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Leibniz is one of the most prominent figures in both the history of philosophy and the history of mathematics.

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Leibniz is one of the most prominent figures in both the history of philosophy and the history of mathematics.

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Leibniz wrote works on philosophy, theology, ethics, politics, law, history and philology.

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Leibniz made major contributions to physics and technology, and anticipated notions that surfaced much later in probability theory, biology, medicine, geology, psychology, linguistics and computer science.

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Leibniz wrote in several languages, primarily in Latin, French and German, but in English, Italian and Dutch.

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Leibniz was a pioneer in the field of mechanical calculators.

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Leibniz refined the binary number system, which is the foundation of nearly all digital computers, including the Von Neumann architecture, which is the standard design paradigm, or "computer architecture", followed from the second half of the 20th century, and into the 21st.

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In philosophy and theology, Leibniz is most noted for his optimism, i e his conclusion that our world is, in a qualified sense, the best possible world that God could have created, a view sometimes lampooned by other thinkers, such as Voltaire in his satirical novella Candide.

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The work of Leibniz anticipated modern logic and still influences contemporary analytic philosophy, such as its adopted use of the term "possible world" to define modal notions.

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Leibniz's father died when he was six years old, and from that point on, Leibniz was raised by his mother.

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Leibniz's father had been a Professor of Moral Philosophy at the University of Leipzig, and the boy later inherited his father's personal library.

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Leibniz then enrolled in the University of Altdorf and quickly submitted a thesis, which he had probably been working on earlier in Leipzig.

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Leibniz next declined the offer of an academic appointment at Altdorf, saying that "my thoughts were turned in an entirely different direction".

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Leibniz knew fairly little about the subject at that time but presented himself as deeply learned.

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Leibniz soon met Johann Christian von Boyneburg, the dismissed chief minister of the Elector of Mainz, Johann Philipp von Schonborn.

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Leibniz then dedicated an essay on law to the Elector in the hope of obtaining employment.

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The stratagem worked; the Elector asked Leibniz to assist with the redrafting of the legal code for the Electorate.

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Leibniz published an essay, under the pseudonym of a fictitious Polish nobleman, arguing for the German candidate for the Polish crown.

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Leibniz proposed to protect German-speaking Europe by distracting Louis as follows.

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Leibniz met Nicolas Malebranche and Antoine Arnauld, the leading French philosophers of the day, and studied the writings of Descartes and Pascal, unpublished as well as published.

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Leibniz befriended a German mathematician, Ehrenfried Walther von Tschirnhaus; they corresponded for the rest of their lives.

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Leibniz met with the Royal Society where he demonstrated a calculating machine that he had designed and had been building since 1670.

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Leibniz had declined the invitation, but had begun corresponding with the duke in 1671.

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Leibniz spent several days in intense discussion with Spinoza, who had just completed his masterwork, the Ethics.

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Leibniz served three consecutive rulers of the House of Brunswick as historian, political adviser, and most consequentially, as librarian of the ducal library.

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Leibniz thenceforth employed his pen on all the various political, historical, and theological matters involving the House of Brunswick; the resulting documents form a valuable part of the historical record for the period.

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Leibniz began promoting a project to use windmills to improve the mining operations in the Harz Mountains.

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Leibniz played a role in the initiatives and negotiations leading up to that Act, but not always an effective one.

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Brunswicks tolerated the enormous effort Leibniz devoted 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.

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Leibniz began working on calculus in 1674; the earliest evidence of its use in his surviving notebooks is 1675.

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Leibniz never finished the project, in part because of his huge output on many other fronts, but 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 genealogy with commentary, to be completed in three years or less.

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Leibniz was eulogized by Fontenelle, before the French Academy of Sciences in Paris, which had admitted him as a foreign member in 1700.

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Leibniz 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.

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On several occasions, Leibniz backdated and altered personal manuscripts, actions which put him in a bad light during the calculus controversy.

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Leibniz was charming, well-mannered, and not without humor and imagination.

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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.

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Leibniz wrote only two book-length philosophical treatises, of which only the Theodicee of 1710 was published in his lifetime.

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Leibniz dated his beginning as a philosopher to his Discourse on Metaphysics, which he composed in 1686 as a commentary on a running dispute between Nicolas Malebranche and Antoine Arnauld.

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In 1695, Leibniz made his public entree into European philosophy with a journal article titled "New System of the Nature and Communication of Substances".

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Leibniz met Spinoza in 1676, read some of his unpublished writings, and has since been suspected of appropriating some of Spinoza's ideas.

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Leibniz was influenced by his Leipzig professor Jakob Thomasius, who supervised his BA thesis in philosophy.

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Leibniz was deeply interested in the new methods and conclusions of Descartes, Huygens, Newton, and Boyle, but viewed their work through a lens heavily tinted by scholastic notions.

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Leibniz variously invoked one or another of seven fundamental philosophical Principles:.

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Leibniz's best known contribution to metaphysics is his theory of monads, as exposited in Monadologie.

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Leibniz proposes his theory that the universe is made of an infinite number of simple substances known as monads.

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Leibniz uses a geometry book as an example to explain his reasoning.

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Leibniz asserted that the truths of theology and philosophy cannot contradict each other, since reason and faith are both "gifts of God" so that their conflict would imply God contending against himself.

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Leibniz describes this perfection later in section VI as the simplest form of something with the most substantial outcome .

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Leibniz then asserts that different principles and geometry cannot simply be from the will of God, but must follow from his understanding.

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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:.

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Leibniz wrote memoranda that can now be read as groping attempts to get symbolic logic—and thus his calculus—off the ground.

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Leibniz attached so much importance to the development of good notations that he attributed all his discoveries in mathematics to this.

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Leibniz's notation for calculus is an example of his skill in this regard.

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Leibniz saw that the uniqueness of prime factorization suggests a central role for prime numbers in the universal characteristic, a striking anticipation of Godel numbering.

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Leibniz was a mathematical novice when he first wrote about the characteristic, at first he did not conceive it as an algebra but rather as a universal language or script.

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Leibniz has been noted as one of the most important logicians between the times of Aristotle and Gottlob Frege.

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Leibniz enunciated the principal properties of what we now call conjunction, disjunction, negation, identity, set inclusion, and the empty set.

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Leibniz published nothing on formal logic in his lifetime; most of what he wrote on the subject consists of working drafts.

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Leibniz regarded such relations as qualities of things : For him, "Mary is the mother of John" describes separate qualities of Mary and of John.

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Notably, Leibniz declared space and time to be inherently relational.

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Leibniz believed that the sum of an infinite number of zeros would be equal to one half using the analogy of the creation of the world from nothing.

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Leibniz was one of the pioneers in actuarial science, calculating the purchase price of life annuities and the liquidation of a state's debt.

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Leibniz arranged the coefficients of a system of linear equations into an array, now called a matrix, in order to find a solution to the system if it existed.

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Leibniz laid down the foundations and theory of determinants, although the Japanese mathematician Seki Takakazu discovered determinants independently of Leibniz.

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Leibniz solved systems of linear equations using determinants, which is called Cramer's rule.

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Leibniz wrote that circles "can most simply be expressed by this series, that is, the aggregate of fractions alternately added and subtracted".

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Leibniz attempted to create a definition for a straight line while attempting to prove the parallel postulate.

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Leibniz is credited, along with Sir Isaac Newton, with the discovery of calculus .

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Leibniz did not publish anything about his calculus until 1684.

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Leibniz expressed the inverse relation of integration and differentiation, later called the fundamental theorem of calculus, by means of a figure in his 1693 paper Supplementum geometriae dimensoriae.

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Leibniz exploited infinitesimals in developing calculus, manipulating them in ways suggesting that they had paradoxical algebraic properties.

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From 1711 until his death, Leibniz was engaged in a dispute with John Keill, Newton and others, over whether Leibniz had invented calculus independently of Newton.

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Leibniz was the first to use the term analysis situs, later used in the 19th century to refer to what is known as topology.

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My Leibniz mania is further reinforced by finding that for one moment its hero attached importance to geometric scaling.

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We 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.

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Leibniz's writings are currently discussed, not only for their anticipations and possible discoveries not yet recognized, but as ways of advancing present knowledge.

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Leibniz contributed a fair amount to the statics and dynamics emerging around him, often disagreeing with Descartes and Newton.

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Leibniz devised a new theory of motion based on kinetic energy and potential energy, which posited space as relative, whereas Newton was thoroughly convinced that space was absolute.

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Leibniz held a relationist notion of space and time, against Newton's substantivalist views.

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One of Leibniz's projects was to recast Newton's theory as a vortex theory.

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Leibniz realized that the total energy would be conserved in certain mechanical systems, so he considered it an innate motive characteristic of matter.

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Leibniz appears to be an "underappreciated pioneer of psychology" Leibniz wrote on topics which are now regarded as fields of psychology: attention and consciousness, memory, learning, motivation, emergent individuality, the general dynamics of development .

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Leibniz found his most important interpreter in Wilhelm Wundt, founder of psychology as a discipline.

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Leibniz thought that there are many petites perceptions, or small perceptions of which we perceive but of which we are unaware.

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Leibniz believed that by the principle that phenomena found in nature were continuous by default, it was likely that the transition between conscious and unconscious states had intermediary steps.

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Leibniz's theory regarding consciousness in relation to the principle of continuity can be seen as an early theory regarding the stages of sleep.

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Leibniz was a direct influence on Ernst Platner, who is credited with originally coining the term Unbewußtseyn .

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Leibniz's ideas regarding music and tonal perception went on to influence the laboratory studies of Wilhelm Wundt.

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Leibniz worked to set up a coherent medical training program, oriented towards public health and preventive measures.

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Leibniz even proposed something akin to what much later emerged as game theory.

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In 1906, Garland published a volume of Leibniz's writings bearing on his many practical inventions and engineering work.

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Nevertheless, it is well understood that Leibniz was a serious inventor, engineer, and applied scientist, with great respect for practical life.

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Leibniz designed wind-driven propellers and water pumps, mining machines to extract ore, hydraulic presses, lamps, submarines, clocks, etc.

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Leibniz interpreted a diagram which showed yin and yang and corresponded it to a zero and one.

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Regardless, Leibniz simplified the binary system and articulated logical properties such as conjunction, disjunction, negation, identity, inclusion, and the empty set.

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In 1961, Norbert Wiener suggested that Leibniz should be considered the patron saint of cybernetics.

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In 1671, Leibniz began to invent a machine that could execute all four arithmetic operations, gradually improving it over a number of years.

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Couturat reported finding an unpublished note by Leibniz, dated 1674, describing a machine capable of performing some algebraic operations.

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Leibniz devised a cipher machine, recovered by Nicholas Rescher in 2010.

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In 1693, Leibniz described a design of a machine which could, in theory, integrate differential equations, which he called "integraph".

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Leibniz was groping towards hardware and software concepts worked out much later by Charles Babbage and Ada Lovelace.

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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.

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Leibniz's predecessor, Tobias Fleischer, had already created a cataloging system for the Duke's library but it was a clumsy attempt.

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At this library, Leibniz focused more on advancing the library than on the cataloging.

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Leibniz was one of the first to consider developing a core collection for a library and felt "that a library for display and ostentation is a luxury and indeed superfluous, but a well-stocked and organized library is important and useful for all areas of human endeavor and is to be regarded on the same level as schools and churches".

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Unfortunately, Leibniz lacked the funds to develop the library in this manner.

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Leibniz was not allowed to make complete changes to the existing closed catalog, but was allowed to improve upon it so he started on that task immediately.

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Leibniz created an alphabetical author catalog and had created other cataloging methods that were not implemented.

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Seemingly, Leibniz paid a good deal of attention to the classification of subject matter, favoring a well-balance library covering a host of numerous subjects and interests.

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Leibniz designed a book indexing system in ignorance of the only other such system then extant, that of the Bodleian Library at Oxford University.

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Leibniz called on publishers to distribute abstracts of all new titles they produced each year, in a standard form that would facilitate indexing.

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Leibniz hoped that this abstracting project would eventually include everything printed from his day back to Gutenberg.

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Leibniz called for the creation of an empirical database as a way to further all sciences.

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Leibniz drew up its first statutes, and served as its first President for the remainder of his life.

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In 1677, Leibniz 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; this is sometimes considered an anticipation of the European Union.

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Leibniz trained as a legal academic, but under the tutelage of Cartesian-sympathiser Erhard Weigel we already see an attempt to solve legal problems by rationalist mathematical methods .

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On reaching Frankfurt am Main Leibniz penned The New Method of Teaching and Learning the Law, by way of application.

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Leibniz's argument that the function of legal teaching was not to impress rules as one might train a dog, but to aid the student in discovering their own public reason, evidently impressed von Schonborn as he secured the job.

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Leibniz devoted considerable intellectual and diplomatic effort to what would now be called an ecumenical endeavor, seeking to reconcile the Roman Catholic and Lutheran churches.

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Leibniz evidently thought that the thoroughgoing application of reason would suffice to heal the breach caused by the Reformation.

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Leibniz refuted the argument, advanced by Swedish scholars in his day, that a form of proto-Swedish was the ancestor of the Germanic languages.

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Leibniz was perhaps the first major European intellectual to take a close interest in Chinese civilization, which he knew by corresponding with, and reading other works by, European Christian missionaries posted in China.

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Leibniz apparently read Confucius Sinarum Philosophus in the first year of its publication.

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Leibniz came to the conclusion that Europeans could learn much from the Confucian ethical tradition.

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Leibniz mulled over the possibility that the Chinese characters were an unwitting form of his universal characteristic.

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Leibniz noted how the I Ching hexagrams correspond to the binary numbers from 000000 to 111111, and concluded that this mapping was evidence of major Chinese accomplishments in the sort of philosophical mathematics he admired.

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Leibniz communicated his ideas of the binary system representing Christianity to the Emperor of China, hoping it would convert him.

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Leibniz was the only major Western philosopher of the time who attempted to accommodate Confucian ideas to prevailing European beliefs.

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Leibniz visited mines, talked with mine engineers, and tried to negotiate export contracts for lead from the ducal mines in the Harz mountains.

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Leibniz was remembered for only one book, the Theodicee, whose supposed central argument Voltaire lampooned in his popular book Candide, which concludes with the character Candide saying, "Non liquet", a term that was applied during the Roman Republic to a legal verdict of "not proven".

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Voltaire's depiction of Leibniz's ideas was so influential that many believed it to be an accurate description.

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Leibniz had an ardent disciple, Christian Wolff, whose dogmatic and facile outlook did Leibniz's reputation much harm.

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Leibniz influenced David Hume, who read his Theodicee and used some of his ideas.

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Much of Europe came to doubt that Leibniz had discovered calculus independently of Newton, and hence his whole work in mathematics and physics was neglected.

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In 1768, Louis 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.

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Shortly thereafter, Louis Couturat published an important study of Leibniz, and edited a volume of Leibniz's heretofore unpublished writings, mainly on logic.

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Leibniz was lampooned as Professor Pangloss, described as "the greatest philosopher of the Holy Roman Empire".

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Leibniz appears as one of the main historical figures in Neal Stephenson's series of novels The Baroque Cycle.

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Leibniz mainly wrote in three languages: scholastic Latin, French and German.

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The amount, variety, and disorder of Leibniz's writings are a predictable result of a situation he described in a letter as follows:.

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