Leibnitz, Or Leibniz, Gottfried Wilhelm, a German philosopher, born in Leipsic at the beginning of July, 1046, died in Hanover, Nov. 14, 1710. His father, a professor in the university, died when he was six years old. He enjoyed by the care of his mother the best privileges of education which Germany then afforded, but declares that he was for the most part self-taught, and relates that he would withdraw from school to shut himself up whole days in his father's library. At the St. Nicholas gymnasium in Leipsic he incurred the remonstrances of his masters by learning Latin and reading the classics in advance of the regular course. Before he was 12, he says, he "understood the Latin authors very well, had begun to lisp Greek, and wrote verses with singular success." He was already studying the greatest modern as well as ancient philosophers, was comparing Bacon and Descartes with Aristotle and Plato, and was aiming to grasp the unity of all the sciences. At the age of 15 he entered the university of Leipsic, applied himself chiefly to mathematics, philosophy, and law, continued his studies for a short time at Jena, returned to Leipsic, and produced remarkable theses on occasion of receiving his degrees.

His treatise Be Principio Indi-vidui, his academic exercise on becoming bachelor of philosophy, is perhaps the most extraordinary demonstration of erudition and power of thought ever achieved by a youth of 17. It was the fruit of severe boyish deliberation whether or not he should give up the substantial forms of the schoolmen, prefigured his future philosophy by its vivid statement of individuality as the fundamental principle of ontology, and was the last noticeable work written in the sense and style of scholasticism. In it he declares for nominalism. His three theses on becoming bachelor and licentiate of law were published, and he wished to crown his studies in jurisprudence with the degree of doctor; but this was refused him on pretence of his youth by the superiors of the college, whose ill will he had in some way incurred. He therefore left his native city, never to return. At the university of Altdorf he maintained his thesis for the doctorate in 1666 with so brilliant success that a professorship was immediately offered him, which he declined.

He fell in with a society of Rosicrucians and alchemists at Nuremberg, became their secretary, recorded their experiments, and explored the hermetic authors for revelations concerning the philosopher's stone, but was soon ready for more hopeful labors. In 1007 he met the baron of Boyneburg, ex-chancellor of the elector of Mentz, who was captivated by his genius, and invited him to Frankfort, where he immediately composed his Nova Methodus Discendce Docendceque Jurisprudential (1008), in which he shows his admiration of the Roman law and proposes the registry of all its enactments in chronological order. In the following year appeared his Corporis Juris Reconcinnandi Ratio, in which the arrangement of Justinian is disapproved, and all law is reduced to nine heads: general principles of rights and actions, rights of persons, judgments, real rights, contracts, successions, crimes, public rights, and sacred rights. In the treatment of these departments he proposes to retain the texts of the Corpus Juris Civilis, but to follow the method of the Pandects rather than of the Institutes. The versatile genius and various pursuits of Leibnitz soon withdrew him from the science of philosophical jurisprudence. "He did but pass over that kingdom," says Lermi-nier, "and he reformed and enlarged it." In 1669 he produced, at the instance of Boyneburg, an anonymous treatise in favor of the claims of the prince of Neuburg to the vacant throne of Poland, in reward for which he was made councillor of the elector of Mentz. This office, which he retained three years, furnished him leisure to prosecute vast studies in politics, physics, and philosophy.

He extended his fame as a philosopher by republishing and annotating the Antibarbarus Philosophus of Nizolius (1670), in which he ranks Aristotle above Descartes; wrote a theological argument in defence of the Trinity, Sacrosancta Trinitus (1671), aimed against the Polish Socinian Wis-sowatius, who had procured the erection of a temple to the harmony of the three Christian confessions; addressed to the academy of sciences of Paris and to the royal society of London two remarkable memoirs on the laws of motion; and entered into correspondence with Spinoza by sending him an account of the progress of optics. One of his projects at this time was for a reunion of the Lutheran and Roman Catholic churches, concerning which he had a long correspondence with Bossuet. In 1672 he was sent by Boyneburg to accompany his son to Paris, then the residence of the most learned men of the age under the patronage of Louis XIV. Associated with Cassini, Huygens, and others, he devoted himself especially to mathematics and physics, and established a European reputation by bold and striking thoughts in all departments of learning. To Colbert he presented a new arithmetical machine, an improvement on that of Pascal, which was favorably noticed by the academy of sciences.

To the king he addressed a memorial for an expedition to Egypt, an eminent instance of political foresight. " The conquest of Egypt," he says, "will give supremacy on the sea, the commerce with India, predominance in Christendom, and even an empire in the Orient on the ruins of the Ottoman power." Another of his suggestions to Louis XIV. was for the publication of a general repertory of human knowledge in the form of a dictionary, thus presenting all the results of scientific labor in their mutual dependences. He proposed illustrated treatises on natural history, and states that his own preference would have been to study the laws established by God in nature rather than the laws and customs created by men for themselves. Several members of the academy of sciences suggested to him that he would be admitted to that body as a pensioner, provided he would become a Catholic; but he declined to accept the offer under this condition. In 1673 he visited England, became personally acquainted with Newton, Boyle, Oldenburg, Wallis, and Collins, and was elected a member of the royal society.

On his return to Paris in the same year he received instructions in the higher mechanics and analysis from Huygens, to whom, in a letter to the countess Kielmans-egge, he acknowledges himself indebted in his mathematical studies which resulted in the discovery of the differential calculus. The death of Boyneburg, soon followed by that of the elector of Mentz (1674), left him without a patron, and he determined to return to Germany. At Paris he received from the duke of Bruns-wick-Luneburg an appointment as councillor, with a pension and with permission to prolong his absence at pleasure. He remained in France till 1676, again visited London, passed through Holland, met with Spinoza at the Hague, and on his arrival in Hanover, the residence of the duke of Brunswick, became his librarian, and was partially occupied for six years in arranging and enriching his library. At the congress of Nimeguen (1677) there was a dispute about the right of precedence between the princes who were electors and those who were not. Leibnitz maintained the cause of the latter in a treatise containing the ultramontrane rather than Protestant declaration that all the states of Christendom should form but a single body, having the pope for their spiritual and the emperor for their temporal head.

This idea of a grand theocracy appears prominently in several of his writings, alike in his views of society and of nature. Theology he defined as the jurisprudence of the kingdom of God, as law and politics transferred to a higher and absolute sphere. He was one of the founders in 1682 of the Acta Eruditorum of Leipsic, to which he furnished numerous articles. Employed to write the history of the house of Brunswick, he explored the principal libraries and archives of Germany and Italy for materials, returning to Hanover in 1690. The fruits of his researches were the Codex Juris Gentium Diplomaticus (2 vols., 1693-1700), a collection of treaties and public documents, with a preface which is one of his masterpieces; Accessions Historicae (2 vols., 1698-1700); Scriptores Rerum Brunsvicensium Illustrations Inservientes (3 vols., 1707-'ll); and the Annates Imperii Occident is Brunsvicenses (first published by Pertz, 2 vols., 1843-'5). His Pro-togaea (first published entire in 1749), a dissertation on the state of the globe before the creation of man, was intended as an introduction to the last work, and was the first important contribution to the science of geology, which he called natural geography.

His hypothesis supposes the prominence of fire in the formation of the earth, the gradual congelation after igneous fusion, the introduction of a vast body of water to cover the surface, and the origin of mountains and valleys by the subsidence of certain portions of the earth breaking in upon vast vaulted caverns. To his influence was chiefly due the foundation of the academy of sciences at Berlin, of which he became the first president in 1702. The first memoir which he presented to the academy was on a binary system of arithmetic, in which the base of the scale of numeration was the number 2 instead of 10, and the only figures used were 1 and 0. He soon after attempted to form a universal alphabet, the elements of which were to be very simple, like algebraic signs, instead of syllables and words, and were directly to represent ideas. This favorite but futile scheme was the subject of long continued meditations. To Augustus, king of Poland and elector of Saxony, he addressed a series of precepts for the advancement of sciences, with a curious preamble; and to this period belong his most important philosophical labors.

In 1704 he composed his examination of Locke, Nouveaux essais sur l'entendement humain; he revealed the great variety of his learning in the first volume of the Miscellanea Berolinensia (1710); was a frequent contributor to the Journal de Trevoux and the Journal des Savants; and published in 1710 in French his Theodicee, the noblest monument of his genius, in which he grapples with the leading problems of philosophy and faith, and which is hardly surpassed as an example at once of metaphysical power and universal erudition. During the latter years of his life he enjoyed the highest personal distinction. A councillor and official historiographer at Hanover, a baron and aulic councillor with a pension at Vienna, he was consulted by Peter the Great at Torgau in 1711, and rewarded by him with the title of councillor of state and a pension of 1,000 rubles. He had for many years corresponded with the most illustrious persons in Europe on almost all public and scientific questions. He united the leading thinkers of Christendom by an interchange of ideas, and from his time the history of philosophy involves more than in any former period the general history of the human mind. To no single person is the civilized world more indebted for the literary commerce between all its parts.

To Spinoza he wrote, suggesting new methods of manufacturing lenses; to Magliabecchi at Florence, urging him in elegant Latin verses to publish his bibliographical discoveries; to the elector of Saxony, on the culture of the silkworm; to Gri-maldi, the Jesuit missionary in China, to impart his researches in Chinese philosophy, and to prevail on the emperor to introduce his new binary arithmetic, suggesting that the latter may be a key to the book Ye-kim, supposed to contain the mysteries of Fo; to Bossuet and Mme. Brinon concerning the union of the Protestant and Catholic churches, and to Span-heim on the union of the Lutheran and Re-formed; to Pere des Bosses on transubstantia-tion, and to Dr. Samuel Clarke on time and space; to Remond de Montmort on Plato, and to Francke on popular education; to the queen of Prussia, his pupil, on free will and predestination; to the electress Sophia, her mother, on English politics; and to the cabinet of Peter the Great on the Slavic and oriental languages. A controversy with Newton concerning the discovery of the differential calculus embittered the latter years of his life.

There is little doubt that Newton's method of fluxions and Leibnitz's method of infinitesimals were both independent and original discoveries; but the priority of publication belongs to Leibnitz, who gave a summary of the principles of the differential calculus in the Acta Eruditorum in 1684. Sir David Brewster's account of this matter, in his "Life of Newton," is, according to the German authorities Gerhart and Guh-rauer, very incomplete, ignoring some important documents, particularly a letter of Leibnitz to Oldenburg dated Aug. 27, 1G76. The royal society of London appointed a commission to examine the question, whose report, Commercium Epistolicum (1712), was in favor of Newton. This is admitted not to have been impartial, and its deficiencies are shown in a revised edition by Biot and Lefort (1856). - The principal metaphysical speculations of Leibnitz are contained in his Theodicee, Nou-veaux essais, Systeme nouveau de la nature (1695), De Ipsa Natura (1608), the fragment on Monadologie (1714), and in portions of his correspondence. He was too much occupied with all the learning of Europe to give a complete and systematic development of his opinions either in this or any other department.

His mind was nurtured in the controversy between the principles of Descartes and Locke, the ultimate tendencies of each of which he was able to perceive, and between which he wished to establish a position. He controverted Locke's rejection of innate ideas, by maintaining that, though no ideas be innate, there is yet an innate faculty for forming ideas independent of and superior to sensation. To the old axiom of sensualism, Nihil est in intellectu, quod non fuerit prius in sensu, he made the revolutionary addition, nisi ipse intellectus. The mind he compares not to a tabula rasa, a blank tablet, but to a block of marble that has certain characteristic veins in it; affirms it to contain potentially in itself the general notions of things, which are unfolded as occasions invite, the germs of our ideas and of the eternal truths which are derived from them. Those necessary truths, which take their origin not from experience, but primarily from the thinking soul, are the elements of all knowledge. Thus, unlike that of Locke, the starting point of his philosophy is not the products of sensation, but the laws of the understanding; and he creates not a system of empiricism, but a system of rationalism.

He departs almost equally from the results of Cartesianism as developed by Malebranche and Spinoza. In Descartes the prominence of the idea of the infinite or absolute tends to cast finite nature into the shade. This tendency appears more decidedly in Malebranche, who denied second causes, and limited all real agency to the Supreme Being, and in Spinoza, who affirmed all thought and substance to be alike parts and modifications of the one sole Existence. Thus the idea of cause was banished from the universe of created things, and all phenomena were regarded only as modes of the divine action. To avoid this result, to vindicate the notion of causality, was the object which Leibnitz had in view in declaring all matter to be necessarily active. He affirmed that one body cannot receive the power of acting from any other, but that the whole force is preexistent in itself. He thus substituted in the study of nature the notion of force for that of mode, the form of dynamics for the form of abstract geometry. This principle is the key to his peculiar system. He begins with maintaining that the pure d priori conceptions of the reason are full and adequate expressions of objective realities.

Logical truth is equivalent to actual truth; rational possibility is necessarily reality; ideas are identical with things. He introduces the two test principles of contradiction and sufficient reason, the former applying to the realm of necessary ideas, the latter to that of contingent facts. Whatsoever abstract conception involves no contradiction with the reason itself is absolutely true. But to determine what ideas are valid in any world of contingent phenomena, in any particular circumstances, there is needed the second principle. For every actual truth a sufficient reason must be rendered, showing that it is that which is best adapted to bring about the intended result. Thus everything must be judged by its final cause. The Cartesian doctrine, that substance consists essentially in extension, does not explain the constant movements and developments of nature. Unless, therefore, every phenomenon be regarded as a direct product of the divine mind, Leibnitz maintains that some inherent, causative, initiative power must be attributed to matter. This power cannot reside in masses as such, since they are infinitely divisible, and may therefore be reduced to a zero of extension, till they lose every material property.

Hence his doctrine of monads, as the simple active elements of things, the veritable, living atoms of nature, the immaterial, indivisible, and final forces of the universe, uninfluenced from without, but continually changing by an inward principle. All monads contain an inward energy by virtue of which they develop themselves spontaneously; they are all different from each other, each having peculiar attributes; all are, properly speaking, souls, being endowed with perception, though those which compose material objects do not possess apperception or consciousness; all are independent of each other, each having its own means of development, and forming a microcosm or living image of the whole universe. In every monad might be read the world's history from beginning to end, each of them being a kind of deity (parvus in suo genere deus). God is the absolute, original monad, from which all the rest are generated; the primitive and necessary substance, in which the detail of changes exists emanantly. Hence follows another doctrine of Leibnitz's philosophy, that of prees-tablished harmony. The dualism of Descartes is rendered unnecessary by the reduction of mind and matter to the same essence, the former being represented by conscious and the latter by unconscious monads.

But these two classes of monads are wholly unlike, and exert no influence on each other. To explain their relation, therefore, Leibnitz reverts to the original constitution of things as perfected by God himself, who, he maintains, has so harmonized all the monads of which the universe is composed, that they work in complete unison in order to accomplish the end for which they were intended. This harmony is not only pre-established by a divine decree, but is produced by virtue of the very nature of monads. In one view every volition of a rational agent finds in the constant procession of physical forces a concurrent event by which it is executed; and in another view, the monads of the human system and of the outward universe are so accommodated to each other, each being a representative of all the rest and a mirror of all things, that each feels all that passes in every other, and all conspire together in every act, more or less effectively in proportion to their nearness to the prime agent. Hence the harmony between all the parts of matter, between the future and the past, between divine decrees and human actions, between the reign of efficient and that of final causes. The transition from these principles to Leibnitz's doctrine of optimism is easy.

Evil is a necessary condition of finite being. The existing universe is one of innumerable possible universes, each of which would have had a different measure of good and evil. The present was made actual, because it presented to the Divine Intelligence the smallest degree of the latter and the largest of the former. Metaphysical evil consists simply in limitation, and moral evil is permitted only for the sake of a greater ultimate good. It follows that he maintained the doctrine of philosophical necessity as the only kind of liberty consistent with the preestablished order of the universe. The want of a logical and connected statement of the philosophy of Leibnitz was supplied by his disciple Wolf. - Leibnitz was of medium stature, of a spare but vigorous frame, was accustomed to eat much and drink little, regulated his meals by his pursuits and not by time, usually studied far into the night, sometimes sat by his desk almost without rising for months, sleeping in his chair, liked to converse with all sorts of people, and was never married.

He wrote very little in his native language, his important treatises being either in Latin or French. His philosophical works were edited by Erdmann (Berlin, 1840). The collective edition by Pertz comprises altogether 12 volumes (Hanover, 1843-'62), consisting of Ge-schichte, prepared by Pertz himself (4 vols., 1843-'7); Philosophie, by Grotefend (1 vol., 1846); and Mathematik, by Gerhardt (7 vols., 1849-'62). See also Foucher de Careil's (Euvres de Leibnitz, from original documents, with annotations (6 vols., Paris, 1859-'65 et seq., the whole to comprise upward of 20 vols.), and the complete edition by Onno Klopp (6 vols., Hanover, 1864-'72 et seq.). The best biography is by Guhrauer (2 vols., Breslau, 1842; with additions, 1846). This is the basis of the "Life of Leibnitz," by J. M. Mackie (Boston, 1845). - Compare Schelling, Leibniz als Denker; Hartenstein, De Materia apud Leibnitz Nrotitione; Helferich, Spinoza und Leibniz, oder das Wesen des Idealismus und Realismus; Feuerbach, Darstellung, Entwick-elung und Kritik der Leibniz' schen Philosophie (Anspach, 1837); Zimmermann, Leibniz und Herbart (Vienna, 1849), and Das Rechtsprin-cip bei Leibniz (1852); Kvet, Leibnizen's Logih (Prague, 1857); the writings relating to his works by Bonifas (Paris, 1863), Thilo (Berlin, 1864), Summer (Gottingen, 1866), and Jacoby (Berlin, 1867); Durdik's Leibniz und Newton (Halle, 1869); and Leibniz"sche Gedanken in der Naturwissenschaft, by Du Bois-Rcymond (Berlin, 1871).