Gottfried Wilhelm Leibniz

Summary

Gottfried Wilhelm Leibniz, born in Leipzig on July 1, 1646 and died in Hanover on November 14, 1716, was a German philosopher, scientist, mathematician, logician, diplomat, jurist, librarian and philologist. A polymathic mind, an important personality of the Frühaufklärung period, he occupies a primordial place in the history of philosophy and the history of science (especially mathematics) and is often considered as the last “universal genius”.

He was born in 1646 in Leipzig into a Lutheran family; his father, Friedrich Leibnütz, was a lawyer and professor of moral philosophy at the city”s university. After his father”s death in 1652, Leibniz studied in the library bequeathed to him by his mother and uncle, in addition to his education. Between 1661 and 1667, he studied at the universities of Leipzig, Jena and Altdorf and obtained degrees in philosophy and law. From 1667 he was employed by Johann Christian von Boyneburg and the Elector of Mainz Jean-Philippe de Schönborn. Between 1672 and 1676 he lived in Paris and traveled to London and The Hague, meeting the scientists of his time and learning about mathematics. After the death of his two employers in 1676, he accepted the offer of employment by the House of Hanover ruling the principality of Calenberg and moved to Hanover where he held the positions of librarian and political advisor. There he carried out research in a wide variety of fields, traveling throughout Europe and corresponding as far as China, until his death in 1716.

In philosophy, Leibniz is, with René Descartes and Baruch Spinoza, one of the main representatives of rationalism. In addition to the principle of non-contradiction, he added three other principles to his reflections: the principle of sufficient reason, the principle of identity of indistinguishables and the principle of continuity. Conceiving thoughts as combinations of basic concepts, he theorized the universal characteristic, a hypothetical language that would allow to express the totality of human thoughts, and that could solve problems by calculation thanks to the calculus ratiocinator, anticipating computer science of more than three centuries. In metaphysics, he invented the concept of monad. Finally, in theology, he established two proofs of the existence of God, called ontological and cosmological proofs. Unlike Spinoza, who thought God was immanent, Leibniz conceived of him as transcendent, in the traditional manner of monotheistic religions. To reconcile the omniscience, omnipotence and benevolence of God with the existence of evil, he invented, within the framework of theodicy, a term that we owe to him, the concept of the best of all possible worlds, which was mocked by Voltaire in the philosophical tale Candide. He will have a major influence on modern logic developed from the 19th century onwards as well as on analytical philosophy in the 20th century.

In mathematics, Leibniz”s main contribution is the invention of the infinitesimal calculus (differential and integral calculus). Although the authorship of this discovery was for a long time the subject of a controversy opposing him to Isaac Newton, historians of mathematics agree today that the two mathematicians developed it more or less independently; Leibniz introduced a new set of notations, more convenient than those of Newton, and still in use today. He also worked on the binary system as a substitute for the decimal system, inspired in particular by old Chinese works, and also carried out research on topology.

Writing continuously – mainly in Latin, French and German – he left a huge literary heritage – Nachlass in German -, listed in the catalog of the Berlin edition (“Arbeitskatalog der Leibniz-Edition”) and kept for the most part in the Hanover library. It consists of about 50,000 documents, including 15,000 letters with more than a thousand different correspondents, and is still not fully published.

Youth (1646-1667)

Gottfried Wilhelm Leibniz was born in Leipzig on July 1, 1646, two years before the end of the Thirty Years” War that ravaged central Europe, into a Lutheran family, “probably of distant Slavic descent. His father, Friedrich Leibnütz, was a jurist and professor of moral philosophy at the city”s university; his mother, Catherina Schmuck, Friedrich”s third wife, was the daughter of law professor Wilhelm Schmuck (de). Leibniz had a half-brother, Johann Friedrich (died 1696), a half-sister, Anna Rosine, and a sister, Anna Catherina (1648-1672) – whose son, Friedrich Simon Löffler, was Leibniz” heir. He was baptized on July 3.

His father died on September 15, 1652, when Leibniz was six years old, and his education was supervised by his mother and uncle, but the young Leibniz also learned on his own in the large library left by his father. In 1653, at the age of 7, Leibniz was enrolled at the Nikolaischule, where he remained until his entrance to the university in 1661 – according to Yvon Belaval, it is nevertheless possible that Leibniz was enrolled even before his father”s death; according to him, his schooling seems to have been as follows: grammar (1652-1655), humanities (1655-1658), philosophy (1658-1661). Although he learned Latin at school, it seems that around the age of twelve, Leibniz taught himself Latin at an advanced level as well as Greek, apparently in order to be able to read the books in his father”s library. Among these books, he was especially interested in metaphysics and theology, both from Catholic and Protestant authors. As his education progressed, he became dissatisfied with Aristotle”s logic and began to develop his own ideas. As he would later recall, he was there unknowingly finding the logical ideas behind rigorous mathematical demonstrations. The young Leibniz became familiar with the works of Latin authors such as Cicero, Quintilian and Seneca, of Greek authors such as Herodotus, Xenophon and Plato, but also of the Scholastic philosophers and theologians.

He is the pupil of Jakob Thomasius who supervises his first philosophical work, which allows him to obtain his baccalaureate in 1663: Disputatio metaphysica de principio individui. In his work, he refuses to define the individual by negation from the universal and “underlines the existential value of the individual, which cannot be explained by its matter alone or its form alone but rather in its whole being”. One finds here the beginnings of his notion of monad.

After his baccalaureate, he had to specialize in order to obtain a doctorate: having the choice between theology, law and medicine, he chose law. Before starting his courses, in the summer of 1663, he studied for a while in Jena, where he was exposed to less classical theories, and had, among others, the neopythagorean mathematician and philosopher Erhard Weigel as a professor of mathematics, who would lead Leibniz to start being interested in mathematical proofs for disciplines such as logic and philosophy. Weigel”s ideas, such as that number is the fundamental concept of the universe, were to have a considerable influence on the young Leibniz.

In October 1663, he returned to Leipzig for his doctorate in law. He had to work on “disputatio” at each stage of his studies and obtained a bachelor”s degree (in 1665). In addition, in 1664, he obtained a Master of Arts in philosophy for a dissertation combining philosophy and law by studying the relations between these fields according to mathematical ideas, as he learned from Weigel.

A few days after his Master of Arts degree, his mother died.

After obtaining his bachelor”s degree in law, Leibniz set out to obtain a habilitation in philosophy. His work, the Dissertatio de arte combinatoria (“Dissertation on the Combinatorial Art”), was published in 1666. In this work, Leibniz intends to reduce all reasoning and discoveries to a combination of basic elements, such as numbers, letters, colors, sounds. Although the habilitation gave him the right to teach, he preferred to pursue a doctorate in law.

Despite his recognized education and growing reputation, he was denied the doctorate in law, for reasons that are partly unexplained. It is true that he was one of the youngest candidates and that there were only twelve law tutors available, but Leibniz suspected that the dean”s wife had persuaded the dean to oppose Leibniz”s doctorate for some unexplained reason. Leibniz was not inclined to accept any delay, so he left for the University of Altdorf where he was enrolled in October 1666. His thesis being already ready, he became a doctor of law in February 1667 with his thesis De Casibus Perplexis in Jure (“Perplexing Cases in Law”). The academics of Altdorf were impressed by Leibniz (he was applauded during his thesis defense, in prose and verse, without notes, with such ease and clarity that his examiners could hardly believe that he had not learned it by heart), and offered him a professorship, which he refused.

While still perhaps a student in Altdorf, Leibniz got his first job, more a temporary solution than a real ambition: secretary of an alchemical society in Nuremberg (whose affiliation or not with the Rosicrucians is debated). He held this position for two years. The exact nature of his obedience is still much debated by historians. He spoke of his passage as a “sweet dream” as early as 1669, and in a joking tone in a letter to Gottfried ThomasiusGottfried Thomasius of 1691. From his membership in this society, he probably hoped for information on his combinatorics.

Early career (1667-1676)

When he left Nuremberg, Leibniz had ambitions to travel, at least to Holland. Shortly afterwards he met Baron Johann Christian von Boyneburg, former chief minister of the Elector of Mainz Johann Philipp von Schönborn, who employed him: in November 1667, Leibniz moved to Boyneburg”s town, Frankfurt am Main, near Mainz. Boyneburg soon obtained for Leibniz a position as assistant to Schönborn”s legal advisor, after Leibniz had dedicated to Schönborn an essay on the reform of the judiciary. Thus, in 1668, he moved to Mainz. However, continuing to work for Boyneburg, he spends as much time in Frankfurt as in Mainz. Together with the legal adviser, he worked on the project of a great recodification of the civil law. With this in mind, he composed his Nova methodus discendæ docendæque jurisprudentiæ, dedicated to the Elector of Mainz, Jean-Philippe of Schönborn, in the hope of obtaining a position at court. He presents the law from a philosophical point of view. Two fundamental rules of jurisprudence appear in it: accept no term without definition and accept no proposition without demonstration. In 1669, Leibniz was promoted to assessor at the Court of Appeal, where he served until 1672.

In addition, Leibniz worked on several works concerning political themes (Model of political demonstrations for the election of the king of Poland) or scientific themes (Hypothesis physica nova (“New Physical Hypotheses”), 1671).

In 1672, he was sent to Paris by Boyneburg on a diplomatic mission to convince Louis XIV to move his conquests to Egypt rather than Germany. His plan failed with the outbreak of the Dutch War in 1672. While waiting for an opportunity to meet with the French government, he was able to meet with the great scholars of the time. He is in contact with Nicolas Malebranche and Antoine Arnauld. With the latter he spoke particularly about the reunification of the churches. From the autumn of 1672, he studied mathematics and physics under the guidance of Christian Huygens. On the advice of the latter, he became interested in the works of Gregory of St. Vincent. He devoted himself to mathematics and published in Paris his manuscript on the arithmetical squaring of the circle (giving π in the form of an alternating series). He also worked on what was to become the infinitesimal calculus (or differential and integral calculus). In 1673, he designed a calculating machine that could perform the four operations, and which inspired many calculating machines of the 19th and 20th centuries (arithmometer, Curta). Before going to Hanover, he went to London to study some of Isaac Newton”s writings; both laid the foundations of integral and differential calculus.

Twice, in 1673 and 1676, Leibniz went to London where he met the mathematicians and physicists of the Royal Society. He himself became a fellow of the Royal Society on April 19, 1673.

Leibniz, having heard of the optical skills of Baruch Spinoza, a rationalist philosopher like himself, sent Spinoza a treatise on optics; Spinoza then sent him a copy of his Treatise on Theology and Politics, which greatly interested Leibniz. Moreover, through his friend Ehrenfried Walther von Tschirnhaus, Leibniz was informed of much of Spinoza”s work on the Ethics (although Tschirnhaus was forbidden to show an advanced copy).

Hanover (1676-1716)

After the death of his two employers, Boyneburg in 1672 and Schönborn in 1673, Leibniz tried to settle in Paris or London, but, not finding any employer, he finally accepted after two years of hesitation the proposal of Duke Jean-Frédéric of Brunswick-Calenberg, who appointed him librarian of the duchy of Brunswick-Luneburg (then, following Leibniz”s requests in February 1677, adviser to the house of Hanover in 1678), a position he held for 40 years, until his death in 1716. On his way to Hanover, he stopped in London, Amsterdam and The Hague, where he met Spinoza, between November 18 and 21, who was then living the last months of his life, suffering from tuberculosis. With Spinoza, they discussed the latter”s Ethics ready for publication, Cartesian physics and Leibniz”s improved version of the ontological argument on the existence of God. He also met the microscopists Jan Swammerdam and Antoni van Leeuwenhoek, meetings that would have a great influence on Leibniz” conception of animals. Leibniz finally arrived in Hanover in December 1676 by mail coach. The city was then populated with 6,500 inhabitants in the old town and 2,000 in the new town on both sides of the Leine.

As librarian, Leibniz had to perform practical tasks: general administration of the library, purchase of new and used books, and inventory of books. In 1679 he had to manage the transfer of the library from Herrenhausen Palace to Hanover itself.

In the years 1680 to 1686, he made numerous trips to the Harz to work on mining. Leibniz spent the equivalent of three years as a mining engineer. He was mainly concerned with the development of devices for extracting water from the mines by means of windmills. He came into conflict with the operators who did not accept his new ideas. This led him to question the origin of fossils, which he initially attributed to the effect of chance, but later recognized their living origin. His book Protogæa was not published until after his death, because the theories he developed on the history of the earth could displease the religious authorities.

In 1682 he founded the journal Acta Eruditorum in Leipzig with Otto Mencke. The following year, he published his article on differential calculus – Nova Methodus pro Maximis et Minimis (en). However, the article contains no demonstration, and Jacques Bernoulli will call it an enigma rather than an explanation. Two years later Leibniz published his article on the integral calculus.

In 1686, he wrote a “Short Discourse on Metaphysics,” now known as the Discourse on Metaphysics. The Discourse is generally considered to be his first mature philosophical work. He sent a summary of the discourse to Arnauld, thus beginning a rich correspondence that would deal mainly with freedom, causality and occasionalism.

The successor of Duke Johann Frederick after his death in 1679, his brother Ernest Augustus, seeking to legitimize his dynastic ambitions historically, asks Leibniz to write a book on the history of the House of Brunswick. Leibniz, busy with the mines of the Harz, could not take care of it right away. In August 1685, Leibniz”s experiments proving to be a failure, the Duke, perhaps in order to keep Leibniz away from the mines, employed him to write the history of the house of Welf, of which the house of Brunswick was a branch, from its origins to the present time, promising him a permanent salary. It was not until December 1686 that Leibniz left the Harz to devote himself fully to his historical research.

Leibniz quickly processed all the material contained in the local archives, and obtained permission to go on a trip to Bavaria, Austria and Italy, which lasted from November 1687 to June 1690.

In Vienna, where he stopped while waiting for the authorization of François II of Modena to consult the archives, he fell ill and had to stay there for a few months. During this time, he read the review of the Philosophiæ naturalis principia mathematica of Isaac Newton, published in the Acta Eruditorum in June 1688. In February 1689, he published the Tentamen de motuum coelestium causis (“Essay on the Causes of Celestial Movements”), in which he tried to explain the movement of the planets using René Descartes” theory of vortices, in order to provide an alternative to Newton”s theory of “remote forces”. He also met with Emperor Leopold I, but failed to obtain a position as imperial advisor or official historian, or permission to found a “universal library. At the same time, he achieved diplomatic success in negotiating the marriage of the daughter of Duke John Frederick, Charlotte Felicita, to the Duke of Modena Renaud III.

In March 1689, Leibniz left for Ferrara, Italy. In this period of religious tensions, Leibniz, who was going to a Catholic country while being a Protestant, was vigilant and foresighted. His secretary, Johann Georg von Eckhart, recounts that when crossing the Po River, the smugglers, knowing that Leibniz was German and therefore most likely Protestant, planned to throw him overboard and seize his luggage. Leibniz, realizing the plot, took out a rosary from his pocket and pretended to pray. The smugglers, seeing this, thought he was a Catholic and abandoned their plan.

From Ferrara, Leibniz left for Rome, where he arrived on April 14, 1689. In addition to his work of studying the archives, he took the time to meet with his scholars and scientists. He had many discussions about the union of the churches and met the Christian missionary Claudio Filippo Grimaldi, who gave him information about China (see section Sinology). He was elected member of the Physico-mathematical Academy and frequented academies and circles, defending in particular the heliocentrism of Nicolaus Copernicus, which was not yet accepted by all. He composed a dialogue, Phoranomus seu de potentia et legibus naturae (“Phoronomy or The power and laws of nature”), phoronomy being the ancestor of what we call today kinematics, i.e. the study of motion without taking into account the causes that produce or modify it, in other words, only in relation to time and space.

From Rome, Leibniz left for Naples, where he arrived on May 4, 1689; the next day he visited the eruption of Vesuvius. In Naples, he did not forget the main purpose of his trip: he asked the learned baron Lorenzo Crasso to show him the archives of Queen Joanna, wife of Otto IV of Brunswick, to make some researches in unpublished annals, where there was a question of these princes, and to give him some information on the Neapolitan genealogists; undoubtedly he obtained satisfaction, because he saw in Naples the Storia Ms. di Matteo Spinelli da Giovinazzo, but as it was former to Otton IV he did not find there anything of what he sought.

In 1690, Leibniz stayed in Florence, where he met Vincenzo Viviani, who had been a student of Galileo, with whom he discussed mathematics. He befriended Rudolf Christian von Bodenhausen, tutor to the sons of the Grand Duke of Tuscany Cosimo III, to whom he entrusted the still unfinished text of the Dynamica (“Dynamics”), in which he defined the concept of force and formulated a principle of conservation. After a brief stay in Bologna, Leibniz went to Modena where he continued his historical research.

Leibniz saw his efforts in his historical research rewarded: in 1692, the Duchy of Brunswick-Luneburg was raised to the rank of electorate. As a reward, Duke Ernest-Augustus made him a private adviser. The other branches of the house of Brunswick were also grateful to him: the co-dukes Rudolf-Augustus and Antony-Ulrich of Brunswick-Wolfenbüttel appointed him librarian at the Herzog August Bibliothek in Wolfenbüttel in 1691, undertook to pay a third of the cost of publishing the history of the house of Welf, and in 1696 appointed him privy councillor. In addition, the Duke of Celle, George William, granted Leibniz an annuity for his historical research. His annuities were then 1,000 thalers in Hanover, 400 from Brunswick-Wolfenbüttel, and 200 from Celle, a comfortable financial situation.

From then on and until the end of his life, he spent as much time in Brunswick, Wolfenbüttel and Celle as in Hanover – the round trips being 200 km long, Leibniz spent a lot of time traveling, owning his own car, and taking advantage of the trips to write his letters.

In 1691, he published in Paris, in the Journal des savants, an Essay on dynamics where he introduced the terms energy and action.

On January 23, 1698, Ernest-Auguste died and his son Georges-Louis succeeded him. Leibniz saw himself increasingly sidelined from his role as advisor by the new prince, far from the cultured man that John Frederick represented in the eyes of Leibniz, who saw in him the “portrait of a Prince”. On the other hand, the friendship that he maintains with Sophie of Hanover and her daughter Sophie-Charlotte, Queen of Prussia, is reinforced

On September 29, 1698, he moved into the house where he lived until his death, located in Schmiedestraße, the new address of the Hanover library.

He convinced the Prince-Elector of Brandenburg (later King of Prussia) to found an Academy of Sciences in Berlin, of which he became the first president in July 1700.

In 1710, he published his Essais de Théodicée, the result of discussions with the philosopher Pierre Bayle.

Recognized as the greatest intellectual of Europe, he was pensioned by several great courts (Peter the Great in Russia, Charles VI in Austria who made him a baron), and corresponded with sovereigns – notably Sophie-Charlotte of Hanover.

The end of Leibniz”s life is not very cheerful.

He faced a controversy with Isaac Newton over which of the two invented the infinitesimal calculus, and was even accused of stealing Newton”s ideas. Most mathematical historians now agree that the two mathematicians developed their theories independently of each other: Newton was the first to develop his ideas, but Leibniz was the first to publish his work.

At court, he was mocked for the outdated appearance (typical of Paris in the 1670s) that his wig and old-fashioned clothes gave him.

In November 1712, he met the Czar in Dresden, then, feeling cramped in Hanover, left for Vienna (without asking Georges-Louis” permission) where he stayed until autumn 1714.

In 1714, he had to face the death of two relatives: on March 27, Antoine-Ulrich of Brunswick-Wolfenbüttel, and on June 8, Sophie of Hanover.

When, on August 12, after the death of Queen Anne, George Louis became King of Great Britain, Leibniz asked to join him in London and even asked to become the official historian of England, but in view of the bad reputation that the philosopher had acquired in England, the new sovereign refused to let Leibniz follow him and ordered him to stay in Hanover.

He considered going to Paris, where Louis XIV had invited him, but the death of the latter, as well as the fact that he had to convert, made him abandon this proposal. He also seriously considered moving to Vienna, where he even started looking for a property. He also considered Berlin, where he was president of the Royal Prussian Academy of Sciences, and St. Petersburg, where he held a position as an advisor. But Leibniz, who was then more than sixty years old, no longer had the health to continue traveling as he had done, or to start a new life elsewhere. His last trip was a meeting with the Czar in Pyrmont in July 1716, after which he never left Hanover.

Very concerned by the history of the Welf house, which he had not written in spite of all the time he had devoted to it, and still hoping to be able to finish it before his death in order to be able to devote himself to his philosophical works, he started to work actively on it again.

Shortly before his death, during the years 1715 and 1716, he corresponded with the English theologian Samuel Clarke, a disciple of Newton, about physics, presenting in its final form his conception of space and time. He also wrote a lot to the French Jesuit Barthélemy Des Bosses.

On November 14, 1716, at nine o”clock in the evening, after having spent a week blocked in his bed with gout and colic, he suffered an excess of gout; he was then made to drink an herbal tea which, rather than curing him, caused him convulsions and severe pain; Less than an hour later he died at the age of 70 in the city where he had resided for 40 years, in the presence of his copyist and his coachman, but in general indifference, while his thought had revolutionized Europe. Nobody cared about his funeral except his personal secretary. The court had been notified, but no one was seen there, despite its relative geographical proximity; this may be explained by the fact that Leibniz was not a zealous religious follower. His burial is that of an insignificant person.

The first, entitled Elogium Godofredi Guilelmi Leibnitii, is the work of Christian Wolff, written in Latin and published in July 1717 in the Acta Eruditorum; the second is a eulogy delivered at the Royal Academy of Sciences in Paris by Bernard Le Bouyer de Fontenelle in November 1717, one year after Leibniz” death.

After Leibniz”s death, Georges-Louis, fearing the revelation of secrets, confiscated Leibniz”s literary heritage (Nachlass), thus allowing its preservation.

Portrait

Leibniz had all his life the impossible ambition to excel in all intellectual and political fields, he loved conversation, though slow to reply and not very eloquent, but more than that he loved reading and meditating alone, working at night did not bother him. He could sit and think for days on end in the same chair, or travel through Europe in all weathers.

Leibniz slept little, often sitting on a chair; as soon as he woke up he resumed his work. He ate a lot and drank little, often taking his meals alone, at irregular hours, depending on his work.

Leibniz was never married, allegedly because he never had the time. It is said that he complained that he had not found the woman he was looking for. When he was about 50 years old, he thought seriously about getting married, but the person he wanted to marry wanted a delay to make his decision, and during this time Leibniz changed his mind.

As was the custom at court, he wore a long black wig. Rare for the time, he attached great importance to his hygiene and regularly visited the baths, which earned him many letters from female admirers.

Leibniz”s physical appearance is indicated by a description written by himself for a medical consultation, as well as by one written by his secretary Johann Georg von Eckhart, who passed it on to Fontenelle for his Praise. Leibniz was a man of medium height, bent over, rather thin, broad-shouldered and bow-legged. He was not very ill, except for occasional dizziness, before he was struck by gout, which caused his death.

Religious and political views

On religious matters, Leibniz is considered a philosophical theist. Although he was raised Protestant, he learned to appreciate some aspects of Catholicism from his employers and colleagues, notably Boyneburg, as he and his relatives were former Lutherans who converted to Catholicism. Although he remained faithful to Lutheranism, and refused to convert to Catholicism, he did frequent Catholic circles. One of his great projects was the reunification of the Catholic and Protestant churches. He never agreed with the Protestant view of the Pope as Antichrist.

Leibniz was a convinced nationalist but also a cosmopolitan. A pacifist, he wanted us to learn from other nations rather than wage war against them. He was a pioneer of the Enlightenment, which believed in the superiority of reason over prejudice and superstition. He tried to promote the use of German, although he wrote little in this language because it was not well suited to philosophical writing (see the Literature section).

He sometimes harbored anti-French sentiments. He mocked the bellicose character of Louis XIV in an anonymous satirical writing of 1684 entitled Mars Christianissimus (a play on the words Mars, god of war, and the expression Rex Christianissimus (“very Christian king”), which referred to Louis XIV).

Concerned with practical political issues, Leibniz tried to convince the Hanoverians to introduce fire insurance, and proposed this measure to the court in Vienna for application throughout the empire, but in both cases it was in vain.

Jobs

Leibniz”s first job, while still perhaps a student in Altdorf, was more a temporary solution than a real ambition: secretary of an alchemical society in Nuremberg (whose affiliation or not with the Rosicrucians is debated).

Shortly afterwards he met Baron Johann Christian von Boyneburg, former chief minister of the Elector of Mainz Johann Philipp von Schönborn, who employed him: in November 1667 Leibniz moved to Boyneburg”s town, Frankfurt am Main, near Mainz. Boyneburg soon obtained for Leibniz a position as an assistant to Schönborn”s legal advisor. Thus, in 1668, he moved to Mainz. However, continuing to work for Boyneburg, he spent as much time in Frankfurt as in Mainz. About a year and a half later, Leibniz was promoted to assessor at the court of appeal.

After the death of his two employers, Boyneburg in 1672 and Schönborn in 1673, Leibniz sought to settle in Paris or London, but, finding no employer, he finally accepted after two years of hesitation the proposal of Duke Johann Frederick of Brunswick-Calenberg, who appointed him librarian of the Duchy of Brunswick-Luneburg and advisor to the House of Hanover, a position he held for 40 years, until his death in 1716.

After his historical research was rewarded with the elevation of the Duchy of Brunswick-Luneburg to the rank of electorate in 1692, Duke Ernest-Augustus made him a private adviser. The other branches of the house of Brunswick were also grateful to him: the co-dukes Rudolf-Augustus and Antony-Ulrich of Brunswick-Wolfenbüttel appointed him librarian at the Herzog August Bibliothek in Wolfenbüttel in 1691, undertook to pay a third of the cost of publishing the history of the house of Welf, and in 1696 appointed him privy councillor. In addition, the Duke of Celle, George William, granted Leibniz a salary for his historical research. The annual salaries of Leibniz at that time were 1,000 thalers from Hanover, 400 from Brunswick-Wolfenbüttel, and 200 from Celle. Leibniz was thus very well paid, since even the lowest salary, that of Celle, was higher than what a skilled worker could expect to earn. From then on and until the end of his life, he spent as much time in Brunswick, Wolfenbüttel and Celle as in Hanover.

Place in the scholarly and political world

Leibniz became a fellow of the Royal Society on April 19, 1673. In 1674, he refused the appointment as a member of the Royal Academy of Sciences, since it required him to convert; finally he was appointed foreign associate of the Royal Academy of Sciences by Louis XIV on January 28, 1699. In 1689, he was appointed member of the Physico-mathematical Academy in Rome.

He convinced the Prince-Elector of Brandenburg (the future King of Prussia) to found an Academy of Sciences in Berlin and became its first president in July 1700. He also tried to establish academies in Dresden in 1704 (his idea failed because of the Great Northern War), in St. Petersburg (an idea that was not realized until the foundation of the St. Petersburg Academy of Sciences in 1724-1725, nine years after Leibniz”s death) and in Vienna in 1713 (an idea that was not realized until the foundation of the Austrian Academy of Sciences in 1846-1847).

Leibniz never questioned the feudal system, but was rather casual in the performance of his duties, and sometimes bordered on disobedience, even disloyalty. If after the death of Duke John Frederick, his relations were less good with his successors Ernest-Augustus and George-Louis, he maintained a friendship with Sophie of Hanover and her daughter Sophie-Charlotte, Queen of Prussia, and was always welcome and frequently invited to both. They appreciated Leibniz”s intelligence, and he was able to find support from them, and it was as a result of their discussions that Leibniz wrote two of his major works: the New Essays on Human Understanding and the Essays on Theodicy. Close to powerful political figures, he was also, in his last years, appointed private adviser to the Russian tsar Peter I the Great and to the imperial court in Vienna. However, his wish to be ennobled was never fulfilled.

He never accepted an academic position, disliking the inflexible structure of German universities.

Leibniz traveled frequently – especially between his main residence, Hanover, and the neighboring towns of Brunswick, Wolfenbüttel, and Celle, with round trips of 200 km – and traveled about 20,000 km by horse-drawn carriage. He owned his own carriage and used the trips to write his letters. During his travels he was able to meet scientists and politicians, establish diplomatic relations, learn about new discoveries and inventions, and continue his research on the history of the Welf house.

Unlike the other great philosophers of his time, Leibniz did not produce a magnum opus, a work that expresses in itself the whole heart of an author”s thought. He wrote only two books, the Essays on Theodicy (1710) and the New Essays on Human Understanding (1704 – published posthumously in 1765).

He sometimes used the pseudonyms Caesarinus Fürstenerius and Georgius Ulicovius Lithuanus.

Leibniz wrote on folio pages which he separated into two columns: one for writing his original draft, the other for annotating or adding certain portions of text to his draft. He often annotated his own annotations. The annotation column was frequently as full as the original text. Moreover, his spelling and punctuation were very fancy.

His mind always racing, he was always jotting down ideas on paper, storing his notes in a large closet for later retrieval. In particular, he took notes on everything he read. However, since he was always writing, the accumulation of his drafts prevented him from finding the one he was interested in, and for this reason he rewrote it; as a result, we have several drafts of the same booklet, which have the same basic ideas, do not have the same development and sometimes do not even have the same plan. If one can generally see a certain progression from one draft to the next, the first versions often contain details or views that are missing from the later versions. However, these repetitions between drafts have an advantage: they allow to highlight the evolution in Leibniz”s thought.

Correspondence

Leibniz”s correspondence is an integral part of his work. It spans more than 50 years, from 1663 to 1716. It is perhaps the most extensive among 17th century scholars. A central activity for Leibniz himself, the philosopher carefully classified it, which facilitated its preservation.

Leibniz composed about 20,000 letters, exchanging with about 1,100 correspondents from sixteen different countries, not only in Western and Central Europe, but also in Sweden, Russia, and as far away as China; his correspondents were from very different backgrounds, from the imperial family to artisans. Among his many correspondents, Leibniz counted Baruch Spinoza, Thomas Hobbes, Antoine Arnauld, Jacques-Bénigne Bossuet, Nicolas Malebranche, Jean and Jacques Bernoulli, Pierre Bayle, and Samuel Clarke, as well as the political figures of his time: princes, electors, and emperors of the Holy Roman Empire, and even Tsar Peter the Great.

Leibniz”s correspondence is included in the international Memory of the World register of UNESCO. It is in an exceptional state of preservation thanks to the confiscation by George I, Elector of Hanover and King of Great Britain, who feared the disclosure of secrets. The complete edition of Leibniz”s correspondence is planned for the year 2048.

Publication

Leibniz”s legacy (Nachlass) is still not fully published.

The complete edition of Leibniz”s writings is conducted by the Gottfried Wilhelm Leibniz Library in Hannover together with three other German libraries. Publications began in the early 20th century. It classifies his written work into eight series (Reihe):

It should be noted that the idea of classifying opuscules and works according to their content is not unanimously accepted. Thus Louis Couturat, in the preface to his edition of Leibniz”s Opuscules et fragments inédits, asserts that the only objective classification is the chronological one, and that any other classification amounts to creating divisions in his work where there are none, at the risk of forgetting certain fragments or of misclassifying them and thus providing a distorted vision of the work. He is also opposed to making choices among the manuscripts; according to him, the objective of the projected edition is to bring to light the entirety of the writings, and then for commentators to make their choice among the pieces that interest them.

On the other hand, the classification of the correspondence by date is less synthetic than that of the edition of C. I. Gerhardt, which groups the letters by correspondent and also gives their answers (which the complete edition does not do).

Main works

Often portrayed as the last “universal genius” and one of the greatest thinkers of the 17th and 18th centuries, Leibniz wrote in a wide variety of fields, making important contributions to metaphysics, epistemology, logic, and the philosophy of religion, but also outside the realm of philosophy, to mathematics, physics, geology, jurisprudence, and history. His thought is not grouped in a magnum opus but is made up of a considerable body of essays, unpublished works and letters.

Denis Diderot, who nevertheless opposed Leibniz”s conceptions on many points, wrote about him in the Encyclopedia: “Perhaps no man has ever read, studied, meditated and written as much as Leibniz”. Bernard Le Bouyer de Fontenelle said that “like the ancients who had the ability to drive up to eight horses at once, he drove all the sciences at once”.

Leibniz is classified, along with René Descartes and Baruch Spinoza, as one of the main representatives of the continental rationalism of the early modern era, as opposed to the three main representatives of the British empiricism: John Locke, George Berkeley and David Hume.

Leibniz”s philosophy is inseparable from his mathematical work as well as from logic, which ensures the unity of his system.

“Mathematicians need to be philosophers as much as philosophers need to be mathematicians.”

– Gottfried Wilhelm Leibniz, Letter to Malebranche of 13

Influences

Leibniz was trained in the scholastic tradition. He was also exposed to elements of modernity, notably Renaissance humanism and the work of Francis Bacon.

His professor at the University of Leipzig, Jakob Thomasius, transmitted to him a great respect for ancient and medieval philosophy. As for his professor at Jena, Erhard Weigel, he led him to consider mathematical proofs for disciplines such as logic or philosophy.

From ancient philosophy, he inherited Aristotelianism (especially logic (syllogistics) and the theory of categories). Leibniz was also influenced by orthodox Christianity.

He was inspired by Raymond Lulle and Athanasius Kircher for his thesis of the alphabet of thought, the combination of ideas, and the universal characteristic.

Leibniz met major philosophical figures of the time such as Antoine Arnauld, Nicolas Malebranche (to whom he owed his interest in China), and especially the Dutch mathematician and physicist Christian Huygens, who taught him philosophy, mathematics and physics.

Leibniz”s relationship with the great thinkers of the time gave him access to the unpublished manuscripts of Descartes and Pascal.

Leibniz will oppose Spinoza and Hobbes on the materialist and necessitarian aspect as well as on their conception of God of their respective doctrines.

Like Spinoza, Leibniz is an heir to Descartes, while also criticizing him to a large extent. Leibniz said of Niels Stensen (Nicolas Sténon) that he “disabused us of Cartesianism”.

Spinoza and Leibniz, in spite of a common heritage, also strongly oppose each other: notably, the former thinks God immanent (Deus sive Natura), the latter transcendent. But Leibniz studied Spinozism so much to criticize it – we find many annotations and critical comments by Leibniz on Spinoza”s Ethics written after he had received Spinoza”s posthumous publications – and for so long – we know of notes written by Leibniz in 1708 on Spinoza”s propositions, proof that the Spinozian system was not just a youthful interest for the German philosopher – that later commentators will wonder to what extent this study will eventually influence the Leibnizian system.

Leibniz opposes Descartes in that he preserves the achievements of Aristotelianism; and affirms, contrary to Descartes and according to an Aristotelian inspiration, that God must respect the principles of logic.

Finally, Leibniz will write the New Essays on Human Understanding and the Essays on Theodicy in opposition to contemporary philosophers, respectively John Locke and Pierre Bayle.

Principles

In the Monadology, Leibniz writes:

“Our reasoning is based on two great principles, that of contradiction and that of sufficient reason.”

– Gottfried Wilhelm Leibniz, Monadology

However, we can, throughout his writings, find four other great principles: the principle of the best, the principle of the predicate inherent in the subject, the principle of identity of indiscernibles and the principle of continuity. Leibniz explains that there is a relation between the six principles while privileging the preponderance of the principles of contradiction and sufficient reason.

The best principle states that God always acts for the best. Therefore, the world we live in would also be the best of all worlds. God is thus an optimizer of the collection of all original possibilities. Therefore, if He is good and all-powerful and since He has chosen this world out of all possibilities, this world must be good and, therefore, this world is the best of all possible worlds. Voltaire, in his work Candide among others, widely criticizes this principle which he sees as too much optimism not considering the suffering of our world.

The principle of the predicate inherent in the subject, originating in Aristotle”s Organon, asserts that in every true proposition the predicate is contained in the concept of the subject itself. Leibniz states: “Praedicatum inest subjecto”. Without such a link between the subject and the predicate, no truth can be demonstrated, whether it is contingent or necessary, universal or particular.

The principle of contradiction (also called “principle of non-contradiction”) comes from Aristotle in his Metaphysics (IV.3) and simply states that a proposition cannot be true and false at the same time. Thus, A cannot be A and ¬A at the same time.

The principle of sufficient reason: this principle states that “nothing is without reason” (nihil est sine ratione) or that “there is no effect without a cause”. For Leibniz, this principle is considered to be the most useful and necessary for human knowledge, since it has constructed a large part of metaphysics, physics and moral science. However, in his Monadology, Leibniz admits that most of these reasons are not known to us.

The principle of identity of indistinguishables (or simply “principle of indistinguishables”): states that if two things have all their properties in common, then they are identical. This principle, which is very controversial, is the reciprocal of the principle of indistinguishability of identical things, which states that if two things are identical, they share all their properties. The two principles together therefore state that: “two things are identical if and only if they share all their properties”.

The principle of continuity says that things change gradually. Leibniz wrote: Natura non facit saltus (“Nature does not make a jump”). Each change goes through an intermediate change which is actualized in an infinity of things. This principle will also be used to show that a motion can start from a state of complete rest and change quietly by degrees.

Logic and combinatorial art

Logic is an important part of Leibniz”s work, although it was neglected by philosophers and mathematicians who were each interested in Leibniz”s work on their respective disciplines, even though in Leibniz”s case these subjects form an indissociable whole, whose cohesion is assured by logic.

“Logic is for Leibniz the Key to Nature

– Yvon Belaval, Leibniz : introduction to his philosophy

The importance of the logic developed by Leibniz makes him for some the greatest logician since Aristotle.

Leibniz considered Aristotle to be the “first person who wrote mathematically outside of mathematics”. He had a great admiration for his work. However, he considered it imperfect; he thought that Aristotelian logic was flawed. He was particularly interested in syllogistics and his first contributions in this field are found in De arte combinatoria.

Leibniz”s logic is inspired by that of the medieval philosopher Raymond Lulle. Lulle, in his Ars magna, puts forward the idea that concepts and propositions can be expressed in the form of combinations. Inspired by Lulle, Leibniz explains in the De arte combinatoria how one could, in a first step, constitute an “Alphabet of human thoughts”, composed of all the basic ideas, and then discover new truths by combining the concepts to form judgments in an exhaustive way and methodically evaluate their truth.

On this principle, Leibniz theorized a universal language that he called characteristica universalis ((lingua) characteristica), which would allow concepts to be expressed in the form of the basic concepts of which they are composed, and to be represented in such a way as to make them comprehensible to all readers, regardless of their mother tongue. Leibniz studied Egyptian hieroglyphs and Chinese ideograms because of their method of representing words in the form of drawings. The universal characteristic is supposed to express not only mathematical knowledge, but also jurisprudence (he established the correspondences at the basis of deontics), ontology (Leibniz criticized René Descartes” definition of substance), even music. Leibniz was not the first to theorize this type of language: before him, the French mathematician François Viète (16th century), the French philosopher René Descartes and the English philologist George Dalgarno (17th century) had already suggested such a project, notably in the field of mathematics, but also for Viète for communication. Moreover, the Leibnizian project will inspire the projects of universal language of the end of the XIXth century with the esperanto, then the interlingue, not degraded version of the Latin created by Giuseppe Peano. It will also inspire Gottlob Frege”s ideography, the logical language loglan and the programming language Prolog.

Leibniz also dreamed of a logic that would be algorithmic and therefore mechanically decidable: the calculus ratiocinator. Such a calculation could be performed by machines and would therefore not be subject to errors. Leibniz thus announces the same ideas that will inspire Charles Babbage, William Stanley Jevons, Charles Sanders Peirce and his student Allan Marquand in the 19th century, and that will be the basis of the development of computers after the Second World War.

“Leibniz believes he can invent, for the verification of logical calculations, technical procedures analogous to the proof by 9 used in Arithmetic. So he calls his Characteristic the judge of controversies, and considers it as an art of infallibility. He paints an attractive picture of what will be, thanks to it, the philosophical discussions of the future. To resolve a question or end a controversy, opponents will only have to take up the pen, if necessary adding a friend as an arbitrator, and say “Let”s calculate!”

– Louis Couturat, The Logic of Leibniz

At the same time, he was aware of the limits of formal logic by affirming that any modeling, to be correct, must be done strictly in analogy with the modeled phenomenon.

Leibniz is for many the most important logician between Aristotle and the 19th century logicians at the origin of modern logic: Auguste De Morgan, George Boole, Ernst Schröder and Gottlob Frege. For Louis Couturat, Leibnizian logic anticipated the principles of modern logical systems, and even surpassed them on certain points.

Nevertheless, most of his texts on logic consist of sketches that were published only very late or even forgotten. The question arises whether Leibniz just anticipated modern logic or whether he influenced it. It seems that the logic of the 19th century was indeed inspired by Leibnizian logic.

Metaphysics

Written in French in 1714 and unpublished during the author”s lifetime, the Monadology represents one of the last stages of Leibniz”s thought. Despite its apparent similarities with earlier texts, the Monadology is quite distinct from works such as the Discourse on Metaphysics or the New System of the Nature and Communication of Substances. The notion of individual substance present in the Discourse on Metaphysics should not be confused with that of the monad.

For Leibniz, physics has its reason in metaphysics. If physics studies the movements of nature, what reality is this movement? And what is its cause? Motion is relative, that is, a thing moves according to the perspective from which we look at it. Motion is therefore not reality itself; reality is the force that subsists outside of all motion and that is the cause of it: the force subsists, rest and motion being relative phenomenal differences.

Leibniz defines force as “that which is in the present state, which carries with it a change for the future.” This theory leads to a rejection of atomism; indeed, if the atom is an absolutely rigid reality, then it cannot lose force in shocks. It is therefore necessary that what is called atom is, in reality, composed and elastic. The idea of an absolute atom is contradictory:

“Atoms are only the effect of the weakness of our imagination, which likes to rest and hurry to come in subdivisions or analyses.”

Thus force is reality: force is substance, and all substance is force. Force is in a state, and this state changes according to laws of change. This succession of changing states has a regular order, that is to say that each state has a reason (cf. principle of sufficient reason): each state is explained by the one that precedes it, it finds its reason there. To this notion of law is also attached the idea of individuality : individuality is for Leibniz a series of changes, a series that is presented as a formula :

“The law of change makes the individuality of each particular substance.”

Every substance develops in this way according to inner laws, following its own tendency: each one therefore has its own law. Thus, if we know the nature of the individual, we can derive from it all the changing states. This law of individuality implies passages to states that are not only new, but also more perfect.

What exists is thus for Leibniz the individual; there are only units. Neither movements, nor even bodies have this substantiality: the Cartesian extended substance supposes indeed something extended, it is only a compound, an aggregate which does not possess reality by itself. Thus, without absolutely simple and indivisible substance, there would be no reality. Leibniz calls this reality monad. The monad is conceived according to the model of our soul:

“Substantial unity requires an accomplished, indivisible and naturally indestructible being, since its notion envelops all that must happen to it, which cannot be found either in the figure or in the movement… But rather in a substantial soul or form, such as what is called I.”

We make the observation of our internal states, and these states (sensations, thoughts, feelings) are in a perpetual change: our soul is a monad, and it is according to its model that we can conceive the reality of the things, because there are undoubtedly in the nature of other monads which are analogous to us. By the law of analogy (a law which is formulated “just like this”), we conceive of all existence as being only a difference of degree relative to us. Thus, for example, there are lower degrees of consciousness, dark forms of psychic life: there are monads at all degrees of lightness and darkness. There is a continuity of all existences, a continuity which finds its foundation in the principle of reason.

From then on, since there are only beings endowed with more or less clear representations, whose essence is in this representative activity, matter is reduced to the state of a phenomenon. Birth and death are also phenomena in which the monads become darker or lighter. These phenomena have reality insofar as they are connected by laws, but the world, in general, exists only as a representation.

These monads, developing according to an internal law, do not receive any influence from the outside:

Let us add that the concept of monad was influenced by the philosophy of Pierre Gassendi, who took up the atomist tradition embodied by Democritus, Epicurus and Lucretius. Indeed, the atom, from the Greek “atomon” (indivisible) is the simple element of which everything is composed. The major difference with the monad is that the monad is of spiritual essence, whereas the atom is of material essence; and thus the soul, which is a monad in Leibniz, is composed of atoms in Lucretius.

How then can we explain that everything happens in the world as if the monads were really influencing each other? Leibniz explains this concordance by a universal pre-established harmony between all beings, and by a common creator of this harmony:

If the monads seem to take each other into account, it is because God created them to be so. It is by God that the monads are created all at once by fulguration, in a state of individuality that makes them like little gods. Each one has a singular point of view on the world, a view of the universe in miniature, and all its perspectives have together an internal coherence, whereas God has the infinity of points of view which he creates in the form of these individual substances. The intimate force and thought of the monads is thus a divine force and thought. And harmony is from the beginning in the mind of God: it is pre-established.

If some commentators (e.g. Alain Renaut, 1989) wanted to see in the pre-established harmony an abstract scheme that re-establishes, only after the fact, the communication between monads, monads that would then be the signs of a fragmentation of reality into independent units, this interpretation was rejected by one of the most important commentaries of Leibniz”s work, that of Dietrich Mahnke, entitled The Synthesis of the Universal Mathematics and the Metaphysics of the Individual (1925). Inspired by Michel Fichant”s, Mahnke underlines that the universal harmony precedes the monad: the choice of each monad is made not by particular wills of God, but by a primitive will, which chooses the whole of the monads: each complete notion of an individuated monad is thus wrapped in the primitive choice of the world. Thus, “the harmonic universality (…) is inscribed in the primitive internal constitution of each individual”.

Finally, it follows from this idea of the monad that the universe does not exist outside of the monad, but is the totality of all perspectives. These perspectives are born from God. All the problems of philosophy are thus displaced in theology.

This transposition poses problems that are not really solved by Leibniz:

Malebranche will summarize all these problems in one formula: God does not create gods.

His theory of the union of the soul and the body naturally follows his idea of the monad. The body is an aggregate of monads, whose relations with the soul are regulated from the start like two clocks that have been synchronized. Leibniz describes the representation of the body (i.e. of the multiple) by the soul as follows:

“Souls are units and bodies are multitudes. But the units, although they are indivisible, and without part, do not let themselves represent multitudes, about as all the lines of the circumference meet in the center.”

Epistemology

Although not treated as much in terms of quantity as logic, metaphysics, theodicy and natural philosophy, epistemology (here in the Anglo-Saxon sense of the term: study of knowledge) remains a theme of important work by Leibniz. Leibniz is an innateist, and fully assumes to be inspired by Plato, on the question of the origin of ideas and knowledge.

Leibniz”s main work on the subject is the New Essays on Human Understanding, written in French, a commentary on John Locke”s Essay on Human Understanding. The New Essays were completed in 1704. But Locke”s death convinced Leibniz to postpone their publication, as the latter found it inappropriate to publish a refutation of a man who could not defend himself. They were finally published posthumously in 1765.

The English philosopher defends an empiricist position, according to which all our ideas come from experience. Leibniz, in the form of an imaginary dialogue between Philalèthe, who quotes passages from Locke”s book, and Theophilus, who opposes him to the Leibnizian arguments, defends an innateist position: some ideas are in our mind from birth. These are ideas that are constitutive of our very understanding, such as that of causality. Innate ideas can be activated by experience, but for this to happen they must first potentially exist in our understanding.

Philosophical theology

Leibniz became very interested in the ontological argument for the existence of God from the 1670s onwards, and exchanged views on this subject with Baruch Spinoza. He refutes René Descartes” argument in the fifth meditation of the Metaphysical Meditations: God has all perfections, and existence is a perfection, therefore God exists. For Leibniz, it is especially a question of showing that all the perfections are compossible, and that existence is a perfection. Leibniz shows the first premise in his essay Quod ens perfectissimum existit (1676), and the second in another short writing from the same period.

Leibniz”s demonstration, which has similarities with the ontological proof of Gödel, established by Kurt Gödel in the 1970s:

Leibniz was also interested in the cosmological argument. The cosmological argument in Leibniz follows from his principle of sufficient reason. Every truth has a sufficient reason, and the sufficient reason of the whole set of truths is necessarily located outside the set, and it is this ultimate reason that we call God.

In the Essays of Theodicy, Leibniz succeeds in demonstrating the uniqueness of God, his omniscience, his omnipotence and his benevolence.

The term “theodicy” etymologically means “justice of God” (from Greek Θεὸς

The example of Judas the traitor, as analyzed in section 30 of the Discourse on Metaphysics, is enlightening: certainly, it was foreseeable from all eternity that this Judas, whose essence God allowed to come into existence, would sin as he sinned, but it is nevertheless him who sins. The fact that this limited, imperfect being (like all creatures) enters into the general plan of creation, and thus in a sense derives its existence from God, does not in itself cleanse it of its imperfection. It is indeed he who is imperfect, just as the cogwheel in a watch is nothing more than a cogwheel: the fact that the watchmaker uses it to make a watch does not make the watchmaker responsible for the fact that this cogwheel is nothing more than a cogwheel.

The principle of sufficient reason, sometimes called the principle of “determining reason” or the “great principle of why”, is the fundamental principle that guided Leibniz in his research: nothing is without a reason that explains why it is, rather than why it is not, and why it is so, rather than otherwise. Leibniz does not deny that evil exists. However, he asserts that all evils cannot be less: these evils find their explanation and justification in the whole, in the harmony of the picture of the universe. “The apparent defects of the whole world, these spots of a sun of which ours is only a ray, raise its beauty far from diminishing it” (Théodicée, 1710 – publication in 1747).

Answering Pierre Bayle, he establishes the following demonstration: if God exists, he is perfect and unique. Now, if God is perfect, he is “necessarily” all-powerful, all goodness and all justice, all wisdom. Thus, if God exists, he could, by necessity, have created the least imperfect of all imperfect worlds; the world best adapted to the supreme ends.

In 1759, in the philosophical tale Candide, Voltaire makes his character Pangloss the supposed spokesman of Leibniz. In truth, he deliberately distorts his doctrine by reducing it to the formula: “everything is at its best in the best of all possible worlds”. This formula is a misinterpretation: Leibniz does not claim that the world is perfect, but that evil is reduced to a minimum. Jean-Jacques Rousseau reminded Voltaire of the binding aspect of Leibniz”s demonstration: “These questions all relate to the existence of God (if one denies it, one should not discuss its consequences). (Letter of August 18, 1756). However, Voltaire”s text does not oppose Leibniz on a theological or metaphysical level: the tale of Candide originates in the opposition between Voltaire and Rousseau, and its content seeks to show that “it is not the reasoning of metaphysicians that will put an end to our ills”, making the apology of a voluntarist philosophy inviting men to “organize earthly life for themselves” and where work is presented as “the source of material and moral progress that will make men happier”.

Ethics

If ethics is the only traditional field of philosophy to which Leibniz is not generally considered an important contributor, like Spinoza, Hume or Kant, Leibniz was very interested in this field. It is true that in comparison with his metaphysics, Leibniz”s ethical thought is not particularly distinguished by its scope or originality. Nevertheless, he engaged in central debates in ethics on the foundations of justice and the question of altruism.

For Leibniz, justice is the a priori science of the good, i.e. there are rational and objective bases for justice. He rejects the position that justice is the decree of the strongest, a position he associates with Thrasymachus who defends it against Socrates in Plato”s Republic, but also with Samuel von Pufendorf and Thomas Hobbes. Indeed, applying this conception, one comes to the conclusion that divine commands are just only because God is the most powerful of all lawmakers. For Leibniz, this is a rejection of God”s perfection; for him, God acts in the best way, not just arbitrarily. God is not only perfect in his power, but also in his wisdom. The a priori and eternal standard of justice to which God adheres must be the basis of the theory of natural law.

Leibniz defines justice as the charity of the wise person. Although this definition may seem strange to those who are used to a distinction between justice and charity, the real originality of Leibniz is his definition of charity and love. Indeed, in the 17th century, the question of the possibility of a disinterested love was raised. It seems that each being acts in a way to persevere in existence, which Hobbes and Spinoza designate under the term of conatus at the base of their respective psychologies. According to this point of view, the one who loves is the one who sees in this love a way to improve his existence; love is then reduced to a form of egoism, and even if it were benevolent, it would lack an altruistic component. To resolve this incompatibility between egoism and altruism, Leibniz defines love as taking pleasure in the happiness of others. Thus, Leibniz does not deny the fundamental principle of each individual”s conduct, the search for pleasure and self-interest, but manages to link it to the altruistic concern for the well-being of others. Thus, love is defined as the coincidence of altruism and self-interest; justice is the charity of the wise person; and the wise person, says Leibniz, is the one who loves everything.

Leibniz”s mathematical works can be found in the Journal des savants de Paris, the Acta Eruditorum of Leipzig (which he helped found) as well as in his abundant correspondence with Christian Huygens, the brothers Jean and Jacques Bernoulli, the Marquis de L”Hôpital, Pierre Varignon, etc.

Infinitesimal calculus

Isaac Newton and Leibniz are often credited with the invention of infinitesimal calculus. In truth, the first steps of this type of calculation can be found as early as Archimedes (3rd century BC). It was later developed by Pierre de Fermat, François Viète and his codification of algebra, and René Descartes and his algebraization of geometry.

The entire 17th century studied the indivisible and the infinitely small. Like Newton, Leibniz dominated early on the indeterminacies in the calculus of derivatives. Moreover, he developed an algorithm that is the major tool for the analysis of a whole and its parts, based on the idea that everything integrates small elements whose variations contribute to the unity. His work on what he called the “specious superior” was continued by the Bernoulli brothers, the Marquis de L”Hôpital, Euler and Lagrange.

Ratings

According to Leibniz, mathematical symbolism is nothing more than a sample, concerning arithmetic and algebra, of his more general project of universal characteristic. According to him, the development of mathematics depends above all on the use of an appropriate symbolism; thus he considers that the progress he made in mathematics is due to the fact that he succeeded in finding adequate symbols for the representation of quantities and their relations. The main advantage of his method of infinitesimal calculation over Newton”s (method of fluxions) is indeed its more judicious use of signs.

It is the origin of several terms:

It also creates several new ratings:

We also owe him a logical definition of equality.

It also evolves the notation in elementary arithmetic:

Binary system

Leibniz was very interested in the binary system. He is sometimes seen as its inventor, although this is not the case. Indeed, Thomas Harriot, an English mathematician and scientist, had already worked on non-decimal systems: binary, ternary, quaternary and quinary, but also higher base systems. According to Robert Ineichen of the University of Freiburg, Harriot is “probably the first inventor of the binary system. According to Ineichen, Mathesis biceps vetus et nova by the Spanish churchman Juan Caramuel y Lobkowitz is the first known publication in Europe on non-decimal systems, including binary. Finally, John Napier discusses binary arithmetic in the Rabdologiæ (1617) and Blaise Pascal states in the De numeris multiplicibus (1654

Leibniz looked for a replacement for the decimal system from the end of the 17th century. He discovered binary arithmetic in a 2,500-year-old Chinese book, the Yi Jing (“Classic of Changes”). He wrote an article which he called “Explanation of Binary Arithmetic, which uses only the characters 1 and 0, with some remarks on its usefulness, and on the light it throws on the ancient Chinese figures of Fu Xi” – Fu Xi being the legendary author of the I Ching. During a stay in Wolfenbüttel, he presented his system to Duke Rudolf Augustus, who was very impressed. He related it to the creation of the world. In the beginning was nothingness (after 7 days (in binary notation, 7 is written 111), everything existed, since there were no more 0. Leibniz also created a coin with, on the obverse, a representation of the duke and, on the reverse, an allegory of the creation of binary numbers.

When he was made a member of the Royal Academy of Sciences in Paris in 1699, Leibniz sent a paper presenting the binary system. Although the academicians were interested in the discovery, they considered it very difficult to handle and waited for Leibniz to present examples of its application. Several years later, he presented his study again, which was better received; this time he linked it to the hexagrams of the I Ching. His article appears in the Histoire de l”Académie royale des sciences of 1703, as well as an account written by a contemporary, “Nouvelle Arithmétique binaire”. Recognizing this way of representing numbers as a very distant heritage of the founder of the Chinese Empire “Fohy”, Leibniz wondered at length about the usefulness of the concepts he had just presented, particularly with regard to the arithmetic rules he was developing.

Finally, he seems to conclude that the only utility he sees in all this is a kind of essential beauty, which reveals the intrinsic nature of numbers and their mutual connections.

Other works

Leibniz was interested in systems of equations and foresaw the use of determinants. In his treatise on the combinatorial art, the general science of form and formulas, he developed substitution techniques for solving equations. He worked on the convergence of series, the development in whole series of functions such as the exponential, the logarithm, the trigonometric functions (1673). He discovered the brachistochrone curve and was interested in the rectification of curves (calculation of their length). He studied Pascal”s treatise on conics and wrote on the subject. He was the first to create the function x↦ax{displaystyle xmapsto a^{x}} (conspectus calculi). He studied the envelopes of curves and the search for extremum for a function (Nova methodus pro maximis et minimis, 1684).

He also attempts a foray into graph theory and topology (analysis situs).

Physics

Leibniz, like many mathematicians of his time, was also a physicist. Although he is known today for his metaphysics and his theory of optimism, Leibniz established himself as one of the main figures of the scientific revolution along with Galileo, Descartes, Huygens, Hooke and Newton. Leibniz became a mechanist very early on, around 1661, when he was studying in Leipzig, as he relates in a letter to Nicolas Rémond. However, a profound difference separates him from Isaac Newton: while Newton considered that “physics is free from metaphysics” and sought to predict phenomena through his physics, Leibniz sought to discover the hidden essence of things and of the world, without trying to obtain precise calculations about any phenomena. He thus came to reproach René Descartes and Newton for not knowing how to do without a Deus ex machina (a hidden divine reason) in their physics, because these did not explain everything that is, what is possible and what is not.

Leibniz invented the concept of kinetic energy, under the name of “living force”. He opposed Descartes” idea that the quantity mv (which at that time was called motive force or momentum) was conserved in shocks, regardless of the directions of motion.

“It is found by reason and by experience that it is the absolute living force that is conserved and by no means the quantity of motion.”

– Gottfried Wilhelm Leibniz, Essay on Dynamics (1691)

The principle of least action was discovered in 1740 by Maupertuis. In 1751, Samuel König claimed to have a letter from Leibniz, dated 1707, in which he stated the same principle, thus well before Maupertuis. The Berlin Academy asked Leonhard Euler to investigate the authenticity of this letter. Euler wrote a report in 1752 in which he concluded that the letter was a forgery: König had invented the existence of this letter from Leibniz. This did not prevent Leibniz from having put forward a statement in optics (without mathematical formalism) close to Fermat”s principle.

In his Philosophiae naturalis principia mathematica, Isaac Newton conceived space and time as absolute things. In his correspondence with Samuel Clarke, who advocated Newton”s ideas, Leibniz refuted these ideas and proposed an alternative system. According to him, space and time are not things in which objects are situated, but a system of relations between these objects. Space and time are “beings of reason”, that is, abstractions from the relations between objects.

“I have more than once marked that I hold space to be something purely relative, like time; for an order of coexistences as time is an order of successions… I do not believe that there is any space without matter. The experiences that we call of the vacuum, exclude only a coarse matter “.

– Third writing of M. Leibniz or answer to the second reply of M. Clarke, 27 February 1716, trans. L. Prenant.

Biology

Leibniz was very interested in biology. His meeting with the microscopists Jan Swammerdam and Antoni van Leeuwenhoek in The Hague in 1676 will have a great influence on his conceptions of the animal body.

In the 1670s and early 1680s, Leibniz devoted himself to vivisections on a macroscopic scale and studied mainly the functions and relationships between organs. At that time, he conceived of animals in the manner of René Descartes, that is, as machines obeying mechanical principles, with the parts structured and ordered for the proper functioning of the whole. According to Leibniz, the determining characteristics of an animal are autonomous nutrition and locomotion. Leibniz believes that these two faculties are the result of internal thermodynamic processes: animals are therefore hydraulic, pneumatic and pyrotechnic machines.

Leibniz”s vision changed radically in the 1690s when he devoted himself to the microscopic study of the various parts of an animal body as a microorganism in its own right. Inspired by the discoveries of Swammerdam and Leeuwenhoek, which revealed that the world is populated by living organisms invisible to the naked eye, and adopting the then emerging view that organisms living within a larger organism are not merely “inhabitants” but constituent parts of the host organism, Leibniz now conceived of the animal as a machine made up of machines, this relationship being true ad infinitum. Unlike artificial machines, animal machines, which Leibniz calls “divine machines”, therefore have no individual parts. To answer the question of the unity of such an infinite imbrication, Leibniz answers that the constituents of the divine machine are in a relation of dominant to dominated. For example, the heart is the part of the body responsible for pumping blood to keep the body alive, and the parts of the heart are responsible for keeping the heart going. This relationship of dominance ensures the unity of the animal machine. It should be noted that it is the bodies of animals, not the animals themselves, that comprise the other animals. Indeed, to do otherwise would contradict the Leibnizian conception of substance, since animals, consisting of autonomous parts, would lose their unity as bodily substances.

Medicine

Leibniz tried to keep abreast of medical progress and to suggest improvements to this science, which was still at a very elementary stage. Blood circulation had only been discovered a hundred years earlier, and it would be nearly two centuries before doctors systematically washed their hands before an operation. In 1691, when Justel learned of the existence of a remedy for dysentery, he did everything possible to obtain this root (ipecacuana) from South America and promoted its use in Germany. A few years later, in a letter to Princess Sophie, he proposed a series of medical recommendations that we take for granted today.

To advance medicine, medical research and the dissemination of results had to be promoted. It was essential that diagnosis preceded treatment. It was also necessary to observe the symptoms of the disease and to record a written history of its evolution and of the patient”s reactions to treatment. In addition, it was important to disclose reports on the most interesting cases: in this sense, it was essential that hospitals had adequate funds and personnel. Finally, he defended the need for preventive medicine and the creation of a Health Council, made up of politicians and doctors capable of proposing a number of measures for diseases of great social spread, such as periodic epidemics. The physician and philosopher Ramazzini, whom he met in Modena, drew his attention to the importance of medical statistics. Leibniz was convinced that the diffusion of such statistics would lead to a substantial improvement, in that doctors would be better equipped to treat the most frequent diseases. He insisted on this theme in different instances and even proposed to the Journal des savants to publish these statistics annually, following the model established by Ramazzini.

Geology

Leibniz constantly showed a keen interest in the study of the evolution of the Earth and of species. During his travels, he was always interested in curiosity cabinets, where he could observe fossils and mineral residues. During his stay in the Harz region and his travels in Germany and Italy, he collected numerous samples of minerals and fossils. He met Niels Stensen in Hanover and read Kircher. As part of his unfinished work on the history of the house of Brunswick, Leibniz wrote a preface entitled Protogaea dealing with natural history and geology, written in 1691 but not published until 1749. He also included a summary of his theory of the evolution of the Earth in Theodicy.

Protogéa is the first work to cover a wide range of major geological issues: the origin of the planet Earth, the formation of relief, the causes of tides, strata and minerals, and the organic origin of fossils. Leibniz recognized the igneous origin of the planet and the existence of a central fire. However, contrary to Descartes who indicated that fire was the cause of terrestrial transformations, he also considered water as a geological agent. The mountains came, according to him, from eruptions prior to the Flood, caused not only by rainfall, but also by the irruption of water from the subsoil. He also cited water and wind as modellers of the relief and distinguished two types of rocks: magmatic and sedimentary.

He was also one of the pioneers of the theory of evolution, putting forward the idea that the differences observed between existing animals and the fossils found were explained by the transformation of species throughout the geological revolutions.

Library Science

Leibniz was librarian in Hanover from 1676 and in Wolfenbüttel from 1691. He was also offered this position in the Vatican in 1686 and in Paris in 1698 (as well as possibly in Vienna), but he refused out of loyalty to Lutheranism, since these positions required conversion to Catholicism.

In his Representation to H.S.H. the Duke of Wolfenbüttel to encourage him in the maintenance of his Library, Leibniz explains how he intended to carry out his duties. In a letter to Duke Friedrich in 1679, Leibniz wrote: “A library must be an encyclopedia”, and he attached two plans for a library classification based on the classification of sciences, which was also to serve as a basis for the Encyclopedia:

Louis Couturat, in La Logique de Leibniz, points out the order and distinction of the three parts of philosophy (metaphysics, mathematics and physics), a distinction based on that of their objects, i.e. our faculties of knowledge: objects of pure understanding, of the imagination, of the senses.

He conceived the project of an encyclopedia or “universal library”:

“It is important to the happiness of the human race that an Encyclopedia be founded, that is to say, an ordered collection of truths sufficient, as far as possible, for the deduction of all useful things.

– Gottfried Wilhelm Leibniz, Initia et specimina scientiæ generalis, 1679-1680

History

From the 1670s onwards, Leibniz was also an important historian. It was initially linked to his interest in law, which led him to develop works on the history of law, and to publish, in the 1690s, an important collection of medieval legal documents. It is also linked to the commission given to him in 1685 by the Elector of Hanover: a history of the house of Brunswick. Convinced that this aristocratic family had in part similar origins to the Italian house of Este, Leibniz undertook important work on the history of Europe from the ninth to the eleventh century. He went to southern Germany and Austria at the end of 1687 to gather the necessary documentation for his investigation. A discovery made in Augsburg in April 1688 significantly broadened his perspectives; he was able to consult the codex Historia de guelfis principibus in the Benedictine monastery of this locality, in which he found evidence of the links between the Guelphs, founders of the duchy of Brunswick-Luneburg, and the house of Este, Italian nobles of the duchy of Ferrara and Modena. This discovery forced him to extend his trip to Italy, in particular to Modena, until 1690. Leibniz”s historical work was much more complex than he had expected and, in 1691, he explained to the Duke that the work could be completed in a few years if he had the benefit of collaboration, which he obtained by recruiting a secretary. He nevertheless wrote the part relating to his discoveries; although three volumes were indeed published, the work was never completed before his death in 1716. Leibniz thus participated in the works of the time, which founded, with Jean Mabillon, Étienne Baluze or Papebrocke, historical criticism; he brought important elements to the questions of chronology and genealogy of the sovereign families of Europe. On the subject of the house of Este, he engaged in a famous polemic with the great Italian scholar Antonio Muratori.

Politics and diplomacy

Leibniz was very interested in political questions.

Shortly after his arrival in Mainz, he published a short treaty in which he tried to settle the question of the succession to the Polish throne by deduction.

In 1672, Boyneburg sent him on a diplomatic mission to Paris to convince Louis XIV to take his conquests to Egypt rather than Germany, according to the plan conceived by Leibniz himself. Beyond the objective of negotiating peace in Europe, he went to Paris with other aims: to meet the royal librarian Pierre de Carcavi, to tell him about the arithmetic machine he was working on, and to enter the Paris Academy of Sciences.

As an irenist, Leibniz sought the reunification of the Catholic and Protestant Christian churches, as well as the unification of the Lutheran and Reformed branches of Protestantism. He sought as much support as possible, especially among the powerful, knowing that if he did not succeed in involving the pope, the emperor or a reigning prince, his chances of success would remain slim. In the course of his life, he wrote various papers in support of this idea, including Systema theologicum, a work that proposed reunification from a Catholic point of view, which was not published until 1845. Together with his friend, Bishop Cristóbal de Rojas y Spínola, who also advocated the reunification of Protestant denominations, they planned to promote a diplomatic coalition between the electors of Brunswick-Luneburg and Saxony against the Emperor, who had expressed his opposition to the project of religious reunification.

Technology and engineering

Leibniz, as an engineer, designed many inventions.

He designed an arithmetic machine capable of multiplying, and for this purpose invented the storage of the multiplicand thanks to his famous fluted cylinders, used until the 1960s. After having built three first models, he built a fourth one later, in 1690, which was found in 1894 at the University of Göttingen and is now kept in the Gottfried Wilhelm Leibniz library in Hanover.

He was also a pioneer in the use of wind power, attempting, unsuccessfully, to replace the pump-driven water wheels long used in Germany with windmills to drain the Harz mines. In the field of mining, he is also the inventor of the endless chain technique.

Leibniz also designed the highest fountain in Europe in the royal gardens of Herrenhausen. He also improved transportation over rough terrain with iron-covered wheels.

Leibniz also drew plans for a submarine, for a chain mail, or for a kind of peg consisting of a nail with sharp edges.

Linguistics and philology

Beyond the philosophical interest in the ideal language of 17th century scholars, Leibniz practiced linguistics primarily as an auxiliary science of history. His goal was to identify ethnic groups and their migrations in order to reconstruct history before the written tradition. Moreover, Leibniz, as part of his history of the house of Brunswick, plans to write two prefaces to it, the first, Protogæa, dealing with geology, the second with the migrations of European tribes, based on linguistic research.

His goal is to establish relationships between languages, based on the postulate that the language of a people depends on its origin. His interest is therefore focused on etymology and toponymy.

Leibniz practiced linguistics on a much broader scale than his contemporaries. His lexical material ranges from German dialects to distant languages such as Manchu. He based all this material on pre-existing bibliography, on his personal observations or on his correspondents, notably the Christian missionaries in China or the members of the Dutch East India Company. He gathered this lexical material in his Collectanea etymologica.

If this desire for universality is the strength of the Leibnizian project, it is also its weakness, because the study of such a quantity of material is beyond the capacity of a single individual. However, the lexical collections that he was able to establish have made it possible to save evidence of languages that would have been lost without Leibniz”s work.

In 1696, with the intention of promoting the study of German, he proposed the creation of the German Society in Wolfenbüttel, under the aegis of Duke Antony-Ulrich, who ruled alongside his brother Rudolf-Augustus, both friends of Leibniz. One of his main works in this field was Unvorgreissliche Gedanken, betreffend die Ausübung und Verbesserung der teutschen Sprache (“Considerations on the cultivation and perfection of the German language”), written in 1697 and published in 1717. He wanted German to become a vehicle for cultural and scientific expression, pointing out that, since the Thirty Years” War, the language had deteriorated and was in danger of being altered by French.

The definitive state of his theories on the descent of languages is known to us from a table of 1710: from the original language (Ursprache), two branches break off: the Japhaic (covering northwestern Asia and Europe) and the Aramaic (Persian, Aramaic, and Georgian descending from both. The Aramaic branch splits into Arabic and Egyptian (which in turn splits into other smaller groups), while the Japhaic branch splits into Scythian and Celtic; Scythian gives Turkish, Slavic, Finnish and Greek, and Celtic gives Celtic and Germanic; when the two mix, they give the Apennine, Pyrenean, and Western European languages (including French and Italian) which have taken on elements from Greek.

Leibniz initially thought that all European languages came from a single language, perhaps Hebrew. Eventually, his research led him to abandon the hypothesis of a single European language group. Furthermore, Leibniz refuted the assumption of Swedish scholars that Swedish was the oldest (and therefore the noblest) European language.

Sinology

Nicolas Malebranche, one of the first Europeans to take an interest in sinology towards the end of his career, played a primordial role in Leibniz”s interest in China.

As early as 1678, Leibniz knew something of the language and considered it the best representation of the ideal language he was looking for. According to him, European civilization is the most perfect in that it is based on Christian revelation, and Chinese civilization represents the best example of non-Christian civilization. In 1689, his meeting with the Jesuit Claudio Filippo Grimaldi, a Christian missionary in Peking who was visiting Rome, broadened and strengthened Leibniz”s interest in China.

Initially, he was most interested in the use of the Chinese language by deaf-mutes, the idea that it might be the memory of a long-forgotten calculus, and the question of whether its construction followed logical-mathematical laws similar to those of Leibniz”s project of universal characteristic. The meeting with Grimaldi made Leibniz aware of the importance of the intellectual exchange that could take place between Europe and China through the travels of missionaries.

In April 1697, he published the Novissima Sinica (“Last News from China”), a collection of letters and essays from Jesuit missionaries in China. Thanks to Father Verjus, director of the Jesuit mission in China, to whom he sent a copy, the book ended up in the hands of Father Joachim Bouvet, a missionary who had returned from China and was staying in Paris. The relationship between Leibniz and Bouvet was very spontaneous and gave rise to the more general development of the binary system. After becoming familiar with Leibniz”s philosophy, Bouvet came to compare it to ancient Chinese philosophy, since the latter had established the principles of natural law. It was also Bouvet who invited him to study the hexagrams of the I Ching, a system similar to the binary created by Fuxi, the legendary Chinese emperor and considered the founder of Chinese culture.

Leibniz pleads with various authorities for a rapprochement between Europe and China through Russia. Maintaining good relations with Moscow, he hoped to exchange discoveries and culture. He even urged the Berlin Academy to set up a Protestant mission in China. A few months before his death, he published his major work on China, entitled Discourse on the Natural Theology of the Chinese, the last part of which finally exposes his binary system and its links with the I Ching.

Psychology

Psychology was one of Leibniz”s main interests. He appears as an “underestimated precursor of psychology”. He was interested in several themes that are now part of psychology: attention and consciousness, memory, learning, motivation, individuality and the role of evolution. He strongly influenced the founder of psychology as a discipline in its own right, Wilhelm Wundt, who published a monograph on Leibniz, and took up the term “perception” introduced by Leibniz.

Games

As early as 1670, texts show Leibniz”s interest in games, and from 1676 until his death, he will engage in an in-depth study of games.

Leibniz was an excellent chess player; he was particularly interested in the scientific and logical aspect of the game (as opposed to games that include an element of chance), and was the first to consider it as a science.

He also invented a reverse solitaire game.

Literature

Leibniz tried to promote the use of the German language and proposed the creation of an Academy for the enrichment and promotion of German. Despite these opinions, he wrote little in German but mostly in Latin and French, because of the lack of abstract technical terms in German. Thus, when he wrote in German, he was often forced to use Latin terms, although he occasionally tried to do without them, in the spirit of the eighteenth-century movements for linguistic purity.

Although he had a scientific career, Leibniz continued to dream of a literary career. He wrote poetry (mostly in Latin) of which he took great pride, and boasted that he could recite most of Virgil”s Aeneid. He had a very elaborate style of writing Latin, typical of the late Renaissance humanists.

He is the author of an edition of the Antibarbarus by the sixteenth-century Italian humanist Mario Nizzoli. In 1673 he undertook the edition ad usum Delphini of the works of Martianus Capella, a 15th century author. In 1676 he translated two dialogues of Plato, the Phaedo and the Theaetetus, into Latin.

He was the first modern to note the profound differences between Plato”s philosophy and the mystical and superstitious questions of Neoplatonism – which he called “pseudo-Platonism”.

Music

Patrice Bailhache was interested in Leibniz”s particular relationship to music. He considered it as “a hidden practice of arithmetic, the mind not being aware that it counts” (“musica est exercitium arithmeticae occultum nescientis se numerare animi”).

His correspondence with the civil servant Conrad Henfling shows a keen interest in this subject, although not in detail. He discusses in particular the notion of consonance as well as the classification of intervals and consonant chords, and the concept of temperament.

However, Leibniz warns against it, because as a pleasure of the mind, one can lose too much time in it. He explains it as follows: “the pleasures of the senses that come closest to the pleasures of the mind <, and that are the purest and the purest>, are those of music” and “the only thing one can fear is to spend too much time on it”.

Also, Leibniz grants it a subordinate role, compared to other disciplines. This probably explains the fact that he did not produce in-depth musicological studies. Patriche Bailhache argues in this sense, quoting Leibniz: “the pleasures of the senses are reduced to intellectual pleasures confusedly known. Music charms us” (GP, VI, p. 605).

In these conditions, according to Patriche Bailhache “mathematics, philosophy, religion are disciplines much higher in dignity than music, and even than the theory of music (because this theory looks at an object of lower value)”.

Legacy, criticism and controversy

At his death, Leibniz did not enjoy a good image. He was involved in a dispute with Isaac Newton about his authorship of the infinitesimal calculus: Newton and Leibniz had both found the techniques of derivation and integration. Leibniz published the first one in 1684, whereas Newton only published in 1711 work that he had done nearly 40 years earlier, in the years 1660-1670.

Leibniz and his disciple Christian Wolff will strongly influence Immanuel Kant. It is not clear, however, in what way Leibnizian ideas will influence Kant”s theses. In particular, it is not clear whether Kant, in his commentary on Leibnizian themes, is commenting directly on Leibniz or his heirs.

In 1765, the publication of the New Essays on Human Understanding offered for the first time a direct access to Leibnizian thought, independently of the image transmitted by Wolff. This event had a decisive effect on Kant”s philosophy and on the German Enlightenment (Aufklärung).

Among the Enlightenment, views on Leibniz were divided. On the one hand, Jean-Jacques Rousseau drew part of his learning from Leibniz; Denis Diderot praised him in the Encyclopédie, and despite numerous oppositions between the two philosophers, there were notable similarities between Leibniz”s New Essays on Human Understanding and Diderot”s Thoughts on the Interpretation of Nature. However, at the same time, Leibniz”s theodicy and his idea of the best of all possible worlds were strongly criticized by Voltaire in his philosophical tale Candide through the character of Pangloss.

Leibniz also strongly influenced the neurophysiologist, psychologist and philosopher Wilhelm Wundt, known as the founder of psychology as an experimental discipline. The latter devoted a monograph to him in 1917.

In the 20th century, the logician Kurt Gödel was strongly influenced by Leibniz (as well as by Kant and Husserl) and studied the latter”s work intensively between 1943 and 1946. He was also convinced that a conspiracy was behind the suppression of some of Leibniz”s work. Gödel considered that the universal characteristic was feasible.

According to the Mathematics Genealogy Project, Leibniz has more than 110,000 descendants in mathematics, including two students: Nicolas Malebranche (to whom he shared his infinitesimal calculus during their talks in Paris in 1672.

In 1968, Michel Serres published his first book, Le Système de Leibniz et ses modèles mathématiques. The reading of Leibniz will accompany him all his life, declaring for example “Internet is Leibniz without God”.

Distinctions and tributes

Several institutions have been named in his honor:

In addition, a prize named in his honor, the Gottfried-Wilhelm-Leibniz-Prize, awarded annually since 1986 by the German Research Foundation, is one of the most prestigious awards in Germany for scientific research.

In mathematics, he gave his name:

In astronomy, it gave its name :

In Paris, he gave his name to the rue Leibniz and the square Leibniz in the 18th arrondissement.

The Bahlsen cookie factory has been selling cookies called “Leibniz-Keks” since 1891, the cookie factory being based in Hanover where the philosopher lived for 40 years.

The house in which he lived from September 29, 1698 until his death in 1716, dating from 1499, was destroyed by aerial bombing on the night of October 8-9, 1943. A faithful reproduction (Leibnizhaus, “Leibniz”s house”) – not located on the original site, which was not available, but still nearby in the old town – was built between 1981 and 1983.

On the occasion of the 370th anniversary of his birth and the 300th anniversary of his death, which also corresponds to the 10th anniversary of the renaming of the University of Hannover and the 50th anniversary of the Gottfried Wilhelm Leibniz Society, the city of Hannover declares 2016 the “Year of Leibniz.”

Two monuments are dedicated to his memory in Hannover: the Leibniz Memorial, a bronze plaque carved to represent his face, and the Leibniz Temple, located in the Georgengarten Park. In addition, mentions of the philosopher can be found in various places in the city.

Ernst Hähnel created a statue of Leibniz in Leipzig (the philosopher”s home town), the Leibniz Forum, in 1883. First displayed in St. Thomas Church, it was moved to the courtyard of the city”s university in 1896-1897, and miraculously survived the bombings of December 1943. In 1968, during the construction of the new university building, the statue was moved again.

Bibliography

Translations into French of mathematical works :

: document used as a source for the writing of this article.

External links

Sources

  1. Gottfried Wilhelm Leibniz
  2. Gottfried Wilhelm Leibniz