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.

SUPPLEMENTARY BIBLIOGRAPHY

WORKS BY LEIBNIZ

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.

OTHER SOURCES

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