LEIBNITZ (Godfrey-William)

, an eminent mathematician and philosopher, was born at Leipsic in Saxony in 1646. At the age of 15, he applied himself to mathematics at Leipsic and Jena; and in 1663, maintained a thesis de Principiis Individuationis. The year following he was admitted Master of Arts. He read with great attention the Greek philosophers; and endeavoured to reconcile Plato with Aristotle, as he afterwards did Aristotle with Des Cartes. But the study of the law was his principal view; in which faculty he was admitted Bachelor in 1665. The year following he would have taken the degree of Doctor; but was refused it on pretence that he was too young, though in reality because he had raised himself several enemies by rejecting the principles of Aristotle and the Schoolmen.

Upon this he repaired to Altorf, where he maintained a thesis de Casibus Perplexis, with such applause, that he had the degree of Doctor conferred on him.

In 1672 he went to Paris, to manage some affairs at the French Court for the baron Boinebourg. Here he became acquainted with all the Literati, and made farther and considerable progress in the study of mathematics and philosophy, chiefly, as he says, by the works of Pascal, Gregory St. Vincent, and Huygens. In this course, having observed the imperfection of Pascal's arithmetical machine, he invented a new one, as he called it, which was approved of by the minister Colbert, and the Academy of Sciences, in which he was offered a seat as a member, but refused the offers made to him, as it would have been necessary to embrace the Catholic religion.

In 1673, he came over to England; where he became acquainted with Mr. Oldenburg, secretary of the Royal Society, and Mr. John Collins, a distinguished member of the Society; from whom it seems he received some hints of the method of fluxions, which had been invented, in 1664 or 1665, by the then Mr. Isaac Newton.

The same year he returned to France, where he resided till 1676, when he again passed through England, and Holland, in his journey to Hanover, where he proposed to settle. Upon his arrival there, he applied himself to enrich the duke's library with the best books of all kinds. The duke dying in 1679, his successor Ernest Augustus, then bishop of Osnaburgh, shewed Mr. Leibnitz the same favour as his predecessor had done, and engaged him to write the History of the House of Brunswick. To execute this task, he travelled over Germany and Italy, to collect materials, While he was in Italy, he met with a pleasant adventure, which might have proved a more serious affair, Passing in a small bark from Venice to Mesola, a storm arose; during which the pilot, imagining he was not understood by a German, whom, being a heretic, he looked on as the cause of the tempest, proposed to strip him of his cloaths and money, and throw him overboard. Leibuitz hearing this, without discovering the least emotion, drew a set of beads from his pocket, and began turning them over with great seeming devotion. The artisice succeeded; one of the sailors observing to the pilot, that, since the man was no heretic, he ought not to be drowned.

In 1700 he was admitted a member of the Royal Academy of Sciences at Paris. The same year the elector of Brandenburg, afterwards king of Prussia, founded an academy at Berlin by his advice; and he was appointed perpetual President, though his affairs would not permit him to reside constantly at that place. He projected an academy of the same kind at Dresden; and this design would have been executed, if it had not been prevented by the confusions in Poland. He was engaged likewise in a scheme for an universal language, and other literary projects. Indeed his writings had made him long before famous over all Europe, and he had many honours and rewards conferred on him. Beside the office of Privy Counsellor of Justice, which the elector of Hanover had given him, the emperor appointed him, in 1711, Aulic Counsellor; and the czar made him Privy Counsellor of Justice, with a pension of 1000 ducats. Leibnitz undertook at the same time to establish an academy of sciences at Vienna; but the plague prevented the execution of it. However, the emperor, as a mark of his favour, settled a pension on him of 2000 florins, and promised him one of 4000 if he would come and reside at Vienna; an offer he was inclined to comply with, but was prevented by his death.

Meanwhile, the History of Brunswick being interrupted by other works which he wrote occasionally, he found, at his return to Hanover in 1714, that the elector had appointed Mr. Eccard for his colleague in writing that history. The elector was then raised to the throne of Great Britain, which place Leibnitz visited the latter end of that year, when he received particular marks of friendship from the king, and was frequently at court. He now was engaged in a dispute with Dr. Samuel Clarke, upon the subjects of free-will, the reality of space, and other philosophical subjects. This was conducted with great candour and learning; and the papers, which were published by Clarke, will ever be esteemed by men of genius and learning. The controversy ended only with the death of Leibnitz, Nov. 14, 1716, which was occasioned by the gout and stone, in the 70th year of his age.

As to his character and person: He was of a middle stature, and a thin habit of body. He had a studious air, and a sweet aspect, though near-sighted. He was indefatigably industrious to the end of his life. He eat and drank little. Hunger alone marked the time of his meals, and his diet was plain and strong.| He had a very good memory, and it was said could re. peat the Æneid from beginning to end. What he wanted to remember, he wrote down, and never read it afterwards. He always professed the Lutheran religion, but never went to sermons; and when in his last sickness his favourite servant desired to send for a minister, he would not permit it, saying he had no occasion for one. He was never married, nor ever attempted it but once, when he was about 50 years old; and the lady desiring time to consider of it, gave him an opportunity of doing the same: he used to say, “that marriage was a good thing, but a wise man ought to consider of it all his life.”

Leibnitz was author of a great multitude of writings; several of which were published separately, and many othersin the memoirs of different academies. He invented a binary arithmetic, and many other ingenious matters. His claim to the invention of Fluxions, has been spoken of under that article. Hanschius collected, with great care, every thing that Leibnitz had said, in different passages of his works, upon the principles of philosophy; and formed of them a complete system, under the title of G. G. Leibnitzii Principia Philosaphiæ more geometrico demonstrata &c, 1728, in 4to. There came out a collection of our author's letters in 1734 and 1735, intitled, Epistolæ ad diversos theologici, juridici, medici, philosophici, mathematici, historici, & philologici argumenti e MSS. auctores : cum annotationibus suis primum divulgavit Christian Cortholtus. But all his works were collected, distributed into classes by M. Dutens, and published at Geneva in six large volumes 4to, in 1768, intitled, Gothofredi Guillelmi Leibnitii Opera Omnia &c.

Lei<*>nitzian Philosophy, or the Philosophy of Leibnitz, is a system formed and published by its author in the last century, partly in emendation of the Cartesian, and partly in opposition to the Newtonian philosophy. In this philosophy, the author retained the Cartesian subtile matter, with the vortices and universal plenum; and he represented the universe as a machine that should proceed for ever, by the laws of mechanism, in the most perfect state, by an absolute inviolable necessity. After Newton's philosophy was published, in 1687, Leibnitz printed an Essay on the celestial motions in the Act. Erud. 1689, where he admits the circulation of the ether with Des Cartes, and of gravity with Newton; though he has not reconciled these principles, nor shewn how gravity arose from the impulse of this ether, nor how to account for the planetary revolutions in their respective orbits. His system is also defective, as it does not reconcile the circulation of the ether with the free motions of the comets in all directions, or with the obliquity of the planes of the planetary orbits; nor resolve other objections to which the hypothesis of the vortices and plenum is liable.

Soon after the period just mentioned, the dispute commenced concerning the invention of the method of Fluxions, which led Mr. Leibnitz to take a very decided part in opposition to the philosophy of Newton. From the goodness and wisdom of the Deity, and his principle of a sufficient reason, he concluded, that the universe was a perfect work, or the best that could possibly have been made; and that other things, which are evil or incommodious, were permitted as necessary consequences of what was best: that the material sys- tem, considered as a perfect machine, can never fall into disorder, or require to be set right; and to suppose that God interposes in it, is to lessen the skill of the author, and the perfection of his work. He expressly charges an impious tendency on the philosophy of Newton, because he asserts, that the fabric of the universe and course of nature could not continue for ever in its present state, but in process of time would<*>require to be re-established or renewed by the hand of its first framer. The perfection of the universe, in consequence of which it is capable of continuing for ever by mechanical laws in its present state, led Mr. Leibnitz to distinguish between the quantity of motion and the force of bodies; and, whilst he owns in opposition to Des Cartes that the former varies, to maintain that the quantity of force is for ever the same in the universe; and to measure the forces of bodies by the squares of their velocities.

Mr. Leibnitz proposes two principles as the foundation of all our knowledge; the first, that it is impossible for a thing to be, and not to be at the same time, which he says is the foundation of speculative truth; and secondly, that nothing is without a sufficient reason why it should be so, rather than otherwise; and by this principle he says we make a transition from abstracted truths to natural philosophy. Hence he concludes that the mind is naturally determined, in its volitions and elections, by the greatest apparent good, and that it is impossible to make a choice between things perfectly like, which he calls indiscernibles; from whence he infers, that two things perfectly like could not have been produced even by the Deity himself: and one reason why he rejects a vacuum, is because the parts of it must be supposed perfectly like to each other. For the same reason too, he rejects atoms, and all similar parts of matter, to each of which, though divisible ad infinitum, he ascribes a monad (Act. Lipsiæ 1698, pa. 435) or active kind of principle, endued with perception and appetite. The essence of substance he places in action or activity, or, as he expresses it, in something that is between acting and the faculty of acting. He affirms that absolute rest is impossible, and holds that motion, or a sort of nisus, is essential to all material substances. Each monad he deseribes as representative of the whole universe from its point of sight; and yet he tells us, in one of his letters, that matter is not a substance, but a substantiatum, or phenomené bien fondé. See also Maclaurin's View of Newton's Philosophical Discoveries, book 1, chap. 4.