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Encyclopedia > Gottfried Leibniz

"Leibniz" redirects here. For other uses, see Leibniz (disambiguation).
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) 1646 – November 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

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Please improve this section by adding citations to reliable sources. Unverifiable material may be challenged and removed.

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

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
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