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| The neutrality of this article is greatly disputed, clearly written by someone who believes Leibniz is RIGHT, and calls any critic a "lay person." | |||
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| |name = Gottfried Wilhelm Leibniz | |||
| |birth = ] (] ]) ], ], ] | |||
| |death = {{death date|1716|11|14|mf=y}}, ], ] | |||
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| | doctoral_students = ]</br>]</br> | |||
| | influences = ], ], ], ], ], ], ] | |||
| | influenced = Many later mathematicians, ], ], ], ] | |||
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| '''Gottfried Wilhelm Leibniz''' (also ''Leibnitz'' or ''von Leibniz''<ref name="pronunciation">{{pronounced|ˈlaɪpnɪts}}.</ref> (] (] ]) ] – ] ]) was a ]<ref></ref> ] who wrote primarily in ] and ]. | |||
| He occupies an equally grand place in both the ] and the ]. He invented ] independently of ], and his ] is the one in general use since. He also discovered the ], foundation of virtually all modern computer architectures. In philosophy, he is most remembered for ], ''i.e''. his conclusion that our universe is, in a restricted sense, the best possible one ] could have made. He was, along with ] and ], one of the three great 17th century ], but his philosophy also looks back to the ] tradition and anticipates modern ] and ]. Leibniz also made major contributions to ] and ], and anticipated notions that surfaced much later in ], ], ], ], ], ], and ]. He also wrote on ], ], ], ], ], and ], even occasional verse. His contributions to this vast array of subjects are scattered in journals and in tens of thousands of letters and unpublished manuscripts. To date, there is no complete edition of Leibniz's writings. | |||
| ==Biography== | |||
| {{Unreferencedsection|date=March 2008}} | |||
| The outline of Leibniz's career is as follows: | |||
| * 1646-1666: Formative years | |||
| * 1666–74: Mainly in service to the ] of ], ], and his minister, Baron von Boineburg. | |||
| ** 1672–76. Resides in Paris, making two important sojourns to London. | |||
| * 1676–1716. In service to the ]. | |||
| **1677–98. Courtier, first to ], then to his brother, Duke, then Elector, ]. | |||
| ***1687–90. Travels extensively in Germany, Austria, and Italy, researching a book the Elector has commissioned him to write on the history of the House of Brunswick. | |||
| **1698–1716: Courtier to Elector ]. | |||
| ***1712–14. Resides in ]. Appointed Imperial Court Councillor in 1713 by ], at the ] court in ]. | |||
| **1714–16: Georg Ludwig, upon becoming ], forbids Leibniz to follow him to London. Leibniz ends his days in relative neglect. | |||
| ===Early life=== | |||
| Gottfried Leibniz was born on ] (] ]) ] in ] to Friedrich Leibniz and Catherina Schmuck. The name Leibniz was originally Slavonic - Lubeniecz . His father had passed away when he was six, so he learned his religious and moral values from his mother. These would exert a profound influence on his philosophical thought in later life. As an adult, he often styled himself "von Leibniz", and many posthumous editions of his works gave his name on the title page as "Freiherr G. W. von Leibniz." However, no document has been found confirming that he was ever granted a patent of nobility.<ref>Aiton 1985: 312</ref> | |||
| When Leibniz was six years old, his father, a Professor of Moral Philosophy at the ], died, leaving a personal library to which Leibniz was granted free access from age seven onwards. By 12, he had taught himself ], which he used freely all his life, and had begun studying ]. | |||
| He entered his father's university at age 14, and completed university studies by 20, specializing in law and mastering the standard university courses in classics, logic, and scholastic philosophy. However, his education in mathematics was not up to the French and British standards. In 1666 (age 20), he published his first book, also his ] thesis in philosophy, '']''. When ] declined to assure him a position teaching law upon graduation, Leibniz submitted the thesis he had intended to submit at Leipzig to the ] instead, and obtained his doctorate in law in five months. He then declined an offer of academic appointment at Altdorf, and spent the rest of his life in the service of two major German noble families. | |||
| ===1666–74=== | |||
| Leibniz's first position was as a salaried alchemist in ], even though he knew nothing about the subject. He soon met Johann Christian von Boineburg (1622–1672), the dismissed chief minister of the Elector of ], ]. Von Boineburg hired Leibniz as an assistant, and shortly thereafter reconciled with the Elector and introduced Leibniz to him. Leibniz then dedicated an essay on law 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 for his Electorate. In 1669, Leibniz was appointed Assessor in the Court of Appeal. Although von Boineburg died late in 1672, Leibniz remained under the employment of his widow until she dismissed him in 1674. | |||
| Von Boineburg did much to promote Leibniz's reputation, and the latter's memoranda and letters began to attract favorable notice. Leibniz's service to the Elector soon took on a ]ic role. He published an essay, under the pseudonym of a fictitious ] nobleman, arguing (unsuccessfully) for the German candidate for the Polish crown. The main European geopolitical reality during Leibniz's adult life was the ambition of ], backed by French military and economic might. Meanwhile, the ] had left German-speaking Europe exhausted, fragmented, and economically backward. Leibniz proposed to protect German-speaking Europe by distracting Louis as follows. France would be invited to take ] as a stepping stone towards an eventual conquest of the ]. In return, France would agree to leave Germany and the Netherlands undisturbed. This plan obtained the Elector's cautious support. In 1672, the French government invited Leibniz to ] for discussion, but the plan was soon overtaken by events and became irrelevant. Napoleon's failed invasion of Egypt in 1798 can be seen as an unwitting implementation of Leibniz's plan. | |||
| Thus Leibniz began several years in Paris, during which he greatly expanded his knowledge of mathematics and physics, and began contributing to both. He met ] and ], the leading French philosophers of the day, and studied the writings of ] and ], unpublished as well as published. He befriended a German mathematician, ]; they corresponded for the rest of their lives. Especially fateful was Leibniz's making the acquaintance of the ] physicist and mathematician ], then active in Paris. Soon after arriving in Paris, Leibniz received a rude awakening; his knowledge of mathematics and physics was spotty. With Huygens as mentor, he began a program of self-study that soon resulted in his making major contributions to both subjects, including inventing his version of the differential and integral ]. | |||
| When it became clear that France would not implement its part of Leibniz's Egyptian plan, the Elector sent his nephew, escorted by Leibniz, on a related mission to the English government in ], early in 1673. There Leibniz made the acquaintance of ] and ]. After demonstrating to the ] a calculating machine he had been designing and building since 1670, the first such machine that could execute all four basic arithmetical operations, the Society made him an external member. The mission ended abruptly when news reached it of the Elector's death, whereupon Leibniz promptly returned to Paris and not, as had been planned, to Mainz. | |||
| The sudden deaths of Leibniz's two patrons in the same winter meant that Leibniz had to find a new basis for his career. In this regard, a 1669 invitation from the Duke of ] to visit Hanover proved fateful. Leibniz declined the invitation, but began corresponding with the Duke in 1671. In 1673, ] offered him the post of Counsellor which Leibniz very reluctantly accepted two years later, only after it became clear that no employment in Paris, whose intellectual stimulation he relished, or with the ] imperial court was forthcoming. | |||
| ===House of Hanover 1676–1716=== | |||
| Leibniz managed to delay his arrival in Hanover until the end of 1676, after making one more short journey to London, where he possibly was shown some of Newton's unpublished work on the calculus. This fact was deemed evidence supporting the accusation, made decades later, that he had stolen the calculus from Newton. On the journey from London to Hanover, Leibniz stopped in ] where he met ], the discoverer of microorganisms. He also spent several days in intense discussion with ], who had just completed his masterwork, the '']''. Leibniz respected Spinoza's powerful intellect, but was dismayed by his conclusions that contradicted both Christian and Jewish orthodoxy. | |||
| In 1677, he was promoted, at his request, to Privy Counselor of Justice, a post he held for the rest of his life. Leibniz served three consecutive rulers of the House of Brunswick as historian, political adviser, and most consequentially, as librarian of the ] library. He thenceforth employed his pen on all the various political, historical, and ] matters involving the House of Brunswick; the resulting documents form a valuable part of the historical record for the period. | |||
| ] | |||
| Among the few people in north Germany to warm to Leibniz were the Electress ] (1630–1714), her daughter ] (1668–1705), the Queen of Prussia and her avowed disciple, and ], the consort of her grandson, the future ]. To each of these women he was correspondent, adviser, and friend. In turn, they all warmed to him more than did their spouses and the future king ].<ref>For a recent study of Leibniz's correspondence with Sophia Charlotte, see (1998).</ref> | |||
| The population of Hanover was only about 10,000, and its provinciality eventually grated on Leibniz. Nevertheless, to be a major courtier to the House of ] was quite an honor, especially in light of the meteoric rise in the prestige of that House during Leibniz's association with it. In 1692, the Duke of Brunswick became a hereditary Elector of the ]. The British ] designated the Electress Sophia and her descent as the royal family of the United Kingdom, once both King ] and his sister-in-law and successor, ], were dead. Leibniz played a role in the initiatives and negotiations leading up to that Act, but not always an effective one. For example, something he published anonymously in England, thinking to promote the Brunswick cause, was formally censured by the ]. | |||
| The Brunswicks tolerated the enormous effort Leibniz devoted to intellectual pursuits unrelated to his duties as a courtier, pursuits such as perfecting the calculus, writing about other mathematics, logic, physics, and philosophy, and keeping up a vast correspondence. He began working on the calculus in 1674; the earliest evidence of its use in his surviving notebooks is 1675. By 1677 he had a coherent system in hand, but did not publish it until 1684. Leibniz's most important mathematical papers were published between 1682 and 1692, usually in a journal which he and Otto Mencke founded in 1682, the '']''. That journal played a key role in advancing his mathematical and scientific reputation, which in turn enhanced his eminence in diplomacy, history, theology, and philosophy. | |||
| The Elector ] commissioned Leibniz to write a history of the House of ], going back to the time of ] or earlier, 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 by but no history appeared; the next Elector became quite annoyed at Leibniz's apparent dilatoriness. Leibniz never finished the project, in part because of his huge output on many other fronts, but also because he insisted on writing a meticulously researched and erudite book based on archival sources, when his patrons would have been quite happy with a short popular book, one perhaps little more than a ] with commentary, to be completed in three years or less. They never knew that he had in fact carried out a fair part of his assigned task: when the material Leibniz had written and collected for his history of the House of Brunswick was finally published in the 19th century, it filled three volumes. | |||
| In 1711, John Keill, writing in the journal of the Royal Society and with Newton's presumed blessing, accused Leibniz of having plagiarized Newton's calculus. Thus began the ] which darkened the remainder of Leibniz's life. A formal investigation by the Royal Society (in which Newton was an unacknowledged participant), undertaken in response to Leibniz's demand for a retraction, upheld Keill's charge. Historians of mathematics writing since 1900 or so have tended to acquit Leibniz, pointing to important differences between Leibniz's and Newton's versions of the calculus. | |||
| In 1711, while traveling in northern Europe, the Russian ] ] stopped in Hanover and met Leibniz, who then took some interest in matters Russian over the rest of his life. In 1712, Leibniz began a two year residence in ], where he was appointed Imperial Court Councillor to the ]s. On the death of Queen Anne in 1714, Elector Georg Ludwig became King ], under the terms of the 1701 ]. 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 of Wales, ], George I forbade Leibniz to join him in London until he completed at least one volume of the history of the Brunswick family his father had commissioned nearly 30 years earlier. Moreover, for George I to include 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 in British official circles could not have been higher. Finally, his dear friend and defender, the dowager Electress ], died in 1714. | |||
| Leibniz died in ] in 1716: at the time, he was so out of favor that neither George I (who happened to be near Hanover at the time) nor any fellow courtier other than his personal secretary attended the funeral. Even though Leibniz was a life member of the Royal Society and the ], neither organization saw fit to honor his passing. His grave went unmarked for more than 50 years. Leibniz was eulogized by ], before the Academie des Sciences in Paris, which had admitted him as a foreign member in 1700. The eulogy was composed at the behest of the ], a niece of the Electress Sophia. | |||
| Leibniz never married. He complained on occasion about money, but the fair sum he left to his sole heir, his sister's stepson, proved that the Brunswicks had, by and large, paid him well. In his diplomatic endeavors, he at times verged on the unscrupulous, as was all too often the case with professional diplomats of his day. On several occasions, Leibniz backdated and altered personal manuscripts, actions which cannot be excused or defended and which put him in a bad light during the calculus controversy. On the other hand, he was charming and well-mannered, with many friends and admirers all over Europe. | |||
| ==Writings and edition== | |||
| Leibniz mainly wrote in three languages: scholastic Latin (ca. 40%), French (ca. 35%), and German (less than 25%).{{Fact|date=April 2008}} During his lifetime, he published many pamphlets and scholarly articles, but only two "philosophical" books, the ''Combinatorial Art'' and the '']''. (He published numerous pamphlets, often anonymous, on behalf of the House of ], most notably the "De jure suprematum" a major consideration of the nature of ].) One substantial book appeared posthumously, his '']'', which Leibniz had withheld from publication after the death of ]. Only in 1895, when Bodemann completed his catalogues of Leibniz's manuscripts and correspondence, did the enormous extent of Leibniz's '']'' become clear: about 15,000 letters to more than 1000 recipients plus more than 40,000 other items. Moreover, quite a few of these letters are of essay length. Much of his vast correspondence, especially the letters dated after 1685, remains unpublished, and much of what is published has been so only in recent decades. The amount, variety, and disorder of Leibniz's writings are a predictable result of a situation he described as follows: | |||
| {{quote|"''I cannot tell you how extraordinarily distracted and spread out I am. I am trying to find various things in the archives; I look at old papers and hunt up unpublished documents. From these I hope to shed some light on the history of the Brunswick. I receive and answer a huge number of letters. At the same time, I have so many mathematical results, philosophical thoughts, and other literary innovations that should not be allowed to vanish that I often do not know where to begin''". (1695 letter to ] in Gerhardt)}} | |||
| The extant parts of the of Leibniz's writings (see photograph there) are organized as follows: | |||
| *Series 1. ''Political, Historical, and General Correspondence''. 21 vols., 1666–1701. | |||
| *Series 2. ''Philosophical Correspondence''. 1 vol., 1663–85. | |||
| *Series 3. ''Mathematical, Scientific, and Technical Correspondence''. 6 vols., 1672–96. | |||
| *Series 4. ''Political Writings''. 6 vols., 1667–98. | |||
| *Series 5. ''Historical and Linguistic Writings''. Inactive. | |||
| *Series 6. ''Philosophical Writings''. 7 vols., 1663–90, and '']''. | |||
| *Series 7. ''Mathematical Writings''. 3 vols., 1672–76. | |||
| *Series 8. ''Scientific, Medical, and Technical Writings''. In preparation. | |||
| The systematic cataloguing of all of Leibniz's ] was begun in 1901. Two World wars, the NS dictatorship (with Jewish genocide, including an employee of the project, and other personal consequences), and decades of German division (two states with the cold war's "iron curtain" in between, separating scholars and also scattered portions of his literary estates), greately hampered the ambitious edition project which had and has to deal with seven languages used on ca. 200 000 pages of written and printed paper. In 1985 it was reorganized and included in a joint program of German federal and state ("Länder") academies. Since then the branches in ], ], ] and ] have jointly published 25 volumes of the critical edition (until 2006) with an average of 870 pages (compared to only 19 volumes since 1923), plus preparing index and ] works (so, had that "speed" of work been possible from the beginning, the project would already be completed). | |||
| ==Posthumous reputation== | |||
| When Leibniz died, his reputation was in decline. He was remembered for only one book, the ''Théodicée'', whose supposed central argument ] lampooned in his '']''. Voltaire's depiction of Leibniz's ideas was so influential that many believed it to be an accurate description (this misapprehension may still be the case among certain lay people). Thus Voltaire and his ''Candide'' bear some of the blame for the lingering failure to appreciate and understand Leibniz's ideas. Leibniz had an ardent disciple, ], whose dogmatic and facile outlook did Leibniz's reputation much harm. In any event, philosophical fashion was moving away from the rationalism and system building of the 17th century, of which Leibniz had been such an ardent exponent. His work on law, diplomacy, and history was seen as of ephemeral interest. The vastness and richness of his correspondence went unrecognized. | |||
| Much of Europe came to doubt that Leibniz had discovered the calculus independently of Newton, and hence his whole work in mathematics and physics was neglected. Voltaire, an admirer of Newton, also wrote ''Candide'' at least in part to discredit Leibniz's claim to having discovered the calculus and Leibniz's charge that Newton's theory of universal gravitation was incorrect. The rise of relativity and subsequent work in the history of mathematics has put Leibniz's stance in a more favorable light. | |||
| Leibniz's long march to his present glory began with the 1765 publication of the ''Nouveaux Essais'', which ] read closely. In 1768, Dutens edited the first multi-volume edition of Leibniz's writings, followed in the 19th century by a number of editions, including those edited by Erdmann, Foucher de Careil, Gerhardt, Gerland, Klopp, and Mollat. Publication of Leibniz's correspondence with notables such as ], ], ], and her daughter ], began. | |||
| In 1900, ] published a critical study of Leibniz's metaphysics. Shortly thereafter, ] published an important of Leibniz, and edited a volume of Leibniz's heretofore unpublished writings, mainly on logic. While their conclusions, especially Russell's, were subsequently challenged and often dismissed, they made Leibniz somewhat respectable among 20th century analytical and linguistic philosophers in the English speaking world (Leibniz had already been of great influence to many Germans such as ]). For example, Leibniz's phrase '']'', meaning interchangeability without loss of or compromising the truth, recurs in ]'s writings. Nevertheless, the secondary English-language literature on Leibniz did not really blossom until after ]. This is especially true of English speaking countries; in Gregory Brown's bibliography<ref>Gregory Brown's bibliography </ref> fewer than 30 of the English language entries were published before 1946. American Leibniz studies owe much to Leroy Loemker (1904–85) through his translations {{Harv|Loemker}} and his interpretive essays in {{Harv|LeClerc}}. | |||
| Nicholas Jolley {{Harv|Jolley|217–19}} has surmised that Leibniz's reputation as a philosopher is now perhaps higher than at any time since he was alive because: | |||
| *Work in the history of 17th and 18th century ] has revealed more clearly the 17th century "Intellectual Revolution" that preceded the better known ] and commercial revolutions of the 18th and 19th centuries. | |||
| *The doctrinaire contempt for ], characteristic of ] and ], has faded; | |||
| *] and contemporary philosophy continue to invoke his notions of ], ], and ]; | |||
| *The 17th and 18th century belief that natural science, especially ], differs from philosophy mainly in degree and not in kind, is no longer dismissed out of hand. That modern ] includes a "]" as well as a "radical ]" element is more accepted now than in the early 20th century; | |||
| *He is now seen as a major prolongation of the mighty endeavor begun by ] and ]: the ] and man's place in it are amenable to human ]. | |||
| The University of Hannover (German spelling) is named after him. | |||
| In 1985, the ] government created the ], annual awards of 1.55 million Euros for experimental results, and 770,000 Euros for theoretical ones. It is the world's largest prize for scientific achievement. | |||
| == Philosopher == | |||
| Leibniz's philosophical thinking appears fragmented, because his philosophical writings consist mainly of a multitude of short pieces: journal articles, manuscripts published long after his death, and many letters to many correspondents. He wrote only two philosophical treatises, and the one he published in his lifetime, the ''Théodicée'' of 1710, is as much theological as philosophical. | |||
| Leibniz dated his beginning as a philosopher to his '']'', which he composed in 1686 as a commentary on a running dispute between ] and ]. This led to an extensive and valuable correspondence with Arnauld ({{Harvnb|Ariew & Garber|69}}, {{Harvnb|Loemker|§§36,38}}); it and the ''Discourse'' were not published until the 19th century. In 1695, Leibniz made his public entrée into European philosophy with a journal article titled "New System of the Nature and Communication of Substances" ({{Harvnb|Ariew & Garber|138}}, {{Harvnb|Loemker|§47}}, {{Harvnb|Wiener|II.4}}). Over 1695–1705, he composed his '']'', a lengthy commentary on ]'s 1690 '']'', but upon learning of Locke's 1704 death, lost the desire to publish it, so that the ''New Essays'' were not published until 1765. The '']'', composed in 1714 and published posthumously, consists of 90 aphorisms. | |||
| Leibniz met ] in 1676, read some of his unpublished writings, and has since been suspected of appropriating some of Spinoza's ideas. While Leibniz admired Spinoza's powerful intellect, he was also forthrightly dismayed by Spinoza's conclusions, ({{Harvnb|Ariew & Garber| 272–84}}, {{Harvnb|Loemker|§§14,20,21}}, {{Harvnb|Wiener|III.8}}) especially when these were inconsistent with Christian orthodoxy. | |||
| Unlike Descartes and Spinoza, Leibniz had a thorough university education in philosophy. His lifelong ] and ] turn of mind betrayed the strong influence of one of his ] professors, ], who also supervised his BA thesis in philosophy. Leibniz also eagerly read ], a Spanish ] respected even in ] universities. Leibniz was deeply interested in the new methods and conclusions of Descartes, Huygens, Newton, and ], but viewed their work through a lens heavily tinted by scholastic notions. Yet it remains the case that Leibniz's methods and concerns often anticipate the ], and ] and ] of the 20th century. | |||
| ===The Principles=== | |||
| Leibniz variously invoked one or another of seven fundamental philosophical Principles (Mates 1986: chpts. 7.3, 9): | |||
| *]/]. If a proposition is true, then its negation is false and vice versa. | |||
| *]. Two things are identical if and only if they share the same properties. Frequently invoked in modern logic and philosophy. | |||
| *]. "There must be a sufficient reason for anything to exist, for any event to occur, for any truth to obtain." (LL 717). | |||
| *]. See Jolley (1995: 129–31), Woolhouse and Francks (1998), and Mercer (2001). "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. | |||
| *]. ''Natura non saltum facit''. A mathematical analog to this principle would go as follows. If a ] describes a ] of something to which continuity applies, then its ] and ] are both ]s. | |||
| *]. "God assuredly always chooses the best." (LL 311). | |||
| *]. "Leibniz believed that the best of all possible worlds would actualize every genuine possibility, and argued in ] 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." (From ].) | |||
| The second principle here is often referred to as ] . The Identity of Indiscernibles has attracted the most controversy and criticism, especially from corpuscular philosophy and quantum mechanics. | |||
| Leibniz would on occasion give a speech for a specific principle, but more often took them for granted. For a precis of what Leibniz meant by these and other Principles, see Mercer (2001: 473–84). For a classic discussion of ] and ], see Lovejoy (1957). | |||
| ===The monads=== | |||
| Leibniz's best known contribution to ] is his theory of ]s, as exposited in '']''. Monads are to the metaphysical realm what ]s are to the physical/phenomenal. Monads are the ultimate elements of the ]. The monads are "substantial forms of being" with the following properties: they are eternal, indecomposable, individual, subject to their own laws, un-interacting, and each reflecting the entire universe in a ] (a historically important example of ]). Monads are centers of ]; substance is force, while ], ], and ] are merely phenomenal. | |||
| The ] essence of a monad is its irreducible simplicity. Unlike atoms, monads possess no material or spatial character. They also differ from atoms by their complete mutual independence, so that interactions among monads are only apparent. Instead, by virtue of the principle of pre-established harmony, each monad follows a preprogrammed set of "instructions" peculiar to itself, so that a monad "knows" what to do at each moment. (These "instructions" may be seen as analogs of the ]s governing ]s.) By virtue of these intrinsic instructions, each monad is like a little mirror of the universe. Monads need not be "small"; e.g., each human being constitutes a monad, in which case ] is problematic. ], too, is a monad, and the ] can be inferred from the harmony prevailing among all other monads; God wills the pre-established harmony. | |||
| Monads are purported to having gotten rid of the problematic: | |||
| *Interaction between ] and ] arising in the system of ]; | |||
| *Lack of ] inherent to the system of ], which represents individual creatures as merely ]al. | |||
| The monadology was thought arbitrary, even eccentric, in Leibniz's day and since. | |||
| ===Theodicy and optimism=== | |||
| The ''Théodicée'' tries to justify the apparent imperfections of the world by claiming that it is ]. It must be the best possible and most balanced world, because it was created by a perfect God. Rutherford (1998) is a detailed scholarly study of Leibniz's theodicy. | |||
| The statement that "we live in the best of all possible worlds" drew scorn, most notably from ], who lampooned it in his comic novel '']'' by having the character '']'' (a parody of Leibniz) repeat it like a ]. Thus the adjective "panglossian", describing one so naive as to believe that the world about us is the best possible one. | |||
| The mathematician Paul du Bois-Reymond, in his "Leibnizian Thoughts in Modern ]," wrote that Leibniz thought of God as a ].<blockquote> "As is well known, the theory of the ] of ] was indebted to him for the greatest progress through the discovery of the method of ]s. Well, he conceives God in the creation of the world like a mathematician who is solving a minimum problem, or rather, in our modern phraseology, a problem in the ] — the question being to determine among an ] number of possible worlds, that for which the sum of necessary ] is a minimum."</blockquote> | |||
| A cautious defense of Leibnizian ] would invoke certain scientific principles that emerged in the two centuries since his death and that are now thoroughly established: the ], the ], and the ]. In addition, the modern observations that lead to the ] arguments seem to support his view: | |||
| #The 3+1 dimensional structure of ] may be ideal. In order to sustain ] such as ], a ] probably requires three ] and one ] ]. Most universes deviating from 3+1 either violate some fundamental ]s, or are impossible. The mathematically richest number of spatial dimensions is also 3 (in the sense of topological nontriviality). | |||
| #The ], ], and ] are the "best possible" in that they enable intelligent life to exist. Such life has evolved on Earth only because the ], ], and ] possess a number of unusual characteristics; see ], Morris (2003: chpts. 5,6). | |||
| #The most sweeping form of ] derives from the ] (Barrow and Tipler 1986). Physical reality can be seen as grounded in the numerical values of a handful of ], the best known of which are the ] and the ratio of the ] of the ] to the ]. Were the numerical values of these constants to differ by a few percent from their observed values, it is unlikely that the resulting universe would contain ]. | |||
| Our ]s, ], ], and ] are all "best" in the sense that they enable ] such as ], ]s, and, ultimately, ]. On the other hand, it is also reasonable to believe that life might be more intelligent given some other set of circumstances. Further, some modern proponents of Leibnizian optimism seem to confuse the term "best" with terms like "good" or "better"; by definition, there can be only one "best". | |||
| ===Symbolic thought=== | |||
| Leibniz believed that much of human reasoning could be reduced to calculations of a sort, and that such calculations could resolve many differences of opinion: | |||
| <blockquote>"The only way to rectify our reasonings is to make them as tangible as those of the Mathematicians, so that we can find our error at a glance, and when there are disputes among persons, we can simply say: Let us calculate , without further ado, to see who is right." (''The Art of Discovery'' 1685, W 51) </blockquote> | |||
| Leibniz's ], which resembles ], can be viewed as a way of making such calculations feasible. Leibniz wrote memoranda (many of which are translated in Parkinson 1966) that can now be read as groping attempts to get symbolic logic—and thus his ''calculus''—off the ground. But Gerhard and Couturat did not publish these writings until modern formal logic had emerged in Frege's '']'' and in writings by ] and his students in the 1880s, and hence well after ] and ] began that logic in 1847. | |||
| Leibniz thought ]s were important for human understanding. He attached so much importance to the invention of good notations that he attributed all his discoveries in mathematics to this. His notation for the ] is an example of his skill in this regard. ], a 19th century pioneer of ], shared Leibniz's passion for symbols and notation, and his belief that these are essential to a well-running logic and mathematics. | |||
| But Leibniz took his speculations much further. Defining a ] as any written sign, he then defined a "real" character as one that represents an idea directly and not simply as the word embodying the idea. Some real characters, such as the notation of logic, serve only to facilitate reasoning. Many characters well-known in his day, including ], ]s, and the symbols of ] and ], he deemed not real. (Loemker, however, who translated some of Leibniz's works into English, said that the symbols of chemistry were real characters so there is disagreement among Leibniz scholars on this point.<!--is this paragraph correct up to this point?-->) Instead, he proposed the creation of a '']'' or "universal characteristic," built on an ] in which each fundamental concept would be represented by a unique "real" character. | |||
| <blockquote>"It is obvious that if we could find characters or signs suited for expressing all our thoughts as clearly and as exactly as arithmetic expresses numbers or geometry expresses lines, we could do in all matters ''insofar as they are subject to reasoning'' all that we can do in arithmetic and geometry. For all investigations which depend on reasoning would be carried out by transposing these characters and by a species of calculus." (''Preface to the General Science'', 1677. Revision of Rutherford's translation in Jolley 1995: 234. Also W I.4) </blockquote> | |||
| Complex thoughts would be represented by combining characters for simpler thoughts. Leibniz saw that the uniqueness of ] suggests a central role for ] in the universal characteristic, a striking anticipation of ]. Granted, there is no intuitive or ] way to number any set of elementary concepts using the prime numbers. | |||
| Because Leibniz was a mathematical novice when he first wrote about the ''characteristic'', at first he did not conceive it as an ] but rather as a ] or script. Only in 1676 did he conceive of a kind of "algebra of thought," modeled on and including conventional algebra and its notation. The resulting ''characteristic'' included a logical calculus, some combinatorics, algebra, his ''analysis situs'' (geometry of situation) discussed in 3.2, a universal concept language, and more. | |||
| What Leibniz actually intended by his ] and ], and the extent to which modern formal ] does justice to the calculus, may never be established. A good introductory discussion of the "characteristic" is Jolley (1995: 226–40). An early, yet still classic, discussion of the "characteristic" and "calculus" is Couturat (1901: chpts. 3,4). | |||
| ===Formal logic=== | |||
| {{main|algebraic logic}} | |||
| Leibniz is the most important logician between Aristotle and 1847, when ] and ] each published books that began modern formal logic. Leibniz enunciated the principal properties of what we now call ], ], ], ], set ], and the ]. The principles of Leibniz's logic and, arguably, of his whole philosophy, reduce to two: | |||
| #All our ideas are compounded from a very small number of simple ideas, which form the ]. | |||
| #Complex ideas proceed from these simple ideas by a uniform and symmetrical combination, analogous to arithmetical multiplication. | |||
| With regard to (1), the number of simple ideas is much greater than Leibniz thought. As for (2), logic can indeed be grounded in a symmetrical combining operation, but that operation is analogous to either of addition or multiplication. The formal logic that emerged early in the 20th century also requires, at minimum, unary ] and ] ]s ranging over some ]. | |||
| Leibniz published nothing on formal logic in his lifetime; most of what he wrote on the subject consists of working drafts. | |||
| In his book '']'', ] went as far as claiming that Leibniz had developed logic in his unpublished writings to a level which was reached only 200 years later. | |||
| ===Mathematician=== | |||
| Although the mathematical notion of ] was implicit in trigonometric and logarithmic tables, which existed in his day, Leibniz was the first, in 1692 and 1694, to employ it explicitly, to denote any of several geometric concepts derived from a curve, such as ], ], ], ], and the ] (Struik 1969: 367). In the 18th century, "function" lost these geometrical associations. | |||
| Leibniz was the first to see that the coefficients of a system of ]s could be arranged into an array, now called a ], which can be manipulated to find the solution of the system, if any. This method was later called ]. Leibniz's discoveries of ] and of ], also relevant to mathematics, are discussed in the preceding section. | |||
| A comprehensive scholarly treatment of Leibniz's mathematical writings has yet to be written, perhaps because Series 7 of the Academy edition is very far from complete. | |||
| ===Calculus=== | |||
| Leibniz is credited, along with ], with the discovery of ]. According to Leibniz's notebooks, a critical breakthrough occurred on ], ], when he employed integral calculus for the first time to find the area under the function ''y = x''. He introduced several notations used to this day, for instance the ] ∫ representing an elongated S, from the Latin word ''summa'' and the ''d'' used for ], from the Latin word ''differentia''. This ingenious and suggestive notation for the calculus is probably his most enduring mathematical legacy. Leibniz did not publish anything about his calculus until 1684. For an English translation of this paper, see Struik (1969: 271–84), who also translates parts of two other key papers by Leibniz on the calculus. The ] of ] is still called "Leibniz's law." In addition, the theorem that tells how and when to differentiate under the integral sign is called ]. | |||
| Leibniz's approach to the calculus fell well short of later standards of rigor (the same can be said of Newton's). We now see a Leibniz "proof" as being in truth mostly a ] hodgepodge mainly grounded in geometric intuition. Leibniz also freely invoked mathematical entities he called ]s, manipulating them in ways suggesting that they had ]ical ]ic properties. ], in a tract called ''The Analyst'' and elsewhere, ridiculed this and other aspects of the early calculus, pointing out that natural science grounded in the calculus required just as big of a leap of ] as ] grounded in ] ]. | |||
| From 1711 until his death, Leibniz's life was envenomed by a long dispute with John Keill, Newton, and others, over whether Leibniz had invented the calculus independently of Newton, or whether he had merely invented another notation for ideas that were fundamentally Newton's. Hall (1980) gives a thorough scholarly discussion of the ]. | |||
| Modern, rigorous calculus emerged in the 19th century, thanks to the efforts of ], ], ], and others, who based their work on the definition of a ] and on a precise understanding of ]s. Their work discredited the use of ]s to ''justify'' calculus. Yet, infinitesimals survived in science and engineering, and even in rigorous mathematics, via the fundamental computational device known as the ]. Beginning in 1960, ] worked out a rigorous foundation for Leibniz's infinitesimals, using ]. The resulting ] can be seen as a belated vindication of Leibniz's mathematical reasoning. | |||
| ===Topology=== | |||
| Leibniz was the first to use the term ''analysis situs'' (LL §27), later used in the 19th century to refer to what is now known as ]. There are two takes on this situation. On the one hand, Mates (1986: 240), citing a 1954 paper in German by ], argues: | |||
| <blockquote>"Although for the situs of a sequence of points is completely determined by the distance between them and is altered if those distances are altered, his admirer ], in the famous 1736 paper solving the ] and its generalizations, used the term ''geometria situs'' in such a sense that the situs remains unchanged under topological deformations. He mistakenly credits Leibniz with originating this concept. ...it is sometimes not realized that Leibniz used the term in an entirely different sense and hence can hardly be considered the founder of that part of mathematics."</blockquote> | |||
| But Hirano (1997) argues differently, quoting Mandelbrot (1977: 419): | |||
| <blockquote>"...To sample Leibniz' scientific works is a sobering experience. Next to calculus, and to other thoughts that have been carried out to completion, the number and variety of premonitory thrusts is overwhelming. We saw examples in 'packing,'... My Leibniz mania is further reinforced by finding that for one moment its hero attached importance to geometric scaling. In "Euclidis Prota"..., which is an attempt to tighten Euclid's axioms, he states,...: 'I have diverse definitions for the straight line. The straight line is a curve, any part of which is similar to the whole, and it alone has this property, not only among curves but among sets.' This claim can be proved today."</blockquote> | |||
| Thus the fractal geometry promoted by Mandelbrot drew on Leibniz's notions of self-similarity and the principle of continuity: ''natura non facit saltus''. We also see that when Leibniz wrote, in a metaphysical vein, that "the straight line is a curve, any part of which is similar to the whole..." he was anticipating topology by more than two centuries. As for "packing," Leibniz told to his friend and correspondent Des Bosses to imagine a circle, then to inscribe within it three congruent circles with maximum radius; the latter smaller circles could be filled with three even smaller circles by the same procedure. This process can be continued infinitely, from which arises a good idea of self-similarity. Leibniz's improvement of Euclid's axiom contains the same concept. | |||
| == Scientist and engineer == | |||
| Leibniz's writings are currently discussed, not only for their anticipations and possible discoveries not yet recognized, but as ways of advancing present knowledge. Much of his writing on physics is included in Gerhardt's ''Mathematical Writings''. His writings on other scientific and technical subjects are mostly scattered and relatively little known, because the Academy edition has yet to publish any volume in its Series ''Scientific, Medical, and Technical Writings'' . | |||
| ===Physics=== | |||
| {{seealso|dynamism (metaphysics)}} | |||
| Leibniz contributed a fair amount to the statics and dynamics emerging about him, often disagreeing with ] and ]. He devised a new theory of ] (]) based on ] and ], which posited space as relative, whereas Newton felt strongly space was absolute. An important example of Leibniz's mature physical thinking is his ''Specimen Dynamicum'' of 1695. (AG 117, LL §46, W II.5) On Leibniz and physics, see the chapter by Garber in Jolley (1995) and Wilson (1989). | |||
| Until the discovery of subatomic particles and the ] governing them, many of Leibniz's speculative ideas about aspects of nature not reducible to statics and dynamics made little sense. For instance, he anticipated ] by arguing, against Newton, that ], ] and motion are relative, not absolute. ] in interacting theories plays a role in ] and in the lattices of ]. The ] has been invoked in recent ], and his ] in ], a field some even credit him with having anticipated in some sense. Those who advocate ], a recent direction in cosmology, claim Leibniz as a precursor. | |||
| ====The ''vis viva''==== | |||
| {{main|vis viva}} | |||
| Leibniz 's ''vis viva'' (Latin for ''living force'') is mv<sup>2</sup>, twice the modern ]. He realized that the total energy would be conserved in certain mechanical systems, so he considered it an innate motive characteristic of matter (see AG 155–86, LL §§53–55, W II.6–7a). Here too his thinking gave rise to another regrettable nationalistic dispute. His "vis viva" was seen as rivaling the ] championed by Newton in England and by ] in France; hence ] in those countries tended to neglect Leibniz's idea. ]s eventually found "vis viva" useful, so that the two approaches eventually were seen as complementary. | |||
| ===Other natural science=== | |||
| By proposing that the earth has a molten core, he anticipated modern ]. In ], he was a preformationist, but also proposed that organisms are the outcome of a combination of an infinite number of possible microstructures and of their powers. In the ] and ], he revealed an amazing transformist intuition, fueled by his study of comparative anatomy and fossils. He worked out a primal organismic theory. On Leibniz and biology, see Loemker (1969a: VIII). In ], he exhorted the physicians of his time—with some results—to ground their theories in detailed comparative observations and verified experiments, and to distinguish firmly scientific and metaphysical points of view. | |||
| ===Social science=== | |||
| In ] he anticipated the distinction between ] and ] states. On Leibniz and psychology, see Loemker (1969a: IX). In public health, he advocated establishing a medical administrative authority, with powers over ] and ]. He worked to set up a coherent medical training programme, oriented towards public health and preventive measures. In economic policy, he proposed tax reforms and a national insurance scheme, and discussed the balance of trade. He even proposed something akin to what much later emerged as ]. In ] he laid the ground for ]. | |||
| ===Technology=== | |||
| In 1906, Garland published a volume of Leibniz's writings bearing on his many practical inventions and engineering work. To date, few of these writings have been translated into English. Nevertheless, it is well understood that Leibniz was a serious inventor, engineer, and applied scientist, with great respect for practical life. Following the motto ''theoria cum praxis'', he urged that theory be combined with practical application, and thus has been claimed as the father of ]. He designed wind-driven propellers and water pumps, mining machines to extract ore, hydraulic presses, lamps, submarines, clocks, etc. With ], he invented a ]. He even proposed a method for desalinating water. From 1680 to 1685, he struggled to overcome the chronic flooding that afflicted the ducal ] mines in the ], but did not succeed. (Aiton 1985: 107–114, 136) | |||
| ====Information technology==== | |||
| Leibniz may have been the first computer scientist and information theorist. Early in life, he discovered the ] system (base 2), which was later (and is now) used on most computers, then revisited that system throughout his career. (See Couturat, 1901: 473–78.) He anticipated ] and ]. His ] anticipated aspects of the ]. In 1934, ] claimed to have found in Leibniz's writings a mention of the concept of ], central to Wiener's later ] theory. | |||
| In 1671, Leibniz began to invent a machine that could execute all four arithmetical operations, gradually improving it over a number of years. This ']' attracted fair attention and was the basis of his election to the ] in 1673. A number of such machines were made during his years in ], by a craftsman working under Leibniz's supervision. It was not an unambiguous success because it did not fully mechanize the operation of carrying. Couturat (1901: 115) reported finding an unpublished note by Leibniz, dated 1674, describing a machine capable of performing some algebraic operations. | |||
| Leibniz was groping towards hardware and software concepts worked out much later in 1830-1845 by ] and ]. In 1679, while mulling over his binary arithmetic, Leibniz imagined a machine in which binary numbers were represented by marbles, governed by a rudimentary sort of punched cards. Modern electronic digital computers replace Leibniz's marbles moving by gravity with shift registers, voltage gradients, and pulses of electrons, but otherwise they run roughly as Leibniz envisioned in 1679. Davis (2000) discusses Leibniz's prophetic role in the emergence of calculating machines and of formal languages. | |||
| ===Librarian=== | |||
| While serving as librarian of the ducal libraries in ] and ], Leibniz effectively became one of the founders of ]. The latter library was enormous for its day, as it contained more than 100,000 volumes, and Leibniz helped design a new building for it, believed to be the first building explicitly designed to be a library. He also designed a book ] in ignorance of the only other such system then extant, that of the ] at ]. He also called on publishers to distribute abstracts of all new titles they produced each year, in a standard form that would facilitate indexing. He hoped that this abstracting project would eventually include everything printed from his day back to ]. Neither proposal met with success at the time, but something like them became standard practice among English language publishers during the 20th century, under the aegis of the ] and the ]. | |||
| He called for the creation of an ] ] as a way to further all sciences. His ], ], and a "community of minds"—intended, among other things, to bring political and religious unity to Europe—can be seen as distant unwitting anticipations of artificial languages (e.g., ] and its rivals), ], even the ]. | |||
| ===Advocate of scientific societies=== | |||
| Leibniz emphasized that ] was a collaborative endeavor. Hence he warmly advocated the formation of national scientific societies along the lines of the British Royal Society and the French Academie Royale des Sciences. More specifically, in his correspondence 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 ] was created. Leibniz drew up its first statutes, and served as its first President for the remainder of his life. That Academy evolved into the German Academy of Sciences, the publisher of the ongoing critical edition of his works. On Leibniz’s projects for scientific societies, see Couturat (1901: App. IV). | |||
| ==Lawyer, moralist== | |||
| No philosopher has ever had as much experience with practical affairs of state as Leibniz, except possibly ]. Leibniz's writings on law, ethics, and politics (e.g., AG 19, 94, 111, 193; Riley 1988; LL §§2, 7, 20, 29, 44, 59, 62, 65; W I.1, IV.1–3) were long overlooked by English speaking scholars, but this has changed of late; see (in order of difficulty) Jolley (2005: chpt. 7), Gregory Brown's chapter in Jolley (1995), Hostler (1975), and Riley (1996). | |||
| While Leibniz was no apologist for absolute monarchy like ], or for tyranny in any form, neither did he echo the political and constitutional views of his contemporary ], views invoked in support of democracy, in 18th century America and later elsewhere. The following excerpt from a 1695 letter to Baron J. C. Boineburg's son Philipp is very revealing of Leibniz's political sentiments: | |||
| <blockquote>"As for.. the great question of the power of sovereigns and the obedience their peoples owe them, I usually say that it would be good for princes to be persuaded that their people have the right to resist them, and for the people, on the other hand, to be persuaded to obey them passively. I am, however, quite of the opinion of ], that one ought to obey as a rule, the evil of revolution being greater beyond comparison than 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 to endure ceases. This is most rare, however, and the theologian who authorizes violence under this pretext should take care against excess; excess being infinitely more dangerous than deficiency." (LL: 59, fn 16. Translation revised.)</blockquote> | |||
| Leibniz foresaw the ]. In 1677, he (LL: 58, fn 9) called for a European confederation, governed by a council or senate, whose members would represent entire nations and would be free to vote their consciences. Europe would adopt a uniform religion. He reiterated these proposals in 1715. | |||
| ===Ecumenism=== | |||
| Leibniz devoted considerable intellectual and diplomatic effort to what would now be called ] endeavor, seeking to reconcile first the ] and ] churches, later the Lutheran and ] churches. In this respect, he followed the example of his early patrons, Baron von Boineburg and the Duke ], both cradle Lutherans who converted to Catholicism as adults, who did what they could to encourage the reunion of the two faiths, and who warmly welcomed such endeavors by others. (The House of ] remained Lutheran because the Duke's children did not follow their father.) These efforts included corresponding with the French bishop ], and involved Leibniz in a fair bit of theological controversy. He evidently thought that the thoroughgoing application of reason would suffice to heal the breach caused by the ]. | |||
| ==Philologist== | |||
| Leibniz was an avid student of languages, eagerly latching on to any information about ] and ] that came his way. He refuted the belief, widely held by Christian scholars in his day, that ] was the primeval language of the ]. He also refuted the argument, advanced by Swedish scholars in his day, that some sort of proto-] was the ancestor of the ]. He puzzled over the origins of the ],{{Fact|date=February 2007}} was aware of the existence of ], and was fascinated by ]. Scholarly appreciation of Leibniz the ] is hampered by the fact that no volume of the planned Academy edition series "Historical and Linguistic Writings" has appeared. | |||
| ==Sinophile== | |||
| Leibniz was perhaps the first major European intellect to take a close interest in ] civilization, which he knew by corresponding with, and reading other work by, European Christian missionaries posted in China. He concluded that Europeans could learn much from the ] ethical tradition. He mulled over the possibility that the ]s were an unwitting form of his ]. He noted with fascination how the ] hexagrams correspond to the ] from 0 to 111111, and concluded that this mapping was evidence of major Chinese accomplishments in the sort of philosophical mathematics he admired. | |||
| On Leibniz, the I Ching, and binary numbers, see Aiton (1985: 245–48). Leibniz's writings on Chinese civilization are collected and translated in Cook and Rosemont (1994), and discussed in Perkins (2004). | |||
| == As polymath == | |||
| The following episode from the life of Leibniz illustrates the breadth of his genius, and the difficulties awaiting those who try to come to terms with it. While making his grand tour of European ]s to research the Brunswick family history he never completed, Leibniz stopped in ], May 1688 – February 1689, where he did much ] and ] work for the Brunswicks. He visited ], talked with mine ], and tried to negotiate export contracts for ] from the ducal mines in the ]. His proposal that the streets of Vienna be lit with lamps burning ] was implemented. During a formal audience with the ] and in subsequent memoranda, he advocated reorganizing the Austrian economy, reforming the coinage of much of central Europe, negotiating a ] between the ]s and the ], and creating an imperial research library, official archive, and public insurance fund. He wrote and published an important paper on ]. | |||
| Leibniz also wrote a short paper, first published by ] in 1903, later translated as LL 267 and WF 30, summarizing his views on ]. The paper is undated; that he wrote it while in Vienna was determined only in 1999, when the ongoing finally published Leibniz's philosophical writings for the period 1677–90. Couturat's reading of this paper was the launching point for much 20th century thinking about Leibniz, especially among ]. But after a meticulous study of all of Leibniz's philosophical writings up to 1688—a study the 1999 additions to the critical edition made possible—Mercer (2001) begged to differ with Couturat's reading; the jury is still out. | |||
| Leibniz was not devoid of humor and imagination; see W IV.6 and LL § 40. Also see a curious passage titled "Leibniz's Philosophical Dream," first published by Bodemann in 1895 and translated on p. 253 of Morris, Mary, ed. and trans., 1934. ''Philosophical Writings''. Dent & Sons Ltd. | |||
| == References == | |||
| {{Morefootnotes|date=February 2008}} | |||
| {{reflist}} | |||
| == Works == | |||
| Four important collections of English translations are W (Wiener 1951), LL (Loemker 1969), AG (Ariew and Garber 1989), and WF (Woolhouse and Francks, 1998). | |||
| The ongoing critical edition of all of Leibniz's writings is | |||
| Selected works; major ones in bold. The year shown is usually the year in which the work was completed, not of its eventual publication. | |||
| * 1666. ''De Arte Combinatoria'' (On the Art of Combination). Partially translated in LL §1 and Parkinson (1966). | |||
| * 1671. ''Hypothesis Physica Nova'' (New Physical Hypothesis). LL §8.I (part) | |||
| * 1673 '']'' (A Philosopher's Creed, ]) | |||
| * 1684. ''Nova methodus pro maximis et minimis'' (New Method for maximums and minimums). Translation in Struik, D. J., 1969. ''A Source Book in Mathematics, 1200–1800''. Harvard Uni. Press: 271–81. | |||
| * 1686. '']''. Martin and Brown (1988). AG 35, LL §35, W III.3, WF 1. | |||
| * 1703. ''Explication de l'Arithmétique Binaire'' (Explanation of Binary Arithmetic). Gerhardt, ''Mathematical Writings'' VII.223. | |||
| * 1710. '''Théodicée'''. Farrer, A.M., and Huggard, E.M., trans., 1985 (1952). Open Court. W III.11 (part). | |||
| * 1714. '''Monadologie'''. ], trans., 1991. ''The Monadology: An Edition for Students''. Uni. of Pittsburg Press. AG 213, LL §67, W III.13, WF 19. | |||
| * 1765. '']''. Completed 1704. Remnant, Peter, and Bennett, Jonathan, trans., 1996. ''New Essays on Human Understanding''. Cambridge Uni. Press. W III.6 (part). | |||
| Collections of shorter works in translation: | |||
| *{{Harvard reference|Surname1=Ariew|Given1=R|Authorlink1=|Surname2=Garber|Given2=D|Year=1989|Title=Leibniz: Philosophical Essays|Publisher=Hackett}} | |||
| * Bennett, Jonathan. | |||
| * Cook, Daniel, and Rosemont, Henry Jr., 1994. ''Leibniz: Writings on China''. Open Court. | |||
| * Dascal, Marcelo, 1987. ''Leibniz: Language, Signs and Thought''. John Benjamins. | |||
| * {{Harvard reference|Surname=Loemker|Given=Leroy|Authorlink=|Year=1969 (1956)|Title=Leibniz: Philosophical Papers and Letters|Publisher=Reidel}} | |||
| * Martin, R.N.D., and Brown, Stuart, 1988. ''Discourse on Metaphysics and Related Writings''. St. Martin's Press. | |||
| * Parkinson, G.H.R., 1966. ''Leibniz: Logical Papers.'' Oxford Uni. Press. | |||
| * ———, and Morris, Mary, 1973. '''Leibniz: Philosophical Writings''. London: J M Dent & Sons. | |||
| * Riley, Patrick, 1988 (1972). ''Leibniz: Political Writings''. Cambridge Uni. Press. | |||
| * Rutherford, Donald. | |||
| * Strickland, Lloyd, 2006. ''Shorter Leibniz Texts''. Continuum Books. | |||
| * {{Harvard reference|Surname=Wiener|Given=Philip|Year=1951|Title=Leibniz: Selections|Place=|Publisher=Scribner|ID=|URL=}} Regrettably out of print and lacks index. | |||
| * Woolhouse, R.S., and Francks, R., 1998. ''Leibniz: Philosophical Texts''. Oxford Uni. Press. | |||
| Donald Rutherford's | |||
| == Secondary literature == | |||
| A modern biography in English is Aiton (1985). An 1845 English biography by John M. Mackie is available on Google Books . A lively short account of Leibniz’s life, one also taking a critical approach to his philosophy, is Mates (1986: 14–35), who cites the German biographies extensively. Also see , the chapter by Ariew in Jolley (1995), and Jolley (2005: chpt. 1). For a biographical glossary of Leibniz's intellectual contemporaries, see AG 350. | |||
| For a first introduction to Leibniz's philosophy, turn to the Introduction of an anthology of his writings in English translation, e.g., Wiener (1951), Loemker (1969a), Woolhouse and Francks (1998). Then turn to the monographs and Jolley (2005). For an introduction to Leibniz's metaphysics, see the chapters by Mercer, Rutherford, and Sleigh in Jolley (1995); see Mercer (2001) for an advanced study. For an introduction to those aspects of Leibniz's thought of most value to the philosophy of logic and of language, see Jolley (1995, chpts. 7, 8); Mates (1986) is more advanced. MacRae (Jolley 1995: chpt. 6) discusses Leibniz's theory of knowledge. For glossaries of the philosophical terminology recurring in Leibniz's writings and the secondary literature, see Woolhouse and Francks (1998: 285–93) and Jolley (2005: 223–29). | |||
| Introductory: | |||
| *Jolley, Nicholas, 2005. ''Leibniz''. Routledge. | |||
| *MacDonald Ross, George, 1984. ''''. Oxford Univ. Press. | |||
| *], 1908. , 4th ed. (see ]) | |||
| Intermediate: | |||
| *Aiton, Eric J., 1985. ''Leibniz: A Biography''. Hilger (UK). | |||
| *Brown, Gregory, 2004, "Leibniz's Endgame and the Ladies of the Courts," ''Journal of the History of Ideas 65'': 75–100. | |||
| *Hall, A. R., 1980. ''Philosophers at War: The Quarrel between Newton and Leibniz''. Cambridge Univ. Press. | |||
| *Hostler, J., 1975. ''Leibniz's Moral Philosophy''. UK: Duckworth. | |||
| *Jolley, Nicholas, ed., 1995. ''The Cambridge Companion to Leibniz''. Cambridge Univ. Press. | |||
| *LeClerc, Ivor, ed., 1973. ''The Philosophy of Leibniz and the Modern World''. Vanderbilt Univ. Press. | |||
| *Loemker, Leroy, 1969a, "Introduction" to his ''Leibniz: Philosophical Papers and Letters''. Reidel: 1–62. | |||
| *Luchte, James, 2006, 'Mathesis and Analysis: Finitude and the Infinite in the ''Monadology'' of Leibniz,' London: Heythrop Journal. | |||
| *], 1957 (1936). "Plenitude and Sufficient Reason in Leibniz and Spinoza" in his ''The Great Chain of Being''. Harvard Uni. Press: 144–82. Reprinted in Frankfurt, H. G., ed., 1972. ''Leibniz: A Collection of Critical Essays''. Anchor Books. | |||
| *MacDonald Ross, George, 1999, "Leibniz and Sophie-Charlotte" in Herz, S., Vogtherr, C.M., Windt, F., eds., ''Sophie Charlotte und ihr Schloß''. München: Prestel: 95–105. | |||
| *Perkins, Franklin, 2004. ''Leibniz and China: A Commerce of Light''. Cambridge Univ. Press. | |||
| *Riley, Patrick, 1996. ''Leibniz's Universal Jurisprudence: Justice as the Charity of the Wise''. Harvard Univ. Press. | |||
| *Strickland, Lloyd, 2006. ''Leibniz Reinterpreted''. Continuum: London and New York | |||
| Advanced | |||
| *Adams, Robert M., 1994. ''Leibniz: Determinist, Theist, Idealist''. Oxford Uni. Press. | |||
| *Bueno, Gustavo, 1981. ''''. Oviedo: Pentalfa. | |||
| *], 1901. ''La Logique de Leibniz''. Paris: Felix Alcan. | |||
| *Ishiguro, Hide, 1990 (1972). ''Leibniz's Philosophy of Logic and Language''. Cambridge Univ. Press. | |||
| *Lenzen, Wolfgang, 2004. in Gabbay, D., and Woods, J., eds., ''Handbook of the History of Logic, Vol. 3''. North Holland: 1–84. | |||
| *Mates, Benson, 1986. ''The Philosophy of Leibniz: Metaphysics and Language''. Oxford Univ. Press. | |||
| *Mercer, Christia, 2001. ''Leibniz's metaphysics: Its Origins and Development''. Cambridge Univ. Press. | |||
| *Robinet, André, 2000. ''Architectonique disjonctive, automates systémiques et idéalité transcendantale dans l'oeuvre de G.W. Leibniz: Nombreux textes inédits''. | |||
| *Rutherford, Donald, 1998. ''Leibniz and the Rational Order of Nature''. Cambridge Univ. Press. | |||
| *Wilson, Catherine, 1989. ''Leibniz's Metaphysics''. Princeton Univ. Press. | |||
| *Woolhouse, R. S., ed., 1993. ''G. W. Leibniz: Critical Assessments'', 4 vols. Routledge. A remarkable one-stop collection of many valuable articles. | |||
| by Gregory Brown. | |||
| == Other works cited == | |||
| *] and ], 1986. '']''. Oxford Univ. Press. | |||
| *], 2000. ''The Universal Computer: The Road from Leibniz to ]''. W W Norton. | |||
| *Du Bois-Reymond, Paul, 18nn, "Leibnizian Thoughts in Modern Science," ???.<!--details, please--> | |||
| *], 1997. ''The Norton History of the Mathematical Sciences''. W W Norton. | |||
| *Hirano, Hideaki, 1997, "Cultural Pluralism And Natural Law." Unpublished. | |||
| *Reinhard Finster, Gerd van den Heuvel: Gottfried Wilhelm Leibniz. Mit Selbstzeugnissen und Bilddokumenten. 4. Auflage. Rowohlt, Reinbek bei Hamburg 2000 (Rowohlts Monographien, 50481), ISBN 3-499-50481-2 | |||
| *], 1977. ''The Fractal Geometry of Nature''. Freeman. | |||
| *], 2003. ''Life's Solution: Inevitable Humans in a Lonely Universe''. Cambridge Uni. Press. | |||
| *Ward, P. D., and Brownlee, D., 2000. '']''. Springer Verlag. | |||
| *Zalta, E. N., 2000, "," ''Philosophiegeschichte und logische Analyse / Logical Analysis and History of Philosophy 3'': 137–183. | |||
| == Quotations == <!--Please move the following to Wikiquote, if not already there--> | |||
| {{Wikiquote}} | |||
| Wiener (1951: 567–70) lists 44 quotable "proverbs" beginning with "Justice is the charity of the wise." | |||
| *"In the realm of spirit, seek clarity; in the material world, seek utility." Mates's (1986: 15) translation of Leibniz's motto. | |||
| *"God is the final reason of salvation, of grace, of faith and of election in Jesus Christ." (Theodicy: Essays on the Justice of God and the Freedom of Man in the Origin of Evil, Part I, 126) | |||
| *"With every lost hour, a part of life perishes." "Deeds make people." Loemker's (1969: 58) translation of other Leibniz mottoes. | |||
| *"The ''monad''... is nothing but a simple substance which enters into compounds. ''Simple'' means without parts... Monads have no windows through which anything could enter or leave." ''Monadology'' (LL §67.1,7) | |||
| *"I maintain that men could be incomparably happier than they are, and that they could, in a short time, make great progress in increasing their happiness, if they were willing to set about it as they should. We have in hand excellent means to do in 10 years more than could be done in several centuries without them, if we apply ourselves to making the most of them, and do nothing else except what must be done." (Translated in Riley 1972: 104, and quoted in Mates 1986: 120) | |||
| *"It is unworthy of excellent men to lose hours like slaves in the labour of calculation which could safely be relegated to anyone else if machines were used." | |||
| *"Truths of reason are necessary and their opposite is impossible: truths of fact are contingent and their opposite possible." | |||
| *"It is one of my most important and very best verified maxims that nature makes no leaps. This I have called the law of continuity." | |||
| *"Why is there something, rather than nothing?" | |||
| *"There are two kinds of truths: truths of reasoning and truths of fact." | |||
| *"The soul is the mirror of an indestructible universe." | |||
| == See also == | |||
| <div class="references-small" style="-moz-column-count:4; column-count:4;"> | |||
| *] | |||
| *] | |||
| *] | |||
| *] | |||
| *] | |||
| *] | |||
| *] | |||
| *] | |||
| *] | |||
| *] for differentiation under the integral sign | |||
| *] | |||
| *] | |||
| * ] | |||
| *] | |||
| *] | |||
| * ] a biscuit named for Leibniz | |||
| * ] | |||
| </div> | |||
| == External links == | |||
| {{Commons|Gottfried Wilhelm Leibniz}} | |||
| {{wikisource author|Gottfried Leibniz}} | |||
| * Full text of John M. Mackie's 1845 biography of Leibniz from Google Books. | |||
| * {{gutenberg author| id=Leibniz+Gottfried+Wilhelm+Freiherr+von | name=Gottfried Leibniz}} | |||
| * in easier-to-read versions. | |||
| * — Gregory Brown. | |||
| * Scroll down for many Leibniz links. | |||
| * — Original Leibniz translations of many works including many never before translated into English | |||
| * : useful links | |||
| * ]: "" — Douglas Burnham. | |||
| * ]. Leibniz on: | |||
| ** — Andrew Youpa. | |||
| ** — Marc Bobro. | |||
| ** — Michael Murray. | |||
| ** — Kulstad and Carlin. | |||
| *], 11th ed.: "" | |||
| * | |||
| * for the ''Leibniz Review'', 1998–. | |||
| * | |||
| * {{MacTutor Biography|id=Leibniz}} | |||
| * Books and Writers: | |||
| *Sundry , often mentioning Leibniz, prompted by: | |||
| **Schirrmacher, Frank, "" ''Frankfurter Allgemeine'', 10.07.00. | |||
| * Harry Maugan's blog: compared to Voltaire via ''Candide''. | |||
| * : text with concordances and frequency list | |||
| * : Lecture series by French philosopher Gilles Deleuze on Leibniz from 1980 in English and other languages. | |||
| <!-- Metadata: see ] --> | |||
| {{Enlightenment}} | |||
| {{BD|1646|1716|Leibniz, Gottfried}} | |||
| {{Refimprove|date=March 2008}} | |||
| {{Original research|date=March 2008}} | |||
| {{Persondata | |||
| |NAME=Leibniz, Gottfried Wilhelm | |||
| |ALTERNATIVE NAMES=Leibnitz, Gottfried Wilhelm; Leibniz, Gottfried Wilhelm von; von Leibniz, Gottfried Wilhelm | |||
| |SHORT DESCRIPTION=German philoospher | |||
| |DATE OF BIRTH={{birth date|1646|7|1|mf=y}} | |||
| |PLACE OF BIRTH=], ] | |||
| |DATE OF DEATH={{death date|1716|11|14|mf=y}} | |||
| |PLACE OF DEATH=], ] | |||
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Revision as of 21:48, 22 May 2008
The neutrality of this article is greatly disputed, clearly written by someone who believes Leibniz is RIGHT, and calls any critic a "lay person."