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Encyclopedia > Gottfried Leibniz
Western Philosophy
18th-century philosophy
Gottfried Wilhelm Leibniz
Name
Gottfried Wilhelm Leibniz
Birth July 1 (June 21 Old Style) 1646, Leipzig, Electorate of Saxony
Death November 14, 1716, Hanover, Electorate of Hanover
School/tradition Rationalism
Main interests Metaphysics, Mathematics, Theodicy
Notable ideas Infinitesimal calculus, Calculus, Monadology, Theodicy, Optimism
Influenced by Plato, Aristotle, Aquinas, Suárez, Descartes, Spinoza, Ramon Llull
Influenced Many later mathematicians, Christian Wolff, Kant, Bertrand Russell, Martin Heidegger
Signature

Gottfried Wilhelm Leibniz (also Leibnitz or von Leibniz[1] (July 1 (June 21 Old Style) 1646November 14, 1716) was a German[2] polymath who wrote primarily in Latin and French. Gottfried Leibniz (July 1, 1646 – November 14, 1716) was a German polymath. ... Western philosophy is a modern claim that there is a line of related philosophical thinking, beginning in ancient Greece (Greek philosophy) and the ancient Near East (the Abrahamic religions), that continues to this day. ... (Redirected from 18th century philosophy) 17th-century Western philosophy is conventionally seen as being dominated by the coming of symbolic mathematics and rationalism to philosophy, many of the most noted philosophers were also mathematicians. ... Image File history File links Gottfried_Wilhelm_von_Leibniz. ... is the 182nd day of the year (183rd in leap years) in the Gregorian calendar. ... is the 172nd day of the year (173rd in leap years) in the Gregorian calendar. ... Old Style redirects here. ... 1646 (MDCXLVI) was a common year starting on Monday (see link for calendar) of the Gregorian calendar (or a common year starting on Thursday of the 10-day slower Julian calendar). ... Leipzig ( ; Sorbian/Lusatian: Lipsk from the Sorbian word for Tilia) is, with a population of over 506,000, the largest city in the federal state of Saxony, Germany. ... The examples and perspective in this article or section may not represent a worldwide view. ... is the 318th day of the year (319th in leap years) in the Gregorian calendar. ... // Events August 5 - In the Battle of Peterwardein 40. ... , Hanover(i) (German: , IPA: ), on the river Leine, is the capital of the federal state of Lower Saxony (Niedersachsen), Germany. ... Capital Hanover Head of State King of Hanover Hanover (German: Hannover) is a historical territory in todays Germany. ... In epistemology and in its broadest sense, rationalism is any view appealing to reason as a source of knowledge or justification (Lacey 286). ... Plato (Left) and Aristotle (right), by Raphael (Stanza della Segnatura, Rome) Metaphysics is the branch of philosophy concerned with explaining the ultimate nature of reality, being, and the world. ... For other meanings of mathematics or uses of math and maths, see Mathematics (disambiguation) and Math (disambiguation). ... Theodicy (IPA: ) (adjectival form theodicean) is a specific branch of theology and philosophy that attempts to reconcile the existence of evil or suffering in the world with the belief in an omniscient, omnipotent, and benevolent God, i. ... Infinitesimal calculus is an area of mathematics pioneered by Gottfried Leibniz based on the concept of infinitesimals, as opposed to the calculus of Isaac Newton, which is based upon the concept of the limit. ... For other uses, see Calculus (disambiguation). ... The Monadology (Monadologie, 1714) is one of Gottfried Leibniz’s works that best define his philosophy, monadism. ... Theodicy (IPA: ) (adjectival form theodicean) is a specific branch of theology and philosophy that attempts to reconcile the existence of evil or suffering in the world with the belief in an omniscient, omnipotent, and benevolent God, i. ... “Positive Attitude” redirects here. ... For other uses, see Plato (disambiguation). ... For other uses, see Aristotle (disambiguation). ... Aquinas redirects here. ... Francisco Suárez (1548–1617) was a Spanish philosopher and theologian, generally regarded as having been the greatest scholastic after Thomas Aquinas. ... René Descartes René Descartes (IPA: , March 31, 1596 – February 11, 1650), also known as Cartesius, worked as a philosopher and mathematician. ... Baruch de Spinoza (‎, Portuguese: , Latin: ) (November 24, 1632 – February 21, 1677) was a Dutch philosopher of Portuguese Jewish origin. ... Ramon Llull. ... Christian Wolff (less correctly Wolf; also known as Wolfius) (January 24, 1679 - April 9, 1754) was a German philosopher. ... Immanuel Kant Immanuel Kant (April 22, 1724 – February 12, 1804) was a Prussian philosopher, generally regarded as one of Europes most influential thinkers and the last major philosopher of the Enlightenment. ... Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS, (18 May 1872 – 2 February 1970), was a British philosopher, logician, mathematician, advocate for social reform, and pacifist. ... Martin Heidegger (September 26, 1889 – May 26, 1976) (IPA ) was a highly influential German philosopher. ... Image File history File links No higher resolution available. ... is the 182nd day of the year (183rd in leap years) in the Gregorian calendar. ... is the 172nd day of the year (173rd in leap years) in the Gregorian calendar. ... Old Style redirects here. ... 1646 (MDCXLVI) was a common year starting on Monday (see link for calendar) of the Gregorian calendar (or a common year starting on Thursday of the 10-day slower Julian calendar). ... is the 318th day of the year (319th in leap years) in the Gregorian calendar. ... // Events August 5 - In the Battle of Peterwardein 40. ... Leonardo da Vinci, a polymath, is seen as the epitome of the related term, Renaissance Man A polymath (Greek polymathÄ“s, πολυμαθής, having learned much)[1][2] is a person with encyclopedic, broad, or varied knowledge or learning. ... For other uses, see Latins and Latin (disambiguation). ...


He occupies an equally grand place in both the history of philosophy and the history of mathematics. He invented calculus independently of Newton, and his notation is the one in general use since. He also discovered the binary system, foundation of virtually all modern computer architectures. In philosophy, he is most remembered for optimism, i.e. his conclusion that our universe is, in a restricted sense, the best possible one God could have made. He was, along with René Descartes and Baruch Spinoza, one of the three great 17th century rationalists, but his philosophy also looks back to the Scholastic tradition and anticipates modern logic and analysis. Leibniz also made major contributions to physics and technology, and anticipated notions that surfaced much later in biology, medicine, geology, probability theory, psychology, linguistics, and information science. He also wrote on politics, law, ethics, theology, history, and philology, 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. The history of philosophy is the study of philosophical ideas and concepts through time. ... For a timeline of events in mathematics, see timeline of mathematics. ... For other uses, see Calculus (disambiguation). ... Sir Isaac Newton FRS (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ... In calculus, Leibnizs notation, named in honor of the 17th century German philosopher and mathematician Gottfried Wilhelm Leibniz, was originally the use of expressions such as dx and dy and to represent infinitely small (or infinitesimal) increments of quantities x and y, just as Δx and Δy represent finite... The binary numeral system, or base-2 number system, is a numeral system that represents numeric values using two symbols, usually 0 and 1. ... “Positive Attitude” redirects here. ... This article is about the term God in the context of monotheism and henotheism. ... Descartes redirects here. ... Baruch de Spinoza (‎, Portuguese: , Latin: ) (November 24, 1632 – February 21, 1677) was a Dutch philosopher of Portuguese Jewish origin. ... In epistemology and in its broadest sense, rationalism is any view appealing to reason as a source of knowledge or justification (Lacey 286). ... Scholastic redirects here. ... Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration. ... Analytic philosophy (sometimes, analytical philosophy) is a generic term for a style of philosophy that came to dominate English-speaking countries in the 20th century. ... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... By the mid 20th century humans had achieved a mastery of technology sufficient to leave the surface of the Earth for the first time and explore space. ... For the song by Girls Aloud see Biology (song) Biology studies the variety of life (clockwise from top-left) E. coli, tree fern, gazelle, Goliath beetle Biology (from Greek: Βιολογία - βίος, bio, life; and λόγος, logos, speech lit. ... For the chemical substances known as medicines, see medication. ... This article includes a list of works cited but its sources remain unclear because it lacks in-text citations. ... Probability theory is the branch of mathematics concerned with analysis of random phenomena. ... {redirect|Psychological science|the journal|Psychological Science (journal)}} Not to be confused with Phycology. ... For the journal, see Linguistics (journal). ... Not to be confused with informatics or information theory. ... For other uses, see Politics (disambiguation). ... For other uses, see Law (disambiguation). ... For other uses, see Ethics (disambiguation). ... Theology finds its scholars pursuing the understanding of and providing reasoned discourse of religion, spirituality and God or the gods. ... HIStory – Past, Present and Future, Book I is a double album by American singer Michael Jackson released in June 1995 and remains Jacksons most conflicting and controversial release. ... Philology, etymologically, is the love of words. It is most accurately defined as an affinity toward the learning of the backgrounds as well as the current usages of spoken or written methods of human communication. The commonality of studied languages is more important than their origin or age (that is...

Contents

Biography

The outline of Leibniz's career is as follows: Image File history File links Question_book-3. ...

  • 1646-1666: Formative years
  • 1666–74: Mainly in service to the Elector of Mainz, Johann Philipp von Schönborn, and his minister, Baron von Boineburg.
    • 1672–76. Resides in Paris, making two important sojourns to London.
  • 1676–1716. In service to the House of Hanover.
    • 1677–98. Courtier, first to John Frederick, Duke of Brunswick-Lüneburg, then to his brother, Duke, then Elector, Ernst August of Hanover.
      • 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 Georg Ludwig of Hanover.
    • 1714–16: Georg Ludwig, upon becoming George I of Great Britain, forbids Leibniz to follow him to London. Leibniz ends his days in relative neglect.

The prince-electors or electoral princes of the Holy Roman Empire — German: Kurfürst (singular) Kurfürsten (plural) — were the members of the electoral college of the Holy Roman Empire, having the function of electing the Emperors of Germany. ... Mainz is a city in Germany and the capital of the German federal state of Rhineland-Palatinate. ... Schönborn is the name of a German noble family, many members of which were prelates of the Church. ... The House of Hanover (the Hanoverians) is a German royal dynasty which has ruled the Duchy of Braunschweig-Lüneburg, the Kingdom of Hanover and the Kingdom of Great Britain and Ireland. ... John Frederick (German: Johann Friedrich; 25 April 1625, Herzberg am Harz – 18 December 1679, Augsburg) was duke of Brunswick-Lüneburg and ruled over the Calenberg subdivision of the duchy from 1665 until his death. ... Ernest Augustus (German: Ernst August; 20 November 1629, Herzberg – 23 January 1698, Herrenhausen) was duke of Brunswick-Lüneburg and ruled over the Calenberg (or Hanover) subdivision of the duchy. ... George I (George Louis; 28 May 1660 – 11 June 1727)[1] was King of Great Britain and Ireland, from 1 August 1714 until his death. ... For other uses, see Vienna (disambiguation). ... Holy Roman Emperor Charles VI Charles VI, (German Karl VI; in full Karl Josef Franz)Holy Roman Emperor (October 1, 1685 – October 20, 1740) was Holy Roman Emperor from 1711 to 1740 and the second son of Leopold I with his third wife, Eleonore-Magdalena of Pfalz-Neuburg. ... Flag of the Habsburg Monarchy; also used as the flag of the Austrian Empire until the Ausgleich of 1867. ... For other uses, see Vienna (disambiguation). ... George I (George Louis; 28 May 1660 – 11 June 1727)[1] was King of Great Britain and Ireland, from 1 August 1714 until his death. ...

Early life

Gottfried Leibniz was born on 1 July 1646 in Leipzig to Friedrich Leibniz and Catherina Schmuck. The name Leibniz was originally Slavonic - Lubeniecz [1]. 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 [Baron] G. W. von Leibniz." However, no document has been found confirming that he was ever granted a patent of nobility.[3] is the 182nd day of the year (183rd in leap years) in the Gregorian calendar. ... 1646 (MDCXLVI) was a common year starting on Monday (see link for calendar) of the Gregorian calendar (or a common year starting on Thursday of the 10-day slower Julian calendar). ... Leipzig ( ; Sorbian/Lusatian: Lipsk from the Sorbian word for Tilia) is, with a population of over 506,000, the largest city in the federal state of Saxony, Germany. ...


When Leibniz was six years old, his father, a Professor of Moral Philosophy at the University of Leipzig, died, leaving a personal library to which Leibniz was granted free access from age seven onwards. By 12, he had taught himself Latin, which he used freely all his life, and had begun studying Greek. The University of Leipzig (German Universität Leipzig), located in Leipzig in the Free State of Saxony (former Kingdom of Saxony), Germany, is one of the oldest universities in Europe. ... Latin was the language originally spoken in the region around Rome called Latium. ...


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 habilitation thesis in philosophy, On the Art of Combinations. When Leipzig declined to assure him a position teaching law upon graduation, Leibniz submitted the thesis he had intended to submit at Leipzig to the University of Altdorf 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. Habilitation is the highest academic qualification a person can achieve by his/her own pursuit in certain European countries. ... The Dissertatio de arte combinatoria was published by Gottfried Leibniz in 1666. ... Leipzig ( ; Sorbian/Lusatian: Lipsk from the Sorbian word for Tilia) is, with a population of over 506,000, the largest city in the federal state of Saxony, Germany. ... The University of Altdorf was a university in Altdorf bei Nürnberg, a small town outside Nuremberg. ...


1666–74

Leibniz's first position was as a salaried alchemist in Nuremberg, 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 Mainz, Johann Philipp von Schönborn. 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. Nürnberg redirects here. ... Mainz is a city in Germany and the capital of the German federal state of Rhineland-Palatinate. ... Schönborn is the name of a German noble family, many members of which were prelates of the Church. ...


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 diplomatic role. He published an essay, under the pseudonym of a fictitious Polish 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 Louis XIV of France, backed by French military and economic might. Meanwhile, the Thirty Years' War 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 Egypt as a stepping stone towards an eventual conquest of the Dutch East Indies. In return, France would agree to leave Germany and the Netherlands undisturbed. This plan obtained the Elector's cautious support. In 1672, the French government invited Leibniz to Paris 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. This page is about negotiations; for the board game, see Diplomacy (game). ... Louis XIV redirects here. ... Combatants Sweden  Bohemia Denmark-Norway[1] Dutch Republic France Scotland England Saxony  Holy Roman Empire Catholic League Austria Bavaria Spain Commanders Frederick V Buckingham Leven Gustav II Adolf â€  Johan Baner Cardinal Richelieu Louis II de Bourbon Vicomte de Turenne Christian IV of Denmark Bernhard of Saxe-Weimar Johann Georg I... This article does not cite any references or sources. ... This article is about the capital of France. ...


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 Malebranche and Antoine Arnauld, the leading French philosophers of the day, and studied the writings of Descartes and Pascal, unpublished as well as published. He befriended a German mathematician, Ehrenfried Walther von Tschirnhaus; they corresponded for the rest of their lives. Especially fateful was Leibniz's making the acquaintance of the Dutch physicist and mathematician Christiaan Huygens, 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 calculus. Nicolas Malebranche (August 6, 1638 – October 13, 1715) was a French philosopher of the Cartesian school. ... Antoine Arnauld, (1612 - August 8, 1694) — le grand as contemporaries called him, to distinguihs him from his father — was a French Roman Catholic theologian and writer. ... René Descartes René Descartes (IPA: , March 31, 1596 – February 11, 1650), also known as Cartesius, worked as a philosopher and mathematician. ... Blaise Pascal (pronounced ), (June 20 [[1624 // ]] – August 19, 1662) was a French mathematician, physicist, and religious philosopher. ... Ehrenfried Walther von Tschirnhaus (or Tschirnhausen) (April 10, 1651–October 11, 1708) was a German mathematician. ... Christiaan Huygens (pronounced in English (IPA): ; in Dutch: ) (April 14, 1629 – July 8, 1698), was a Dutch mathematician, astronomer and physicist; born in The Hague as the son of Constantijn Huygens. ... For other uses, see Calculus (disambiguation). ...


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 London, early in 1673. There Leibniz made the acquaintance of Henry Oldenburg and John Collins. After demonstrating to the Royal Society 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. This article is about the capital of England and the United Kingdom. ... Categories: Royal Society | Stub ... John Collins (25 March 1625– 10 November 1683) was an English mathematician. ... For other uses, see Royal Society (disambiguation). ...


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 Brunswick to visit Hanover proved fateful. Leibniz declined the invitation, but began corresponding with the Duke in 1671. In 1673, the Duke 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 Habsburg imperial court was forthcoming. Brunswick-Lüneburg was an historical state within the Holy Roman Empire. ... John Frederick (German: Johann Friedrich; 25 April 1625, Herzberg am Harz – 18 December 1679, Augsburg) was duke of Brunswick-Lüneburg and ruled over the Calenberg subdivision of the duchy from 1665 until his death. ... Flag of the Habsburg Monarchy; also used as the flag of the Austrian Empire until the Ausgleich of 1867. ...


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 The Hague where he met Leeuwenhoek, the discoverer of microorganisms. He also spent several days in intense discussion with Spinoza, who had just completed his masterwork, the Ethics. Leibniz respected Spinoza's powerful intellect, but was dismayed by his conclusions that contradicted both Christian and Jewish orthodoxy. Hague redirects here. ... Anton von Leeuwenhoek Anton van Leeuwenhoek (October 24, 1632 - August 26, 1723) was a tradesman and scientist from Delft, in the Netherlands. ... Baruch Spinoza Benedictus de Spinoza (November 24, 1632 - February 21, 1677), named Baruch Spinoza by his synagogue elders and known as Bento de Spinoza or Bento dEspiñoza in the community in which he grew up. ... Ethics is a philosophical book written by Baruch Spinoza. ...


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 ducal library. He 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. This article is about the nobility title. ... Theology is literally rational discourse concerning God (Greek θεος, theos, God, + λογος, logos, rational discourse). By extension, it also refers to the study of other religious topics. ...

Leibniz

Among the few people in north Germany to warm to Leibniz were the Electress Sophia of Hanover (1630–1714), her daughter Sophia Charlotte of Hanover (1668–1705), the Queen of Prussia and her avowed disciple, and Caroline of Ansbach, the consort of her grandson, the future George II. 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 George I of Great Britain.[4] Image File history File links Leibniz_231. ... Image File history File links Leibniz_231. ... Electress Sophia of Hanover (born Sophia, Countess Palatine of Simmern; 14 October 1630 – 8 June 1714) was the youngest daughter of Frederick V, Elector Palatine, of the House of Wittelsbach, the Winter King of Bohemia, and Elizabeth Stuart. ... Sophia Charlotte of Hanover was born on October 30, 1668, at Schloss Iburg near Osnabrück. ... Caroline of Ansbach (later Queen Caroline; Wilhelmina Charlotte Caroline; 1 March 1683 – 20 November 1737) was the queen consort of George II. // Margravine Caroline of Brandenburg-Ansbach was born on 1 March 1683, at Ansbach in Germany, the daughter of Johann Friedrich, Margrave of Brandenburg-Ansbach and his second wife... George II (George Augustus; 10 November 1683 – 25 October 1760) was King of Great Britain and Ireland, Duke of Brunswick-Lüneburg (Hanover) and Archtreasurer and Prince-Elector of the Holy Roman Empire from 11 June 1727 until his death. ... George I (George Louis; 28 May 1660 – 11 June 1727)[1] was King of Great Britain and Ireland, from 1 August 1714 until his death. ...


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 Brunswick 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 Holy Roman Empire. The British Act of Settlement 1701 designated the Electress Sophia and her descent as the royal family of the United Kingdom, once both King William III and his sister-in-law and successor, Queen Anne, 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 British Parliament. Brunswick-Lüneburg was an historical state within the Holy Roman Empire. ... This article is about the medieval empire. ... Act of Settlement The Electress Sophia of Hanover The Act of Settlement (12 & 13 Wm 3 c. ... William III (14 November 1650 – 8 March 1702) was the Prince of Orange from his birth, Stadtholder of the main provinces of the Dutch Republic from 28 June 1672, King of England and King of Ireland from 13 February 1689, and King of Scots (under the name William II) from... Anne (6 February 1665 – 1 August 1714) became Queen of England, Scotland and Ireland on 8 March 1702, succeeding William III of England and II of Scotland. ... The Parliament of the United Kingdom of Great Britain and Northern Ireland is the supreme legislative institution in the United Kingdom and British overseas territories (it alone has parliamentary sovereignty). ...


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 Acta Eruditorum. 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. Acta Eruditorum (Latin: reports, acts of the scholars) was the first scientific journal of the German lands, published from 1682 to 1782. ...


The Elector Ernst August commissioned Leibniz to write a history of the House of Brunswick, going back to the time of Charlemagne 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 genealogy 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. Ernest Augustus (German: Ernst August; 20 November 1629, Herzberg – 23 January 1698, Herrenhausen) was duke of Brunswick-Lüneburg and ruled over the Calenberg (or Hanover) subdivision of the duchy. ... Brunswick-Lüneburg was an historical state within the Holy Roman Empire. ... For the American band, see Charlemagne (band). ... Genealogy (from Greek: γενεα, genea, family; and λόγος, logos, knowledge) is the study and tracing of family pedigrees. ...


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 calculus priority dispute 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. Isaac Newton began working on a form of the calculus in 1666. ...


In 1711, while traveling in northern Europe, the Russian Tsar Peter the Great 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 Vienna, where he was appointed Imperial Court Councillor to the Habsburgs. On the death of Queen Anne in 1714, Elector Georg Ludwig became King George I of Great Britain, under the terms of the 1701 Act of Settlement. 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, Caroline of Ansbach, 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 Sophia, died in 1714. Tsar (Bulgarian, Serbian and Macedonian цар, Russian  , in scientific transliteration respectively car and car ), occasionally spelled Czar or Tzar and sometimes Csar or Zar in English, is a Slavonic term designating certain monarchs. ... Peter the Great or Pyotr Alexeyevich Romanov (Russian: Пётр I Алексеевич Pyotr I Alekse`yevich, Пётр Великий Pyotr Veli`kiy) (9 June 1672 – 8 February 1725 [30 May 1672–28 January 1725 O.S.][1]) ruled Russia from 7 May (27 April O.S.) 1682 until his death, jointly ruling before 1696 with his... For other uses, see Vienna (disambiguation). ... Flag of the Habsburg Monarchy; also used as the flag of the Austrian Empire until the Ausgleich of 1867. ... George I (George Louis; 28 May 1660 – 11 June 1727)[1] was King of Great Britain and Ireland, from 1 August 1714 until his death. ... Act of Settlement The Electress Sophia of Hanover The Act of Settlement (12 & 13 Wm 3 c. ... Caroline of Ansbach (later Queen Caroline; Wilhelmina Charlotte Caroline; 1 March 1683 – 20 November 1737) was the queen consort of George II. // Margravine Caroline of Brandenburg-Ansbach was born on 1 March 1683, at Ansbach in Germany, the daughter of Johann Friedrich, Margrave of Brandenburg-Ansbach and his second wife... Electress Sophia of Hanover (born Sophia, Countess Palatine of Simmern; 14 October 1630 – 8 June 1714) was the youngest daughter of Frederick V, Elector Palatine, of the House of Wittelsbach, the Winter King of Bohemia, and Elizabeth Stuart. ...


Leibniz died in Hanover 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 Berlin Academy of Sciences, neither organization saw fit to honor his passing. His grave went unmarked for more than 50 years. Leibniz was eulogized by Fontenelle, 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 Duchess of Orleans, a niece of the Electress Sophia. , Hanover(i) (German: , IPA: ), on the river Leine, is the capital of the federal state of Lower Saxony (Niedersachsen), Germany. ... The Prussian Academy of Sciences (German: ) was an academy established in Berlin on July 11, 1700. ... For other uses of Fontenelle, see Fontenelle (disambiguation). ... Liselotte of the Palatinate Elizabeth Charlotte, Countess Palatine of Simmern (Heidelberg, May 27, 1652 – October 9 or December 8, 1722 at the Château de Saint-Cloud near Paris), known in French as la princesse palatine and in German as Liselotte von der Pfalz, was a princess of the electoral...


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%).[citation needed] During his lifetime, he published many pamphlets and scholarly articles, but only two "philosophical" books, the Combinatorial Art and the Théodicée. (He published numerous pamphlets, often anonymous, on behalf of the House of Brunswick-Lüneburg, most notably the "De jure suprematum" a major consideration of the nature of sovereignty.) One substantial book appeared posthumously, his Nouveaux essais sur l'entendement humain, which Leibniz had withheld from publication after the death of John Locke. Only in 1895, when Bodemann completed his catalogues of Leibniz's manuscripts and correspondence, did the enormous extent of Leibniz's Nachlass 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: Theodicy is a branch of theology that studies how the existence of a good or benevolent God is reconciled with the existence of evil. ... Brunswick-Lüneburg was an historical state within the Holy Roman Empire. ... “Sovereign” redirects here. ... Nouveaux essais sur lentendement humain (New Essays on Human Understanding) was a chapter-by-chapter rebuttal by Gottfried Leibniz of the John Locke book Essays on Human Understanding. ... For other persons named John Locke, see John Locke (disambiguation). ... A literary executor is a person with decision-making power in respect of the literary estate of an author who has died. ...

"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 [House of] 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 Vincent Placcius in Gerhardt)

The extant parts of the critical edition 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 Nouveaux essais sur l'entendement humain.
  • 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 Nachlass 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 Potsdam, Münster, Hannover and Berlin 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 concordance works (so, had that "speed" of work been possible from the beginning, the project would already be completed). Nouveaux essais sur lentendement humain (New Essays on Human Understanding) was a chapter-by-chapter rebuttal by Gottfried Leibniz of the John Locke book Essays on Human Understanding. ... A literary executor is a person with decision-making power in respect of the literary estate of an author who has died. ... Potsdam is the capital city of the federal state of Brandenburg in Germany. ... For other places with the same or similar names, and other uses of the word, see Munster (disambiguation) Münster is a city in North Rhine-Westphalia, Germany. ... Map of Germany showing Hanover Hanover (in German: Hannover [haˈnoːfɐ]), on the river Leine, is the capital of the state of Lower Saxony (Niedersachsen), Germany. ... This article is about the capital of Germany. ... Look up Concordance on Wiktionary, the free dictionary see Concordance system for usage in politics. ...


Posthumous reputation

When Leibniz died, his reputation was in decline. He was remembered for only one book, the Théodicée, whose supposed central argument Voltaire lampooned in his Candide. 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, Christian Wolff, 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. For other uses, see Voltaire (disambiguation). ... For the Bernstein operetta based on the book, see Candide (operetta). ... Christian Wolff (less correctly Wolf; also known as Wolfius) (January 24, 1679 - April 9, 1754) was a German philosopher. ...


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 Kant 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 Antoine Arnauld, Samuel Clarke, Sophia of Hanover, and her daughter Sophia Charlotte of Hanover, began. Immanuel Kant Immanuel Kant (April 22, 1724 – February 12, 1804) was a Prussian philosopher, generally regarded as one of Europes most influential thinkers and the last major philosopher of the Enlightenment. ... Antoine Arnauld, (1612 - August 8, 1694) — le grand as contemporaries called him, to distinguihs him from his father — was a French Roman Catholic theologian and writer. ... Samuel Clarke. ... Electress Sophia of Hanover (born Sophia, Countess Palatine of Simmern; 14 October 1630 – 8 June 1714) was the youngest daughter of Frederick V, Elector Palatine, of the House of Wittelsbach, the Winter King of Bohemia, and Elizabeth Stuart. ... Sophia Charlotte of Hanover was born on October 30, 1668, at Schloss Iburg near Osnabrück. ...


In 1900, Bertrand Russell published a critical study of Leibniz's metaphysics. Shortly thereafter, Louis Couturat published an important study 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 Bernhard Riemann). For example, Leibniz's phrase salva veritate, meaning interchangeability without loss of or compromising the truth, recurs in Willard Quine's writings. Nevertheless, the secondary English-language literature on Leibniz did not really blossom until after World War II. This is especially true of English speaking countries; in Gregory Brown's bibliography[5] 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 (Loemker) and his interpretive essays in (LeClerc). Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS, (18 May 1872 – 2 February 1970), was a British philosopher, logician, mathematician, advocate for social reform, and pacifist. ... Louis Couturat (January 17, 1868 - August 3, 1914) was a French logician, mathematician, philosopher, and linguist. ... Bernhard Riemann. ... This page is a candidate to be copied to Wiktionary using the Transwiki process. ... W. V. Quine Willard Van Orman Quine (June 25, 1908 - December 25, 2000) was one of the most influential American philosophers and logicians of the 20th century. ... Combatants Allied powers: China France Great Britain Soviet Union United States and others Axis powers: Germany Italy Japan and others Commanders Chiang Kai-shek Charles de Gaulle Winston Churchill Joseph Stalin Franklin Roosevelt Adolf Hitler Benito Mussolini Hideki Tōjō Casualties Military dead: 17,000,000 Civilian dead: 33,000...


Nicholas Jolley (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 ideas has revealed more clearly the 17th century "Intellectual Revolution" that preceded the better known Industrial and commercial revolutions of the 18th and 19th centuries.
  • The doctrinaire contempt for metaphysics, characteristic of analytic and linguistic philosophy, has faded;
  • Analytic and contemporary philosophy continue to invoke his notions of identity, individuation, and possible worlds;
  • The 17th and 18th century belief that natural science, especially physics, differs from philosophy mainly in degree and not in kind, is no longer dismissed out of hand. That modern science includes a "scholastic" as well as a "radical empiricist" 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 Plato and Aristotle: the universe and man's place in it are amenable to human reason.

The University of Hannover (German spelling) is named after him. The history of ideas is a field of research in history that deals with the expression, preservation, and change of human ideas over time. ... A Watt steam engine, the steam engine that propelled the Industrial Revolution in Britain and the world. ... Plato (Left) and Aristotle (right), by Raphael (Stanza della Segnatura, Rome) Metaphysics is the branch of philosophy concerned with explaining the ultimate nature of reality, being, and the world. ... Analytic philosophy (sometimes, analytical philosophy) is a generic term for a style of philosophy that came to dominate English-speaking countries in the 20th century. ... Ordinary language philosophy is less a philosophical doctrine or school than it is a loose network of approaches to traditional philosophical problems. ... Analytic philosophy (sometimes, analytical philosophy) is a generic term for a style of philosophy that came to dominate English-speaking countries in the 20th century. ... In philosophy, identity is whatever makes an entity definable and recognizable, in terms of possessing a set of qualities or characteristics that distinguish it from entities of a different type. ... Individuation comprises the processes whereby the undifferentiated becomes or develops individual characteristics, or the opposite process, by which components of an individual are integrated into a more indivisible whole. ... Possible Worlds is: Possible Worlds (play) a play by John Mighton Possible Worlds (poetry book) a book of poems by Peter Porter (poet) Possible Worlds (book) a book by J. B. S. Haldane This is a disambiguation page: a list of articles associated with the same title. ... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... Scholastic is the official student publication of the University of Notre Dame. ... Empiricism is generally regarded as being at the heart of the modern scientific method, that our theories should be based on our observations of the world rather than on intuition or faith; that is, empirical research and a posteriori inductive reasoning rather than purely deductive logic. ... For other uses, see Plato (disambiguation). ... For other uses, see Aristotle (disambiguation). ... For other uses, see Universe (disambiguation). ... For other uses, see Reason (disambiguation). ...


In 1985, the German government created the Leibniz Prize, 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. The Gottfried Wilhelm Leibniz Prize (complete German title Förderpreis für deutsche Wissenschaftler im Gottfried Wilhelm Leibniz-Programm der Deutschen Forschungsgemeinschaft) is a research prize awarded by the Deutsche Forschungsgemeinschaft every year since 1985 to scientists working in Germany. ...


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 Discourse on Metaphysics, which he composed in 1686 as a commentary on a running dispute between Malebranche and Antoine Arnauld. This led to an extensive and valuable correspondence with Arnauld (Ariew & Garber 69, 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" (Ariew & Garber 138, Loemker §47, Wiener II.4). Over 1695–1705, he composed his New Essays on Human Understanding, a lengthy commentary on John Locke's 1690 An Essay Concerning Human Understanding, 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 Monadologie, composed in 1714 and published posthumously, consists of 90 aphorisms. The Discourse on Metaphysics (Discours de métaphysique, 1686) is a short (60 pages in translation) book by Gottfried Leibniz in which he develops a philosophy concerning physical substance, motion and resistance of bodies, and Gods role within the universe. ... Nicolas Malebranche (August 6, 1638 – October 13, 1715) was a French philosopher of the Cartesian school. ... Antoine Arnauld, (1612 - August 8, 1694) — le grand as contemporaries called him, to distinguihs him from his father — was a French Roman Catholic theologian and writer. ... Nouveaux Essais sur Lentendement humaine (New Essays on Human Understanding) was a chapter-by-chapter rebuttal by Gottfried Leibniz of the John Locke book Essays on Human Understanding. ... For other persons named John Locke, see John Locke (disambiguation). ... An Essay Concerning Human Understanding is one of John Lockes two most famous works, the other being his Second Treatise on Civil Government. ... The Monadology (Monadologie, 1714) is one of Gottfried Leibniz’s works that best define his philosophy, monadism. ...


Leibniz met Spinoza 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, (Ariew & Garber 272–84, Loemker §§14,20,21, Wiener III.8) especially when these were inconsistent with Christian orthodoxy. Baruch Spinoza Benedictus de Spinoza (November 24, 1632 - February 21, 1677), named Baruch Spinoza by his synagogue elders and known as Bento de Spinoza or Bento dEspiñoza in the community in which he grew up. ...


Unlike Descartes and Spinoza, Leibniz had a thorough university education in philosophy. His lifelong scholastic and Aristotelian turn of mind betrayed the strong influence of one of his Leipzig professors, Jakob Thomasius, who also supervised his BA thesis in philosophy. Leibniz also eagerly read Francisco Suárez, a Spanish Jesuit respected even in Lutheran universities. 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. Yet it remains the case that Leibniz's methods and concerns often anticipate the logic, and analytic and linguistic philosophy of the 20th century. Scholastic redirects here. ... For other uses, see Aristotle (disambiguation). ... Leipzig ( ; Sorbian/Lusatian: Lipsk from the Sorbian word for Tilia) is, with a population of over 506,000, the largest city in the federal state of Saxony, Germany. ... Jakob Thomasius (1622–1684) was a German academic philosopher and jurist. ... Francisco Suárez (1548–1617) was a Spanish philosopher and theologian, generally regarded as having been the greatest scholastic after Thomas Aquinas. ... The Society of Jesus (Latin: Societas Iesu), commonly known as the Jesuits, is a Roman Catholic religious order. ... The Lutheran movement is a group of denominations of Protestant Christianity by the original definition. ... For the American art director and production designer, see Robert F. Boyle Robert Boyle (25 January 1627 – 30 December 1691) was a natural philosopher, chemist, physicist, inventor, and early gentleman scientist, noted for his work in physics and chemistry. ... Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration. ... Analytic philosophy (sometimes, analytical philosophy) is a generic term for a style of philosophy that came to dominate English-speaking countries in the 20th century. ... Ordinary language philosophy is less a philosophical doctrine or school than it is a loose network of approaches to traditional philosophical problems. ...


The Principles

Leibniz variously invoked one or another of seven fundamental philosophical Principles (Mates 1986: chpts. 7.3, 9):

  • Identity / Contradiction. If a proposition is true, then its negation is false and vice versa.
  • Identity of indiscernibles. Two things are identical if and only if they share the same properties. Frequently invoked in modern logic and philosophy.
  • Sufficient reason. "There must be a sufficient reason [often known only to God] for anything to exist, for any event to occur, for any truth to obtain." (LL 717).
  • Pre-established harmony. See Jolley (1995: 129–31), Woolhouse and Francks (1998), and Mercer (2001). "[T]he appropriate nature of each substance brings it about that what happens to one corresponds to what happens to all the others, without, however, their acting upon one another directly." (Discourse on Metaphysics, XIV) A dropped glass shatters because it "knows" it has hit the ground, and not because the impact with the ground "compels" the glass to split.
  • Continuity. Natura non saltum facit. A mathematical analog to this principle would go as follows. If a function describes a transformation of something to which continuity applies, then its domain and range are both dense sets.
  • Optimism. "God assuredly always chooses the best." (LL 311).
  • Plenitude. "Leibniz believed that the best of all possible worlds would actualize every genuine possibility, and argued in Théodicée that this best of all possible worlds will contain all possibilities, with our finite experience of eternity giving no reason to dispute nature's perfection." (From Plenitude.)

The second principle here is often referred to as Leibniz's Law [2]. The Identity of Indiscernibles has attracted the most controversy and criticism, especially from corpuscular philosophy and quantum mechanics. In mathematics, the term identity has several important uses: An identity is an equality that remains true regardless of the values of any variables that appear within it, to distinguish it from an equality which is true under more particular conditions. ... Broadly speaking, a contradiction is an incompatibility between two or more statements, ideas, or actions. ... The identity of indiscernibles is an ontological principle; i. ... The principle of sufficient reason states that anything that happens does so for a definite reason. ... Gottfried Leibnizs theory of pre-established harmony is a philosophical theory about causation under which every substance only affects itself, but all the substances (both bodies and minds) in the world nevertheless seem to causally interact with each other because they have been programmed by God in advance to... Continuum mechanics is a branch of physics (specifically mechanics) that deals with continuous matter, including both solids and fluids (i. ... This article is about functions in mathematics. ... Look up transformation in Wiktionary, the free dictionary. ... In mathematics, the domain of a function is the set of all input values to the function. ... In mathematics, the range of a function is the set of all output values produced by that function. ... In topology and related areas of mathematics, a subset A of a topological space X is called dense (in X) if, intuitively, any point in X can be well-approximated by points in A. Formally, A is dense in X if for any point x in X, any neighborhood of... “Positive Attitude” redirects here. ... The plenitude principle or principle of plenitude asserts that everything that can happen will happen. ... Theodicy is a branch of theology that studies how the existence of a good or benevolent God is reconciled with the existence of evil. ... The plenitude principle or principle of plenitude asserts that everything that can happen will happen. ... The identity of indiscernibles is an ontological principle; i. ...


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 Sufficient Reason and Plenitude, see Lovejoy (1957). The principle of sufficient reason states that anything that happens does so for a definite reason. ... The plenitude principle or principle of plenitude asserts that everything that can happen will happen. ...


The monads

Leibniz's best known contribution to metaphysics is his theory of monads, as exposited in Monadologie. Monads are to the metaphysical realm what atoms are to the physical/phenomenal. Monads are the ultimate elements of the universe. 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 pre-established harmony (a historically important example of panpsychism). Monads are centers of force; substance is force, while space, matter, and motion are merely phenomenal. Plato (Left) and Aristotle (right), by Raphael (Stanza della Segnatura, Rome) Metaphysics is the branch of philosophy concerned with explaining the ultimate nature of reality, being, and the world. ... For other uses, see Monist (disambiguation). ... The Monadology (Monadologie, 1714) is one of Gottfried Leibniz’s works that best define his philosophy, monadism. ... For other uses, see Atom (disambiguation). ... For other uses, see Universe (disambiguation). ... Gottfried Leibnizs theory of pre-established harmony is a philosophical theory about causation under which every substance only affects itself, but all the substances (both bodies and minds) in the world nevertheless seem to causally interact with each other because they have been programmed by God in advance to... Panpsychism, in philosophy, is either the view that all parts of matter involve mind, or the more holistic view that the whole universe is an organism that possesses a mind. ... For other uses, see Force (disambiguation). ... This article is about the idea of space. ... This article is about matter in physics and chemistry. ... This article or section is in need of attention from an expert on the subject. ...


The ontological 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 scientific laws governing subatomic particles.) 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 free will is problematic. God, too, is a monad, and the existence of God can be inferred from the harmony prevailing among all other monads; God wills the pre-established harmony. This article is about ontology in philosophy. ... A scientific law, is a law-like statement that generalizes across a set of conditions. ... Helium atom (schematic) Showing two protons (red), two neutrons (green) and two electrons (yellow). ... Free-Will is a Japanese independent record label founded in 1986. ... This article is about the term God in the context of monotheism and henotheism. ... Arguments for and against the existence of God have been proposed by philosophers, theologians, and others. ...


Monads are purported to having gotten rid of the problematic:

The monadology was thought arbitrary, even eccentric, in Leibniz's day and since. For other uses, see Mind (disambiguation). ... This article is about matter in physics and chemistry. ... René Descartes René Descartes (IPA: , March 31, 1596 – February 11, 1650), also known as Cartesius, worked as a philosopher and mathematician. ... Individuation comprises the processes whereby the undifferentiated becomes or develops individual characteristics, or the opposite process, by which components of an individual are integrated into a more indivisible whole. ... Baruch Spinoza Benedictus de Spinoza (November 24, 1632 - February 21, 1677), named Baruch Spinoza by his synagogue elders and known as Bento de Spinoza or Bento dEspiñoza in the community in which he grew up. ... A railing accidentally collapses at a college football game, spilling fans onto the sidelines An accident is something going wrong unexpectedly. ...


Theodicy and optimism

The Théodicée tries to justify the apparent imperfections of the world by claiming that it is optimal among all possible worlds. 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 phrase the best of all possible worlds (French:le meilleur des mondes possibles) was coined by the German philosopher Gottfried Leibniz in his 1710 work Essais de Théodicée sur la bonté de Dieu, la liberté de lhomme et lorigine du mal (Theodicy). ...


The statement that "we live in the best of all possible worlds" drew scorn, most notably from Voltaire, who lampooned it in his comic novel Candide by having the character Dr. Pangloss (a parody of Leibniz) repeat it like a mantra. Thus the adjective "panglossian", describing one so naive as to believe that the world about us is the best possible one. For other uses, see Voltaire (disambiguation). ... For the Bernstein operetta based on the book, see Candide (operetta). ... Voltaire Pangloss is a character in Voltaires novel Candide. ... For other uses, see Mantra (disambiguation). ...


The mathematician Paul du Bois-Reymond, in his "Leibnizian Thoughts in Modern Science," wrote that Leibniz thought of God as a mathematician. A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... Leonhard Euler, considered one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is the field of mathematics. ...

"As is well known, the theory of the maxima and minima of functions was indebted to him for the greatest progress through the discovery of the method of tangents. 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 calculus of variations — the question being to determine among an infinite number of possible worlds, that for which the sum of necessary evil is a minimum." Local and global maxima and minima for cos(3Ï€x)/x, 0. ... This article is about functions in mathematics. ... For other uses, see tangent (disambiguation). ... Calculus of variations is a field of mathematics that deals with functionals, as opposed to ordinary calculus which deals with functions. ... Infinity is a word carrying a number of different meanings in mathematics, philosophy, theology and everyday life. ... For other uses, see Evil (disambiguation). ...

A cautious defense of Leibnizian optimism would invoke certain scientific principles that emerged in the two centuries since his death and that are now thoroughly established: the principle of least action, the conservation of mass, and the conservation of energy. In addition, the modern observations that lead to the Fine-tuned Universe arguments seem to support his view: “Positive Attitude” redirects here. ... The principle of least action was first formulated by Pierre-Louis Moreau de Maupertuis, who said that Nature is thrifty in all its actions. See action (physics). ... The law of conservation of mass/matter, also known as law of mass/matter conservation (or the Lomonosov-Lavoisier law), states that the mass of a closed system of substances will remain constant, regardless of the processes acting inside the system. ... This article is about the law of conservation of energy in physics. ... The deepest visible-light image of the cosmos. ...

  1. The 3+1 dimensional structure of spacetime may be ideal. In order to sustain complexity such as life, a universe probably requires three spatial and one temporal dimension. Most universes deviating from 3+1 either violate some fundamental physical laws, or are impossible. The mathematically richest number of spatial dimensions is also 3 (in the sense of topological nontriviality).
  2. The universe, solar system, and Earth are the "best possible" in that they enable intelligent life to exist. Such life has evolved on Earth only because the Earth, solar system, and Milky Way possess a number of unusual characteristics; see Ward & Brownlee (2000), Morris (2003: chpts. 5,6).
  3. The most sweeping form of optimism derives from the Anthropic Principle (Barrow and Tipler 1986). Physical reality can be seen as grounded in the numerical values of a handful of dimensionless constants, the best known of which are the fine structure constant and the ratio of the rest mass of the proton to the electron. 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 complex structures.

Our physical laws, universe, solar system, and home planet are all "best" in the sense that they enable complex structures such as galaxies, stars, and, ultimately, intelligent life. 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". For other uses of this term, see Spacetime (disambiguation). ... Complexity in general usage is the opposite of simplicity. ... This article is about life in general. ... For other uses, see Universe (disambiguation). ... This article is about the idea of space. ... This article is about the concept of time. ... 2-dimensional renderings (ie. ... For a list of set rules, see Laws of science. ... For other uses, see Universe (disambiguation). ... This article is about the Solar System. ... This article is about Earth as a planet. ... This article is about Earth as a planet. ... This article is about the Solar System. ... For other uses, see Milky Way (disambiguation). ... The Rare Earth hypothesis is a hypothesis in planetary astronomy and astrobiology which argues that the emergence of complex multicellular life (metazoa) on Earth required an extremely unlikely combination of astrophysical and geological events and circumstances. ... “Positive Attitude” redirects here. ... In physics and cosmology, the anthropic principle states that we should take into account the constraints that our existence as observers imposes on the sort of universe that we could observe. ... In physics, fundamental physical constants are physical constants that are independent of systems of units and are in general dimensionless numbers. ... The fine-structure constant or Sommerfeld fine-structure constant, usually denoted , is the fundamental physical constant characterizing the strength of the electromagnetic interaction. ... The term mass in special relativity is used in a couple of different ways, occasionally leading to a great deal of confusion. ... For other uses, see Proton (disambiguation). ... For other uses, see Electron (disambiguation). ... Complexity in general usage is the opposite of simplicity. ... For a list of set rules, see Laws of science. ... For other uses, see Universe (disambiguation). ... This article is about the Solar System. ... This article is about Earth as a planet. ... Complexity in general usage is the opposite of simplicity. ... For other uses, see Galaxy (disambiguation). ... This article is about the astronomical object. ... Intelligent Life is an upmarket magazine launched by the editors of The Economist in 2004. ...


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:

"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 [calculemus], without further ado, to see who is right." (The Art of Discovery 1685, W 51)

Leibniz's calculus ratiocinator, which resembles symbolic logic, 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 Begriffsschrift and in writings by Charles Peirce and his students in the 1880s, and hence well after Boole and De Morgan began that logic in 1847. The Calculus Ratiocinator is a concept appearing in the writings of Gottfried Leibniz, usually paired with his characteristica universalis, which he mentioned much more frequently. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... Begriffsschrift is the title of a short book on logic by Gottlob Frege, published in 1879, and is also the name of the formal system set out in that book. ... Charles Sanders Peirce (IPA: /pɝs/), (September 10, 1839 – April 19, 1914) was an American polymath, physicist, and philosopher, born in Cambridge, Massachusetts. ... Not to be confused with George Boolos. ... The tone or style of this article or section may not be appropriate for Wikipedia. ...


Leibniz thought symbols 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 infinitesimal calculus is an example of his skill in this regard. Charles Peirce, a 19th century pioneer of semiotics, shared Leibniz's passion for symbols and notation, and his belief that these are essential to a well-running logic and mathematics. Infinitesimal calculus is an area of mathematics pioneered by Gottfried Leibniz based on the concept of infinitesimals, as opposed to the calculus of Isaac Newton, which is based upon the concept of the limit. ... Charles Sanders Peirce (IPA: /pɝs/), (September 10, 1839 – April 19, 1914) was an American polymath, physicist, and philosopher, born in Cambridge, Massachusetts. ... Semiotics, semiotic studies, or semiology is the study of signs and symbols, both individually and grouped into sign systems. ...


But Leibniz took his speculations much further. Defining a character 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 Egyptian hieroglyphics, Chinese characters, and the symbols of astronomy and chemistry, 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.) Instead, he proposed the creation of a characteristica universalis or "universal characteristic," built on an alphabet of human thought in which each fundamental concept would be represented by a unique "real" character. Hieroglyphs are a system of writing used by the Ancient Egyptians, using a combination of logographic, syllabic, and alphabetic elements. ... Japanese name Kanji: Hiragana: Korean name Hangul: Hanja: Vietnamese name Quốc ngữ: Hán tá»±: A Chinese character or Han character (simplified Chinese: ; traditional Chinese: ; pinyin: ) is a logogram used in writing Chinese, Japanese, rarely Korean, and formerly Vietnamese. ... For other uses, see Astronomy (disambiguation). ... For other uses, see Chemistry (disambiguation). ... Universal characteristic redirects here. ... The idea of an alphabet of human thought originates in the 17th century, when proposals were first made for a universal language. ...

"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)

Complex thoughts would be represented by combining characters for simpler thoughts. Leibniz saw that the uniqueness of prime factorization suggests a central role for prime numbers in the universal characteristic, a striking anticipation of Gödel numbering. Granted, there is no intuitive or mnemonic way to number any set of elementary concepts using the prime numbers. In mathematics, the integer prime-factorization (also known as prime decomposition) problem is this: given a positive integer, write it as a product of prime numbers. ... In mathematics, a prime number, or prime for short, is a natural number greater than one and whose only distinct positive divisors are 1 and itself. ... In formal number theory a Gödel numbering is a function which assigns to each symbol and formula of some formal language a unique natural number called a Gödel number (GN). ... For other uses, see Mnemonic (disambiguation). ...


Because 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. 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. This article is about the branch of mathematics. ... The idea of a universal language is at least as old as the Biblical story of Babel and its fall — the mythical point of which is that there was once a time of a universal Adamic language (and then something happened, analogous to the Fall of Man). ...


What Leibniz actually intended by his characteristica universalis and calculus ratiocinator, and the extent to which modern formal logic 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). Universal characteristic redirects here. ... The Calculus Ratiocinator is a concept appearing in the writings of Gottfried Leibniz, usually paired with his characteristica universalis, which he mentioned much more frequently. ... Logic (from Classical Greek λόγος logos; meaning word, thought, idea, argument, account, reason, or principle) is the study of the principles and criteria of valid inference and demonstration. ...


Formal logic

Main article: algebraic logic

Leibniz is the most important logician between Aristotle and 1847, when George Boole and Augustus De Morgan each published books that began modern formal logic. Leibniz enunciated the principal properties of what we now call conjunction, disjunction, negation, identity, set inclusion, and the empty set. The principles of Leibniz's logic and, arguably, of his whole philosophy, reduce to two: Algebraic logic has at least two meanings: the early study of Boolean algebra; and abstract algebraic logic, a branch of contemporary mathematical logic. ... Not to be confused with George Boolos. ... The tone or style of this article or section may not be appropriate for Wikipedia. ... Logical disjunction (usual symbol or) is a logical operator that results in true if either of the operands is true. ... Negation (i. ... In mathematics, the term identity has several important uses: An identity is an equality that remains true regardless of the values of any variables that appear within it, to distinguish it from an equality which is true under more particular conditions. ... Superset redirects here. ... The empty set is the set containing no elements. ...

  1. All our ideas are compounded from a very small number of simple ideas, which form the alphabet of human thought.
  2. 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 negation and quantified variables ranging over some universe of discourse. The idea of an alphabet of human thought originates in the 17th century, when proposals were first made for a universal language. ... Negation (i. ... In language and logic, quantification is a construct that specifies the extent of validity of a predicate, that is the extent to which a predicate holds over a range of things. ... In computer science and mathematics, a variable (pronounced ) (sometimes called an object or identifier in computer science) is a symbolic representation used to denote a quantity or expression. ... The term universe of discourse generally refers to the entire set of terms used in a specific discourse, i. ...


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


In his book History of Western Philosophy, Bertrand Russell went as far as claiming that Leibniz had developed logic in his unpublished writings to a level which was reached only 200 years later. A History of Western Philosophy And Its Connection with Political and Social Circumstances from the Earliest Times to the Present Day (1945) by the philosopher Bertrand Russell is a guide to Western philosophy from the pre-Socratic philosophers to the early 20th century. ... Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS, (18 May 1872 – 2 February 1970), was a British philosopher, logician, mathematician, advocate for social reform, and pacifist. ...


Mathematician

Although the mathematical notion of function was implicit in trigonometric and logarithmic tables, which existed in his day, Leibniz was the first, in 1692 and 1694, to employ it explicitly, to denote any of several geometric concepts derived from a curve, such as abscissa, ordinate, tangent, chord, and the perpendicular (Struik 1969: 367). In the 18th century, "function" lost these geometrical associations. This article is about functions in mathematics. ... Abscissa means the x coordinate on an (x, y) graph; the input of a mathematical function against which the output is plotted. ... Ordinate means the y coordinate on an (x, y) graph; the plotted output of a mathematical function. ... For other uses, see tangent (disambiguation). ... A chord of a curve is a geometric line segment whose endpoints both lie on the curve. ... In mathematics, normal can have several meanings: Surface normal, a line that is perpendicular to a surface Normal distribution, a type of random variable in statistics Normal extension, in abstract algebra, a certain type of algebraic field extensions Normal family, a pre-compact family of holomorphic functions Normal function, a...


Leibniz was the first to see that the coefficients of a system of linear equations could be arranged into an array, now called a matrix, which can be manipulated to find the solution of the system, if any. This method was later called Gaussian elimination. Leibniz's discoveries of Boolean algebra and of symbolic logic, also relevant to mathematics, are discussed in the preceding section. Graph sample of linear equations A linear equation is an algebraic equation in which each term is either a constant or the product of a constant times the first power of a variable. ... In mathematics, a matrix (plural matrices) is a rectangular table of elements (or entries), which may be numbers or, more generally, any abstract quantities that can be added and multiplied. ... In linear algebra, Gaussian elimination is an algorithm that can be used to determine the solutions of a system of linear equations, to find the rank of a matrix, and to calculate the inverse of an invertible square matrix. ... Boolean algebra is the finitary algebra of two values. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ...


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 Isaac Newton, with the discovery of infinitesimal calculus. According to Leibniz's notebooks, a critical breakthrough occurred on November 11, 1675, 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 integral sign ∫ representing an elongated S, from the Latin word summa and the d used for differentials, 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 product rule of differential calculus is still called "Leibniz's law." In addition, the theorem that tells how and when to differentiate under the integral sign is called Leibniz integral rule. Sir Isaac Newton FRS (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ... Infinitesimal calculus is an area of mathematics pioneered by Gottfried Leibniz based on the concept of infinitesimals, as opposed to the calculus of Isaac Newton, which is based upon the concept of the limit. ... is the 315th day of the year (316th in leap years) in the Gregorian calendar. ... Year 1675 (MDCLXXV) was a common year starting on Tuesday (link will display the full calendar) of the Gregorian calendar (or a common year starting on Friday of the 10-day slower Julian calendar). ... The correct title of this article is Å¿. It appears incorrectly here due to technical restrictions. ... The differential dy In calculus, a differential is an infinitesimally small change in a variable. ... In calculus, the product rule also called Leibnizs law (see derivation), governs the differentiation of products of differentiable functions. ... Differential calculus is the theory of and computations with differentials; see also derivative and calculus. ... The Leibniz integral rule, or Leibniz formula (for differentiation of definite integrals), is Notice that the boundaries of integration are variable (that is, functions of t). ...


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 heuristic hodgepodge mainly grounded in geometric intuition. Leibniz also freely invoked mathematical entities he called infinitesimals, manipulating them in ways suggesting that they had paradoxical algebraic properties. George Berkeley, 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 faith as theology grounded in Christian revelation. For other uses, see Heuristic (disambiguation). ... Infinitesimals have been used to express the idea of objects so small that there is no way to see them or to measure them. ... Look up paradox in Wiktionary, the free dictionary. ... This article is about the branch of mathematics. ... For the second husband of Henrietta Howard, Countess of Suffolk, see George Berkeley (MP). ... For other uses, see Faith (disambiguation). ... Theology finds its scholars pursuing the understanding of and providing reasoned discourse of religion, spirituality and God or the gods. ... Topics in Christianity Movements · Denominations Ecumenism · Relation to other religions Preaching · Prayer Music · Liturgy · Calendar Symbols · Art · Criticism Christianity Portal This box:      Christianity is a monotheistic[1] religion centered on the life and teachings of Jesus of Nazareth as presented in the New Testament. ... Revelation of the Last Judgment by Jacob de Backer Revelation is an uncovering or disclosure via communication from the divine of something that has been partially or wholly hidden or unknown, which could not be known apart from the unveiling (Goswiller 1987 p. ...


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 calculus priority dispute. Isaac Newton began working on a form of the calculus in 1666. ...


Modern, rigorous calculus emerged in the 19th century, thanks to the efforts of Augustin Louis Cauchy, Bernhard Riemann, Karl Weierstrass, and others, who based their work on the definition of a limit and on a precise understanding of real numbers. Their work discredited the use of infinitesimals to justify calculus. Yet, infinitesimals survived in science and engineering, and even in rigorous mathematics, via the fundamental computational device known as the differential. Beginning in 1960, Abraham Robinson worked out a rigorous foundation for Leibniz's infinitesimals, using model theory. The resulting nonstandard analysis can be seen as a belated vindication of Leibniz's mathematical reasoning. Augustin Louis Cauchy (August 21, 1789 – May 23, 1857) was a French mathematician. ... Bernhard Riemann. ... Karl Theodor Wilhelm Weierstrass (Weierstraß) (October 31, 1815 – February 19, 1897) was a German mathematician who is often cited as the father of modern analysis. // Karl Weierstrass was born in Ostenfelde, Westphalia (today Germany). ... Wikibooks Calculus has a page on the topic of Limits In mathematics, the concept of a limit is used to describe the behavior of a function as its argument either gets close to some point, or as it becomes arbitrarily large; or the behavior of a sequences elements as... In mathematics, the real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2. ... Infinitesimals have been used to express the idea of objects so small that there is no way to see them or to measure them. ... In mathematics, differential has several meanings: Differential (infinitesimal), an infinitesimal change in the value of a function In differential topology: Differential form, a generalization that accommodates multiplication and differentiation of differentials In addition, differentials and differential forms on manifolds come with the following notions of differentiation: Exterior derivative, a notion... Abraham Robinson Abraham Robinson (October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of non-standard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were incorporated into mathematics. ... In mathematics, model theory is the study of the representation of mathematical concepts in terms of set theory, or the study of the structures that underlie mathematical systems. ... In the most restricted sense, nonstandard analysis or non-standard analysis is that branch of mathematics that formulates analysis using a rigorous notion of infinitesimal, where an element of an ordered field F is infinitesimal if and only if its absolute value is smaller than any element of F of...


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 topology. There are two takes on this situation. On the one hand, Mates (1986: 240), citing a 1954 paper in German by Jacob Freudenthal, argues: For other uses, see Topology (disambiguation). ... Jacob Freudenthal (born June 20, 1839, at Bodenfelde, province of Hanover, Prussia -) is a German philosopher. ...

"Although for [Leibniz] 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 Euler, in the famous 1736 paper solving the Königsberg Bridge Problem 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." Leonhard Euler aged 49 (oil painting by Emanuel Handmann, 1756) Leonhard Euler (April 15, 1707 - September 18, 1783) (pronounced oiler) was a Swiss mathematician and physicist. ... Map of Königsberg in Eulers time showing the actual layout of the seven bridges, highlighting the river Pregolya and the bridges. ...

But Hirano (1997) argues differently, quoting Mandelbrot (1977: 419):

"...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."

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

See also: dynamism (metaphysics).

Leibniz contributed a fair amount to the statics and dynamics emerging about him, often disagreeing with Descartes and Newton. He devised a new theory of motion (dynamics) based on kinetic energy and potential energy, 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). René Descartes René Descartes (IPA: , March 31, 1596 – February 11, 1650), also known as Cartesius, worked as a philosopher and mathematician. ... Sir Isaac Newton FRS (4 January 1643 – 31 March 1727) [ OS: 25 December 1642 – 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ... This article or section is in need of attention from an expert on the subject. ... In physics, dynamics is the branch of classical mechanics that is concerned with the effects of forces on the motion of objects. ... The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. ... Potential energy can be thought of as energy stored within a physical system. ...


Until the discovery of subatomic particles and the quantum mechanics 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 Albert Einstein by arguing, against Newton, that space, time and motion are relative, not absolute. Leibniz's rule in interacting theories plays a role in supersymmetry and in the lattices of quantum mechanics. The principle of sufficient reason has been invoked in recent cosmology, and his identity of indiscernibles in quantum mechanics, a field some even credit him with having anticipated in some sense. Those who advocate digital philosophy, a recent direction in cosmology, claim Leibniz as a precursor. For a generally accessible and less technical introduction to the topic, see Introduction to quantum mechanics. ... “Einstein” redirects here. ... This article is about the idea of space. ... This article is about the concept of time. ... At least two results in calculus are called Leibnizs rule or the Leibniz rule, in honor of Gottfried Leibniz. ... This article or section is in need of attention from an expert on the subject. ... For a generally accessible and less technical introduction to the topic, see Introduction to quantum mechanics. ... The principle of sufficient reason states that anything that happens does so for a definite reason. ... Cosmology, from the Greek: κοσμολογία (cosmologia, κόσμος (cosmos) order + λογια (logia) discourse) is the study of the Universe in its totality, and by extension, humanitys place in it. ... The identity of indiscernibles is an ontological principle; i. ... For a generally accessible and less technical introduction to the topic, see Introduction to quantum mechanics. ... To meet Wikipedias quality standards, this article or section may require cleanup. ...


The vis viva

Main article: vis viva

Leibniz 's vis viva (Latin for living force) is mv2, twice the modern Kinetic energy. 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 conservation of momentum championed by Newton in England and by Descartes in France; hence academics in those countries tended to neglect Leibniz's idea. Engineers eventually found "vis viva" useful, so that the two approaches eventually were seen as complementary. Vis Viva is the principle that the difference between the aggregate work of the accelerating forces of a system and that of the retarding forces is equal to one half the vis viva accumulated or lost in the system while the work is being done. ... The cars of a roller coaster reach their maximum kinetic energy when at the bottom of their path. ... In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. ... René Descartes René Descartes (IPA: , March 31, 1596 – February 11, 1650), also known as Cartesius, worked as a philosopher and mathematician. ... Plato is credited with the inception of academia: the body of knowledge, its development and transmission across generations. ... Look up engineer in Wiktionary, the free dictionary. ...


Other natural science

By proposing that the earth has a molten core, he anticipated modern geology. In embryology, 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 life sciences and paleontology, 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 medicine, 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. This article includes a list of works cited but its sources remain unclear because it lacks in-text citations. ... This article or section is in need of attention from an expert on the subject. ... Biology studies the variety of life (clockwise from top-left) E. coli, tree fern, gazelle, Goliath beetle Biology is the science of life (from the Greek words bios = life and logos = word). ... Paleontology, palaeontology or palæontology (from Greek: paleo, ancient; ontos, being; and logos, knowledge) is the study of prehistoric life forms on Earth through the examination of plant and animal fossils. ... For the chemical substances known as medicines, see medication. ...


Social science

In psychology he anticipated the distinction between conscious and unconscious states. On Leibniz and psychology, see Loemker (1969a: IX). In public health, he advocated establishing a medical administrative authority, with powers over epidemiology and veterinary medicine. 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 game theory. In sociology he laid the ground for communication theory. {redirect|Psychological science|the journal|Psychological Science (journal)}} Not to be confused with Phycology. ... Consciousness is a quality of the mind generally regarded to comprise qualities such as subjectivity, self-awareness, sentience, sapience, and the ability to perceive the relationship between oneself and ones environment. ... This article does not adequately cite its references or sources. ... Epidemiology is the study of factors affecting the health and illness of populations, and serves as the foundation and logic of interventions made in the interest of public health and preventive medicine. ... Veterinary medicine is the application of medical, diagnostic, and therapeutic principles to companion, domestic, exotic, wildlife, and production animals. ... Game theory is a branch of applied mathematics that is often used in the context of economics. ... Sociology (from Latin: socius, companion; and the suffix -ology, the study of, from Greek λόγος, lógos, knowledge [1]) is the scientific or systematic study of society, including patterns of social relationships, social interaction, and culture[2]. Areas studied in sociology can range from the analysis of brief contacts between anonymous... There is much discussion in the academic world of communication as to what actually constitutes communication. ...


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 applied science. He designed wind-driven propellers and water pumps, mining machines to extract ore, hydraulic presses, lamps, submarines, clocks, etc. With Denis Papin, he invented a steam engine. He even proposed a method for desalinating water. From 1680 to 1685, he struggled to overcome the chronic flooding that afflicted the ducal silver mines in the Harz Mountains, but did not succeed. (Aiton 1985: 107–114, 136) For the song by 311, see Grassroots Applied science is the exact science of applying knowledge from one or more natural scientific fields to practical problems. ... Denis Papin Denis Papin (22 August 1647 - c. ... // The term steam engine may also refer to an entire railroad steam locomotive. ... This article is about the chemical element. ... The Harz is a mountain range in northern Germany. ...


Information technology

Leibniz may have been the first computer scientist and information theorist. Early in life, he discovered the binary number 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 Lagrangian interpolation and algorithmic information theory. His calculus ratiocinator anticipated aspects of the universal Turing machine. In 1934, Norbert Wiener claimed to have found in Leibniz's writings a mention of the concept of feedback, central to Wiener's later cybernetic theory. The binary or base-two numeral system is a system for representing numbers in which a radix of two is used; that is, each digit in a binary numeral may have either of two different values. ... In numerical analysis, a Lagrange polynomial, named after Joseph Louis Lagrange, is the interpolation polynomial for a given set of data points in the Lagrange form. ... This article or section is in need of attention from an expert on the subject. ... The Calculus Ratiocinator is a concept appearing in the writings of Gottfried Leibniz, usually paired with his characteristica universalis, which he mentioned much more frequently. ... The Turing machine is an abstract machine introduced in 1936 by Alan Turing to give a mathematically precise definition of algorithm or mechanical procedure. As such it is still widely used in theoretical computer science, especially in complexity theory and the theory of computation. ... Norbert Wiener Norbert Wiener (November 26, 1894, Columbia, Missouri – March 18, 1964, Stockholm Sweden) was an American theoretical and applied mathematician. ... For other uses, see Feedback (disambiguation). ... For other uses, see Cybernetics (disambiguation). ...


In 1671, Leibniz began to invent a machine that could execute all four arithmetical operations, gradually improving it over a number of years. This 'Stepped Reckoner' attracted fair attention and was the basis of his election to the Royal Society in 1673. A number of such machines were made during his years in Hanover, 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. In the 1670s, a German Baron called Gottfried von Leibniz (sometimes von Leibnitz) took mechanical calculation a step beyond his predecessors. ... For other uses, see Royal Society (disambiguation). ... , Hanover(i) (German: , IPA: ), on the river Leine, is the capital of the federal state of Lower Saxony (Niedersachsen), Germany. ...


Leibniz was groping towards hardware and software concepts worked out much later in 1830-1845 by Charles Babbage and Ada Lovelace. 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.[3] 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. Babbage redirects here. ... Augusta Ada King, Countess of Lovelace (December 10, 1815 London, England – November 27, 1852 Marylebone, London, England [1]), born Augusta Ada Byron, is mainly known for having written a description of Charles Babbages early mechanical general-purpose computer, the analytical engine. ...


Librarian

While serving as librarian of the ducal libraries in Hanover and Wolfenbuettel, Leibniz effectively became one of the founders of library science.[4] 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 indexing system in ignorance of the only other such system then extant, that of the Bodleian Library at Oxford University. 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 Gutenberg. 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 Library of Congress and the British Library. , Hanover(i) (German: , IPA: ), on the river Leine, is the capital of the federal state of Lower Saxony (Niedersachsen), Germany. ... Wolfenbüttel Wolfenbüttel is a town in Lower Saxony, Germany. ... Library science is an interdisciplinary science incorporating the humanities, law and applied science to study topics related to libraries, the collection, organization, preservation and dissemination of information resources, and the political economy of information. ... Library classification forms part of the field of library and information science. ... Entrance to the Library, with the coats-of-arms of several Oxford colleges The Bodleian Library, the main research library of the University of Oxford, is one of the oldest libraries in Europe, and in England is second in size only to the British Library. ... The University of Oxford, located in the city of Oxford in England, is the oldest university in the English-speaking world. ... This article is about the inventor of printing in Europe; for other uses, see Guttenberg (disambiguation) and Gutenberg. ... Construction of the Thomas Jefferson Building, from July 8, 1888 to May 15, 1894. ... British Library main building, London The British Library (BL) is the national library of the United Kingdom. ...


He called for the creation of an empirical database as a way to further all sciences. His characteristica universalis, calculus ratiocinator, 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., Esperanto and its rivals), symbolic logic, even the World Wide Web. A central concept in science and the scientific method is that all evidence must be empirical, or empirically based, that is, dependent on evidence or consequences that are observable by the senses. ... This article is about computing. ... Universal characteristic redirects here. ... The Calculus Ratiocinator is a concept appearing in the writings of Gottfried Leibniz, usually paired with his characteristica universalis, which he mentioned much more frequently. ... This article is about the language. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... The World Wide Web and WWW redirect here. ...


Advocate of scientific societies

Leibniz emphasized that research 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 Berlin Academy of Sciences 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). This article is about the concept. ... The Prussian Academy of Sciences (German: ) was an academy established in Berlin on July 11, 1700. ...


Lawyer, moralist

No philosopher has ever had as much experience with practical affairs of state as Leibniz, except possibly Marcus Aurelius. 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). Marcus Aurelius Antoninus Augustus (called the Wise) (April 26, 121[2] – March 17, 180) was Roman Emperor from 161 to his death in 180. ...


While Leibniz was no apologist for absolute monarchy like Hobbes, or for tyranny in any form, neither did he echo the political and constitutional views of his contemporary John Locke, 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: This article is about the philosopher Thomas Hobbes. ... For other persons named John Locke, see John Locke (disambiguation). ...

"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 Grotius, 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.) Hugo Grotius Hugo Grotius (Huig de Groot, or Hugo de Groot; 10th April 1583 - 28th August 1645) worked as a jurist in the Dutch Republic and laid the foundations for international law, based on natural law. ...

Leibniz foresaw the European Union. 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 ecumenical endeavor, seeking to reconcile first the Roman Catholic and Lutheran churches, later the Lutheran and Reformed churches. In this respect, he followed the example of his early patrons, Baron von Boineburg and the Duke John Frederick, 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 Brunswick remained Lutheran because the Duke's children did not follow their father.) These efforts included corresponding with the French bishop Bossuet, 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 Reformation. Topics in Christianity Movements · Denominations Ecumenism · Relation to other religions Preaching · Prayer Music · Liturgy · Calendar Symbols · Art · Criticism Christianity Portal This box:      Ecumenism (also oecumenism, Å“cumenism) refers to initiatives aimed at greater religious unity or cooperation. ... The Roman Catholic Church, most often spoken of simply as the Catholic Church, is the largest Christian church, with over one billion members. ... The Lutheran movement is a group of denominations of Protestant Christianity by the original definition. ... The Reformed churches are a group of Protestant denominations historically related by a similar Zwinglian or Calvinist system of doctrine but organizationally independent. ... John Frederick (German: Johann Friedrich; 25 April 1625, Herzberg am Harz – 18 December 1679, Augsburg) was duke of Brunswick-Lüneburg and ruled over the Calenberg subdivision of the duchy from 1665 until his death. ... Brunswick-Lüneburg was an historical state within the Holy Roman Empire. ... Jacques_Benigne Bossuet (September 27, 1627 - April 12, 1704) was a French bishop, theologian, and court preacher. ... The Protestant Reformation was a movement which began in the 16th century as a series of attempts to reform the Roman Catholic Church, but ended in division and the establishment of new institutions, most importantly Lutheranism, Reformed churches, and Anabaptists. ...


Philologist

Leibniz was an avid student of languages, eagerly latching on to any information about vocabulary and grammar that came his way. He refuted the belief, widely held by Christian scholars in his day, that Hebrew was the primeval language of the human race. He also refuted the argument, advanced by Swedish scholars in his day, that some sort of proto-Swedish was the ancestor of the Germanic languages. He puzzled over the origins of the Slavic languages,[citation needed] was aware of the existence of Sanskrit, and was fascinated by classical Chinese. Scholarly appreciation of Leibniz the philologist is hampered by the fact that no volume of the planned Academy edition series "Historical and Linguistic Writings" has appeared. The vocabulary of a person is defined either as the set of all words that are understood by that person or the set of all words likely to be used by that person when constructing new sentences. ... For the rules of the English language, see English grammar. ... Hebrew redirects here. ... The Human Race could be: The Human race. ... The Germanic languages are a group of related languages constituting a branch of the Indo-European (IE) language family. ...  Countries where a West Slavic language is the national language  Countries where an East Slavic language is the national language  Countries where a South Slavic language is the national language The Slavic languages (also called Slavonic languages), a group of closely related languages of the Slavic peoples and a subgroup... Sanskrit ( , for short ) is a classical language of India, a liturgical language of Hinduism, Buddhism, Sikhism, and Jainism, and one of the 23 official languages of India. ... Classical Chinese or Literary Chinese is a traditional style of written Chinese based on the grammar and vocabulary of very old forms of Chinese , making it very different from any modern spoken form of Chinese. ... Philology is the study of ancient texts and languages. ...


Sinophile

Leibniz was perhaps the first major European intellect to take a close interest in Chinese 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 Confucian ethical tradition. He mulled over the possibility that the Chinese characters were an unwitting form of his universal characteristic. He noted with fascination how the I Ching hexagrams correspond to the binary numbers from 0 to 111111, and concluded that this mapping was evidence of major Chinese accomplishments in the sort of philosophical mathematics he admired. A Confucian temple in Wuwei, Peoples Republic of China. ... Japanese name Kanji: Hiragana: Korean name Hangul: Hanja: Vietnamese name Quốc ngữ: Hán tá»±: A Chinese character or Han character (simplified Chinese: ; traditional Chinese: ; pinyin: ) is a logogram used in writing Chinese, Japanese, rarely Korean, and formerly Vietnamese. ... Universal characteristic redirects here. ... Alternative meaning: I Ching (monk) The I Ching (Traditional Chinese: 易經, pinyin y jīng; Cantonese IPA: jɪk6gɪŋ1; Cantonese Jyutping: jik6ging1; alternative romanizations include I Jing, Yi Ching, Yi King) is the oldest of the Chinese classic texts. ... The binary numeral system represents numeric values using two symbols, typically 0 and 1. ...


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 archives to research the Brunswick family history he never completed, Leibniz stopped in Vienna, May 1688 – February 1689, where he did much legal and diplomatic work for the Brunswicks. He visited mines, talked with mine engineers, and tried to negotiate export contracts for lead from the ducal mines in the Harz mountains. His proposal that the streets of Vienna be lit with lamps burning rapeseed oil was implemented. During a formal audience with the Austrian Emperor and in subsequent memoranda, he advocated reorganizing the Austrian economy, reforming the coinage of much of central Europe, negotiating a Concordat between the Habsburgs and the Vatican, and creating an imperial research library, official archive, and public insurance fund. He wrote and published an important paper on mechanics. Leibniz also wrote a short paper, first published by Louis Couturat in 1903, later translated as LL 267 and WF 30, summarizing his views on metaphysics. The paper is undated; that he wrote it while in Vienna was determined only in 1999, when the ongoing critical edition 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 analytic philosophers. 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. Archive of the AMVC An archive refers to a collection of historical records, and also refers to the location in which these records are kept. ... For other uses, see Vienna (disambiguation). ... For other uses, see Law (disambiguation). ... This article is about negotiations. ... This article is about mineral extractions. ... Engineering is the discipline and profession of applying scientific knowledge and utilizing natural laws and physical resources in order to design and implement materials, structures, machines, devices, systems, and processes that realize a desired objective and meet specified criteria. ... General Name, Symbol, Number lead, Pb, 82 Chemical series Post-transition metals or poor metals Group, Period, Block 14, 6, p Appearance bluish gray Standard atomic weight 207. ... The Harz is a mountain range in northern Germany. ... Binomial name Brassica napus L. Rapeseed Brassica napus, also known as Rape, Oilseed Rape, Rapa, Rapaseed and (one particular cultivar) Canola, is a bright yellow flowering member of the family Brassicaceae. ... The Holy Roman Emperor was, with some variation, the ruler of the Holy Roman Empire, the predecessor of modern Germany, during its existence from the 10th century until its collapse in 1806. ... A concordat is an agreement between the pope and a government or sovereign on religious matters. ... Flag of the Habsburg Monarchy; also used as the flag of the Austrian Empire until the Ausgleich of 1867. ... For other uses, see Mechanic (disambiguation). ... Louis Couturat (January 17, 1868 - August 3, 1914) was a French logician, mathematician, philosopher, and linguist. ... Plato (Left) and Aristotle (right), by Raphael (Stanza della Segnatura, Rome) Metaphysics is the branch of philosophy concerned with explaining the ultimate nature of reality, being, and the world. ... Analytic philosophy (sometimes, analytical philosophy) is a generic term for a style of philosophy that came to dominate English-speaking countries in the 20th century. ...


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

  1. ^ pronounced [ˈlaɪpnɪts].
  2. ^ Gottfried Leibniz
  3. ^ Aiton 1985: 312
  4. ^ For a recent study of Leibniz's correspondence with Sophia Charlotte, see MacDonald Ross (1998).
  5. ^ Gregory Brown's bibliography bibliography

Image File history File links This is a lossless scalable vector image. ...

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 Sämtliche Schriften und Briefe.


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 Confessio philosophi (A Philosopher's Creed, English translation)
  • 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. Discours de métaphysique. Martin and Brown (1988). Jonathan Bennett's translation. AG 35, LL §35, W III.3, WF 1.
  • 1703. Explication de l'Arithmétique Binaire (Explanation of Binary Arithmetic). Gerhardt, Mathematical Writings VII.223. Lloyd Strickland's translation.
  • 1710. Théodicée. Farrer, A.M., and Huggard, E.M., trans., 1985 (1952). Theodicy. Open Court. W III.11 (part).
  • 1714. Monadologie. Nicholas Rescher, trans., 1991. The Monadology: An Edition for Students. Uni. of Pittsburg Press. Jonathan Bennett's translation. Latta's translation. AG 213, LL §67, W III.13, WF 19. French, latin and spanish edition, with facsimil of Leibniz's manuscript.
  • 1765. Nouveaux essais sur l'entendement humain. Completed 1704. Remnant, Peter, and Bennett, Jonathan, trans., 1996. New Essays on Human Understanding. Cambridge Uni. Press. W III.6 (part). Jonathan Bennett's translation.

Collections of shorter works in translation: The Discourse on Metaphysics is a short (60 pages in translation) book by Gottfried Leibniz in which he develops a philosophy concerning physical substance, motion and resistance of bodies, and Gods role within the universe. ... Nicholas Rescher (born July 15, 1928 in Hagen, Germany) is an American philosopher, affiliated for many years with the University of Pittsburgh, where he is currently University Professor of Philosophy and Chairman of the Center for the Philosophy of Science. ... Nouveaux essais sur lentendement humain (New Essays on Human Understanding) was a chapter-by-chapter rebuttal by Gottfried Leibniz of the John Locke book Essays on Human Understanding. ...

  • Ariew, R & D Garber (1989), Leibniz: Philosophical Essays, Hackett
  • Bennett, Jonathan. Various texts.
  • Cook, Daniel, and Rosemont, Henry Jr., 1994. Leibniz: Writings on China. Open Court.
  • Dascal, Marcelo, 1987. Leibniz: Language, Signs and Thought. John Benjamins.
  • Loemker, Leroy (1969 (1956)), Leibniz: Philosophical Papers and Letters, 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. Various texts.
  • Strickland, Lloyd, 2006. Shorter Leibniz Texts. Continuum Books. Online.
  • Wiener, Philip (1951), Leibniz: Selections, Scribner Regrettably out of print and lacks index.
  • Woolhouse, R.S., and Francks, R., 1998. Leibniz: Philosophical Texts. Oxford Uni. Press.

Donald Rutherford's online bibliography.


Secondary literature

A modern biography in English is Aiton (1985). An 1845 English biography by John M. Mackie is available on Google Books here. 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 MacDonald Ross (1984: chpt. 1), 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 MacDonald Ross (1984), 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:

Intermediate: Walter William Rouse Ball (1850 August 14–1925 April 4) was a Brtish mathematician, and a fellow at Trinity College, Cambridge from 1878 to 1905. ...

  • 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.
  • Arthur O. Lovejoy, 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. English translation.
  • 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 Arthur Oncken Lovejoy (Berlin, October 10, 1873 - Baltimore, December 30, 1962) was an influential intellectual historian, and the founder of the subdiscipline known as the history of ideas. ...

  • Adams, Robert M., 1994. Leibniz: Determinist, Theist, Idealist. Oxford Uni. Press.
  • Bueno, Gustavo, 1981. Introducción a la Monadología de Leibniz. Oviedo: Pentalfa.
  • Louis Couturat, 1901. La Logique de Leibniz. Paris: Felix Alcan. Donald Rutherford's English translation in progress.
  • Ishiguro, Hide, 1990 (1972). Leibniz's Philosophy of Logic and Language. Cambridge Univ. Press.
  • Lenzen, Wolfgang, 2004. "Leibniz's Logic," 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. Vrin
  • 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.

Online bibliography by Gregory Brown. Louis Couturat (January 17, 1868 - August 3, 1914) was a French logician, mathematician, philosopher, and linguist. ...


Other works cited

  • John D. Barrow and Frank J. Tipler, 1986. The Anthropic Cosmological Principle. Oxford Univ. Press.
  • Martin Davis, 2000. The Universal Computer: The Road from Leibniz to Turing. W W Norton.
  • Du Bois-Reymond, Paul, 18nn, "Leibnizian Thoughts in Modern Science," ???.
  • Ivor Grattan-Guinness, 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
  • Benoît Mandelbrot, 1977. The Fractal Geometry of Nature. Freeman.
  • Simon Conway Morris, 2003. Life's Solution: Inevitable Humans in a Lonely Universe. Cambridge Uni. Press.
  • Ward, P. D., and Brownlee, D., 2000. Rare Earth: Why Complex Life is Uncommon in the Universe. Springer Verlag.
  • Zalta, E. N., 2000, "A (Leibnizian) Theory of Concepts," Philosophiegeschichte und logische Analyse / Logical Analysis and History of Philosophy 3: 137–183.

John David Barrow FRS (born November 29, 1952, London) is an English cosmologist, theoretical physicist, and mathematician. ... Frank J. Tipler (born in 1947 in Andalusia, Alabama) is a professor of mathematical physics at Tulane University in New Orleans, Louisiana. ... In physics and cosmology, the anthropic principle states that we should take into account the constraints that our existence as observers imposes on the sort of universe that we could observe. ... Martin Davis, (born 1926, New York City) is an American mathematician, known for his work on Hilberts tenth problem. ... Turing may refer to: Alan Turing Turing (programming language) Turing (cipher) Turing machine Turing completeness Turing test Reverse Turing test Turing Award Turing Police Church-Turing thesis TURing interface Turing (novel), by Christos Papadimitrou, published in 2003 Turing Scholars Category: ... Ivor Grattan-Guinness (Born 23 June 1941, in Bakewell, England) is a prolific historian of mathematics and logic, at Middlesex University. ... Benoît B. Mandelbrot, PhD, (born November 20, 1924) is a Franco-American mathematician, best known as the father of fractal geometry. Benoît Mandelbrot was born in Poland, but his family moved to France when he was a child; he is a dual French and American citizen and was... Simon Conway Morris is a British paleontologist. ... The Rare Earth hypothesis is a hypothesis in planetary astronomy and astrobiology which argues that the emergence of complex multicellular life (metazoa) on Earth required an extremely unlikely combination of astrophysical and geological events and circumstances. ...

Quotations

Wikiquote has a collection of quotations related to:
Gottfried Leibniz

Wiener (1951: 567–70) lists 44 quotable "proverbs" beginning with "Justice is the charity of the wise." Image File history File links This is a lossless scalable vector image. ... Wikiquote is one of a family of wiki-based projects run by the Wikimedia Foundation, running on MediaWiki software. ...

  • "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

The Monadology (Monadologie, 1714) is one of Gottfried Leibniz’s works that best define his philosophy, monadism. ... Universal characteristic redirects here. ... The idea of a universal language is at least as old as the Biblical story of Babel. ... The Calculus Ratiocinator is a concept appearing in the writings of Gottfried Leibniz, usually paired with his characteristica universalis, which he mentioned much more frequently. ... The idea of an alphabet of human thought originates in the 17th century, when proposals were first made for a universal language. ... Isaac Newton began working on a form of the calculus in 1666. ... The Leibniz-Gemeinschaft (complete title: Wissenschaftsgemeinschaft Gottfried Wilhelm Leibniz . ... The Gottfried Wilhelm Leibniz Prize (complete German title Förderpreis für deutsche Wissenschaftler im Gottfried Wilhelm Leibniz-Programm der Deutschen Forschungsgemeinschaft) is a research prize awarded by the Deutsche Forschungsgemeinschaft every year since 1985 to scientists working in Germany. ... In linear algebra, the determinant is a function that associates a scalar det(A) to every square matrix A. The fundamental geometric meaning of the determinant is as the scale factor for volume when A is regarded as a linear transformation. ... The Leibniz integral rule, or Leibniz formula (for differentiation of definite integrals), is Notice that the boundaries of integration are variable (that is, functions of t). ... The alternating series test is a method used to prove that infinite series of terms converge. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... In physics and cosmology, the anthropic principle states that we should take into account the constraints that our existence as observers imposes on the sort of universe that we could observe. ... In the 1670s, a German Baron called Gottfried von Leibniz (sometimes von Leibnitz) took mechanical calculation a step beyond his predecessors. ... The problem of the futures contingents designs a logical paradox first posed by Diodorus Cronus from the Megarian school of philosophy, under the name of the dominator, and then reactualized by Aristotle in chapter 9 of De Interpretatione. ... The Leibniz-Keks is a German brand of biscuit (or cookie in American English) produced by the Bahlsen food company since 1891. ... The Leibniz harmonic triangle is a triangular arrangement of fractions in which the outermost diagonals consist of the reciprocals of the row numbers and each inner cell is the absolute value of the cell above minus the cell to the left. ...

External links

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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 July 1, 1646(1646-07-01)
PLACE OF BIRTH Leipzig, Germany
DATE OF DEATH November 14, 1716
PLACE OF DEATH Hanover, Germany
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World map showing the Americas CIA political map of the Americas in an equal-area projection The Americas are the lands of the Western hemisphere or New World, consisting of the continents of North America and South America with their associated islands and regions. ... The American Enlightenment is a term sometimes employed to describe the intellectual culture of the British North American colonies and the early United States (as they became following the American Revolution). ... Benjamin Franklin (January 17 [O.S. January 6] 1706 – April 17, 1790) was one of the most well known Founding Fathers of the United States. ... David Rittenhouse (April 8, 1732 – June 26, 1796) was a renowned American astronomer, inventor, mathematician, surveyor, scientific instrument craftsman, and public official. ... For other persons named John Adams, see John Adams (disambiguation). ... 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Natural philosophy or the philosophy of nature, known in Latin as philosophia naturalis, is a term applied to the objective study of nature and the physical universe that was regnant before the development of modern science. ... Rationality as a term is related to the idea of reason, a word which following Websters may be derived as much from older terms referring to thinking itself as from giving an account or an explanation. ... For other uses, see Reason (disambiguation). ... A magnet levitating above a high-temperature superconductor demonstrates the Meissner effect. ... This article is about secularism. ... The Encyclopédistes were a group of 18th century writers in France who compiled the Encyclopédie (Encyclopedia) edited by Denis Diderot and Jean le Rond dAlembert. ... Weimar Classicism is, as many historians and scholars argue, a disputed literary movement that took place in Germany and Continental Europe. ... 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Gottfried Wilhelm Leibniz -- Metaphysics [Internet Encyclopedia of Philosophy] (10590 words)
Leibniz also claims that a statement is true for all time--that is, whenever the statement is made.
Leibniz states: "For they [free or intelligent substances] are not bound by any certain subordinate laws of the universe, but act as it were by a private miracle" ("Necessary and Contingent Truths").
Leibniz's analogy is of the roar of the waves of the beach: the seemingly singular sound of which one is conscious is in fact made up of a vast number of individual sounds of which one is not conscious--droplets of water smacking into one another.
Gottfried Leibniz - Wikipedia, the free encyclopedia (9971 words)
Leibniz died in Hanover 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.
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.
Leibniz was the first to see that the coefficients of a system of linear equations could be arranged into arrays, now called matrices, which can be manipulated to find the solution of the system, if any.
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