莱布尼兹其实离开我们并不遥远

莱布尼兹其实离开我们并不遥远

大家知道，莱布尼兹离开我们已经有300多年了，但是，他的思想至今仍然活跃在我们身旁

众所周知，微积分的运算符号dx、dy，二进制计算机，符号形式逻辑，超实数系统（原型），这些东西至今仍然萦绕在我们的脑际，……

但是，中国人都知道康熙皇帝的故事，对于西方科学家莱布尼兹的贡献却知之甚少。我并不想重复陈述莱布尼兹的伟大之处，只是把他的生平事迹列举如下，供读者自己阅读、判断。

袁萌  12月24日

   

"Leibniz" redirectshere. For other uses, see Gottfried Wilhelm (von) Leibniz(/ˈlaɪbnɪts/;^[5] German: [ˈɡɔtfʁiːt ˈvɪlhɛlm fɔn ˈlaɪbnɪts]^[6] or [ˈlaɪpnɪts];^[7] French: GodefroiGuillaume Leibnitz;^[8] 1 July1646 [O.S. 21 June] – 14 November 1716) was a German polymath andphilosopher who occupies a prominent place in the history of mathematics and the history of philosophy, having developed differential and integral calculus independently of Isaac Newton.^[9] Leibniz's notation has been widely used ever since it waspublished. It was only in the 20th century that his Law of Continuityand Transcendental Law of Homogeneity foundmathematical implementation (by means of non-standard analysis). He became one of the most prolificinventors in the field of mechanical calculators. While working on adding automaticmultiplication and division to Pascal's calculator, he was the first to describe a pinwheel calculator in 1685^[10] andinvented the Leibnizwheel, used in the arithmometer, thefirst mass-produced mechanical calculator. He also refined the binary numbersystem, which is the foundation of virtually all digital computers.

In philosophy, Leibniz is most noted for his optimism, i.e. his conclusion that our Universe is, in arestricted sense, the best possible one that God could have created,an idea that was often lampooned by others such as Voltaire. Leibniz,along with RenéDescartes and BaruchSpinoza, was one of the three great 17th-century advocates of rationalism. Thework of Leibniz anticipated modern logicand analytic philosophy, but his philosophy also looks back to thescholastictradition, in which conclusions are produced by applying reason to firstprinciples or prior definitions rather than to empirical evidence.

Leibniz made major contributions to physics andtechnology, and anticipated notions that surfaced much later in philosophy, probability theory, biology, medicine,geology, psychology, linguistics, and computer science.He wrote works on philosophy, politics, law, ethics, theology, history, and philology. Leibnizalso contributed to the field of library science. While serving as overseer ofthe Wolfenbüttel library in Germany, he devised a cataloging system that wouldserve as a guide for many of Europe's largest libraries.^[11]Leibniz's contributions to this vast array of subjects were scattered invarious learnedjournals, in tens of thousands of letters, and in unpublishedmanuscripts. He wrote in several languages, but primarily in Latin, French, and German.^[12] There isno complete gathering of the writings of Leibniz translated into English.^[13]

Contents

• 1 Biography
• • 1.1 Early life
  • 1.2 1666–1676
  • 1.3 House of Hanover, 1676–1716
  • 1.4 Death
  • 1.5 Personal life
• 2 Philosopher
• • 2.1 The Principles
  • 2.2 The monads
  • 2.3 Theodicy and optimism
  • 2.4 Discourse on Metaphysics

2.5 Fundamental question ofmetaphysics

• • 2.6 Symbolic thought
  • 2.7 Formal logic
• 3 Mathematician
• • 3.1 Calculus
  • 3.2 Topology
• 4 Scientist and engineer
• • 4.1 Physics
  • • 4.1.1 The vis viva
  • 4.2 Other natural science
  • 4.3 Psychology
  • 4.4 Social science
  • 4.5 Technology
  • • 4.5.1 Computation
  • 4.6 Librarian
  • 4.7 Advocate of scientific societies
• 5 Lawyer and moralist
• • 5.1 Ecumenism
• 6 Philologist
• 7 Sinophile
• 8 As polymath
• 9 Posthumous reputation

10 Writings and edition

• • 10.1 Selected works

10.1.1 Posthumous works

10.2 Collections

• 11 See also
• 12 Notes
• 13 References
• • 13.1 Bibliographies
  • 13.2 Primary literature
  • 13.3 Secondary literature up to 1950
  • 13.4 Secondary literature post-1950
• 14 External links

Biography

Early life

Gottfried Leibniz was born on 1 July 1646, toward theend of the Thirty Years' War, in Leipzig, Saxony, to Friedrich Leibnizand Catharina Schmuck. Friedrich noted in his family journal:

21. Juny am Sontag 1646 Ist mein Sohn GottfriedWilhelm, post sextam vespertinam 1/4 uff 7 uhr abents zur welt gebohren, imWassermann.

In English:

On Sunday 21 June [NS: 1 July] 1646,my son Gottfried Wilhelm is born into the world a quarter after six in theevening, in Aquarius.^[14][15]

Leibniz was baptized on 3 July of that year at St. Nicholas Church, Leipzig; his godfather wasthe Lutheran theologianMartin Geier (de).^[16] Hisfather died when he was six and a half years old, and from that point on he wasraised by his mother. Her teachings influenced Leibniz's philosophical thoughtsin his later life.^{[citation needed]}

Leibniz's father had been a Professor of MoralPhilosophy at the University of Leipzig, and the boy later inherited his father'spersonal library. He was given free access to it from the age of seven. WhileLeibniz's schoolwork was largely confined to the study of a small canon of authorities, his father's library enabled him tostudy a wide variety of advanced philosophical and theological works—ones thathe would not have otherwise been able to read until his college years.^[17] Accessto his father's library, largely written in Latin, also led to his proficiency in theLatin language, which he achieved by the age of 12. He also composed 300 hexameters of Latin verse, in asingle morning, for a special event at school at the age of 13.^[18]

In April 1661 he enrolled in his father's formeruniversity at age 15,^[1][19] andcompleted his bachelor's degree in Philosophy in December 1662. He defendedhis Disputatio Metaphysica de Principio Individui (MetaphysicalDisputation on the Principle of Individuation),^[20] whichaddressed the principle of individuation, on 9 June 1663.Leibniz earned his master's degree in Philosophy on 7 February 1664. Hepublished and defended a dissertationSpecimen Quaestionum Philosophicarum ex Jure collectarum (An Essay ofCollected Philosophical Problems of Right),^[20] arguingfor both a theoretical and a pedagogical relationship between philosophy andlaw, in December 1664. After one year of legal studies, he was awarded hisbachelor's degree in Law on 28 September 1665.^[21] Hisdissertation was titled De conditionibus (On Conditions).^[20]

In early 1666, at age 19, Leibniz wrote his firstbook, De Arte Combinatoria (On the Combinatorial Art),the first part of which was also his habilitation thesisin Philosophy, which he defended in March 1666.^[20][22] His nextgoal was to earn his license and Doctorate in Law, which normally requiredthree years of study. In 1666, the University of Leipzig turned down Leibniz'sdoctoral application and refused to grant him a Doctorate in Law, most likelydue to his relative youth.^[23][24] Leibnizsubsequently left Leipzig.^[25]

Leibniz then enrolled in the University of Altdorf and quickly submitted a thesis, which hehad probably been working on earlier in Leipzig.^[26] Thetitle of his thesis was Disputatio Inauguralis de Casibus Perplexis in Jure(Inaugural Disputation on Ambiguous Legal Cases).^[20] Leibnizearned his license to practice law and his Doctorate in Law in November 1666.He next declined the offer of an academic appointment at Altdorf, saying that"my thoughts were turned in an entirely different direction".^[27]

As an adult, Leibniz often introduced himself as"Gottfried von Leibniz".Many posthumously published editions of his writings presented his name on thetitle page as "FreiherrG. W. von Leibniz." However, no document has ever been found from anycontemporary government that stated his appointment to any form of nobility.^[28]

1666–1676

Engraving of Gottfried WilhelmLeibniz

Leibniz's first position was as a salaried secretaryto an alchemical societyin Nuremberg.^[29] He knewfairly little about the subject at that time but presented himself as deeplylearned. He soon met Johann Christian von Boyneburg (1622–1672), thedismissed chief minister of the Elector of Mainz, Johann Philipp von Schönborn.^[30] VonBoyneburg hired Leibniz as an assistant, and shortly thereafter reconciled withthe Elector and introduced Leibniz to him. Leibniz then dedicated an essay onlaw to the Elector in the hope of obtaining employment. The stratagem worked;the Elector asked Leibniz to assist with the redrafting of the legal code forthe Electorate.^[31] In 1669,Leibniz was appointed assessor in the Court of Appeal. Although von Boyneburgdied late in 1672, Leibniz remained under the employment of his widow until shedismissed him in 1674.^{[citation needed]}

Von Boyneburg did much to promote Leibniz'sreputation, and the latter's memoranda and letters began to attract favorablenotice. After Leibniz's service to the Elector there soon followed a diplomaticrole. He published an essay, under the pseudonym of a fictitious Polishnobleman, arguing (unsuccessfully) for the German candidate for the Polishcrown. The main force in European geopolitics during Leibniz's adult life wasthe ambition of Louis XIV of France, backed by French military and economicmight. Meanwhile, the Thirty Years' War had left German-speaking Europe exhausted, fragmented, and economicallybackward. Leibniz proposed to protect German-speaking Europe by distracting Louisas follows. France would be invited to take Egypt as a stepping stone towards aneventual conquest of the Dutch East Indies.In return, France would agree to leave Germany and the Netherlands undisturbed.This plan obtained the Elector's cautious support. In 1672, the Frenchgovernment invited Leibniz to Paris for discussion,^[32] but theplan was soon overtaken by the outbreak of the Franco-Dutch Warand became irrelevant. Napoleon's failed invasion of Egypt in 1798 can be seen asan unwitting, late implementation of Leibniz's plan, after the Easternhemisphere colonial supremacy in Europe had already passed from the Dutch tothe British.^{[citation needed]}

Thus Leibniz went to Paris in 1672. Soon afterarriving, he met Dutch physicist and mathematician Christiaan Huygens and realised that his own knowledge ofmathematics and physics was patchy. With Huygens as his mentor, he began aprogram of self-study thatsoon pushed him to making major contributions to both subjects, includingdiscovering his version of the differential and integral calculus. He met Nicolas Malebranche and Antoine Arnauld,the leading French philosophers of the day, and studied the writings of Descartes and Pascal, unpublishedas well as published. He befriended a German mathematician, Ehrenfried Walther von Tschirnhaus; theycorresponded for the rest of their lives.

 

Stepped reckoner

When it became clear that France would not implementits part of Leibniz's Egyptian plan, the Elector sent his nephew, escorted byLeibniz, on a related mission to the English government in London, early in1673.^[33] ThereLeibniz came into acquaintance of Henry Oldenburg andJohn Collins. He met with the Royal Society wherehe demonstrated a calculating machine that he had designed and had beenbuilding since 1670. The machine was able to execute all four basic operations(adding, subtracting, multiplying, and dividing), and the society quickly madehim an external member.

The mission ended abruptly when news of the Elector'sdeath (12 February 1673) reached them. Leibniz promptly returned to Paris andnot, as had been planned, to Mainz.^[34] Thesudden deaths of his two patrons in the same winter meant that Leibniz had tofind a new basis for his career.

In this regard, a 1669 invitation from the John Frederick of Brunswickto visit Hanover proved to have been fateful. Leibniz had declined theinvitation, but had begun corresponding with the duke in 1671. In 1673, theduke offered Leibniz the post of counsellor. Leibniz very reluctantly acceptedthe position two years later, only after it became clear that no employment inParis, whose intellectual stimulation he relished, or with the Habsburg imperialcourt, was forthcoming.^{[citation needed]}

In 1675 he tried to get admitted to the French Academy of Sciences as a foreignhonorary member, but it was considered that there were already enoughforeigners there and so no invitation came. He left Paris in October 1676.

House of Hanover, 1676–1716

Leibniz managed to delay his arrival in Hanover untilthe end of 1676 after making one more short journey to London, where Newtonaccused him of having seen Newton's unpublished work on calculus in advance.^[35] This wasalleged to be evidence supporting the accusation, made decades later, that hehad stolen calculus from Newton. On the journey from London to Hanover, Leibnizstopped in The Hague where hemet vanLeeuwenhoek, the discoverer of microorganisms. He also spent severaldays in intense discussion with Spinoza, who hadjust completed his masterwork, the Ethics.^[36]

In 1677, he was promoted, at his request, to PrivyCounselor of Justice, a post he held for the rest of his life. Leibniz servedthree consecutive rulers of the House of Brunswick as historian, politicaladviser, and most consequentially, as librarian of the ducal library. He thenceforth employed hispen on all the various political, historical, and theological mattersinvolving the House of Brunswick; the resulting documents form a valuable partof the historical record for the period.

Among the few people in north Germany to acceptLeibniz were the Electress Sophia of Hanover(1630–1714), her daughter Sophia Charlotte of Hanover (1668–1705), theQueen of Prussia and his avowed disciple, and Caroline of Ansbach, the consort of her grandson, the future George II. To each of these women he wascorrespondent, adviser, and friend. In turn, they all approved of Leibniz morethan did their spouses and the future king George I of Great Britain.^[37]

The population of Hanover was only about 10,000, andits provinciality eventually grated on Leibniz. Nevertheless, to be a majorcourtier to the House of Brunswickwas quite an honor, especially in light of the meteoric rise in the prestige ofthat House during Leibniz's association with it. In 1692, the Duke of Brunswickbecame a hereditary Elector of the Holy Roman Empire.The British Act of Settlement 1701 designated the Electress Sophia and herdescent as the royal family of England, once both King William III and his sister-in-law and successor, Queen Anne, were dead. Leibniz played a role inthe initiatives and negotiations leading up to that Act, but not always aneffective one. For example, something he published anonymously in England,thinking to promote the Brunswick cause, was formally censured by the British Parliament.

The Brunswicks tolerated the enormous effort Leibnizdevoted to intellectual pursuits unrelated to his duties as a courtier,pursuits such as perfecting calculus, writing about other mathematics, logic,physics, and philosophy, and keeping up a vast correspondence. He began workingon calculus in 1674; the earliest evidence of its use in his survivingnotebooks is 1675. By 1677 he had a coherent system in hand, but did notpublish it until 1684. Leibniz's most important mathematical papers werepublished between 1682 and 1692, usually in a journal which he and Otto Mencke foundedin 1682, the ActaEruditorum. That journal played a key role in advancing hismathematical and scientific reputation, which in turn enhanced his eminence indiplomacy, history, theology, and philosophy.

 

Leibniz's correspondence, papersand notes from 1669 to 1704, National Library of Poland.

The Elector Ernest Augustus commissioned Leibniz towrite a history of the House of Brunswick, going back to the time of Charlemagne orearlier, hoping that the resulting book would advance his dynastic ambitions.From 1687 to 1690, Leibniz traveled extensively in Germany, Austria, and Italy,seeking and finding archival materials bearing on this project. Decades went bybut no history appeared; the next Elector became quite annoyed at Leibniz'sapparent dilatoriness. Leibniz never finished the project, in part because ofhis huge output on many other fronts, but also because he insisted on writing ameticulously researched and erudite book based on archival sources, when hispatrons would have been quite happy with a short popular book, one perhapslittle more than a genealogywith commentary, to be completed in three years or less. They never knew thathe had in fact carried out a fair part of his assigned task: when the materialLeibniz had written and collected for his history of the House of Brunswick wasfinally published in the 19th century, it filled three volumes.

In 1708, John Keill, writingin the journal of the Royal Society and with Newton's presumed blessing,accused Leibniz of having plagiarised Newton's calculus.^[38] Thusbegan the calculus priority dispute which darkenedthe remainder of Leibniz's life. A formal investigation by the Royal Society(in which Newton was an unacknowledged participant), undertaken in response toLeibniz's demand for a retraction, upheld Keill's charge. Historians ofmathematics writing since 1900 or so have tended to acquit Leibniz, pointing toimportant differences between Leibniz's and Newton's versions of calculus.

In 1711, while traveling in northern Europe, theRussian Tsar Peter the Greatstopped in Hanover and met Leibniz, who then took some interest in Russianmatters for the rest of his life. In 1712, Leibniz began a two-year residencein Vienna, where hewas appointed Imperial Court Councillor to the Habsburgs. On thedeath of Queen Anne in 1714, Elector George Louis became King George I of Great Britain, under the terms of the 1701 Act ofSettlement. Even though Leibniz had done much to bring about this happy event,it was not to be his hour of glory. Despite the intercession of the Princess ofWales, Caroline of Ansbach, George I forbade Leibniz to join him in Londonuntil he completed at least one volume of the history of the Brunswick familyhis father had commissioned nearly 30 years earlier. Moreover, for George I toinclude Leibniz in his London court would have been deemed insulting to Newton,who was seen as having won the calculus priority dispute and whose standing inBritish official circles could not have been higher. Finally, his dear friendand defender, the Dowager Electress Sophia, died in 1714.

Death

Leibniz died in Hanover in 1716: atthe time, he was so out of favor that neither George I (who happened to be nearHanover at that time) nor any fellow courtier other than his personal secretaryattended the funeral. Even though Leibniz was a life member of the RoyalSociety and the Berlin Academy of Sciences, neither organizationsaw fit to honor his passing. His grave went unmarked for more than 50 years.Leibniz was eulogized by Fontenelle, before the French Academy of Sciences in Paris, which hadadmitted him as a foreign member in 1700. The eulogy was composed at the behestof the Duchess of Orleans, a niece of theElectress Sophia.

Personal life

Leibniz never married. He complained on occasion aboutmoney, but the fair sum he left to his sole heir, his sister's stepson, provedthat the Brunswicks had, by and large, paid him well. In his diplomaticendeavors, he at times verged on the unscrupulous, as was all too often thecase with professional diplomats of his day. On several occasions, Leibnizbackdated and altered personal manuscripts, actions which put him in a badlight during the calculus controversy. On the other hand,he was charming, well-mannered, and not without humor and imagination.^[39] He hadmany friends and admirers all over Europe. On Leibniz's religious views, thoughhe was a protestant, Leibnizlearned to appreciate the good sides of Catholicism throughhis patrons and colleagues. He never admitted the Protestant view of Pope as anAntichrist.^[40] Leibnizwas claimed as a philosophical theist.^{[41][42][43][44]}

Philosopher

Leibniz's philosophical thinking appears fragmented,because his philosophical writings consist mainly of a multitude of shortpieces: journal articles, manuscripts published long after his death, and manyletters to many correspondents. He wrote only two book-length philosophicaltreatises, of which only the Théodicée of 1710 was published in hislifetime.

Leibniz dated his beginning as a philosopher to his Discourse on Metaphysics, which he composed in 1686 as acommentary on a running dispute between Nicolas Malebranche and Antoine Arnauld.This led to an extensive and valuable correspondence with Arnauld;^[45] it andthe Discourse were not published until the 19th century. In 1695,Leibniz made his public entrée into European philosophy with a journal articletitled "New System of the Nature and Communication of Substances".^[46] Between1695 and 1705, he composed his New Essays on Human Understanding, alengthy commentary on JohnLocke's 1690 An Essay Concerning Human Understanding,but upon learning of Locke's 1704 death, lost the desire to publish it, so thatthe New Essays were not published until 1765. The Monadologie,composed in 1714 and published posthumously, consists of 90 aphorisms.

Leibniz met Spinoza in 1676,read some of his unpublished writings, and has since been suspected ofappropriating some of Spinoza's ideas. While Leibniz admired Spinoza's powerfulintellect, he was also forthrightly dismayed by Spinoza's conclusions,^[47]especially when these were inconsistent with Christian orthodoxy.

Unlike Descartes and Spinoza, Leibniz had a thoroughuniversity education in philosophy. He was influenced by his Leipzig professor Jakob Thomasius,who also supervised his BA thesis in philosophy.^[4] Leibnizalso eagerly read FranciscoSuárez, a Spanish Jesuit respectedeven in Lutheranuniversities. Leibniz was deeply interested in the new methods and conclusionsof Descartes, Huygens, Newton, and Boyle, but viewedtheir work through a lens heavily tinted by scholastic notions. Yet it remainsthe case that Leibniz's methods and concerns often anticipate the logic, and analytic and linguistic philosophy of the 20th century.

The Principles

Leibniz variously invoked one or another of sevenfundamental philosophical Principles:^[48]

• Identity/contradiction. If a proposition is true, then its negation is false and vice versa.
• Identity of indiscernibles. Two distinct things cannot have all their properties in common. If every predicate possessed by x is also possessed by y and vice versa, then entities x and y are identical; to suppose two things indiscernible is to suppose the same thing under two names. Frequently invoked in modern logic and philosophy, the "identity of indiscernibles" is often referred to as Leibniz's Law. It has attracted the most controversy and criticism, especially from corpuscular philosophy and quantum mechanics.
• Sufficient reason. "There must be a sufficient reason for anything to exist, for any event to occur, for any truth to obtain."^[49]
• Pre-established harmony.^[50] "[T]he appropriate nature of each substance brings it about that what happens to one corresponds to what happens to all the others, without, however, their acting upon one another directly." (Discourse on Metaphysics, XIV) A dropped glass shatters because it "knows" it has hit the ground, and not because the impact with the ground "compels" the glass to split.
• Law of Continuity. Natura non facit saltus^[51] (literally, "Nature does not make jumps").
• Optimism. "God assuredly always chooses the best."^[52]
• Plenitude. Leibniz believed that the best of all possible worlds would actualize every genuine possibility, and argued in Théodicée that this best of all possible worlds will contain all possibilities, with our finite experience of eternity giving no reason to dispute nature's perfection.^[53]

Leibniz would on occasion give a rational defense of aspecific principle, but more often took them for granted.^[54]

The monads

Leibniz's best known contribution to metaphysics is histheory of monads, as exposited in Monadologie.According to Leibniz, monads are elementary particles with blurred perceptions of one another.Monads can also be compared to the corpuscles of the Mechanical Philosophy of René Descartes and others. Monads arethe ultimate elements of the universe.The monads are "substantial forms of being" with the followingproperties: they are eternal, indecomposable, individual, subject to their ownlaws, un-interacting, and each reflecting the entire universe in a pre-established harmony (a historically important example of panpsychism).Monads are centers of force;substance is force, while space,matter, and motion are merelyphenomenal.

The ontologicalessence of a monad is its irreducible simplicity. Unlike atoms, monads possessno material or spatial character. They also differ from atoms by their completemutual independence, so that interactions among monads are only apparent. Instead,by virtue of the principle of pre-established harmony, each monad follows apreprogrammed set of "instructions" peculiar to itself, so that amonad "knows" what to do at each moment. By virtue of these intrinsicinstructions, each monad is like a little mirror of the universe. Monads neednot be "small"; e.g., each human being constitutes a monad, in whichcase free will isproblematic.

Monads are purported to have gotten rid of theproblematic:

• interaction between mind and matter arising in the system of Descartes;
• lack of individuation inherent to the system of Spinoza, which represents individual creatures as merely accidental.

Theodicy and optimism

Further information: Best of all possible worlds and Philosophical optimism

The Theodicy^[55] tries tojustify the apparent imperfections of the world by claiming that it is optimal among all possible worlds. It must bethe best possible and most balanced world, because it was created by an allpowerful and all knowing God, who would not choose to create an imperfect worldif a better world could be known to him or possible to exist. In effect,apparent flaws that can be identified in this world must exist in every possibleworld, because otherwise God would have chosen to create the world thatexcluded those flaws.

Leibniz asserted that the truths of theology(religion) and philosophy cannot contradict each other, since reason and faithare both "gifts of God" so that their conflict would imply Godcontending against himself. The Theodicy is Leibniz's attempt toreconcile his personal philosophical system with his interpretation of thetenets of Christianity.^[56] Thisproject was motivated in part by Leibniz's belief, shared by many conservativephilosophers and theologians during the Enlightenment, in the rational and enlightened nature of theChristian religion as compared to its purportedly less advanced non-Westerncounterparts. It was also shaped by Leibniz's belief in the perfectibility ofhuman nature (if humanity relied on correct philosophy and religion as aguide), and by his belief that metaphysical necessity must have a rational orlogical foundation, even if this metaphysical causality seemed inexplicable interms of physical necessity (the natural laws identified by science).

Because reason and faith must be entirely reconciled,any tenet of faith which could not be defended by reason must be rejected.Leibniz then approached one of the central criticisms of Christian theism:^[57] if Godis all good, all wise and all powerful, howdid evilcome into the world? The answer (according to Leibniz) is that,while God is indeed unlimited in wisdom and power, his human creations, ascreations, are limited both in their wisdom and in their will (power to act).This predisposes humans to false beliefs, wrong decisions and ineffectiveactions in the exercise of their free will. God doesnot arbitrarily inflict pain and suffering on humans; rather he permits both moralevil (sin) and physical evil (pain and suffering) as the necessaryconsequences of metaphysical evil (imperfection), as a means by whichhumans can identify and correct their erroneous decisions, and as a contrast totrue good.

Further, although human actions flow from prior causesthat ultimately arise in God, and therefore are known as a metaphysicalcertainty to God, an individual's free will is exercised within natural laws,where choices are merely contingently necessary, to be decided in the event bya "wonderful spontaneity" that provides individuals an escape fromrigorous predestination.

Discourse on Metaphysics

For Leibniz, "God is an absolutely perfectbeing." He describes this perfection later in section VI as the simplestform of something with the most substantial outcome (VI). Along these lines, hedeclares that every type of perfection "pertains to him (God) in thehighest degree" (I). Even though his types of perfections are notspecifically drawn out, Leibniz highlights the one thing that, to him, doescertify imperfections and proves that God is perfect: "that one actsimperfectly if he acts with less perfection than he is capable of", andsince God is a perfect being, he cannot act imperfectly (III). Because Godcannot act imperfectly, the decisions he makes pertaining to the world must beperfect. Leibniz also comforts readers, stating that because he has doneeverything to the most perfect degree; those who love him cannot be injured.However, to love God is a subject of difficulty as Leibniz believes that we are"not disposed to wish for that which God desires" because we have theability to alter our disposition (IV). In accordance with this, many act asrebels, but Leibniz says that the only way we can truly love God is by beingcontent "with all that comes to us according to his will" (IV).

Because God is "an absolutely perfect being"(I), Leibniz argues that God would be acting imperfectly if he acted with anyless perfection than what he is able of (III). His syllogism then ends with thestatement that God has made the world perfectly in all ways. This also effectshow we should view God and his will. Leibniz states that, in lieu of God’swill, we have to understand that God "is the best of all masters" andhe will know when his good succeeds, so we, therefore, must act in conformityto his good will – or as much of it as we understand (IV). In our view of God,Leibniz declares that we cannot admire the work solely because of the maker,lest we mar the glory and love God in doing so. Instead, we must admire themaker for the work he has done (II). Effectively, Leibniz states that if we saythe earth is good because of the will of God, and not good according to somestandards of goodness, then how can we praise God for what he has done ifcontrary actions are also praiseworthy by this definition (II). Leibniz thenasserts that different principles and geometry cannot simply be from the willof God, but must follow from his understanding.^[58]

Fundamental question ofmetaphysics

Leibniz wrote: "Why is there something rather than nothing?The sufficient reason ... is found in a substance which ... is a necessarybeing bearing the reason for its existence within itself."^[59] Martin Heideggercalled this question "the fundamental question of metaphysics".^[60][61]

Symbolic thought

Leibniz believed that much of human reasoning could bereduced to calculations of a sort, and that such calculations could resolvemany differences of opinion:

The only way to rectify our reasonings is to make themas tangible as those of the Mathematicians, so that we can find our error at aglance, and when there are disputes among persons, we can simply say: Let uscalculate [calculemus], without further ado, to see who is right.^[62]

Leibniz's calculus ratiocinator, which resembles symbolic logic, can be viewed as a way of making suchcalculations feasible. Leibniz wrote memoranda^[63] that cannow be read as groping attempts to get symbolic logic—and thus his calculus—offthe ground. These writings remained unpublished until the appearance of aselection edited by C.I. Gerhardt (1859). L. Couturat published a selection in1901; by this time the main developments of modern logic had been created by Charles Sanders Peirce and by Gottlob Frege.

Leibniz thought symbols wereimportant for human understanding. He attached so much importance to thedevelopment of good notations that he attributed all his discoveries inmathematics to this. His notation for calculus is anexample of his skill in this regard. Peirce, a 19th-century pioneer of semiotics, sharedLeibniz's passion for symbols and notation, and his belief that these areessential to a well-running logic and mathematics.

But Leibniz took his speculations much further.Defining a character as anywritten sign, he then defined a "real" character as one thatrepresents an idea directly and not simply as the word embodying the idea. Somereal characters, such as the notation of logic, serve only to facilitatereasoning. Many characters well known in his day, including Egyptian hieroglyphics, Chinese characters,and the symbols of astronomyand chemistry, hedeemed not real.^[64] Instead,he proposed the creation of a characteristica universalis or"universal characteristic", built on an alphabet of human thought in which each fundamental conceptwould be represented by a unique "real" character:

It is obvious that if we could find characters orsigns suited for expressing all our thoughts as clearly and as exactly asarithmetic expresses numbers or geometry expresses lines, we could do in allmatters insofar as they are subject to reasoning all that we can do inarithmetic and geometry. For all investigations which depend on reasoning wouldbe carried out by transposing these characters and by a species of calculus.^[65]

Complex thoughts would be represented by combiningcharacters for simpler thoughts. Leibniz saw that the uniqueness of prime factorization suggests a central role for prime numbers inthe universal characteristic, a striking anticipation of Gödelnumbering. Granted, there is no intuitive or mnemonic way tonumber any set of elementary concepts using the prime numbers. Leibniz's ideaof reasoning through a universal language of symbols and calculations, however,remarkably foreshadows great 20th century developments in formal systems, suchas Turing completeness, where computation was used to defineequivalent universal languages (see Turing degree).

Because Leibniz was a mathematical novice when hefirst wrote about the characteristic, at first he did not conceive it asan algebra but ratheras a universal language or script. Only in 1676 did he conceive ofa kind of "algebra of thought", modeled on and including conventionalalgebra and its notation. The resulting characteristic included alogical calculus, some combinatorics, algebra, his analysis situs(geometry of situation), a universal concept language, and more.

What Leibniz actually intended by his characteristicauniversalis and calculus ratiocinator, and the extent to which modernformal logic does justice to calculus, may never be established.^[66]

Formal logic

Main article: Algebraic logic

Leibniz is one of the most important logicians betweenAristotle and 1847, when GeorgeBoole and Augustus De Morgan each published books that began modernformal logic. Leibniz enunciated the principal properties of what we now call conjunction, disjunction, negation, identity, set inclusion,and the empty set. Theprinciples of Leibniz's logic and, arguably, of his whole philosophy, reduce totwo:

1. All our ideas are compounded froma very small number of simple ideas, which form the alphabet of human thought.

2. Complex ideas proceed from thesesimple ideas by a uniform and symmetrical combination, analogous toarithmetical multiplication.

The formal logic that emerged early in the 20thcentury also requires, at minimum, unary negation and quantified variables ranging over some universe of discourse.

Leibniz published nothing on formal logic in hislifetime; most of what he wrote on the subject consists of working drafts. Inhis book History of Western Philosophy, Bertrand Russellwent so far as to claim that Leibniz had developed logic in his unpublishedwritings to a level which was reached only 200 years later.

Russell's principal work on Leibniz found that many ofLeibniz's most startling philosophical ideas and claims (e.g., that each of thefundamental monads mirrors the whole universe) follow logically fromLeibniz's conscious choice to reject relations between things as unreal.He regarded such relations as (real) qualities of things (Leibnizadmitted unary predicates only): For him "Mary is themother of John" describes separate qualities of Mary and of John. Thisview contrasts with the relational logic of De Morgan, Peirce, Schröder andRussell himself, now standard in predicate logic.Notably, Leibniz also declared space and time to be inherently relational.^[67]

Mathematician

Although the mathematical notion of function was implicit in trigonometric and logarithmic tables,which existed in his day, Leibniz was the first, in 1692 and 1694, to employ itexplicitly, to denote any of several geometric concepts derived from a curve,such as abscissa, ordinate, tangent, chord, and the perpendicular.^[68] In the18th century, "function" lost these geometrical associations.

Leibniz was the first to see that the coefficients ofa system of linearequations could be arranged into an array, now called a matrix, which can be manipulated to find the solution of thesystem, if any. This method was later called Gaussian elimination. Leibniz's discoveries of Boolean algebra and of symbolic logic, also relevant to mathematics, are discussed inthe preceding section. The best overview of Leibniz's writings on calculus maybe found in Bos (1974).^[69]

Calculus

Leibniz is credited, along with Sir Isaac Newton, withthe discovery of calculus(differential and integral calculus). According to Leibniz's notebooks, acritical breakthrough occurred on 11 November 1675, when he employed integralcalculus for the first time to find the area under the graph of a function y= f(x).^[70] Heintroduced several notations used to this day, for instance the integral sign ∫,representing an elongated S, from the Latin word summa, and the d usedfor differentials, from the Latin word differentia.This cleverly suggestive notation for calculus is probably his most enduringmathematical legacy. Leibniz did not publish anything about his calculus until1684.^[71] Leibnizexpressed the inverse relation of integration and differentiation, later calledthe fundamental theorem of calculus, by means of afigure^[72] in his1693 paper Supplementum geometriae dimensoriae....^[73] However,James Gregory is credited for the theorem'sdiscovery in geometric form, Isaac Barrow proveda more generalized geometric version, and Newton developedsupporting theory. The concept became more transparent as developed throughLeibniz's formalism and new notation.^[74] The product rule of differential calculus is still called "Leibniz'slaw". In addition, the theorem that tells how and when to differentiateunder the integral sign is called the Leibniz integral rule.

Leibniz exploited infinitesimals indeveloping calculus, manipulating them in ways suggesting that they had paradoxical algebraicproperties. GeorgeBerkeley, in a tract called The Analyst andalso in De Motu, criticized these. A recent study argues that Leibniziancalculus was free of contradictions, and was better grounded than Berkeley'sempiricist criticisms.^[75]

From 1711 until his death, Leibniz was engaged in adispute with John Keill, Newton and others, over whether Leibniz had inventedcalculus independently of Newton. This subject is treated at length in thearticle Leibniz–Newton calculus controversy.

The use of infinitesimals in mathematics was frownedupon by followers of KarlWeierstrass,^{[citation needed]} but survived in science and engineering,and even in rigorous mathematics, via the fundamental computational deviceknown as the differential. Beginning in 1960, Abraham Robinsonworked out a rigorous foundation for Leibniz's infinitesimals, using model theory, inthe context of a field of hyperreal numbers.The resulting non-standard analysis can be seen as a belated vindication ofLeibniz's mathematical reasoning. Robinson's transfer principle is a mathematical implementation ofLeibniz's heuristic law of continuity, while the standard part function implements the Leibnizian transcendental law of homogeneity.

Topology

Leibniz was the first to use the term analysissitus,^[76] laterused in the 19th century to refer to what is now known as topology. There aretwo takes on this situation. On the one hand, Mates, citing a 1954 paper inGerman by Jacob Freudenthal, argues:

Although for Leibniz the situs of a sequence of pointsis completely determined by the distance between them and is altered if thosedistances are altered, his admirer Euler,in the famous 1736 paper solving the Königsberg Bridge Problem and itsgeneralizations, used the term geometria situs in such a sense that thesitus remains unchanged under topological deformations. He mistakenly creditsLeibniz with originating this concept. ... [It] is sometimes not realized thatLeibniz used the term in an entirely different sense and hence can hardly beconsidered the founder of that part of mathematics.^[77]

But Hideaki Hirano argues differently, quoting Mandelbrot:^[78]

To sample Leibniz' scientific works is a soberingexperience. Next to calculus, and to other thoughts that have been carried outto completion, the number and variety of premonitory thrusts is overwhelming.We saw examples in "packing", ... My Leibniz mania is furtherreinforced by finding that for one moment its hero attached importance togeometric scaling. In Euclidis Prota ..., which is an attempt totighten Euclid's axioms, he states ...: "I have diverse definitionsfor the straight line. The straight line is a curve, any part of which issimilar to the whole, and it alone has this property, not only among curves butamong sets." This claim can be proved today.^[79]

Thus the fractal geometrypromoted by Mandelbrot drew on Leibniz's notions of self-similarity andthe principle of continuity: Natura non facit saltus.^[51] We alsosee that when Leibniz wrote, in a metaphysical vein, that "the straightline is a curve, any part of which is similar to the whole", he wasanticipating topology by more than two centuries. As for "packing",Leibniz told his friend and correspondent Des Bosses to imagine a circle, thento inscribe within it three congruent circles with maximum radius; the lattersmaller circles could be filled with three even smaller circles by the sameprocedure. This process can be continued infinitely, from which arises a goodidea of self-similarity. Leibniz's improvement of Euclid's axiom contains thesame concept.

Scientist and engineer

Leibniz's writings are currently discussed, not onlyfor their anticipations and possible discoveries not yet recognized, but asways of advancing present knowledge. Much of his writing on physics is includedin Gerhardt's Mathematical Writings.

Physics

See also: Dynamism (metaphysics) and Conatus § In Leibniz

Leibniz contributed a fair amount to the statics anddynamics emerging around him, often disagreeing with Descartes and Newton. He deviseda new theory of motion(dynamics) based on kinetic energy and potential energy,which posited space as relative, whereas Newton was thoroughly convinced thatspace was absolute. An important example of Leibniz's mature physical thinkingis his Specimen Dynamicum of 1695.^[80]

Until the discovery of subatomic particles and the quantum mechanicsgoverning them, many of Leibniz's speculative ideas about aspects of nature notreducible to statics and dynamics made little sense. For instance, heanticipated AlbertEinstein by arguing, against Newton, that space, time and motion are relative, notabsolute: "As for my own opinion, I have said more than once, that I holdspace to be something merely relative, as time is, that I hold it to be anorder of coexistences, as time is an order of successions."^[81]

Leibniz held a relationist notionof space and time, against Newton's substantivalist views.^[82][83][84]According to Newton's substantivalism, space and time are entities in their ownright, existing independently of things. Leibniz's relationism, on the other hand,describes spaceand time as systems of relations that exist between objects. Therise of general relativity and subsequent work in the history of physics has put Leibniz's stance in a morefavorable light.

One of Leibniz's projects was to recast Newton'stheory as a vortex theory.^[85] However,his project went beyond vortex theory, since at its heart there was an attemptto explain one of the most difficult problems in physics, that of the origin ofthe cohesion of matter.^[85]

The principle of sufficient reason has been invokedin recent cosmology, and his identity of indiscernibles in quantummechanics, a field some even credit him with having anticipated in some sense.Those who advocate digital philosophy, a recent direction in cosmology, claimLeibniz as a precursor. In addition to his theories about the nature ofreality, Leibniz's contributions to the development of calculus have also had amajor impact on physics.

The vis viva

Leibniz's vis viva (Latinfor "living force") is mv², twice the modern kinetic energy. Herealized that the total energy would be conserved in certain mechanicalsystems, so he considered it an innate motive characteristic of matter.^[86] Here toohis thinking gave rise to another regrettable nationalistic dispute. His visviva was seen as rivaling the conservation of momentum championed by Newton in England andby Descartes inFrance; hence academicsin those countries tended to neglect Leibniz's idea. In reality, both energyand momentum areconserved, so the two approaches are equally valid.

Other natural science

By proposing that the earth has a molten core, heanticipated modern geology. In embryology, he wasa preformationist, but also proposed that organisms are the outcome of acombination of an infinite number of possible microstructures and of theirpowers. In the lifesciences and paleontology,he revealed an amazing transformist intuition, fueled by his study ofcomparative anatomy and fossils. One of his principal works on this subject, Protogaea,unpublished in his lifetime, has recently been published in English for thefirst time. He worked out a primal organismic theory.^[87] Inmedicine, he exhorted the physicians of his time—with some results—to groundtheir theories in detailed comparative observations and verified experiments,and to distinguish firmly scientific and metaphysical points of view.

Psychology

Psychology had been a central interest of Leibniz.^[88][89] Heappears to be an "underappreciated pioneer of psychology" ^[90] He wroteon topics which are now regarded as fields of psychology: attention and consciousness, memory, learning (association), motivation (the actof "striving"), emergent individuality, thegeneral dynamics of development (evolution). Hisdiscussions in the New Essays and Monadology often rely oneveryday observations such as the behaviour of a dog or the noise of the sea,and he develops intuitive analogies (the synchronous running of clocks or thebalance spring of a clock). He also devised postulates and principles thatapply to psychology: the continuum of the unnoticed petite perceptionsto the distinct, self-aware apperception,and psychophysical parallelism from the point ofview of causality and of purpose: “Souls act according to the laws of finalcauses, through aspirations, ends and means. Bodies act according to the lawsof efficient causes, i.e. the laws of motion. And these two realms, that ofefficient causes and that of final causes, harmonize with one another.” ^[91] Thisidea refers to the mind-body problem, stating that the mind and brain do notact upon each other, but act alongside each other separately but in harmony.^[92] Leibniz,however, did not use the term psychologia.^[93] Leibniz’epistemological position – against John Locke andEnglish empiricism (sensualism) – wasmade clear: “Nihil est in intellectu quod non fuerit in sensu, nisi intellectuipse.” – “Nothing is in the intellect that was not first in the senses, exceptthe intellect itself.” ^[94]Principles that are not present in sensory impressions can be recognised inhuman perception and consciousness: logical inferences, categories of thought,the principle of causalityand the principle of purpose(teleology).

Leibniz found his most important interpreter in Wilhelm Wundt,founder of psychology as a discipline. Wundt used the "… nisi intellectuipse" quotation 1862 on the title page of his Beiträge zur Theorie derSinneswahrnehmung (Contributions on the Theory of Sensory Perception) andpublished a detailed and aspiring monograph on Leibniz^[95] Wundtshaped the term apperception,introduced by Leibniz, into an experimental psychologically based apperceptionpsychology that included neuropsychological modelling – an excellent example ofhow a concept created by a great philosopher could stimulate a psychologicalresearch program. One principle in the thinking of Leibniz played a fundamentalrole: “the principle of equality of separate but corresponding viewpoints.”Wundt characterized this style of thought (perspectivism) in away that also applied for him – viewpoints that "supplement one another,while also being able to appear as opposites that only resolve themselves whenconsidered more deeply."^[96][97] Much ofLeibniz's work went on to have a great impact on the field of psychology.^[98] Leibnizthought that there are many petites perceptions, or small perceptions of whichwe perceive but of which we are unaware. He believed that by the principle thatphenomena found in nature were continuous by default, it was likely that thetransition between conscious and unconscious states had intermediary steps.^[99] For thisto be true, there must also be a portion of the mind of which we are unaware atany given time. His theory regarding consciousness in relation to the principleof continuity can be seen as an early theory regarding the stages of sleep. Inthis way, Leibniz's theory of perception can be viewed as one of many theoriesleading up to the idea of the unconscious.Leibniz was a direct influence on Ernst Platner, whois credited with originally coining the term Unbewußtseyn (unconscious).^[100]Additionally, the idea of subliminal stimuli can be traced back to his theory of smallperceptions.^[101]Leibniz's ideas regarding music and tonal perception went on to influence thelaboratory studies of Wilhelm Wundt.^[102]

Social science

In public health, he advocated establishing a medicaladministrative authority, with powers over epidemiology and veterinary medicine. He worked to set up a coherent medicaltraining program, oriented towards public health and preventive measures. Ineconomic policy, he proposed tax reforms and a national insurance program, anddiscussed the balanceof trade. He even proposed something akin to what much later emergedas game theory. Insociology he laid the ground for communication theory.

Technology

In 1906, Garland published a volume of Leibniz'swritings bearing on his many practical inventions and engineering work. Todate, few of these writings have been translated into English. Nevertheless, itis well understood that Leibniz was a serious inventor, engineer, and appliedscientist, with great respect for practical life. Following the motto theoriacum praxi, he urged that theory be combined with practical application, andthus has been claimed as the father of applied science. Hedesigned wind-driven propellers and water pumps, mining machines to extractore, hydraulic presses, lamps, submarines, clocks, etc. With Denis Papin, heinvented a steamengine. He even proposed a method for desalinating water. From 1680to 1685, he struggled to overcome the chronic flooding that afflicted the ducalsilver mines in the HarzMountains, but did not succeed.^[103]

Computation

Leibniz may have been the first computer scientist andinformation theorist.^[104] Earlyin life, he documented the binary numeral system (base 2), then revisited that systemthroughout his career.^[105] Heanticipated Lagrangian interpolation and algorithmic information theory. His calculus ratiocinator anticipated aspects of the universal Turing machine. In 1961, Norbert Wienersuggested that Leibniz should be considered the patron saint of cybernetics.^[106]

In 1671, Leibniz began to invent a machine that couldexecute all four arithmetic operations, gradually improving it over a number ofyears. This "steppedreckoner" attracted fair attention and was the basis of hiselection to the RoyalSociety in 1673. A number of such machines were made during hisyears in Hanover by acraftsman working under his supervision. They were not an unambiguous successbecause they did not fully mechanize the carry operation. Couturat reported finding an unpublished noteby Leibniz, dated 1674, describing a machine capable of performing somealgebraic operations.^[107] Leibnizalso devised a (now reproduced) cipher machine, recovered by Nicholas Rescher in2010.^[108] In1693, Leibniz described a design of a machine which could, in theory, integratedifferential equations, which he called "integraph".^[109]

Leibniz was groping towards hardware and softwareconcepts worked out much later by Charles Babbage andAda Lovelace. In1679, while mulling over his binary arithmetic, Leibniz imagined a machine inwhich binary numbers were represented by marbles, governed by a rudimentarysort of punched cards.^[110] Modern electronicdigital computers replace Leibniz's marbles moving by gravity with shiftregisters, voltage gradients, and pulses of electrons, but otherwise they runroughly as Leibniz envisioned in 1679.

Librarian

Later in Leibniz’s career (after the death of vonBoinburg), Leibniz moved to Paris and accepted a position as a librarian in theHanoverian court of Johann Friedrich, Duke of Brunswick-Luneburg. Leibniz’spredecessor, Tobias Fleischer, had already created a cataloging system for theDuke’s library but it was a clumsy attempt. At this library, Leibniz focusedmore on advancing the library than on the cataloging. For instance, within amonth of taking the new position, he developed a comprehensive plan to expandthe library. He was one of the first to consider developing a core collectionfor a library and felt “that a library for display and ostentation is a luxuryand indeed superfluous, but a well-stocked and organized library is importantand useful for all areas of human endeavor and is to be regarded on the samelevel as schools and churches”.^[111]Unfortunately, Leibniz lacked the funds to develop the library in this manner.After working at this library, by the end of 1690 Leibnez was appointed asprivy-councilor and librarian of the Bibliotheca Augusta at Wolfenbuettel. Itwas an extensive library with at least 25,946 printed volumes^[111]. Atthis library, Leibniz sought to improve the catalog. He was not allowed to makecomplete changes to the existing closed catalog, but was allowed to improveupon it so he started on that task immediately. He created an alphabeticalauthor catalog and had also created other cataloging methods that were notimplemented. While serving as librarian of the ducal libraries in Hanover and Wolfenbuettel,Leibniz effectively became one of the founders of library science. Healso designed a book indexing system in ignorance of the only other such systemthen extant, that of the Bodleian Library atOxford University. He also called on publishers to distributeabstracts of all new titles they produced each year, in a standard form thatwould facilitate indexing. He hoped that this abstracting project wouldeventually include everything printed from his day back to Gutenberg. Neither proposal met with success at the time, butsomething like them became standard practice among English language publishersduring the 20th century, under the aegis of the Library of Congress and the British Library.

He called for the creation of an empirical database as a wayto further all sciences. His characteristica universalis, calculus ratiocinator, and a "community ofminds"—intended, among other things, to bring political and religiousunity to Europe—can be seen as distant unwitting anticipations of artificiallanguages (e.g., Esperantoand its rivals), symbolic logic, even the World Wide Web.

Advocate of scientific societies

Leibniz emphasized that research was a collaborativeendeavor. Hence he warmly advocated the formation of national scientificsocieties along the lines of the British Royal Societyand the French Academie Royale des Sciences. More specifically, in hiscorrespondence and travels he urged the creation of such societies in Dresden, Saint Petersburg,Vienna, and Berlin. Only one such project came to fruition; in 1700, the Berlin Academy of Sciences was created. Leibnizdrew up its first statutes, and served as its first President for the remainderof his life. That Academy evolved into the German Academy of Sciences, thepublisher of the ongoing critical edition of his works.^[112]

Lawyer and moralist

With the possible exception of Marcus Aurelius, nophilosopher has ever had as much experience with practical affairs of state asLeibniz. Leibniz's writings on law, ethics, and politics^[113] werelong overlooked by English-speaking scholars, but this has changed of late.^[114]

While Leibniz was no apologist for absolute monarchylike Hobbes, or fortyranny in any form, neither did he echo the political and constitutional viewsof his contemporary JohnLocke, views invoked in support of democracy, in 18th-centuryAmerica and later elsewhere. The following excerpt from a 1695 letter to BaronJ. C. Boyneburg's son Philipp is very revealing of Leibniz's politicalsentiments:

As for ... the great question of the power ofsovereigns and the obedience their peoples owe them, I usually say that itwould be good for princes to be persuaded that their people have the right toresist them, and for the people, on the other hand, to be persuaded to obeythem passively. I am, however, quite of the opinion of Grotius, that oneought to obey as a rule, the evil of revolution being greater beyond comparisonthan the evils causing it. Yet I recognize that a prince can go to such excess,and place the well-being of the state in such danger, that the obligation toendure ceases. This is most rare, however, and the theologian who authorizesviolence under this pretext should take care against excess; excess beinginfinitely more dangerous than deficiency.^[115]

In 1677, Leibniz called for a European confederation,governed by a council or senate, whose members would represent entire nationsand would be free to vote their consciences;^[116] this issometimes considered an anticipation of the European Union. Hebelieved that Europe would adopt a uniform religion. He reiterated theseproposals in 1715.

But at the same time, he arrived to propose aninterreligious and multicultural project to create a universal system ofjustice, which required from him a broad interdisciplinary perspective. Inorder to propose it, he combined linguistics, especially sinology, moral andlaw philosophy, management, economics, and politics.^[117]

Ecumenism

Leibniz devoted considerable intellectual anddiplomatic effort to what would now be called ecumenicalendeavor, seeking to reconcile first the Roman Catholic and Lutheran churches,and later the Lutheran and Reformedchurches. In this respect, he followed the example of his early patrons, Baronvon Boyneburg and the Duke John Frederick—both cradle Lutherans whoconverted to Catholicism as adults—who did what they could to encourage thereunion of the two faiths, and who warmly welcomed such endeavors by others.(The House of Brunswickremained Lutheran because the Duke's children did not follow their father.)These efforts included corresponding with the French bishop Jacques-Bénigne Bossuet, and involved Leibniz in sometheological controversy. He evidently thought that the thoroughgoingapplication of reason would suffice to heal the breach caused by the Reformation.

Philologist

Leibniz the philologist was anavid student of languages, eagerly latching on to any information aboutvocabulary and grammar that came his way. He refuted the belief, widely held byChristian scholars in his day, that Hebrew was theprimeval language of the human race. He also refuted the argument, advanced bySwedish scholars in his day, that a form of proto-Swedish was theancestor of the Germanic languages. He puzzled over the origins of the Slavic languages,was aware of the existence of Sanskrit,and was fascinated by classical Chinese.

He published the princeps editio (first modernedition) of the latemedieval Chronicon Holtzatiae, a Latin chronicle of the County of Holstein.

Sinophile

 

A diagram of I Chinghexagrams sent to Leibniz from Joachim Bouvet. TheArabic numerals were added by Leibniz.^[118]

Leibniz was perhaps the first major Europeanintellectual to take a close interest in Chinese civilization, which he knew bycorresponding with, and reading other works by, European Christian missionariesposted in China. Having read Confucius Sinarum Philosophus on the firstyear of its publication,^[119] heconcluded that Europeans could learn much from the Confucian ethicaltradition. He mulled over the possibility that the Chinese characterswere an unwitting form of his universal characteristic. He noted withfascination how the I Chinghexagrams correspond to the binary numbers from000000 to 111111, and concluded that this mapping was evidence of major Chineseaccomplishments in the sort of philosophical mathematics he admired.^[120]

Leibniz's attraction to Chinese philosophy originates from his perception that Chinesephilosophy was similar to his own.^[119] Thehistorian E.R. Hughes suggests that Leibniz's ideas of "simplesubstance" and "pre-established harmony" were directlyinfluenced by Confucianism,pointing to the fact that they were conceived during the period that he wasreading Confucius Sinarum Philosophus.^[119]

As polymath

While making his grand tour of European archives toresearch the Brunswick family history that he never completed, Leibniz stoppedin Vienna between May1688 and February 1689, where he did much legal and diplomatic work for theBrunswicks. He visited mines, talked with mine engineers, and tried to negotiateexport contracts for lead from the ducal mines in the Harz mountains. Hisproposal that the streets of Vienna be lit with lamps burning rapeseed oil wasimplemented. During a formal audience with the Austrian Emperor and in subsequent memoranda, he advocated reorganizingthe Austrian economy, reforming the coinage of much of central Europe,negotiating a Concordatbetween the Habsburgs and the Vatican, andcreating an imperial research library, official archive, and public insurancefund. He wrote and published an important paper on mechanics.

Leibniz also wrote a short paper, Primae veritates,first published by LouisCouturat in 1903 (pp. 518–523)^[121]summarizing his views on metaphysics.The paper is undated; that he wrote it while in Vienna in 1689 was determinedonly in 1999, when the ongoing critical edition finally published Leibniz'sphilosophical writings for the period 1677–90.^[122]Couturat's reading of this paper was the launching point for much 20th-centurythinking about Leibniz, especially among analytic philosophers. But after a meticulous study of all ofLeibniz's philosophical writings up to 1688—a study the 1999 additions to thecritical edition made possible—Mercer (2001) begged to differ with Couturat'sreading; the jury is still out.

Posthumous reputation

When Leibniz died, his reputation was in decline. Hewas remembered for only one book, the Théodicée,^[123] whosesupposed central argument Voltairelampooned in his popular book Candide,which concludes with the character Candide saying, "Non liquet"(it is not clear), a term that was applied during the Roman Republic to a legalverdict of "not proven". Voltaire's depiction of Leibniz's ideas wasso influential that many believed it to be an accurate description. ThusVoltaire and his Candide bear some of the blame for the lingeringfailure to appreciate and understand Leibniz's ideas. Leibniz had an ardentdisciple, Christian Wolff, whose dogmatic and facileoutlook did Leibniz's reputation much harm. He also influenced David Hume who readhis Théodicéeand used some of his ideas.^[124] In anyevent, philosophical fashion was moving away from the rationalism and systembuilding of the 17th century, of which Leibniz had been such an ardentproponent. His work on law, diplomacy, and history was seen as of ephemeralinterest. The vastness and richness of his correspondence went unrecognized.

Much of Europe came to doubt that Leibniz haddiscovered calculus independently of Newton, and hence his whole work inmathematics and physics was neglected. Voltaire, an admirer of Newton, alsowrote Candide at least in part to discredit Leibniz's claim to havingdiscovered calculus and Leibniz's charge that Newton's theory of universal gravitationwas incorrect.^{[citation needed]}

Leibniz's long march to his present glory began withthe 1765 publication of the Nouveaux Essais, which Kant read closely.In 1768, LouisDutens edited the first multi-volume edition of Leibniz's writings,followed in the 19th century by a number of editions, including those edited byErdmann, Foucher de Careil, Gerhardt, Gerland, Klopp, and Mollat. Publicationof Leibniz's correspondence with notables such as Antoine Arnauld, Samuel Clarke, Sophia of Hanover,and her daughter Sophia Charlotte of Hanover, began.

In 1900, Bertrand Russellpublished a critical study of Leibniz's metaphysics.^[125] Shortlythereafter, LouisCouturat published an important study of Leibniz, and edited avolume of Leibniz's heretofore unpublished writings, mainly on logic. They madeLeibniz somewhat respectable among 20th-century analytical and linguistic philosophers in the English-speaking world (Leibnizhad already been of great influence to many Germans such as Bernhard Riemann).For example, Leibniz's phrase salva veritate,meaning interchangeability without loss of or compromising the truth, recurs inWillard Quine'swritings. Nevertheless, the secondary literature on Leibniz did not reallyblossom until after World War II. This is especially true of English speakingcountries; in Gregory Brown's bibliography fewer than 30 of the Englishlanguage entries were published before 1946. American Leibniz studies owe muchto Leroy Loemker (1904–1985) through histranslations and his interpretive essays in LeClerc (1973).

Nicholas Jolley has surmised thatLeibniz's reputation as a philosopher is now perhaps higher than at any timesince he was alive.^[126]Analytic and contemporary philosophy continue to invoke his notions of identity, individuation, and possible worlds.Work in the history of 17th- and 18th-century ideas has revealedmore clearly the 17th-century "Intellectual Revolution" that precededthe better-known Industrial and commercial revolutions of the 18th and 19thcenturies.

In 1985, the German government created the Leibniz Prize, offering an annual award of1.55 million euros forexperimental results and 770,000 euros for theoretical ones. It was the worldslargest prize for scientific achievement prior to the Fundamental Physics Prize.

The collection of manuscript papers of Leibniz at theGottfried Wilhelm Leibniz Bibliothek – Niedersächische Landesbibliothek wereinscribed on UNESCO's Memory of the World Register in 2007.