Gottfried Wilhelm Leibniz

Gottfried Wilhelm Leibniz (born June 21 [July 1, New Style], 1646, Leipzig [Germany]—died November 14, 1716, Hanover [Germany]) was a German philosopher, mathematician, and political adviser, important both as a metaphysician and as a logician and distinguished also for his independent invention of the differential and integral calculus.

Early life and education

Leibniz was born into a pious Lutheran family near the end of the Thirty Years’ War, which had laid Germany in ruins. As a child, he was educated in the Nicolai School but was largely self-taught in the library of his father, who had died in 1652. At Easter time in 1661, he entered the University of Leipzig as a law student; there he came into contact with the thought of scientists and philosophers who had revolutionized their fields—figures such as Galileo, Francis Bacon, Thomas Hobbes, and René Descartes. Leibniz dreamed of reconciling—a verb that he did not hesitate to use time and again throughout his career—these modern thinkers with the Aristotle of the Scholastics. His baccalaureate thesis, De Principio Individui (“On the Principle of the Individual”), which appeared in May 1663, was inspired partly by Lutheran nominalism (the theory that universals have no reality but are mere names) and emphasized the existential value of the individual, who is not to be explained either by matter alone or by form alone but rather by his whole being (entitate tota). This notion was the first germ of the future “monad.” In 1666 he wrote De Arte Combinatoria (“On the Art of Combination”), in which he formulated a model that is the theoretical ancestor of some modern computers: all reasoning, all discovery, verbal or not, is reducible to an ordered combination of elements, such as numbers, words, sounds, or colours.

After completing his legal studies in 1666, Leibniz applied for the degree of doctor of law. He was refused because of his age and consequently left his native city forever. At Altdorf—the university town of the free city of Nürnberg—his dissertation De Casibus Perplexis (“On Perplexing Cases”) procured him the doctor’s degree at once, as well as the immediate offer of a professor’s chair, which, however, he declined. During his stay in Nürnberg, he met Johann Christian, Freiherr von Boyneburg, one of the most distinguished German statesmen of the day. Boyneburg took him into his service and introduced him to the court of the prince elector, the archbishop of Mainz, Johann Philipp von Schönborn, where he was concerned with questions of law and politics.

King Louis XIV of France was a growing threat to the German Holy Roman Empire. To ward off this danger and divert the king’s interests elsewhere, the Archbishop hoped to propose to Louis a project for an expedition into Egypt; because he was using religion as a pretext, he expressed the hope that the project would promote the reunion of the church. Leibniz, with a view toward this reunion, worked on the Demonstrationes Catholicae. His research led him to situate the soul in a point—this was new progress toward the monad—and to develop the principle of sufficient reason (nothing exists or occurs without a reason). His meditations on the difficult theory of the point were related to problems encountered in optics, space, and movement; they were published in 1671 under the general title Hypothesis Physica Nova (“New Physical Hypothesis”). He asserted that movement depends, as in the theory of the German astronomer Johannes Kepler, on the action of a spirit (God).

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In 1672 the prince elector sent the young jurist on a mission to Paris, where he arrived at the end of March. In September, Leibniz met with Antoine Arnauld, a Jansenist theologian known for his writings against the Jesuits (Jansenism was a nonorthodox Roman Catholic movement that spawned a rigoristic form of morality). Leibniz sought Arnauld’s help for the reunion of the church. He was soon left without protectors by the deaths of Freiherr von Boyneburg in December 1672 and of the prince elector in February 1673; he was now, however, free to pursue his scientific studies. In search of financial support, he constructed a calculating machine and presented it to the Royal Society during his first journey to London, in 1673.

Late in 1675 Leibniz laid the foundations of both integral and differential calculus. With this discovery, he ceased to consider time and space as substances—another step closer to monadology. He began to develop the notion that the concepts of extension and motion contained an element of the imaginary, so that the basic laws of motion could not be discovered merely from a study of their nature. Nevertheless, he continued to hold that extension and motion could provide a means for explaining and predicting the course of phenomena. Thus, contrary to Descartes, Leibniz held that it would not be contradictory to posit that this world is a well-related dream. If visible movement depends on the imaginary element found in the concept of extension, it can no longer be defined by simple local movement; it must be the result of a force. In criticizing the Cartesian formulation of the laws of motion, known as mechanics, Leibniz became, in 1676, the founder of a new formulation, known as dynamics, which substituted kinetic energy for the conservation of movement. At the same time, beginning with the principle that light follows the path of least resistance, he believed that he could demonstrate the ordering of nature toward a final goal or cause (see teleology).