Gottfried Leibnitz Biography
LEIBNITZ, (Ger. Leibniz), Gottfried Wilhelm von (1646–1716). A German philosopher and mathematician, born in Leipzig, July 1, 1646. His father, who was professor of law at the university, died when Leibnitz was six years old. He studied at the Nikolaischule of his native city, entered the university with unusual preparation, in his fifteenth year, and selected the law as his profession, but devoted himself also to philosophy and literature. When 17 years old he defended a remarkable thesis entitled Disputatio Metaphysica de Principio Individui, and in the summer of the same year he spent some time at the University of Jena, studying mathematics. In 1664 he published Specimen Difficultatis in Jure, and in 1666 Dissertatio de Arte Combinatoria. In the latter year he presented himself for the degree in law. In consequence of his youth, however, he was not permitted to take it at Leipzig, but a few months later, November, 1666, he received the degree of doctor juris from Altdorf. After pursuing further studies he had the good fortune to become a kind of protégé of Baron yon Boyneburg, ex-Prime Minister to the Elector of Mainz. At Boyneburg's suggestion he dedicated to the Elector an essay, Nova Methodus Discendœ Docendœque Jurisprudentiœ (1667). This gained an appointment for Leibnitz in the Elector's service. Leibnitz now (1668–69) set to work to reform the Corpus Juris (q.v.). Meanwhile he published several theological treatises. In 1670, at the age of 24, he was appointed assessor on the bench of the upper court of appeals, which was the supreme court of the electorate. In 1672 he accompanied Boyneburg's sons to Paris, and there wrote with a view to submission to Louis XIV a plan for the invasion of Egypt. Leibnitz's real intention in this memorandum was to divert Louis's attention from plans against Germany. Louis seemingly never received this document; at any rate he did not act on the advice. It was reserved for Napoleon to make the invasion of Egypt (1798); and five years later (1803) Napoleon discovered to his surprise that he had been anticipated in his plan by the German philosopher. From Paris Leibnitz went to London; both in Paris and in London he formed the acquaintance of the most eminent philosophers, among them Boyle, Huygens, and Malebranche. In 1676 Leibnitz entered the service of the Duke of Brunswick-Lüneberg as librarian and privy councilor. After a tour of historical exploration, he prepared a series of works illustrating the history of the house of Brunswick. He undertook likewise the scientific direction and organization of the mines in the Harz, into which he introduced many improvements; he took an active part in negotiations for Church unions, and in the theological discussions connected therewith, which formed the subject of a protracted correspondence with Bossuet and with Pélisson. His private studies, however, were chiefly philosophical and philological. He was chief organizer in 1700 and first president of the Academy of Sciences of Berlin, which later became the Berlin Academy; and he proposed at Vienna the establishment of a similar organization, which, however, was not established till 1846, the two hundredth anniversary of his birth. It was to him, likewise, that Peter the Great owed the plan of the since celebrated Academy of St. Petersburg. The Czar bestowed on Leibnitz a pension and the title of Privy Councilor. In 1714 Leibnitz wrote the Monadologie in French for Prince Eugene of Savoy. In the same year he was appointed Privy Councilor and Baron of the Empire. Towards the close of his life Leibnitz spent some time in further work on the annals of the house of Brunswick, and was drawn into a philosophical controversy with Samuel Clarke (q.v.). Before the close of the controversy he died rather unexpectedly at Hanover, Nov. 14, 1716. A monument has been erected to him in Hanover, and in 1883 a statue was unveiled in Leipzig.
Leibnitz was eminent in history, divinity, philosophy, political studies, experimental science, mathematics, mining engineering, and even belles-lettres. But it is chiefly through his philosophical and mathematical reputation that he lives in history. He was greatly influenced by the Cartesian philosophy; but he differed from Descartes both in his method and in some of his principles. In epistemology Leibnitz was an opponent of the doctrine that the mind, at birth, is a tabula rasa, a blank tablet to be written on by experience. He maintained, on the contrary, that, although we are not born with ready-made knowledge in the sense of clear, distinct ideas, still there are "small, dark notions of the soul," which are not the mere passive results of impressions. There may be perceptions of which we are not aware, or which are not aware of themselves. Indeed, in the last resort, Leibnitz denies the reality of everything which is not a percipient or a perception. The perception may be very minute, so as not to be self-conscious, or it may be conscious of itself. In the latter case it is called apperception. Growth in knowledge consists in the process of clarification and distinction of ideas. Sense is not fundamentally different from intellect; it is only confused intellect. Nothing comes to the soul from without. Everything it seems to acquire in the process of learning is originally possessed in obscure form. Virtually, therefore, all ideas are innate in the sense that they are not acquired; but the explicit consciousness of them is acquired. That which has presentations is called by Leibnitz a monad, or a unity, just because it is thus a self-contained system of perceptions, not influénceable from without. It is described as having no windows through which it can look out upon the rest of the universe, but as mirroring the whole universe within itself. But because each monad mirrors the whole universe, each is in so far like the others; the perceptions in each are precisely alike in content; the only difference is that these perceptions may vary indefinitely in clearness and distinctness. Those monads in which all perceptions are obscure are called matter; from matter up to God there is no difference in kind, merely a difference in degree of clearness and distinctness of presentations. Monads are found in all stages of clearness of presentation (see Continuity, Law Of), and each monad tends towards clarification and distinction of these presentations. Those presentations which are merely clear, but not distinct, i.e., which are not confused with others, but are not adequately known in themselves, are objects of empirical or contingent knowledge; those presentations which are both clear and distinct are objects of rational or necessary knowledge. The validity of rational knowledge is guaranteed by the principle of contradiction; that of empirical knowledge by the principle of sufficient reason, which Leibnitz was the first to introduce into a system of philosophy. In other words, necessary truths are analytical, contingent truths synthetical. The latter must have authentication from without; an adequate reason must be given for their validity. The former are authenticated by the fact that it is impossible to think their opposites. The changes that take place at the same time in various monads have no influence on each other. There is no interaction. But there is a preëstablished harmony of such sort that presentations in one monad correspond to those in another. The relation between any two monads is likened to that between two clocks keeping perfect time. They do not influence each other's movements, but they keep together. This correspondence is due to the fact that God, the monad of monads, created all other monads in such a way that in their subsequent course of development their changes should harmonize. These monads are immortal. In choosing to create this world of monads, God selected the best of all possible worlds. God's wisdom gave Him an infinite range of choice; His goodness determined the selection He made. This is Leibnitz's peculiar optimism, which does not assert that everything is perfectly good, but that the world as a whole is the best of all possible worlds. In this way Leibnitz sought to justify God in creating a world with evil in it. This is Leibnitz's theodicy.
His mathematical work is worth special treatment. He began his work on the calculus (q.v.) about the time of his settling in Hanover in 1676, and two years later he had developed it into a fairly complete discipline. It was not, however, until six years after this that he published (1684) anything upon the subject. Two years earlier (1682) he and Mencke founded the Acta Eruditorum, and it was in this celebrated journal that most of his mathematical memoirs appeared (1682–92). The first one on the new calculus was his Nova Methodus pro Minimis et Maximis (1684). Newton (q.v.) had known and used the principles of the fluxional calculus as early as 1665, and had made them public, although not in print, in 1669. Leibnitz had access to certain letters of Newton's in 1676. He also had the opportunity of knowing of the theory when he was in London in 1673, and with the mathematical acquaintances he met there it might be expected that the new theory would be discussed. There is, however, no exact evidence that he knew anything of Newton's discovery at the time he began his own work. It should, however, be stated that the germs of the theory of the calculus are to be found in the works of Fermat, Wallis, and Cavalieri, all of which were well known at that time in the mathematical world.
The essential differences in the two systems lie in the notation and the method of attack. Newton used x" where Leibnitz used dx, and based his treatment on the notion of velocity of material substances where the latter proceeded from the concept of the infinitesimal. As mathematics developed, the differential notation proved greatly superior to the fluxional, and in the first quarter of the nineteenth century it was adopted in England, as it had been adopted a hundred years earlier on the Continent. With this change of notation the so-called fluxional calculus disappeared and the differential calculus took its place.
The further mathematical work of Leibnitz was not of a high order. His contributions to analytic geometry were noteworthy only for laying the foundation (1692) for the theory of envelopes, and for introducing the terms "coordinates" and "axes of coördinates." He contributed a little to the theory of mechanics, but his work was often inaccurate, and he made no great discoveries.
In addition to Leibnitz’s works already referred to, special mention should be made of Nouveau système de la nature (1695); Essais de théodicée (1710); Principes de la nature et de la grâce (1714); Nouveaux essais sur l’entendement humain (finished by 1704 and published posthumously in 1765); and A Collection of Papers which Passed Between the Late Mr. Leibnitz and Dr. Clarke in the Years 1715 and 1716 (London, 1717). His Latin and French philosophical works have been many times collected, edited, and published. The editions of Erdmann (Berlin, 1840), of Jaret (Paris, 1866; 2d ed., 1900), and of Gerhardt (Berlin, 1875–90) are especially noteworthy. The publishing of a complete edition of all Leibnitz’s works was undertaken by Pertz. This edition, as it now stands, contains four volumes of history (Hanover, 1843–47); seven volumes of mathematics, edited by Gerhardt (Berlin and Halle, 1849–63); but of the philosophical portion only one volume appeared. A satisfactory edition is yet to be published. In 1900 some French and German scholars undertook to prepare for such an edition; but so far only a few isolated volumes have appeared. In the Journal of Speculative Philosophy are to be found translations of the Monadologie and many of the lesser writings; and some of the important philosophical works have been translated by G. M. Duncan (New Haven, 1890); the Nouveaux essais by A. G. Langley (London, 1894); The Monadology and Other Philosophical Writings by R. Latta (Oxford, 1898).
The New International Encyclopaedia, Vol. XIII (New York: Dodd, Mead & Co., 1920) 743-744.