Leibnitz, Godfrey William De

, a very eminent mathematician and philosopher, was born at Leipsic, July 4, 1646. His father, Frederic Leibnitz, was professor of moral philosophy, and secretary to that university; but did not survive the birth of his son above six years. His mother put him under messieurs Homschucius and Bachuchius, to teach him Greek and Latin; and he made so quick a progress as to surpass the expectations of his master; and not content with their tasks, when at home, where there was a well-chosen library left by his father, he read with attention the ancient authors, and “especially Livy. The poets also had a share in his studies, particularly Virgil, many of whose verses he could repeat in his old age, with fluency and accuracy. He had himself also a talent for versifying, and is said to have composed in one day’s time, a poem of three hundred lines, without an elision. This early and assiduous attention to classical learning laid the foundation of that correct and elegant taste which appears in all his writings. At the age of | fifteen, he became a student in the university of Leipsic, and to polite literature joining philosophy and the mathematics, he studied the former under James Thomasius, and the latter under John Kuhnius, at Leipsic. He afterwards went to Jena, where he heard the lectures of professor Bohnius upon polite learning and history, and those of Falcknerius in the law. At his return to Leipsic, in 1663, he maintained, under Thomasius, a thesis,” De Principiis Individuationis.“In 1664, he was admitted M. A.; and observing how useful philosophy might be in illustrating the law, he maintained several philosophical questions taken out of the” Corpus Juris." At the same time he applied himself particularly to the study of the Greek philosophers, and engaged in the task of reconciling Plato with Aristotle; as he afterwards attempted a like reconciliation between Aristotle and Des Cartes. He was so intent on these studies, that he spent whole days in meditating upon them, in a forest near Leipsic.

His views being at this time chiefly fixed upon the law, he commenced bachelor in that faculty in 1665, and the year after supplicated for his doctor’s degree; but was denied, as not being of sufficient standing, that is, not quite twenty; but the real cause of the demur was his rejecting the principles of Aristotle and the schoolmen, against the received doctrine of that time. Resenting the affront, he went to Altorf, where he maintained a thesis, “De Casibus perplexis,” with so much reputation, that he not only obtained his doctor’s degree, but had an offer of being made professor of law extraordinary. This, however, was declined; and he went from Altorf to Nuremberg, to visit the learned in that university. He had heard of some literati there who were engaged in the pursuit of the philosopher’s stone; and his curiosity was raised to be initiated into their mysteries. For this purpose he drew up a letter full of abstruse terms, extracted out of books of chemistry; and, unintelligible as it was to himself, addressed it to the director of that society, desiring to be admitted a member. They were satisfied of his merit, from the proofs given in his letter; and not only admitted him into their laboratory, but even requested him to accept the secretaryship, with a stipend. His office was, to register their processes and experiments, and to extract from the books of the best chemists such things as might be of use to them in their pursuits. | About this time, baron Boinebourg, first minister of the elector of Mentz, passing through Nuremberg, met Leibnitz at a common entertainment; and conceived so great an opinion of his parts and learning from his conversation, that he advised him to apply himself wholly to law and history; giving him at the same time the strongest assurances, that he would engage the elector, John Philip of Schonborn, to send for him to his court. Leibnitz accepted the kindness, promising to do his utmost to render himself worthy of such a patronage; and, to be more within the reach of its happy effects, he repaired to Francfort upon the Maine, in the neighbourhood of Mentz. In 1668, John Casimir, king of Poland, resigning his crown, the elector palatine, among others, became a competitor for that dignity; and, while baron Boinebourg went into Poland to manage the elector’s interests, Leibnitz wrote a treatise to shew that the Polonnois could not make choice of a better person for their king. With this piece the elector palatine was extremely pleased, and invited our author to his court. But baron Boinebourg, resolving to provide for him at the court of Mentz, would not suffer him to accept this last offer from the palatine; and immediately obtained for him the post of counsellor of the chamber of review to the elector of Mentz. Baron Boinebourg had some connexions at the French court; and as his son, who was at Paris, was not of years to be trusted with the management of his affairs, he begged Mr. Leibnitz to undertake that charge.

Leibnitz, charmed with this opportunity of shewing bit gratitude to so zealous a patron, set out for Paris in 1672. He also proposed several other advantages to himself in this tour, and his views were not disappointed. He saw all the literati in that metropolis, made an acquaintance with the greatest part of them, and, besides, applied himself with vigour to the mathematics, in which study he had not yet made any considerable progress. He tells us himself, that he owed his advancement in it principally to the works of Pascal, Gregory, St. Vincent, and above all, to the excellent treatise of Huygens “De Horologio oscillatorio.” In this course, having observed the imperfection of Pascal’s arithmetical machine, which, however, Pascal did not live to finish, he invented a new one, as he called it; the use of which he explained to Mr. Colbert, who was extremely pleased with it and, the invention being approved | likewise by the Academy of sciences, he was offered a seat there as pensionary member. With sucli encouragement he might have settled very advantageously at Paris if he would have turned Roman catholic; but he chose to adhere to the Lutheran religion, in which he was born. In 1673, he lost his patron, M. de Boim-bourg; and, being at liberty by his death, took a tour to England, where he became acquainted with Oldenburg, the secretary, and John Collins, fellow of the royal society, from whom he received some hints of the invention of the method of fluxions, which had been discovered in 1664 or 1665, by Mr. (afterwards) sir Isaac Newton *.

While he was in England he received an account of the death of the elector of Mentz, by which he lost his pension. He then returned to France, whence be wrote to the duke of Brunswick Lunenburg, to inform him of his circumstances. That prince sent him a very gracious answer, assuring him of his favour, and, for the present, appointed him counsellor of his court, with a salary; but gave him leave to stay at Paris, in order to complete his arithmetical machine, which, however, was not completed until after his death. In 1674 be went again to England, whence he passed, through Holland, to Hanover, and from his first

*

The right to this invention is so interesting to our coontry, -that we must not omit this occasion of atserting it The state ef the dispute between the competitors, Leibnitz and Newton, is as follows: Newton discovered it in 1665 aud 1666, and communicated it to Dr. Barrow in 1669. Leibnitz said he had some glimpses of it in 167’2, before he had seen any hint of Newton’s prior discovery, which was communicated by Mr. Collins to several foreigners in 16“3; in the beginning of which year Leibnitz was in England, and commenced an acquaintance with Collins, but at that time only claimed the invention of another differential method, properly so called, which indeed was Newton’s invention; mentioning no other till June 1617: and this was a year after a letter of Newton’s, containing a sufficient description of the nature of the method, had been sent to Paris, to be communicated to him. However, nothing of it wa printed by sir Isaac; which being observed by the other, he first printed it, under the name of the Differential, and sometime* the Infinitesimal method, in the ” Acta Tniditonim I.ipsiar, for the yearlr>84.“And, as be still persisted in his claim to the invention, sir Isaac, at the request of George I. gave his majesty an account of the whole affair, and sent Leibnitz a defiance in express terras, to prore his assertion. This was answered by Leibnitz, in a letter which he sent by Mr. Kemond, at Paris, to be communicated to sir haac, after he had shewn it in France: declaring that he took this method in order to have indifferent and intelligent witnesses. That method being disliked by sir haac, who thought that London, as well as Paris might furnish such witnesses, be resolved to carry the dispute no farther; and, when Leibnitz’s letter came from France, he refuted it, by remarks which be communicated only to some of his friends; but, as soon as he heard of Leibuiu’s death, which happened six months after, be published Leibnitz’s letter, with his own remarks, by way of supplement to RalpUon’s ” History of Fluxions."

| arrival there made it his business to enrich the library of that prince with the best books of all kinds. That duke dying in 1679, his successor, Ernest Augustus, then bishop of Osnabrug, afterwards George I. extended the same patronage to Leibnitz, and directed him to write the history of the house of Brunswick. Leibnitz undertook the task; and, travelling through Germany and Italy to collect materials, returned to Hanover in 1690, with an ample store. While he was in Italy he met with a singular instance of bigotry, which, but for his happy presence of mind, might have proved fatal. 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. Leibnitz hearing this, without discovering the least emotion, pulled out a set of beads, and turned them over with a seeming devotion. The artifice succeeded; one of the sailors observing to the pilot, that, since the man was no heretic, it would be of no use to drown him. 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 the advice of Leibnitz, who was appointed perpetual president of it; and, though his other affairs did not permit him to reside constantly upon the spot, yet he made ample amends by the treasures with which he enriched their memoirs, in several dissertations upon geometry, polite learning, natural philosophy, and physic. He also projected to establish at Dresden another academy like that at Berlin. He communicated his design to the king of Poland in 1703, who was inclined to promote it; but the troubles which arose shortly after in that kingdom, hindered it from being carried into execution.

Besides these projects to promote learning, there is another still behind of a more extensive view, both in its nature and use; he set himself to invent a language so easy and so perspicuous, as to become the common language of all nations of the world. This is what is called “The Universal Language,” and the design occupied the thoughts of our philosopher a long time. The thing had been attempted before by d’Algarme, and Dr. Wilkins, bishop of Chester; but Leibnitz did not approve of their method, and therefore attempted a new one. His | predecessors in his opinion had not reached the point; they might indeed enable nations who did not understand each othe,r, to correspond easily together; but they had not attained the true real characters, which would be the beat instruments of the human mind, and extremely assist both the reason and memory. These characters, he thought, ought to resemble as much as possible those of algebra, which are simple and expressive, and never superfluous and equivocal, but whose varieties are grounded on reason. In order to hasten the execution of this vast project, he employed a young person to put into a regular order the definitions of all things whatsoever; but, though he laboured in it from 1703, yet his life did not prove sufficient to complete it*. In the meantime, his name became famous over Europe; and his merit was rewarded by other princes, besides the elector of Hanover. In 1711, he was made aulic counsellor to the emperor; and the czar of Moscovy appointed him privy-counsellor of justice, with a pension of a thousand ducats f. Leibnitz undertook at the same time to establish an academy of sciences at Vienna; but that project miscarried a disappointment which some have ascribed to the plague. However that be, it is certain he only had the honour of attempting it, and the emperor rewarded him for it with a pension of 2000 florins, promising him to double the sum, if he would come and reside at Vienna, which his death prevented. In the mean time, the History of Brunswick being inter* rupted by other works which he wrote occasionally, he found at his return to Hanover, in 1714, that the elector had appointed Mr. Eckard for his colleague in that history. The elector was then raised to the throne of Great Britain; and soon after his arrival, the electoral princess, then princess of Wales, and afterwards queen Caroline, engaged Leibnitz in a dispute with Dr. Samuel Clarke upon the subject of free-will, the reality of space, and other philosophical subjects. This controversy was carried on by letters which passed through her royal‘ high ness’s bands, and ended only with the death of Leibnitz, Nov. 14, 1716, occasioned by the gout and stone, at the age of seventy.

* He speaks in some places of an “Recueil de Literature.” printed at

alphabet of human thoughts, which Amsterdam, in 1740, which also says

tie was contriving, which, it is very that Leibnitz refused the place of

probable, had some relation to his keeper of Hie Vatican library, offertJ

universal language. him by cardinal Casanata, while hf

f The particulars we have ia the was at Rome.

| Leibnitz was in person of a middle stature, and of a thin habit. He had a studious air, and a sweet aspect, though short-sighted. He was indefatigably industrious, and so continued to the end of his life. He ate and drank little. Hunger alone marked the time of his meals, and his diet was plain and strong. He loved travelling, and different climates never affected his health. In order to impress upon his memory what he had a mind to remember, he wrote it down, and never read it afterwards. His temper was naturally choleric, but on most occasions he had th art to restrain it. As he had the honour of passing for one of the greatest men in Europe, he was sufficiency sensible of it. He was solicitous in procuring the favour of princes, which he turned to his own advantage, as well as to the service of learning. He was affable and polite in conversation, and averse to disputes. He was thought to love money, and is said to have left sixty thousand crowns, yet no more than fifteen or twenty thousand out at interest; the rest being found in crown-pieces and other specie, hoarded in corn-sacks. He always professed himself a Lutheran, but never joined in public worship; and in his last sickness, being desired by his coachman, who was his favourite servant, to send for a minister, he would not hear of it, saying he had no occasion for one. He was never married, and never attempted it but once, when he was about fifty years old; and the lady desiring time to consider of it, gave him an opportunity of doing the same; which produced this conclusion, “that marriage was a good thing, but a wise man ought to consider of it all his life.” Mr. Lcefler, son of his sister, was his sole heir, whose wife died suddenly with joy at the sight of so much money left them by their uncle. It is said he had a natural son in his youth, who afterwards lived with him, was serviceable to him in many ways, and had a considerable share in his confidence. He went by the name of William Dinninger, and extremely resembledhis father.

The following particulars relating to M. Leibnitz are extracted from the works of the abbé Conti, as given in the Gazette Litteraire for 1765

This great man,” says the abbé“,” owed his death to a medicine given him by a Jesuit at Vienna, which he took from a desire to obtain a too speedy cure for the gout. This removed the disorder suddenly from his foot to his stomach, and killed him. At the time of his death, | he was sitting on the side of his bed, with an ink-stand and Barclay’s Argenis beside him. They say that he was continually reading this book, the style of which pleased him exceedingly; and that it was from this taste he intended to form his history.

"He left behind him twelve or thirteen thousand crowns in specie, and a bag full of gold medals. Among his papers was found a manuscript on the Cartesian method, which has not yet appeared; a political tract of Bud, the letters of pope Sylvester II. and Spinoza’s letters. His own manuscripts were in great disorder. There were found many papers filled with his thoughts, and with ban mots either his own, or collected by him. Leibnitz had passed part of his life with almost all the sovereigns of Europe, and expressed himself with much spirit and elegance. He left behind him poems, epigrams, and loveletters. He was connected with the learned of all countries; and carefully preserved all the letters he wrote and received. M. Eckard says, there were found in his letters the history of the inventions, discoveries, and literary disputes during the space of forty years. He applied himself to every thing; having left behind him a book of etymologies in the German language, and he laboured at an universal language to the time of his death. He loved chemistry j and to acquire the secrets of that art, he contrived a language chiefly composed of foreign words, which procured him the acquaintance of several chemists.

"He read all books without exception the more odd and whimsical the title was, the more curious he was to examine the contents. He found a romance written in German by Mr. Eckard: this romance contained the history of a father, who having consulted an astrologer about the future destiny of his son, learnt that to preserve him from death, there was no other method than to make him pass for the son of a hangman. Leibnitz found this romance so excellent that he read it through at one sitting.

The first time he visited Hanover, he never went out of his study. He never spoke of the sacred Scriptures without reverence; they are full, he would say, of lessons useful to mankind. He was unwilling to engage in religious disputes, but when his own principles were attacked, he defended himself with much warmth. He was fond of the Estern manners, had a great esteem for the Arabic and Chinese languages, and recommended the study of | them. He formed a project for making a voyage to China, and the Czar promised to fit him out; but on reflexion, he found himself too far advanced in life to undertake it He collected many Chinese books in which were contained the antiquities of that empire.

Leibnitz was author of a great multitude of writings j several of which were published separately, and many others in the memoirs of different academies. He invented a binary arithmetic, and many other ingenious matters. His claim to the invention of Fluxions, we have already noticed. 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 Philosophise more geometrico demonstrate,“&c. 1728, 4to. There cam*- out a collection of our author’s letters in 1734 and 1735, entitled,” E pis tolas ad diversos theologici, juridici, medici, philosophic!, mathematici, historici, & philologici argument! e Mss. auctores^ cum annotationibus suis priuium divulgavit Christian Cortholtus,“and another collection of his letters was published in 1805 at Hanover, by M. Feder, under the title of” Commercii epistolici Leibnitziani typis nondum vulgati selecta specimina,“8vo. Of his collected works, the best edition, distributed into classes by M. Dutens, was published at Geneva in six large volumes 4to, in 1768, entitled,” Gothofredi Guillelmi Leibnitzii Opera omnia," &c.

As Leibnitz was long the successful teacher of a new system of philosophy, it may be now necessary to give some account of it, which was formed 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 irt all directions, or with the obliquity of the planes of the planetary orbits; nor does it 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 system, 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 indiscernilles; 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 iiifinitum, he ascribes a monad, 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 describes 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 substantial urn, or phenomene bienfondc. From this metaphysical theory, which must be confessed too hypothetical to afford satisfaction, Leibnitz deduced many dogmas respecting the divine nature and operations, the nature of human actions, good and evil, natural and moral, and other subjects which he treats with great subtlety, and in a connected train of reasoning.

The translator of Mosheim’s Ecclesiastical History observes, that the progress of Arminianism has declined in Germany and several parts of Switzerland, in consequence of the influence of the Leibnitzian and Wolfian philosophy. Leibnitz and Wolf, by attacking that liberty of indifference, which is supposed to imply the power of acting not only without, but against motives, struck, he says, at the very foundation of the Arminian system. He adds, that the greatest possible perfection of the universe, considered as the ultimate end of creating goodness, removes from the doctrine of predestination those arbitrary procedures and narrow views, with which the Calvinists are supposed to have loaded it, and gives it a new, a more pleasing, and a more philosophical aspect. As the Leibnitzians laid down this great end as the supreme object of God’s universal dominion, and the scope to which all his dispensations are directed, so they concluded, that, if this end was proposed, it must be accomplished. Hence the doctrine of necessity, to fulfil the purposes of a predestination founded in wisdom and goodness; a necessity, physical and mechanical, in the motions of material and inanimate things; but a necessity, moral and spiritual, in the voluntary determinations of intelligent beings, in consequence of prepollent motives, which produce their effects with certainty, though these effects be contingent, and by no | means the offspring of an absolute and essentially immutable fatality. Tbese principles, says the same writer, are evidently applicable to the main doctrines of Calvinism; by them predestination is confirmed, though modified with respect to its reasons and its end; by them irresistible grace (irresistible in a moral sense) is maintained upon the hypothesis of prepollent motives and a moral necessity; the perseverance of the saints is also explicable upon the same system, by a series of moral causes producing a series of moral effects. But Maclaine adds, that the Leibnitzian system has scarcely been embraced by any of the English Calvmists, because, as he supposes, they adhere firmly to their theology, and blend no pnilosophical principles with their system.

Gibbon has drawn the character of Leibnitz with great force and precision, as a man whose genius and studies have ranked his name with the first philosophic names of his age and country; but he thinks his reputation, perhaps, would have been more pure and permanent, if he had not ambitiously grasped the whole circle of human science. As a theologian, says Gibbon (who is not, perhaps, the most impartial judge of this subject), he successively contended with the sceptics, who believe too little, and with the papists who believe too much; and with the heretics, who believe otherwise than is inculcated by the Lutheran confession of Augsburgh. Yet the philosopher betrayed his love of union and toleration* his faith in revelation was accused, while he proved the Trinity by the principles of logic; and in the defence of the attributes and providence of the Deity, he was suspected of a secret correspondence with his adversary Bayle. The metaphysician expatiated in the fields of air; his pre-established harmony of the soul and body might have provoked the jealousy of Plato; and his optimism, the best of all possible worlds, seems an idea too vast for a mortal mind. He was a physician, in the large and genuine sense of the word like his brethren, he amused him with creating a globe and his Protogæa, or primitive earth, has not been useless to the last hypothesis of Buffon, which prefers the agency of fire to that of water. “I am not worthy,” adds Gibbon, “to praise the mathematician; but his name is mingled in all the problems and discoveries of the times; the masters of the art were his rivals or disciples; and if he borrowed from sir Isaac Newton, the sublime method of | fluxions, Leibnitz was at least the Prometheus who imparted to mankind the sacred fire which he had stolen from the gods. His curiosity extended to every branch of chemistry, mechanics, and the arts; and the thirst of knowledge was always accompanied with the spirit of improvement. The vigour of his youth had been exercised in the schools of jurisprudence; and while he taught, he aspired to reform the laws of nature and nations, of Rome and Germany. The annals of Brunswick, and of the empire, of the ancient and modern world, were presented to the mind of the historian; and he could turn from the solution of a problem, to the dusty parchments and barbarous style of the records of the middle age. His genius was more nobly directed to investigate the origin of languages and nations; nor could he assume the character of a grammarian, without forming the project of an universal idiom and alphabet. These various studies were often interrupted by the occasional politics of the times; and his pen was always ready in the cause of the princes and patrons to whose service he was attached; many hours were consumed in a learned correspondence with all Europe; and the philosopher amused his leisure in the composition of French and Latin poetry. Such an example may display the exte^nt and powers of the human understanding, but even his powers were dissipated by the multiplicity of his pursuits. He attempted more than he could finish; he designed more than he could execute: his imagination was too easily satisfied with a bold and rapid glance on the subject, which he was impatient to leave; and Leibnitz may be compared to those heroes, whose empire has been lost in the ambition of universal conquest.1

1

Gen. Dict. Eloge by Fontenelle. Brucker. —Hutton’s Dictionary. Gibbon’s Miscellaneous Works. —Dict. Hist.Saxii Onomast.