LEIBNIZ, GOTTFRIED WILHELM (1646–1716)

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.

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

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