’s total writings, including the massive edition of Series 6, Volume 4 of the philosophical writings, released in 1999). In part, however, the new picture that has emerged in recent decades is the result of changing historiographical concerns among scholars of early modern science and philosophy. Whereas earlier scholarship had been largely content with a triumphalist account of the history of science, placing Leibniz at the beginning of a few lines of scientific inquiry that have been, as it happens, successful ones, the new historiography has been intent on bringing to light all of the interests of the heroes of the scientific revolution, even those that have turned out in the interim to be dead ends.

One significant part of this change in recent decades has been a growing sensitivity to the different ways in which the various scientific disciplines have been divided up in different times and places. Often—as is the case with Leibniz—proposals for new ways to divide the sciences themselves reflect philosophical convictions about the structure of the world. It is illuminating to consider Leibniz’s division of the sciences presented in his 1700 memorandum to the Elector of Brandenburg for the creation of a scientific society in Berlin. There Leibniz identifies two fundamental branches of the “real sciences,” mathematics and physics, and in turn divides these two as follows: mathematics consists of

  1. geometry, including analysis;
  2. astronomy and its related fields, including geography, chronology, and optics;
  3. civil, military, and naval architecture (along with painting and sculpture); and
  4. mechanics.

Physics, in turn, includes

  1. chemistry;
  2. study of the mineral kingdom, including mining and smelting;
  3. study of the vegetable kingdom, including agriculture and forestry; and
  4. study of the animal kingdom, including anatomy, the science of hunting, and animal husbandry. (Aiton, 1985, p. 251)

We need not follow Leibniz’s schema here, but it can at least serve as a reminder that the traditional view of Leibniz’s scientific concerns, which places a mathematized physics at the foundation of all things, and leaves those things largely untouched, surely does not capture the full range of his concerns. When we say that for Leibniz mathematics underlies physics, what we mean to say is not, as the schema suggests, inter alia that painting underlies forestry, but that Leibniz included much of what we would call “physics” under the heading of mathematics because he, in keeping with the revolution begun by Galileo and others a century earlier, believed that the natural world could best be understood in quantitative terms. But the natural world is carved up into more than just homogeneous bodies in motion: it also contains chemical compounds, crystals, organic bodies, embryos, and so on, none of which traditional mechanical physics had ever been up to the task of describing, and all of which, by the second half of the seventeenth century, had risen to the top of the list of phenomena in need of explanation in scientific terms. Leibniz managed to contribute more to some of these fields than others. Here we shall consider his contributions to chemistry, biology, geology, and ethnography (as these terms are understood in the twenty-first century).

Chemistry . In part because it was not easily subsumable into the new mechanical science—which sought to explain everything in terms of mass, figure, and motion alone—chemistry continued to be inflected by the mystical ideas associated with alchemy well into the seventeenth century. Many mystical thinkers made important discoveries in chemistry, such as Jean-Baptiste van Helmont, the first scientist to correctly describe the motion of gas.

Leibniz was careful to maintain at least a public distance from the alchemists, but it has been proven that he was involved in an alchemical society in 1666–1667, and statements he made at least through 1698 indicate an enduring belief in the possibility of manufacturing gold. He believed in this possibility for sound reasons: as he writes in the Protogaea, “material, which is everywhere identical with itself, can take on any form, since there are no ultimate, non-interchangeable elements” (§ 3]). He himself had seen evidence of radical transformations of physical substances, of the transformation of urine into phosphor, for example.

Leibniz inherited from van Helmont the alchemical view that bodies possess a lightest distillation fraction, which could be obtained through a process of chemical sublimations and which constitutes the core of that entity’s corporeal being. He transforms this to serve his own doctrine that no corporeal substance can ever be taken out of existence, but always remains in some subtle or reduced form. Thus he writes in explicitly alchemical terms: “We shall put off the body, it is true, but not entirely; and we shall retain the most subtle part of its substance (quintessence), in the same way as chemists are able to sublimate a body or mass” (Otium hannoveranum, 411 R 164fn.)

Leibniz is intent to reject the Kabbalistic theory that the spirit of a being may be located in some very hard bone in the body, the luz in Hebrew. He prefers the alchemical doctrine, according to which there always remains some core or flos of a corporeal being, which may be resurrected at any time (hence Leibniz’s interest in experiments on insect palingenesis), but that this core cannot be identified with some particular, indestructibly hard part. Such a view would be too close to traditional atomism, and Leibniz imagines instead that “the clothing or covering” of the body “is in constant fluctuation, and at one time is evaporated, at another is again enlarged by the air or by food” (Sämtliche Schriften und Briefe II 1: 118f).

Biology . Palingenesis, or the regeneration of supposedly dead animals, is an example of a problem of largely theological interest that was long studied empirically by the alchemists. It was also, clearly, a biological problem, but biology did not exist as an independent science, and indeed would not for quite some time.

If biology was not an independent discipline, this does not indicate an absence of scientific interest in the phenomena of living nature. Leibniz, in particular, was intensely interested in the problems of organic structure and the origins, development, and motion of living bodies. Even if he habitually denied that he borrowed any ideas directly from the research of the microscopists Anton van Leeuwenhoek, Jan Swammerdam, Marcello Malpighi, and others, insisting instead that his metaphysical views were derived from higher principles, nonetheless he often credits these researchers for having empirically corroborated what he knew to be true on a priori grounds. Swammerdam’s discovery of insect metamorphosis, and Leeuwenhoek’s of the spermatozoon, seemed to Leibniz to confirm the view that no substance ever exists in a fully non-corporeal state, and that all apparent generations and destructions of corporeal substances are in fact just radical transformations.

Leibniz’s theory of corporeal substances is a theory of nested individuality, according to which there are individual substances constituting the organic bodies of other individual substances. “Every animated thing,” Leibniz writes to Antoine Arnauld in a letter of 30 April 1687, “contains a world of diversity in a true unity.” This view of organic structure—and Leibniz is the first thinker in history to distinguish between organism on the one hand, which he sees as parts within parts to infinity, and mechanism on the other, understood as any structure decomposable in a finite series of steps—also appears to be inspired by the microscopic discovery that what look to be individuals often are but colonies of smaller individuals. In Aristotle’s metaphysical biology, there had been a basic conviction that where there is one organic body, there is only one substance, such as a horse or a man. For Leibniz, in contrast, in the organic body dominated by the soul of the horse there are infinitely many other souls conspiring, each with its own organic body, and so on without end.

For Leibniz, there could be no lower level at which we arrive at rock-bottom, basic living entities. Cells would not be discovered for some time after Leibniz’s death, and in some sense Leibniz’s vision excludes the possibility of these biological building blocks. This would not stop some, such as Charles Bonnet in the eighteenth century, from interpreting Leibniz’s theory of monads materialistically as an anticipation of the view that every part of an organic body contains the code responsible for the generation of the entire body. Yet Leibniz’s theory of nested individuality may be seen as anticipating some trends in biology, to the extent that it calls into question the common-sense view of spatiotemporally separable organisms as the true individuals in living nature, and instead suggests that individuality may be a relative matter, just as today evolutionists identify variously the gene, the organism, and the population each as the unit of selection upon which adaptive forces might work.

Geology . The family of Leibniz’s employer, Duke Johann Friedrich von Braunschweig-Lüneberg, gained much of its revenue from the mining of valuable metals. Leibniz thus was able to try his skills as a mining engineer, attempting to develop a system for the extraction of silver ore from the Harz Mountains. This practical activity, combined with another responsibility his employer placed on him— the writing of the history of the House of Brunswick— yielded a major work on geology. Leibniz, wishing to begin his history of the royal family from the very beginning, and seizing on the fact that the House of Brunswick had its own financial interest in understanding how mountains are formed, wrote his speculative Protogaea, intended to be the first part of his uncompleted royal history, on, among other things, the evolution of the earth, the formation of continents, oceans, and mountains, the origins of fossils, and so on.

By the early eighteenth century, significant evidence had been accumulated to call into doubt the accuracy of the biblical account of cosmogony. Among the most important evidence were the remains of unknown animal species, and seashells discovered at high altitudes. Some, intent on defending the traditional account, argued that these were tricks of the devil, while a naturalistic but still creationist account had it that these were “forms” imposed by astral influx and seared into receptive matter. Leibniz was cautious not to overtly deny the biblical account, but nonetheless sought a consistently naturalistic way of accounting for puzzling natural phenomena such as these. He argues that “fishes expressed in slate are from true fishes, and this proves that they are not tricks of nature” (§ 20]). Leibniz believes that under certain circumstances enclosed soil can be “cooked” within the Earth as in an oven, and rapidly turned into stone. If animal remains happen to be trapped within, these will turn into fossils. Thus Leibniz correctly discerns the source of the fossil remains, but greatly underestimates the length of time required for them to be produced.

Some of his reflections in the Protogaea also indicate a grasp of the epistemological problem of scientifically accounting for processes completed in the distant past, a problem that affects paleontology, cosmology, geology, and archaeology equally. Leibniz believed that fossil evidence could be used together with what was currently known of mechanics and chemistry in order to arrive at a plausible account of the earth’s history. While in some respects speculative, Leibniz’s contribution to the earth sciences is nonetheless noteworthy for his consistent effort to stay within the bounds of the demonstrable, even when the subject in question makes this difficult. While Leibniz continues to presume that a deluge early on changed the face of the Earth, in many passages the Protogaea is also an early example of the uniformitarian approach to geological processes that would gradually come to be favored over the cataclysmic approach.

Ethnography . As with geology, in the early modern period significant new ethnographic evidence was rapidly being accumulated that seemed to dispute the biblical account of origins. On the one hand, new discoveries, particularly in the Americas, made it increasingly difficult to believe that enough time had elapsed from the biblical creation for human beings to wander so far from the presumably Near Eastern Garden of Eden, and to change so much with respect to physical appearance. On the other hand, increasing awareness of the technological achievements of other civilizations, particularly the Chinese, made it increasingly difficult to believe that the revealed truth of Christianity gave Europeans any greater access to scientific truth than their pagan neighbors enjoyed. Interest was also piqued by the fact that some cultures, such as the Chinese, the ancient Persians, and the Mexica (Aztecs) also had alternative chronologies of world history that placed the origin much further back than the Old Testament

had it. In view of these problems, certain libertines advocated a doctrine of multiple creations, holding that revealed scripture was only of relevance for those created from Adam and Eve.

Leibniz was very interested in the Jesuit reports from China, and in the speculations of the missionaries as to the nature and origins of Chinese science and technology. Many Jesuits believed that the Chinese had strayed from the Near East long ago, and they were seen to have a developed legal system and sophisticated machines, but no understanding of the principles underlying either of these. Confucianism was thus portrayed as a system of laudable rules, the reasons for which had been forgotten in the flow of centuries. Early on, Leibniz too entertained the strong monogenetic hypothesis that all human beings have a Middle Eastern pedigree. He writes in the mid-1670s, for example: “Whether the Chinese are from the Egyptians or the latter from the former, I dare not say; certainly the similarity of their institutions and hieroglyphics along with their shared kind of writing and philosophizing suggests that they are consanguineous peoples (Sämtliche Schriften und Briefe, IV i 270–1).

Later, Leibniz grows increasingly agnostic as to the origins of Chinese civilization, but also grows thoroughly convinced of the innate capacity of the Chinese to arrive at the same basic truths that revealed theology would have us believe could only come from genealogical connection to Christ. In the Discourse on the Natural Theology of the Chinese, still unfinished at his death in 1716, he writes that the Chinese, unlike the English, who are inadvertently lapsing into paganism by reintroducing a meddling God or a world soul into nature, are right to “reduce the governance of Heaven and other things to natural causes and distance themselves from the ignorance of the masses, who seek out supernatural miracles” ([§ 2]). Here, it seems almost that Leibniz believes that precisely the isolation of the Chinese from the scriptural tradition, and their consequent need to rely on nature alone for their understanding of the divine, is itself the fortunate cause of their theological superiority to the English.

Ultimately, Leibniz sides with the Jesuits in the so-called “rites controversy,” in which the pope insisted against the missionary sect that the Chinese could not continue their traditional ancestor worship while identifying themselves as Christians. Leibniz and the Jesuits believed that Chinese ritual did not imply any particular theological convictions or other, and thus that it was compatible with Christian dogma. The position Leibniz takes up on this issue reveals a sharp understanding of the nature of cultural distinctiveness and of the still problematic question of the boundary between culture and religion. As with biology, anthropology was not a scientific discipline in Leibniz’s time, and he had no systematic approach to it. But many of his ideas in this area were subtle and prescient.



Otium hannoveranum, sive Miscellanea. 2nd edition. Edited by J. F. Feller. Leipzig: G. G. Leibnitii, 1737.

Sämtliche Schriften und Briefe. Edited by the Prussian Academy of Sciences (later German Academy of Sciences). Darmstadt: O. Reichl, 1923–1999. Among important recent editions of Leibniz’s writings, the most recent volume in the Akademie edition, begun by the Prussian Academy in 1923 and still underway, of Leibniz’s writings deserves first mention. The fourth volume of series six (dedicated to the philosophical writings) appeared in 1999. This volume itself consists in four separate volumes, and is well over a thousand pages long.

Oeuvres de Leibniz. 7 vols. Edited by A. Foucher de Careil. Paris: Firmin Didot, 1861–1865. Reprint, Hildesheim: Olms, 1969.

Philosophical Essays. Edited and translated by Roger Ariew and Daniel Garber. Indianapolis, IN: Hackett, 1989. An edition of Leibniz’s English writings, very useful for instructional purposes.

De Summa Rerum: Metaphysical Papers, 1675–1676. Edited and translated by G. H. R. Parkinson. New Haven, CT: Yale University Press, 1992. A series of bilingual editions (English along with Latin, French or German), organized thematically.

Protogaea: de l’aspect primitif de la terre et des traces d’une histoire très ancienne que renferment les monuments mêmes de la nature. Edited and translated by Bertrand de Saint-Germain. Toulouse: Presses Universitaires du Mirail, 1993. French-Latin bilingual edition of Leibniz’s geological treatise.

The Labyrinth of the Continuum: Writings on the Continuum Problem, 1672–1686. Edited and translated by Richard T. W. Arthur. New Haven, CT: Yale University Press, 2001.

Discours sur la théologie naturelle des Chinois. Edited and translated by Wenchao Li and Hans Poser. Frankfurt: Vittorio Klostermann, 2002. Published as Discourse on the Natural Theology of the Chinese. Translated with an introduction by Henry Rosemont Jr. and Daniel J. Cook. Honolulu: University Press of Hawaii, 1977. Leibniz’s treatise on China.

Confessio Philosophi: Papers concerning the Problem of Evil, 1671–1678. Edited and translated by Robert C. Sleigh Jr. New Haven, CT: Yale University Press, 2004.

The Leibniz-Des Bosses Correspondence. Edited and translated by Brandon Look and Donald Rutherford. New Haven, CT: Yale University Press, 2007.


Aiton, Eric J. Leibniz: A Biography. Boston: A. Hilger, 1985. A good biography chronicling many of the details of Leibniz’s life and work.

Antognazza, Maria Rosa. Leibniz on the Trinity and the Incarnation: Reason and Revelation in the Seventeenth Century. Translated by Gerald Parks. New Haven, CT: Yale University Press, 2008. Intellectual biography.

Ariew, Roger. “Leibniz on the Unicorn and Various Other Curiosities.” Early Science and Medicine 3 (4, 1998): 267–288. Leibniz’s activity in geology and paleontology.

Brown, Stuart. “Some Occult Influences on Leibniz’s Philosophy.” In Leibniz, Mysticism, and Religion, edited by Allison P. Coudert, Richard H. Popkin, and Gordon M. Weiner. Boston: Kluwer, 1998.

Coudert, Allison P. Leibniz and the Kabbalah. Dordrecht: Kluwer, 1995. For Leibniz’s connection to the Kabbalists.

Duchesneau, François. Les modèles du vivant de Descartes à Leibniz. Paris: Vrin, 1998. Leibniz’s place in the history of biology.

Nachtomy, Ohad, Ayelet Shavit, and Justin Smith. “Leibnizian Organisms, Nested Individuals, and Units of Selection.” Theory in Biosciences 121 (2002): 205–230.

Perkins, Franklin. Leibniz and China: A Commerce of Light. Cambridge, U.K.: Cambridge University Press, 2004. Excellent study of Leibniz’s Sinological activity, as well as some insight into his ethnographic ideas in general.

Phemister, Pauline. Leibniz and the Natural World: Activity, Passivity, and Corporeal Substances in Leibniz’s Philosophy. Dordrecht: Springer, 2005.

Ross, George MacDonald. “Leibniz and Alchemy.” Studia Leibnitiana Sonderheft 7 (1978): 166–77. Explores relation of Leibniz to the alchemists.

Smith, Justin E. H., ed. The Problem of Animal Generation in Early Modern Philosophy. Cambridge, U.K.: Cambridge University Press, 2006.

Justin E. H. Smith

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Leibniz, Gottfried Wilhelm

Leibniz, Gottfried Wilhelm

b. Leipzig, Germany, 1 July 1646; d. Hannover, Germany, 14 November 1716)

mathematics, philosophy, metaphysics.

Leibniz was the son of Friedrich Leibniz, who was professor of moral philosophy and held various administrative posts at the University of Leipzig. His mother, Katherina Schmuck, was also from an academic family. Although the Leibniz family was of Slavonic origin, it had been established in the Leipzig area for more than two hundred years, and three generations had been in the service of the local princes.

Leibniz attended the Nicolai school, where his precocity led his teachers to attempt to confine him to materials thought suitable to his age. A sympathetic relative recognized his gifts and aptitude for selfinstruction, and on the death of Friedrich Leibniz, in 1652, recommended that the boy be given unhampered access to the library that his father had assembled. By the time he was fourteen, Leibniz had thus become acquainted with a wide range of classical, scholastic, and even patristic writers, and had, in fact, begun that omnivorous reading that was to be his habit throughout his life. (Indeed, Leibniz’ ability to read almost anything led Fontenelle to remark of him that he bestowed the honor of reading on a great mass of bad books.)

At the age of fifteen Leibniz entered the University of Leipzig, where he received most of his formal education, although that institution was at that time firmly entrenched in the Aristotelian tradition and did little to encourage science. In 1663 he was for a brief time a student at the University of Jena, where Erhard Weigel first taught him to understand Euclidean geometry. Leibniz continued his studies at Altdorf, from which he received the doctorate in 1666, with a dissertation entitled Disputatio de casibus perplexis. He was invited to remain at that university, but chose instead, during the second half of 1667, to undertake a visit to Holland.

Leibniz reached Mainz, where, through the offices of the statesman J. C. von Boyneburg, he met the elector Johann Philipp von Schönborn, who asked him into his service. Leibniz worked on general legal problems, developed his program for legal reform of the Holy Roman Empire, wrote (anonymously) a number of position papers for the elector, and began a vast correspondence that by 1671 had already brought him into contact with the secretaries of the Royal Society of London and the Paris Academy of Sciences, as well as with Athanasius Kircher in Italy and Otto von Guericke in Magdeburg. He also began work on his calculating machine, a device designed to multiply and divide by the mechanical repetition of adding or subtracting. In 1671 Pierre de Carcavi, royal librarian in Paris, asked Leibniz to send him this machine so that it could be shown to Colbert. The machine was, however, only in the design stage at that time (although a model of it was built in 1672 and demonstrated to the Academy three years later).

In the winter of 1671-1672, Leibniz and Boyneburg set forth a plan to forestall French attacks on the Rhineland. By its terms, Louis XIV was to conquer Egypt, create a colonial empire in North Africa, and build a canal across the isthmus of Suez—thereby gratifying his imperial ambitions at no cost to the Netherlands and the German states along the Rhine. Leibniz was asked to accompany a diplomatic mission to Paris to discuss this matter with the king. He never met Louis, but he did immerse himself in the intellectual and scientific life of Paris, forming a lifelong friendship with Christiaan Huygens. He also met Antoine Arnauld and Carcavi. The official mission came to nothing, however, and in December 1672 Leibniz’ patron and collaborator Boyneburg died.

In January 1673 Leibniz went to London with a mission to encourage peace negotiations between England and the Netherlands; while there he became acquainted with Oldenburg, Pell, Hooke, and Boyle, and was elected to the Royal Society. The mission was completed, but the elector Johann Philipp had died, and his successor showed little interest in continuing Leibniz’ salary, especially since Leibniz wanted to return to Paris. Leibniz arrived in the French capital in March 1673, hoping to make a sufficient reputation to obtain for himself a paid post in the Academy of Sciences. Disappointed in this ambition, he visited London briefly, where he saw Oldenburg and Collins, and in October 1676 left Paris for Hannover, where he was to enter the service of Johann Friedrich, duke of Brunswick-Lüneburg. En route, Leibniz stopped in Holland, where he had scientific discussions with Jan Hudde and Leeuwenhoek, and, at The Hague between 18 and 21 November, conducted a momentous series of conversations with Spinoza.

By the end of November Leibniz had arrived in Hannover, where he was initially a member of the duke’s personal staff. He acted as adviser and librarian, as well as consulting on various engineering projects. (One of these, a scheme to increase the yield of the Harz silver mines by employing windmill-powered pumps, was put into operation in 1679, but failed a few years later, through no fault of the engineering principles involved.) Leibniz was soon formally appointed a councillor at court, and when Johann Friedrich died suddenly in 1679 to be succeeded by his brother Ernst August (in March 1680), he was confirmed in this office. Sophia, the wife of the new duke, became Leibniz’ philosophical confidante; Ernst August commissioned him to write a genealogy of the house of Brunswick, Annales imperii occidentes Brunsvicenses, to support the imperial and dynastic claims of that family. Leibniz’ researches on this subject involved him in a series of scholarly travels; his princely support opened the doors of archives and libraries, and he was enabled to meet and discuss science with eminent men throughout Europe.

Leibniz left Hannover in October 1687 and traveled across Germany; in Munich he found an indication that the Guelphs were related to the house of Este, an important point for his genealogy. In May 1688 he arrived in Vienna; in October of that year he had an audience with Emperor Leopold I, to whom he outlined a number of plans for economic and scientific reforms. He also sought an appointment at the Austrian court, which was granted only in 1713. He then proceeded to Venice and thence to Rome. He hoped to meet Queen Christina, but she had died; he did become a member of the Accademia Fisico-matematica that she had founded. In Rome, too, Leibniz met the Jesuit missionary Claudio Filippo Grimaldi, who was shortly to leave for China as mathematician to the court of Peking; Grimaldi awakened in Leibniz what was to become a lasting interest in Chinese culture. Returning north from Rome, Leibniz stopped in Florence for a lively exchange on mathematical problems with Galileo’s pupil Viviani; in Bologna he met Malpighi.

On 30 December 1689 Leibniz reached Modena, his ultimate destination, and set to work in the ducal archives which had been opened to him. (Indeed, he threw himself into his genealogical research with such fervor that he afflicted himself with severe eyestrain.) He interrupted his work long enough to arrange a marriage between Rinaldo d’Este of Modena and Princess Charlotte Felicitas of Brunswick-Lüneburg (celebrated on 2 December 1695), but by February 1690 he was able to prove the original relatedness of the house of Este and the Guelph line, and his research was complete. He returned to Hannover, making various stops along the way; his efforts were influential in the elevation of Hannover to electoral status (1692) and earned Leibniz himself an appointment as privy councillor.

Elector Ernst August died in January 1698 and his successor, Georg Ludwig, although urging Leibniz to complete the history of his house, nevertheless declined to make any other use of his services. Leibniz found support for his project in other courts, however, particularly through the patronage of Sophia Charlotte, daughter of Ernst August and Sophia and electress of Brandenburg. At her invitation Leibniz went to Berlin in 1700, in which year, on his recommendation, the Berlin Academy was founded. Leibniz became its president for life. Sophia Charlotte died in 1705; Leibniz made his last visit to Berlin in 1711. He persisted in his efforts toward religious, political, and cultural reforms, now hoping to influence the Hapsburg court in Vienna and Peter the Great of Russia. In 1712 Peter appointed him privy councillor, and from 1712 to 1714 he served as imperial privy councillor in Vienna.

On 14 September 1714 Leibniz returned to Hannover; he arrived there three days after Georg Ludwig had left for England as King George I. Leibniz petitioned for a post in London as court historian, but the new king refused to consider it until he had finished his history of the house of Brunswick. Leibniz, plagued by gout, spent the last two years of his life trying to finish that monumental work. He died on 14 November 1716, quite neglected by the noblemen he had served. He never married.

Frederick Kreiling

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Leibniz, Gottfried Wilhelm (1646–1716)


LEIBNIZ, GOTTFRIED WILHELM (16461716), 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, 16721676; 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 (16291695), who introduced him to Descartes's geometry and the new algebra, and also made the acquaintance of Nicolas de Malebranche (16381715) and Antoine Arnauld (16121694). 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 (16421727) 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 (16671748) and Jakob (16541705) 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 (17071783), Jean Le Rond d'Alembert (17171783), and Joseph-Louis Lagrange (17361813) 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 16891691, 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.

See also Alembert, Jean Le Rond d' ; Euler, Leonhard ; Huygens Family ; Lagrange, Joseph-Louis ; Mathematics ; Newton, Isaac .


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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Leibniz, Gottfried Wilhelm, Baron von

Gottfried Wilhelm Leibniz, 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.


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.


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.


See Liebniz's political writings, ed. and tr. by P. Riley (1972); biographies by G. M. Ross (1984) and M. R. Antognazza (2008); G. H. Parkinson, Logic and Reality in Leibniz's Metaphysics (1965); H. Ishiguro, Leibniz's Philosophy of Logic and Language (1972).

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