Citizendia

"Leibniz" redirects here. For other uses, see Leibniz (disambiguation).
Western Philosophy
18th-century philosophy
Gottfried Wilhelm Leibniz
Name
Gottfried Wilhelm Leibniz
BirthJuly 1 (June 21 Old Style) 1646, Leipzig, Electorate of Saxony
DeathNovember 14, 1716, Hanover, Electorate of Hanover
School/traditionRationalism
Main interestsMetaphysics, Mathematics, Theodicy
Notable ideasInfinitesimal calculus, Calculus, Monadology, Theodicy, Optimism
Influenced byPlato, Aristotle, Aquinas, Suárez, Descartes, Spinoza, Ramon Llull
InfluencedMany 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. Western philosophy is a term that refers to philosophical thinking in the Western or Occidental world, as distinct from Eastern or Oriental philosophies The Age of Enlightenment or The Enlightenment is a term used to describe a phase in Western philosophy and cultural life centered upon the eighteenth century "July 1st" redirects here For the Ayumi Hamasaki song see H (song. Events 524 - Godomar, King of the Burgundians defeats the Franks at the Battle of Vézeronce. Old Style (or OS) and New Style (or NS) are used in English language historical studies either to indicate that the start of the Julian year This sort of fix restores section edit linkpoints to where they belong The Electorate of Saxony (Kurfürstentum Sachsen or Duchy of Upper Saxony was an independent hereditary electorate of the Holy Roman Empire from 1356–1806 Events 1533 - Conquistadors from Spain under the leadership of Francisco Pizarro arrive in Cajamarca, Inca Year 1716 ( MDCCXVI) was a Leap year starting on Wednesday (link will display the full calendar of the Gregorian calendar (or a Hanover (i ( haˈnoːfɐ on the river Leine, is the capital of the federal state of Lower Saxony ( Niedersachsen The Electorate of Hanover (or more formally the Electorate of Brunswick-Lüneburg; Kurfürstentum Hannover Kurfürstentum Braunschweig-Lüneburg became the ninth Electorate In Epistemology and in its broadest sense rationalism is "any view appealing to Reason as a source of knowledge or justification" (Lacey 286 Metaphysics is the branch of Philosophy investigating principles of reality transcending those of any particular science Mathematics is the body of Knowledge and Academic discipline that studies such concepts as Quantity, Structure, Space and Theodicy (θiːˈɒdɪsi (adjectival form theodicean) is a specific branch of Theology and Philosophy that attempts to reconcile the existence of Calculus ( Latin, calculus, a small stone used for counting is a branch of Mathematics that includes the study of limits, Derivatives Calculus ( Latin, calculus, a small stone used for counting is a branch of Mathematics that includes the study of limits, Derivatives The Monadology ( Monadologie, 1714 is one of Gottfried Leibniz ’s works that best define his philosophy monadism. Theodicy (θiːˈɒdɪsi (adjectival form theodicean) is a specific branch of Theology and Philosophy that attempts to reconcile the existence of Biography Early life Birth and family Plato was born in Athens Greece Aristotle (Greek Aristotélēs) (384 BC – 322 BC was a Greek philosopher a student of Plato and teacher of Alexander the Great. Francisco Suárez ( 5 January 1548, Granada, Spain - 25 September 1617, Lisbon, Portugal) was a Baruch or Benedict de Spinoza (ברוך שפינוזה Bento de Espinosa Benedictus de Spinoza ( November 24, 1632 – February 21, Ramon Llull (1232 &ndash June 29, 1315) (sometimes Raymond Lully, Raymond Lull, in Latin Raimundus or Christian Wolff (less correctly Wolf; also known as Wolfius) baron ( 24 January 1679 - 9 April 1754) was a German Immanuel Kant (ɪmanuəl kant 22 April 1724 12 February 1804 was an 18th-century German Philosopher from the Prussian city of Königsberg Bertrand Arthur William Russell 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970 was a British Philosopher, Historian Martin Heidegger ( September 26, 1889 &ndash May 26, 1976) (ˈmaɐ̯tiːn ˈhaɪ̯dɛgɐ was an influential German philosopher "July 1st" redirects here For the Ayumi Hamasaki song see H (song. Events 524 - Godomar, King of the Burgundians defeats the Franks at the Battle of Vézeronce. Old Style (or OS) and New Style (or NS) are used in English language historical studies either to indicate that the start of the Julian year Events 1533 - Conquistadors from Spain under the leadership of Francisco Pizarro arrive in Cajamarca, Inca Year 1716 ( MDCCXVI) was a Leap year starting on Wednesday (link will display the full calendar of the Gregorian calendar (or a Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. A polymath ( Greek polymathēs, πολυμαθής "having learned much" is a person whose knowledge is not restricted to one subject area Latin ( lingua Latīna, laˈtiːna is an Italic language, historically spoken in Latium and Ancient Rome. French ( français,) is a Romance language spoken around the world by 118 million people as a native language and by about 180 to 260 million people

He occupies an equally grand place in both the history of philosophy and the history of mathematics. The history of Philosophy is the study of philosophical ideas and concepts through time The area of study known as the history of mathematics is primarily an investigation into the origin of new discoveries in Mathematics and to a lesser extent an investigation He invented calculus independently of Newton, and his notation is the one in general use since then. Calculus ( Latin, calculus, a small stone used for counting is a branch of Mathematics that includes the study of limits, Derivatives Sir Isaac Newton, FRS (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements In Calculus, Leibniz's notation, named in honor of the 17th-century German philosopher and mathematician Gottfried Wilhelm Leibniz He also discovered the binary system, foundation of virtually all modern computer architectures. The binary numeral system, or base-2 number system, is a Numeral system that represents numeric values using two symbols usually 0 and 1. In philosophy, he is mostly remembered for optimism, i. e. his conclusion that our universe is, in a restricted sense, the best possible one God could have made. God is the principal or sole Deity in Religions and other belief systems that worship one deity. He was, along with René Descartes and Baruch Spinoza, one of the three greatest 17th century rationalists, but his philosophy also looks back to the scholastic tradition and anticipates modern logic and analysis. Baruch or Benedict de Spinoza (ברוך שפינוזה Bento de Espinosa Benedictus de Spinoza ( November 24, 1632 – February 21, In Epistemology and in its broadest sense rationalism is "any view appealing to Reason as a source of knowledge or justification" (Lacey 286 Scholasticism was the dominant form of theology and philosophy in the Latin West in the Middle Ages, particularly in the 12th 13th and 14th centuries Logic is the study of the principles of valid demonstration and Inference. 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 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. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. Technology is a broad concept that deals with a Species ' usage and knowledge of Tools and Crafts and how it affects a species' ability to control and adapt Foundations of modern biology There are five unifying principles Medicine is the art and science of healing It encompasses a range of Health care practices evolved to maintain and restore Human Health by the Geology (from Greek γη gê, "earth" and λόγος Logos, "speech" lit Probability theory is the branch of Mathematics concerned with analysis of random phenomena Psychology (from Greek grc ψῡχή psȳkhē, "breath life soul" and grc -λογία -logia) is an Academic and Linguistics is the scientific study of Language, encompassing a number of sub-fields Information science is an interdisciplinary science primarily concerned with the collection classification, manipulation storage retrieval and dissemination He also wrote on politics, law, ethics, theology, history, and philology, even occasional verse. Politics Politics is the process by which groups of people make decisions Law is a system of rules enforced through a set of Institutions used as an instrument to underpin civil obedience politics economics and society Ethics is a major branch of Philosophy, encompassing right conduct and good life Theology is the study of a god or the gods from a religious perspective History is the study of the past particularly the written record Those who study history as a Profession are called Historians Etymology See Comparative linguistics for the narrower field of "comparative philology" 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.

Contents

Biography

The outline of Leibniz's career is as follows:

Early life

Gottfried Leibniz was born on 1 July (21 June Old Style) 1646 in Leipzig to Friedrich Leibniz and Catherina Schmuck. "July 1st" redirects here For the Ayumi Hamasaki song see H (song. Events 524 - Godomar, King of the Burgundians defeats the Franks at the Battle of Vézeronce. Old Style (or OS) and New Style (or NS) are used in English language historical studies either to indicate that the start of the Julian year This sort of fix restores section edit linkpoints to where they belong 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]

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. The University of Leipzig (Universität Leipzig located in Leipzig in the Free State of Saxony, Germany, is one of the oldest universities By 12, he had taught himself Latin, which he used freely all his life, and had begun studying Greek. Latin ( lingua Latīna, laˈtiːna is an Italic language, historically spoken in Latium and Ancient Rome. Greek (el ελληνική γλώσσα or simply el ελληνικά — "Hellenic" is an Indo-European language, spoken today by 15-22 million people mainly

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. Habilitation is the highest academic qualification a person can achieve by their own pursuit in certain European and Asian countries The Dissertatio de arte combinatoria was published by Gottfried Leibniz in 1666. 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. This sort of fix restores section edit linkpoints to where they belong The University of Altdorf (Universität Altdorf was a University in Altdorf bei Nürnberg, a small town outside Nuremberg. He then declined an offer of academic appointment at Altdorf, and spent the rest of his life in the service of two major German noble families.

1666–74

Leibniz's first position was as a salaried alchemist in 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. Mainz (ˈmaɪ̯nʦ (Mayence is a City in Germany and the capital of the German federal state of Rhineland-Palatinate. Johann Philipp von Schönborn ( 6 August 1605 - 12 February 1673) was the Archbishop of Mainz from 1647 until 1673 the Bishop Von Boineburg hired Leibniz as an assistant, and shortly thereafter reconciled with the Elector and introduced Leibniz to him. Leibniz then dedicated an essay on law to the Elector in the hope of obtaining employment. The stratagem worked; the Elector asked Leibniz to assist with the redrafting of the legal code for his Electorate. In 1669, Leibniz was appointed Assessor in the Court of Appeal. Although von Boineburg died late in 1672, Leibniz remained under the employment of his widow until she dismissed him in 1674.

Von Boineburg did much to promote Leibniz's reputation, and the latter's memoranda and letters began to attract favorable notice. Leibniz's service to the Elector soon followed a diplomatic role. Diplomacy is the art and practice of conducting Negotiations between representatives of groups or states He published an essay, under the pseudonym of a fictitious Polish nobleman, arguing (unsuccessfully) for the German candidate for the Polish crown. Poland (Polska officially the Republic of Poland 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. Early years Birth and ancestry Louis XIV was born in the Château de Saint-Germain-en-Laye on September 5 1638 and bore the Heir apparent Meanwhile, the Thirty Years' War had left German-speaking Europe exhausted, fragmented, and economically backward. For the Mauritanian Thirty Years' War see Char Bouba war. For the band see The 30 Years War. 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. This article is about the country of Egypt For a topic outline on this subject see List of basic Egypt topics. See http//enwikipediaorg/wiki/WikipediaFootnotes for an explanation of how to generate footnotes using the tags and the template below 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 gone irrelevant. Paris (ˈpærɨs in English; in French) is the Capital of France and the country's largest city Napoleon's failed invasion of Egypt in 1798 can be seen as an unwitting implementation of Leibniz's plan.

Thus Leibniz began several years in Paris, during which he greatly expanded his knowledge of mathematics and physics, and began contributing to both. He met Malebranche and Antoine Arnauld, the leading French philosophers of the day, and studied the writings of Descartes and Pascal, unpublished as well as published. "Malebranche" redirects here For the fictional demons see Malebolge. Antoine Arnauld, ( February 6, 1612 - August 6, 1694) &mdash le Grand as contemporaries called him to distinguish him from his Blaise Pascal (blɛz paskal (June 19 1623 &ndash August 19 1662 was a French Mathematician, Physicist, and religious Philosopher He befriended a German mathematician, Ehrenfried Walther von Tschirnhaus; they corresponded for the rest of their lives. Ehrenfried Walther von Tschirnhaus (or Tschirnhausen) ( April 10, 1651 &ndash October 11, 1708) was a German Mathematician Leibniz was extraordinarily fateful when came into acquaintance of the Dutch physicist and mathematician Christiaan Huygens, who was active in Paris then. The Netherlands ( Dutch:, ˈnedərlɑnt is the European part of the Kingdom of the Netherlands, which consists of the Netherlands the Netherlands Christiaan Huygens (ˈhaɪgənz in English ˈhœyɣəns in Dutch) ( April 14, 1629 &ndash July 8, 1695) was a Dutch Soon after arriving in Paris, Leibniz received a rude awakening; his knowledge of mathematics and physics was spotty. Finding Huygens as mentor, he began a program of self-study that soon pushed him to making major contributions to both subjects, including inventing his version of the differential and integral calculus. Calculus ( Latin, calculus, a small stone used for counting is a branch of Mathematics that includes the study of limits, Derivatives

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. London ( ˈlʌndən is the capital and largest urban area in the United Kingdom. There Leibniz came into acquaintance of Henry Oldenburg and John Collins. Henry Oldenburg (c 1619 - September 1677 worked as a Diplomat and a Natural philosopher. John Collins ( 25 March, 1625 &ndash 10 November 1683) was an English mathematician After demonstrating a calculating machine to the Royal Society 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 Royal Society of London for the Improvement of Natural Knowledge, known simply as The Royal Society, is a Learned society for science that was founded in 1660 The mission ended abruptly when news reached it of the Elector's death, whereupon Leibniz promptly returned to Paris and not, as had been planned, to Mainz.

The sudden deaths of Leibniz's two patrons in the same winter meant that Leibniz had to find a new basis for his career. In this regard, a 1669 invitation from the Duke of Brunswick to visit Hanover proved fateful. Brunswick-Lüneburg (Braunschweig-Lüneburg also Brunswick-Lunenburg was a historical ducal state during the period from the Late Middle Ages through the 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. John Frederick ( German: Johann Friedrich 25 April 1625, Herzberg am Harz &ndash 18 December 1679, Augsburg

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. Antonie Philips van Leeuwenhoek (October 24 1632 &ndash August 30 1723 was a Dutch tradesman and Scientist from Delft, the Netherlands He also spent several days in intense discussion with Spinoza, who had just completed his masterwork, the Ethics. Baruch or Benedict de Spinoza (ברוך שפינוזה Bento de Espinosa Benedictus de Spinoza ( November 24, 1632 – February 21, Ethics is a philosophical book written by Baruch Spinoza. It was written in Latin. Leibniz respected Spinoza's powerful intellect, but was dismayed by his conclusions that contradicted both Christian and Jewish orthodoxy.

In 1677, he was promoted, at his request, to Privy Counselor of Justice, a post he held for the rest of his life. Leibniz served three consecutive rulers of the House of Brunswick as historian, political adviser, and most consequentially, as librarian of the ducal library. A duke is a member of the Nobility, historically of highest rank below the Sovereign, and historically controlled a Duchy or a Dukedom 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. Theology is the study of a god or the gods from a religious perspective

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. Electress Sophia of Hanover (born Sophia Countess Palatine of Simmern; 14 October 1630 – 8 June 1714) was the youngest daughter Sophia Charlotte of Hanover ( 30 October 1668, at Schloss Iburg in Bad Iburg near Osnabrück &ndash 1 February 1705 George II (George Augustus 10 November 1683 &ndash 25 October 1760 was King of Great Britain and Ireland, Duke of Brunswick-Lüneburg ( 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. George I (George Louis German Georg Ludwig; 28 May 1660 &ndash 11 June 1727 For the first year of his life George was the only heir to his father's and three childless [4]

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. Brunswick-Lüneburg (Braunschweig-Lüneburg also Brunswick-Lunenburg was a historical ducal state during the period from the Late Middle Ages through the In 1692, the Duke of Brunswick became a hereditary Elector of the Holy Roman Empire. The Holy Roman Empire ( HRE; German Heiliges Römisches Reich (HRR, Latin Sacrum Romanum Imperium (SRI was a union of territories in 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. The Act of Settlement is an act of the Parliament of England, originally filed in 1700 and passed in 1701 to settle the succession to the English throne William III or William of Orange (14 November 1650 &ndash 8 March 1702 He is informally known in Northern Ireland and Scotland as "King Billy" 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 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. The Parliament of the United Kingdom of Great Britain and Northern Ireland is the supreme legislative body in the United Kingdom and British overseas territories

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. Acta Eruditorum ( Latin for reports acts of the scholars) was the first Scientific journal of the German lands, published from That journal played a key role in advancing his mathematical and scientific reputation, which in turn enhanced his eminence in diplomacy, history, theology, and philosophy.

The Elector 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. Ernest Augustus ( German: Ernst August; Latin: Ernestus Augustus; 20 November 1629 – 23 January 1698 Brunswick-Lüneburg (Braunschweig-Lüneburg also Brunswick-Lunenburg was a historical ducal state during the period from the Late Middle Ages through the Charlemagne (ˈʃɑrlɨmeɪn Carolus Magnus or Karolus Magnus meaning Charles the Great) (747 – 28 January 814 was King of the Franks from 768 to his 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. Genealogy (from Greek: el γενεά el-Latn genea, "descent" and el λόγος el-Latn logos, "knowledge" is the study of They never knew that he had in fact carried out a fair part of his assigned task: when the material Leibniz had written and collected for his history of the House of Brunswick was finally published in the 19th century, it filled three volumes.

In 1711, John Keill, writing in the journal of the Royal Society and with Newton's presumed blessing, accused Leibniz of having plagiarized Newton's calculus. Thus began the calculus priority dispute which darkened the remainder of Leibniz's life. The Calculus controversy was an argument between Seventeenth-century Mathematicians Isaac Newton and Gottfried Leibniz over who had A formal investigation by the Royal Society (in which Newton was an unacknowledged participant), undertaken in response to Leibniz's demand for a retraction, upheld Keill's charge. Historians of mathematics writing since 1900 or so have tended to acquit Leibniz, pointing to important differences between Leibniz's and Newton's versions of the calculus.

In 1711, while traveling in northern Europe, the Russian Tsar Peter the Great stopped in Hanover and met Leibniz, who then took some interest in matters Russian over the rest of his life. Tsar csar and tzar redirect here For other uses see Tsar (disambiguation. In 1712, Leibniz began a two year residence in Vienna, where he was appointed Imperial Court Councillor to the Habsburgs. Vienna ( in Wien; see also other names) is the Capital of Austria, and is also one of the nine States of Austria. 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. George I (George Louis German Georg Ludwig; 28 May 1660 &ndash 11 June 1727 For the first year of his life George was the only heir to his father's and three childless The Act of Settlement is an act of the Parliament of England, originally filed in 1700 and passed in 1701 to settle the succession to the English throne 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. Electress Sophia of Hanover (born Sophia Countess Palatine of Simmern; 14 October 1630 – 8 June 1714) was the youngest daughter

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. Hanover (i ( haˈnoːfɐ on the river Leine, is the capital of the federal state of Lower Saxony ( Niedersachsen 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. The Prussian Academy of Sciences (Preußische Akademie der Wissenschaften was an Academy established in Berlin on July 11 1700. 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. Bernard le Bovier de Fontenelle, also referred to as Bernard le Bouyer de Fontenelle ( 11 February 1657 &ndash 9 January 1757) was The eulogy was composed at the behest of the Duchess of Orleans, a niece of the Electress Sophia.

Leibniz never married. He complained on occasion about money, but the fair sum he left to his sole heir, his sister's stepson, proved that the Brunswicks had, by and large, paid him well. In his diplomatic endeavors, he at times verged on the unscrupulous, as was all too often the case with professional diplomats of his day. On several occasions, Leibniz backdated and altered personal manuscripts, actions which cannot be excused or defended and which put him in a bad light during the calculus controversy. On the other hand, he was charming and well-mannered, with many friends and admirers all over Europe.

Writings and edition

Leibniz mainly wrote in three languages: scholastic Latin (ca. 40%), French (ca. 35%), and German (less than 25%). During his lifetime, he published many pamphlets and scholarly articles, but only two "philosophical" books, the Combinatorial Art and the Théodicée. Essais de Théodicée sur la bonté de Dieu la liberté de l'homme et l'origine du mal ( French: Essays of theodicy on the goodness of God the freedom of (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. Brunswick-Lüneburg (Braunschweig-Lüneburg also Brunswick-Lunenburg was a historical ducal state during the period from the Late Middle Ages through the Sovereignty is the exclusive Right to control a Government, a country, a people or oneself ) One substantial book appeared posthumously, his Nouveaux essais sur l'entendement humain, which Leibniz had withheld from publication after the death of John Locke. New Essays on Human Understanding ("Nouveaux essais sur l'entendement humain" is a chapter-by-chapter rebuttal by Gottfried Leibniz of John Locke John Locke (29 August 1632 – 28 October 1704 was an English Philosopher. 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:

"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:

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), greatly 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). Also see Potsdam New York (in the USA For the Potsdam Conference see Potsdam Conference. Münster ( is a city in North Rhine-Westphalia, Germany. It is located in the northern part of the state and is considered to be the cultural centre of the Hanover (i ( haˈnoːfɐ on the river Leine, is the capital of the federal state of Lower Saxony ( Niedersachsen Berlin is the capital city and one of sixteen states of Germany.

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. François-Marie Arouet ( 21 November 1694 30 May 1778) better known by the Pen name Voltaire, was a French --> Candide ou l'Optimisme (1759 is a French Satire by the Enlightenment Philosopher Voltaire, English translations of which 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. Christian Wolff (less correctly Wolf; also known as Wolfius) baron ( 24 January 1679 - 9 April 1754) was a German In any event, philosophical fashion was moving away from the rationalism and system building of the 17th century, of which Leibniz had been such an ardent exponent. His work on law, diplomacy, and history was seen as of ephemeral interest. The vastness and richness of his correspondence went unrecognized.

Much of Europe came to doubt that Leibniz had discovered the calculus independently of Newton, and hence his whole work in mathematics and physics was neglected. Voltaire, an admirer of Newton, also wrote Candide at least in part to discredit Leibniz's claim to having discovered the calculus and Leibniz's charge that Newton's theory of universal gravitation was incorrect. The rise of relativity and subsequent work in the history of mathematics has put Leibniz's stance in a more favorable light.

Leibniz's long march to his present glory began with the 1765 publication of the Nouveaux Essais, which Kant read closely. Immanuel Kant (ɪmanuəl kant 22 April 1724 12 February 1804 was an 18th-century German Philosopher from the Prussian city of Königsberg 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. Antoine Arnauld, ( February 6, 1612 - August 6, 1694) &mdash le Grand as contemporaries called him to distinguish him from his Samuel Clarke ( 11 October 1675 &ndash 17 May 1729) was an English Philosopher. Electress Sophia of Hanover (born Sophia Countess Palatine of Simmern; 14 October 1630 – 8 June 1714) was the youngest daughter Sophia Charlotte of Hanover ( 30 October 1668, at Schloss Iburg in Bad Iburg near Osnabrück &ndash 1 February 1705

In 1900, Bertrand Russell published a critical study of Leibniz's metaphysics. Bertrand Arthur William Russell 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970 was a British Philosopher, Historian Shortly thereafter, Louis Couturat published an important study of Leibniz, and edited a volume of Leibniz's heretofore unpublished writings, mainly on logic. Louis Couturat ( January 17, 1868 - August 3, 1914) was a French Logician mathematician, philosopher 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. Salva veritate substitution from the Latin for "saving the truth" refers to two expressions that can be interchanged without changing the truth-value of the statements Willard Van Orman Quine (June 25 1908 Akron, Ohio &ndash December 25 2000 (known to intimates as "Van" Nevertheless, the secondary English-language literature on Leibniz did not really blossom until after World War II. World War II, or the Second World War, (often abbreviated WWII) was a global military conflict which involved a majority of the world's nations, including 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).

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:

The University of Hannover (German spelling) is named after him.

In 1985, the German government created the Leibniz Prize, annual awards of 1. Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. The Gottfried Wilhelm Leibniz Prize (complete German title de "Förderpreis für deutsche Wissenschaftler im [[Gottfried Wilhelm Leibniz]]-Programm der Deutschen Forschungsgemeinschaft" 55 million Euros for experimental results, and 770,000 Euros for theoretical ones. It is the world's largest prize for scientific achievement.

Philosopher

Leibniz's philosophical thinking appears fragmented, because his philosophical writings consist mainly of a multitude of short pieces: journal articles, manuscripts published long after his death, and many letters to many correspondents. He wrote only two philosophical treatises, and the one he published in his lifetime, the Théodicée of 1710, is as much theological as philosophical.

Leibniz dated his beginning as a philosopher to his Discourse on Metaphysics, which he composed in 1686 as a commentary on a running dispute between Malebranche and Antoine Arnauld. 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 "Malebranche" redirects here For the fictional demons see Malebolge. Antoine Arnauld, ( February 6, 1612 - August 6, 1694) &mdash le Grand as contemporaries called him to distinguish him from his 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. New Essays on Human Understanding ("Nouveaux essais sur l'entendement humain" is a chapter-by-chapter rebuttal by Gottfried Leibniz of John Locke John Locke (29 August 1632 – 28 October 1704 was an English Philosopher. An Essay Concerning Human Understanding is one of John Locke 's two most famous works the other being his Second Treatise on Civil Government The Monadologie, composed in 1714 and published posthumously, consists of 90 aphorisms. 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. Baruch or Benedict de Spinoza (ברוך שפינוזה Bento de Espinosa Benedictus de Spinoza ( November 24, 1632 – February 21, 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.

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. Scholasticism was the dominant form of theology and philosophy in the Latin West in the Middle Ages, particularly in the 12th 13th and 14th centuries Aristotelianism is a tradition of Philosophy that takes its defining inspiration from the work of Aristotle. This sort of fix restores section edit linkpoints to where they belong Jakob Thomasius (1622–1684 was a German academic philosopher and jurist Leibniz also eagerly read Francisco Suárez, a Spanish Jesuit respected even in Lutheran universities. Francisco Suárez ( 5 January 1548, Granada, Spain - 25 September 1617, Lisbon, Portugal) was a The Society of Jesus ( Latin: Societas Iesu, SJ and SI or SJ, SI) is a Catholic religious order Lutheranism is a major branch of Western Christianity that identifies with the teachings of the sixteenth-century German reformer Martin Luther 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. Robert Boyle was a Natural philosopher, chemist physicist inventor and early Gentleman scientist, noted for his work in Physics and Chemistry Yet it remains the case that Leibniz's methods and concerns often anticipate the logic, and analytic and linguistic philosophy of the 20th century. Logic is the study of the principles of valid demonstration and Inference. 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 a philosophical school that approached traditional philosophical problems as rooted in misunderstandings philosophers develop by forgetting what words actually

The Principles

Leibniz variously invoked one or another of seven fundamental philosophical Principles (Mates 1986: chpts. 7. 3, 9):

The second principle here is often referred to as Leibniz's Law [2]. The identity of indiscernibles is an ontological principle which states that two or more objects or entities are identical (are one and the same entity The Identity of Indiscernibles has attracted the most controversy and criticism, especially from corpuscular philosophy and quantum mechanics.

Leibniz would on occasion give a speech for a specific principle, but more often took them for granted. For a precis of what Leibniz meant by these and other Principles, see Mercer (2001: 473–84). For a classic discussion of Sufficient Reason and Plenitude, see Lovejoy (1957). The principle of sufficient reason (also called the Causal Doctrine) 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. Metaphysics is the branch of Philosophy investigating principles of reality transcending those of any particular science Monism is the metaphysical and Theological view that all is one that all reality is subsumed under the most fundamental category of being or existence The Monadology ( Monadologie, 1714 is one of Gottfried Leibniz ’s works that best define his philosophy monadism. Monads are to the metaphysical realm what atoms are to the physical/phenomenal. History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny Monads are the ultimate elements of the universe. The Universe is defined as everything that Physically Exists: the entirety of Space and Time, all forms of Matter, Energy 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). Gottfried Leibniz 's theory of pre-established harmony is a philosophical theory about causation under which every "substance" only affects itself 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 Monads are centers of force; substance is force, while space, matter, and motion are merely phenomenal. In Physics, a force is whatever can cause an object with Mass to Accelerate. Space is the extent within which Matter is physically extended and objects and Events have positions relative to one another Matter is commonly defined as being anything that has mass and that takes up space. In Physics, motion means a constant change in the location of a body

The ontological essence of a monad is its irreducible simplicity. In Philosophy, ontology (from the Greek, genitive: of being (part 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. A scientific law is a statement that describes the behavior of some particular thing or set of things within the natural world, with an adequately thorough history of successful A subatomic particle is an elementary or composite Particle smaller than an Atom. ) 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. The question of free will 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. God is the principal or sole Deity in Religions and other belief systems that worship one deity. 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.

Theodicy and optimism

The Théodicée tries to justify the apparent imperfections of the world by claiming that it is optimal among all possible worlds. Optimism The phrase " the best of all possible worlds " (le meilleur des mondes possibles was coined by the German philosopher Gottfried Leibniz It must be the best possible and most balanced world, because it was created by a perfect God. Rutherford (1998) is a detailed scholarly study of Leibniz's theodicy.

The statement that "we live in the best of all possible worlds" drew scorn, most notably from Voltaire, who lampooned it in his comic novel Candide by having the character Dr. Pangloss (a parody of Leibniz) repeat it like a mantra. François-Marie Arouet ( 21 November 1694 30 May 1778) better known by the Pen name Voltaire, was a French --> Candide ou l'Optimisme (1759 is a French Satire by the Enlightenment Philosopher Voltaire, English translations of which --> Candide ou l'Optimisme (1759 is a French Satire by the Enlightenment Philosopher Voltaire, English translations of which A mantra ( Devanāgarī मन्त्र (or mantram is a religious or mystical syllable or poem typically from the Sanskrit language Thus the adjective "panglossian", describing one so naive as to believe that the world about us is the best possible one.

The mathematician Paul du Bois-Reymond, in his "Leibnizian Thoughts in Modern Science," wrote that Leibniz thought of God as a mathematician. Science (from the Latin scientia, meaning " Knowledge " or "knowing" is the effort to discover, and increase human understanding 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. In Mathematics, maxima and minima, known collectively as extrema, are the largest value (maximum or smallest value (minimum that The Mathematical concept of a function expresses dependence between two quantities one of which is given (the independent variable, argument of the function For the tangent function see Trigonometric functions. For other uses see Tangent (disambiguation. 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. Calculus of variations is a field of Mathematics that deals with functionals, as opposed to ordinary Calculus which deals with functions. Infinity (symbolically represented with ∞) comes from the Latin infinitas or "unboundedness Evil, in many cultures is used to describe acts or thoughts which are contrary to some particular religion "

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. This article discusses the history of the principle of least action The law of conservation of mass/matter, also known as law of mass/matter conservation (or the Lomonosov - Lavoisier law says that the Mass of In Physics, the law of conservation of energy states that the total amount of Energy in an isolated system remains constant and cannot be created although it may In addition, the modern observations that lead to the Fine-tuned Universe arguments seem to support his view:

  1. The 3+1 dimensional structure of spacetime may be ideal. The fine-tuned Universe is the idea that the conditions that allow Life in the Universe can only occur when certain universal Physical constants lie within SpaceTime is a patent-pending three dimensional graphical user interface that allows end users to search their content such as Google Google Images Yahoo! YouTube eBay Amazon and RSS In order to sustain complexity such as life, a universe probably requires three spatial and one temporal dimension. In general usage complexity often tends to be used to characterize something with many parts in intricate arrangement Life is a state that distinguishes Organisms from non-living objects such as non-life and dead organisms being manifested by growth through Metabolism The Universe is defined as everything that Physically Exists: the entirety of Space and Time, all forms of Matter, Energy Space is the extent within which Matter is physically extended and objects and Events have positions relative to one another For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of In mathematics the dimension of a Space is roughly defined as the minimum number of Coordinates needed to specify every point within it Most universes deviating from 3+1 either violate some fundamental physical laws, or are impossible. A physical law or scientific law is a Scientific generalization based on empirical Observations of physical behavior (i 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. The Universe is defined as everything that Physically Exists: the entirety of Space and Time, all forms of Matter, Energy The Solar System consists of the Sun and those celestial objects bound to it by Gravity. EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 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. EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 The Solar System consists of the Sun and those celestial objects bound to it by Gravity. The Milky Way (a translation of the Latin Via Lactea, in turn derived from the Greek Γαλαξίας (Galaxias sometimes referred to simply In Planetary astronomy and Astrobiology, the Rare Earth hypothesis argues that the emergence of complex Multicellular life ( Metazoa 5,6).
  3. The most sweeping form of optimism derives from the Anthropic Principle (Barrow and Tipler 1986). In Physics and Cosmology, the anthropic principle states that humans should take into account the constraints that human existence imposes on the kind of theoretical 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. The fine-structure constant or Sommerfeld fine-structure constant, usually denoted \alpha \ is the Fundamental physical constant characterizing The proton ( Greek πρῶτον / proton "first" is a Subatomic particle with an Electric charge of one positive The electron is a fundamental Subatomic particle that was identified and assigned the negative charge in 1897 by J 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. In general usage complexity often tends to be used to characterize something with many parts in intricate arrangement

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. A physical law or scientific law is a Scientific generalization based on empirical Observations of physical behavior (i The Universe is defined as everything that Physically Exists: the entirety of Space and Time, all forms of Matter, Energy The Solar System consists of the Sun and those celestial objects bound to it by Gravity. EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001 In general usage complexity often tends to be used to characterize something with many parts in intricate arrangement A galaxy is a massive gravitationally bound system consisting of Stars an Interstellar medium of gas and dust, and Dark matter A star is a massive luminous ball of plasma. The nearest star to Earth is the Sun, which is the source of most of the Energy on Earth Sapience is often defined as Wisdom, or the ability of an organism or entity to act with appropriate judgment. On the other hand, it is also reasonable to believe that life might be more intelligent given some other set of circumstances. Further, some modern proponents of Leibnizian optimism seem to confuse the term "best" with terms like "good" or "better"; by definition, there can be only one "best".

Symbolic thought

Leibniz believed that much of human reasoning could be reduced to calculations of a sort, and that such calculations could resolve many differences of opinion:

"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. The Calculus Ratiocinator is a theoretical universal logical calculation framework a concept described in the writings of Gottfried Leibniz, usually paired with his more frequently Symbolic logic is the area of Mathematics which studies the purely formal properties of strings of symbols 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. Friedrich Ludwig Gottlob Frege ( 8 November 1848, Wismar, Grand Duchy of Mecklenburg-Schwerin  &ndash 26 July 1925 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 Charles Sanders Peirce (pronounced purse) (September 10 1839 &ndash April 19 1914 was an American Logician mathematician, philosopher George Boole (buːl ( November 2, 1815 &ndash December 8, 1864) was a British Mathematician and Philosopher. Augustus De Morgan ( 27 June, 1806 &ndash 18 March, 1871) was a British Mathematician and Logician.

Leibniz thought symbols were important for human understanding. The musical instrument is spelled Cymbal. A symbol is something --- such as an object, Picture, written word a sound a piece 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. Calculus ( Latin, calculus, a small stone used for counting is a branch of Mathematics that includes the study of limits, Derivatives 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. Charles Sanders Peirce (pronounced purse) (September 10 1839 &ndash April 19 1914 was an American Logician mathematician, philosopher Semiotics, semiotic studies, or semiology is the study of sign processes (semiosis or signification and communication signs and Symbols both

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. In Typography, a grapheme is the fundamental unit in written language. 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. Egyptian hieroglyphs (ˈhaɪərəʊɡlɪf from Greek grc-Grek ἱερογλύφος " sacred carving " also hieroglyphic = grc-Grek A Chinese character, also known as a Han character ( is a Logogram used in writing Chinese (hanzi Japanese ( Astronomy (from the Greek words astron (ἄστρον "star" and nomos (νόμος "law" is the scientific study Chemistry (from Egyptian kēme (chem meaning "earth") is the Science concerned with the composition structure and properties (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. The idea of an alphabet of human thought originates in the 17th century when proposals were first made for a universal ''a priori'' 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. In Mathematics, a prime number (or a prime) is a Natural number which has exactly two distinct natural number Divisors 1 In Mathematical logic, a Gödel numbering is a function that assigns to each symbol and Well-formed formula of some Formal language a unique Granted, there is no intuitive or mnemonic way to number any set of elementary concepts using the prime numbers. A mnemonic device (nəˈmɒnɪk is a Memory aid Commonly met mnemonics are often verbal something such as a very short poem or a special word used to help a person remember

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. Algebra is a branch of Mathematics concerning the study of structure, relation, and Quantity. Only in 1676 did he conceive of a kind of "algebra of thought," modeled on and including conventional algebra and its notation. The resulting characteristic included a logical calculus, some combinatorics, algebra, his analysis situs (geometry of situation) discussed in 3. 2, a universal concept language, and more.

What Leibniz actually intended by his characteristica universalis and calculus ratiocinator, and the extent to which modern formal logic does justice to the calculus, may never be established. The Calculus Ratiocinator is a theoretical universal logical calculation framework a concept described in the writings of Gottfried Leibniz, usually paired with his more frequently Logic is the study of the principles of valid demonstration and Inference. A good introductory discussion of the "characteristic" is Jolley (1995: 226–40). An early, yet still classic, discussion of the "characteristic" and "calculus" is Couturat (1901: chpts. 3,4).

Formal logic

Main 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. In Mathematical logic, algebraic logic formalizes logic using the methods of Abstract algebra. George Boole (buːl ( November 2, 1815 &ndash December 8, 1864) was a British Mathematician and Philosopher. Augustus De Morgan ( 27 June, 1806 &ndash 18 March, 1871) was a British Mathematician and Logician. Leibniz enunciated the principal properties of what we now call conjunction, disjunction, negation, identity, set inclusion, and the empty set. In Logic and/or Mathematics, logical conjunction or and is a two-place Logical operation that results in a value of true if both of In Logic and Mathematics, negation or not is an operation on Logical values for example the logical value of a Proposition In Mathematics, the term identity has several different important meanings An identity is an equality that remains true regardless of the values of In Mathematics, and more specifically Set theory, the empty set is the unique set having no ( Zero) members The principles of Leibniz's logic and, arguably, of his whole philosophy, reduce to two:

  1. All our ideas are compounded from a very small number of simple ideas, which form the alphabet of human thought. The idea of an alphabet of human thought originates in the 17th century when proposals were first made for a universal ''a priori'' language.
  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. In Logic and Mathematics, negation or not is an operation on Logical values for example the logical value of a Proposition Quantification has two distinct meanings In Mathematics and Empirical science, it refers to human acts known as Counting and Measuring A variable (ˈvɛərɪəbl is an Attribute of a physical or an abstract System which may change its Value while it is under Observation. The domain of discourse, sometimes called the universe of discourse, logical discourse, or simply discourse, is an analytic tool used in Deductive

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 Arthur William Russell 3rd Earl Russell, OM, FRS (18 May 1872 – 2 February 1970 was a British Philosopher, Historian

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). The Mathematical concept of a function expresses dependence between two quantities one of which is given (the independent variable, argument of the function In Mathematics, the Cartesian coordinate system (also called rectangular coordinate system) is used to determine each point uniquely in a plane In Mathematics, the Cartesian coordinate system (also called rectangular coordinate system) is used to determine each point uniquely in a plane For the tangent function see Trigonometric functions. 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 vector (or line that is perpendicular to a surface In the 18th century, "function" lost these geometrical associations.

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. A linear equation is an Algebraic equation in which each term is either a Constant or the product of a constant and (the first power of a single Variable In Mathematics, a matrix (plural matrices) is a rectangular table of elements (or entries) which may be Numbers or more generally This method was later called Gaussian elimination. In Linear algebra, Gaussian elimination is an efficient Algorithm for solving systems of linear equations, to find the rank of a matrix Leibniz's discoveries of Boolean algebra and of symbolic logic, also relevant to mathematics, are discussed in the preceding section. Boolean algebra (or Boolean logic) is a logical calculus of truth values, developed by George Boole in the late 1830s Symbolic logic is the area of Mathematics which studies the purely formal properties of strings of symbols

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. Sir Isaac Newton, FRS (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements Calculus ( Latin, calculus, a small stone used for counting is a branch of Mathematics that includes the study of limits, Derivatives 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. Events 308 - The Congress of Carnuntum: Attempting to keep peace within the Roman Empire, the leaders of the Tetrarchy declare 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. The ∫ Symbol is used to denote the Integral in Mathematics. In differential calculus, a differential is traditionally an Infinitesimally small change in a Variable. 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 Calculus, the product rule also called Leibniz's law (see derivation) governs the differentiation of products of differentiable Differential Calculus, a field in Mathematics, is the study of how functions change when their inputs change " In addition, the theorem that tells how and when to differentiate under the integral sign is called Leibniz integral rule. In Mathematics, Leibniz's rule for Differentiation under the integral sign, named after Gottfried Leibniz, tells us that if we have an Integral

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. heuristic (hyu̇-ˈris-tik is a method to help solve a problem commonly an informal method Leibniz also freely invoked mathematical entities he called infinitesimals, manipulating them in ways suggesting that they had paradoxical algebraic properties. Infinitesimals (from a 17th century Modern Latin coinage infinitesimus, originally referring to the " Infinite[[ th]]" member of a series have A paradox is a true statement or group of statements that leads to a Contradiction or a situation which defies intuition; or inversely Algebra is a branch of Mathematics concerning the study of structure, relation, and Quantity. 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. George Berkeley (ˈbɑrkli (12 March 1685 14 January 1753 also known as Bishop Berkeley, was a Philosopher. Faith is a Belief in the trustworthiness of an Idea. Formal usage of the word "faith" is usually reserved for concepts of Religion, as in Theology is the study of a god or the gods from a religious perspective Christianity ( Greek Χριστιανισμός from the word Xριστός ( Christ)is a monotheistic Religion centered on the life and teachings Revelation is the act of revealing or disclosing (see etymology or in the theological perception making something obvious and clearly understood through active or passive communication

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. The Calculus controversy was an argument between Seventeenth-century Mathematicians Isaac Newton and Gottfried Leibniz over who had

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. Karl Theodor Wilhelm Weierstrass ( Weierstraß) ( October 31, 1815 &ndash February 19, 1897) was a German mathematician In Mathematics, the concept of a " limit " is used to describe the Behavior of a function as its argument either "gets close" In Mathematics, the real numbers may be described informally in several different ways Their work discredited the use of infinitesimals to justify calculus. Infinitesimals (from a 17th century Modern Latin coinage infinitesimus, originally referring to the " Infinite[[ th]]" member of a series have Yet, infinitesimals survived in science and engineering, and even in rigorous mathematics, via the fundamental computational device known as the differential. In mathematics and more specifically in Differential calculus, the term differential has several interrelated meanings Beginning in 1960, Abraham Robinson worked out a rigorous foundation for Leibniz's infinitesimals, using model theory. Abraham Robinson ( October 6, 1918 &ndash April 11, 1974) was a Mathematician who is most widely known for development of Non-standard In Mathematics, model theory is the study of (classes of mathematical structures such as groups, Fields graphs or even models The resulting nonstandard analysis can be seen as a belated vindication of Leibniz's mathematical reasoning. Non-standard analysis is a branch of Mathematics that formulates analysis using a rigorous notion of an Infinitesimal number

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. Topology ( Greek topos, "place" and logos, "study" is the branch of Mathematics that studies the properties of There are two takes on this situation. On the one hand, Mates (1986: 240), citing a 1954 paper in German by Jacob Freudenthal, argues:

"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. Jacob Freudenthal (born June 20, 1839, at Bodenfelde, province of Hanover, Prussia -1907 was a German Philosopher The Seven Bridges of Königsberg is a famous historical problem in mathematics 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. "

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. Dynamism is a Metaphysical concept conceived by Gottfried Leibniz (1646–1716 and developed into a full System of Cosmology. Sir Isaac Newton, FRS (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements 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. In Physics, motion means a constant change in the location of a body In physics the term dynamics customarily refers to the time evolution of physical processes The kinetic energy of an object is the extra Energy which it possesses due to its motion Potential energy can be thought of as Energy stored within a physical system An important example of Leibniz's mature physical thinking is his Specimen Dynamicum of 1695. (AG 117, LL §46, W II. 5) On Leibniz and physics, see the chapter by Garber in Jolley (1995) and Wilson (1989).

Until the discovery of subatomic particles and the quantum mechanics governing them, many of Leibniz's speculative ideas about aspects of nature not reducible to statics and dynamics made little sense. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons For instance, he anticipated Albert Einstein by arguing, against Newton, that space, time and motion are relative, not absolute. Albert Einstein ( German: ˈalbɐt ˈaɪ̯nʃtaɪ̯n; English: ˈælbɝt ˈaɪnstaɪn (14 March 1879 – 18 April 1955 was a German -born theoretical Space is the extent within which Matter is physically extended and objects and Events have positions relative to one another For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of Leibniz's rule in interacting theories plays a role in supersymmetry and in the lattices of quantum mechanics. In Mathematics, Leibniz's rule for Differentiation under the integral sign, named after Gottfried Leibniz, tells us that if we have an Integral In Particle physics, supersymmetry (often abbreviated SUSY) is a Symmetry that relates elementary particles of one spin to another particle that Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons 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. The principle of sufficient reason (also called the Causal Doctrine) states that anything that happens does so for a definite Reason. Cosmology (from Greek grc κοσμολογία - grc κόσμος kosmos, "universe" and grc -λογία -logia) is study The identity of indiscernibles is an ontological principle which states that two or more objects or entities are identical (are one and the same entity Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons Those who advocate digital philosophy, a recent direction in cosmology, claim Leibniz as a precursor. Digital philosophy is a new direction in Philosophy and cosmology advocated by certain mathematicians and theoretical physicists e

The vis viva

Main article: vis viva

Leibniz 's vis viva (Latin for living force) is mv2, twice the modern Kinetic energy. In the history of Science, vis viva (from the Latin for living force) is an Obsolete scientific theory that served as an elementary The kinetic energy of an object is the extra Energy which it possesses due to its motion 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. In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product Engineers eventually found "vis viva" useful, so that the two approaches eventually were seen as complementary. An engineer is a person professionally engaged in a field of Engineering.

Other natural science

By proposing that the earth has a molten core, he anticipated modern geology. Geology (from Greek γη gê, "earth" and λόγος Logos, "speech" lit 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. Embryology (from Greek grc ἔμβρυον embryon, "unborn embryo" and grc -λογία -logia) is the study of the development In the life sciences and paleontology, he revealed an amazing transformist intuition, fueled by his study of comparative anatomy and fossils. Foundations of modern biology There are five unifying principles Palaeontology redirects here For the Scientific journal, see Palaeontology (journal. 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. Medicine is the art and science of healing It encompasses a range of Health care practices evolved to maintain and restore Human Health by the

Social science

In psychology he anticipated the distinction between conscious and unconscious states. Psychology (from Greek grc ψῡχή psȳkhē, "breath life soul" and grc -λογία -logia) is an Academic and Consciousness has been defined loosely as a constellation of attributes of Mind such as Subjectivity, Self-awareness, Sentience, and the Many observers throughout history have argued that there are influences on Consciousness from other parts of the Mind. 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. 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 Veterinary medicine the application of medical, diagnostic, and therapeutic principles to companion, domestic, exotic, wildlife 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. The balance of trade (or net exports, sometimes symbolized as NX) is the difference between the monetary value of Exports and imports in an He even proposed something akin to what much later emerged as game theory. Game theory is a branch of Applied mathematics that is used in the Social sciences (most notably Economics) Biology, Engineering, In sociology he laid the ground for communication theory. Sociology (from Latin: socius "companion" and the suffix -ology "the study of" from Greek λόγος lógos "knowledge" 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. For the song by 311, see Grassroots. Applied science is the application of knowledge from one or more natural scientific 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. Denis Papin ( 22 August 1647 - c 1712 was a French Physicist, Mathematician and Inventor, best known for his pioneering A steam engine is a Heat engine that performs Mechanical work using Steam as its Working fluid. 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. Silver (ˈsɪlvɚ is a Chemical element with the symbol " Ag " (argentum from the Ancient Greek: ἀργήντος - argēntos gen The Harz is a mountain range in central Germany It is the highest mountain chain in northern Germany occupying parts of the German states of Lower Saxony, Saxony-Anhalt (Aiton 1985: 107–114, 136)

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. The binary numeral system, or base-2 number system, is a Numeral system that represents numeric values using two symbols usually 0 and 1. (See Couturat, 1901: 473–78. ) He anticipated Lagrangian interpolation and algorithmic information theory. In Numerical analysis, a Lagrange polynomial, named after Joseph Louis Lagrange, is the interpolation Polynomial for a given set of data points Algorithmic information theory is a subfield of Information theory and Computer science that concerns itself with the relationship between computation His calculus ratiocinator anticipated aspects of the universal Turing machine. The Calculus Ratiocinator is a theoretical universal logical calculation framework a concept described in the writings of Gottfried Leibniz, usually paired with his more frequently This article is a supplement to the article Turing machine. Alan Turing 's "universal computing machine" (alternately "universal 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. Norbert Wiener ( November 26, 1894, Columbia Missouri – March 18, 1964, Stockholm, Sweden) was an American Feedback is a circular causal Process whereby some proportion of a system's output is returned (fed back to the Input. Cybernetics is the interdisciplinary study of the Structure of Complex systems especially Communication processes control mechanisms and Feedback

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. The Liebniz Stepped Drum (or Step(ped Reckoner, a translation of its German name Staffelwalze, was a digital Mechanical calculator invented by German The Royal Society of London for the Improvement of Natural Knowledge, known simply as The Royal Society, is a Learned society for science that was founded in 1660 A number of such machines were made during his years in Hanover, by a craftsman working under Leibniz's supervision. Hanover (i ( haˈnoːfɐ on the river Leine, is the capital of the federal state of Lower Saxony ( Niedersachsen It was not an unambiguous success because it did not fully mechanize the operation of carrying. Couturat (1901: 115) reported finding an unpublished note by Leibniz, dated 1674, describing a machine capable of performing some algebraic operations.

Leibniz was groping towards hardware and software concepts worked out much later in 1830-1845 by Charles Babbage and Ada Lovelace. Augusta Ada King Countess of Lovelace (10 December 1815 London England &ndash 27 November 1852 Marylebone, London England born Augusta Ada Byron, was the only 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.

Librarian

While serving as librarian of the ducal libraries in Hanover and Wolfenbuettel, Leibniz effectively became one of the founders of library science. Hanover (i ( haˈnoːfɐ on the river Leine, is the capital of the federal state of Lower Saxony ( Niedersachsen Library science is an Interdisciplinary Science incorporating the Humanities, Law and Applied science to study topics related to [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. Library classification forms part of the field of Library and information science. The Bodleian Library ( the main Research library of the University of Oxford, is one of the oldest libraries in Europe, and in England The University of Oxford (informally "Oxford University" or simply "Oxford" located in the city of Oxford, Oxfordshire, England is the 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. Johannes Gensfleisch zur Laden zum Gutenberg ( 1398 &ndash February 3, 1468) was a German Goldsmith and printer who is credited 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. The Library of Congress is the De facto National library of the United States and the research arm of the United States Congress 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. A central concept in Science and the Scientific method is that all Evidence must be empirical, or empirically based that is dependent on evidence A Computer Database is a structured collection of records or data that is stored in a computer system 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. The Calculus Ratiocinator is a theoretical universal logical calculation framework a concept described in the writings of Gottfried Leibniz, usually paired with his more frequently g. , Esperanto and its rivals), symbolic logic, even the World Wide Web. is by far the most widely spoken constructed International auxiliary language in the world Symbolic logic is the area of Mathematics which studies the purely formal properties of strings of symbols The World Wide Web (commonly shortened to the Web) is a system of interlinked Hypertext documents accessed via the Internet.

Advocate of scientific societies

Leibniz emphasized that research was a collaborative endeavor. Research is defined as Human activity based on Intellectual application in the investigation of Matter. 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. The Prussian Academy of Sciences (Preußische Akademie der Wissenschaften was an Academy established in Berlin on July 11 1700. Leibniz drew up its first statutes, and served as its first President for the remainder of his life. That Academy evolved into the German Academy of Sciences, the publisher of the ongoing critical edition of his works. On Leibniz’s projects for scientific societies, see Couturat (1901: App. IV).

Lawyer, moralist

No philosopher has ever had as much experience with practical affairs of state as Leibniz, except possibly Marcus Aurelius. Marcus Aurelius Antoninus Augustus (often referred to as "the wise" ( April 26, 121 – March 17, 180) was Roman Emperor Leibniz's writings on law, ethics, and politics (e. g. , AG 19, 94, 111, 193; Riley 1988; LL §§2, 7, 20, 29, 44, 59, 62, 65; W I. 1, IV. 1–3) were long overlooked by English speaking scholars, but this has changed of late; see (in order of difficulty) Jolley (2005: chpt. 7), Gregory Brown's chapter in Jolley (1995), Hostler (1975), and Riley (1996).

While Leibniz was no apologist for absolute monarchy like 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. Thomas Hobbes (born 5 April 1588died 4 December 1679 was an English philosopher, whose famous 1651 book Leviathan established the foundation John Locke (29 August 1632 – 28 October 1704 was an English Philosopher. The following excerpt from a 1695 letter to Baron J. C. Boineburg's son Philipp is very revealing of Leibniz's political sentiments:

"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. Hugo Grotius or Huig de Groot, or Hugo de Groot; ( Delft, 10 April 1583 Rostock, 28 August 1645 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. )

Leibniz foresaw the European Union. The European Union ( EU) is a political and economic union of twenty-seven member states, located primarily in 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. Ecumenism (also oecumenism, œcumenism) refers to initiatives aimed at greater Religious unity or cooperation Lutheranism is a major branch of Western Christianity that identifies with the teachings of the sixteenth-century German reformer Martin Luther The Reformed churches are a group of Christian Protestant Denominations formally characterized by a similar Calvinist system of doctrine historically 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. John Frederick ( German: Johann Friedrich 25 April 1625, Herzberg am Harz &ndash 18 December 1679, Augsburg (The House of Brunswick remained Lutheran because the Duke's children did not follow their father. Brunswick-Lüneburg (Braunschweig-Lüneburg also Brunswick-Lunenburg was a historical ducal state during the period from the Late Middle Ages through the ) These efforts included corresponding with the French bishop Bossuet, and involved Leibniz in a fair bit of theological controversy. Jacques-Bénigne Bossuet ( September 27, 1627 - April 12, 1704) was a French Bishop and theologian, renowned He evidently thought that the thoroughgoing application of reason would suffice to heal the breach caused by the Reformation. The Protestant Reformation was a reform movement in Europe that began in 1517 though its roots lie further back in time

Philologist

Leibniz was an avid student of languages, eagerly latching on to any information about vocabulary and grammar that came his way. 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 Grammar is the field of Linguistics that covers the Rules governing the use of any given natural language. He refuted the belief, widely held by Christian scholars in his day, that Hebrew was the primeval language of the human race. Human beings, humans or man (Origin 1590–1600 L homō man OL hemō the earthly one (see Humus 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. Swedish ( is a North Germanic language spoken by more than nine million people predominantly in Sweden and parts of Finland, especially along the The Germanic languages are a group of related languages that constitute a branch of the Indo-European (IE Language family. He puzzled over the origins of the Slavic languages, was aware of the existence of Sanskrit, and was fascinated by classical Chinese. The Slavic languages (also called Slavonic languages) a group of closely related Languages of the Slavic peoples and a subgroup of Indo-European languages Sanskrit (sa संस्कृता वाक् saṃskṛtā vāk, for short sa संस्कृतम् saṃskṛtam) is a historical Classical Chinese or Literary Chinese is a traditional style of Written Chinese based on the Grammar and Vocabulary of ancient 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. See Comparative linguistics for the narrower field of "comparative philology"

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. China ( Wade-Giles ( Mandarin) Chung¹kuo² is a cultural region, an ancient Civilization, and depending on perspective a National He concluded that Europeans could learn much from the Confucian ethical tradition. Confucianism ( is a Chinese ethical and philosophical system originally developed from the teachings of the fifth century B He mulled over the possibility that the Chinese characters were an unwitting form of his universal characteristic. A Chinese character, also known as a Han character ( is a Logogram used in writing Chinese (hanzi Japanese ( 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. The I Ching ( Wade-Giles) or “Yì Jīng” ( Pinyin) also called “Classic of Changes” or “Book of Changes” is one of the oldest of the The binary numeral system, or base-2 number system, is a Numeral system that represents numeric values using two symbols usually 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. An archive refers to a collection of historical records and also refers to the location in which these records are kept Vienna ( in Wien; see also other names) is the Capital of Austria, and is also one of the nine States of Austria. Law is a system of rules enforced through a set of Institutions used as an instrument to underpin civil obedience politics economics and society Diplomacy is the art and practice of conducting Negotiations between representatives of groups or states He visited mines, talked with mine engineers, and tried to negotiate export contracts for lead from the ducal mines in the Harz mountains. Mining is the extraction of valuable Minerals or other geological materials from the earth usually (but not always from an Ore body Engineering is the Discipline and Profession of applying technical and scientific Knowledge and Characteristics Lead has a dull luster and is a dense, Ductile, very soft highly The Harz is a mountain range in central Germany It is the highest mountain chain in northern Germany occupying parts of the German states of Lower Saxony, Saxony-Anhalt His proposal that the streets of Vienna be lit with lamps burning rapeseed oil was implemented. Rapeseed ( Brassica napus) also known as rape, oilseed rape, rapa, rapaseed and (in the case of one particular group of 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. The Holy Roman Emperor (Römischer Kaiser or Römisch-Deutscher Kaiser Romanorum Imperator was the elected monarch ruling over the many varying numbers of states A concordat usually refers to an agreement between the Apostolic See and a Government of a certain country on religious matters although it is also used The Holy See is the episcopal jurisdiction of the Bishop of Rome, commonly known as the Pope, and is the preeminent Episcopal see of the Roman Catholic He wrote and published an important paper on mechanics. Mechanics ( Greek) is the branch of Physics concerned with the behaviour of physical bodies when subjected to Forces or displacements 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. Louis Couturat ( January 17, 1868 - August 3, 1914) was a French Logician mathematician, philosopher Metaphysics is the branch of Philosophy investigating principles of reality transcending those of any particular science 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. 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 But after a meticulous study of all of Leibniz's philosophical writings up to 1688—a study the 1999 additions to the critical edition made possible—Mercer (2001) begged to differ with Couturat's reading; the jury is still out.

Leibniz was not devoid of humor and imagination; see W IV. 6 and LL § 40. Also see a curious passage titled "Leibniz's Philosophical Dream," first published by Bodemann in 1895 and translated on p. 253 of Morris, Mary, ed. and trans. , 1934. Philosophical Writings. Dent & Sons Ltd.

References

  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

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.

Collections of shorter works in translation:

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:

Advanced

Online bibliography by Gregory Brown.

Other works cited

Quotations

Wiener (1951: 567–70) lists 44 quotable "proverbs" beginning with "Justice is the charity of the wise. "

See also

External links



Persondata
NAMELeibniz, Gottfried Wilhelm
ALTERNATIVE NAMESLeibnitz, Gottfried Wilhelm; Leibniz, Gottfried Wilhelm von; von Leibniz, Gottfried Wilhelm
SHORT DESCRIPTIONGerman philoospher
DATE OF BIRTHJuly 1, 1646(1646-07-01)
PLACE OF BIRTHLeipzig, Germany
DATE OF DEATHNovember 14, 1716
PLACE OF DEATHHanover, Germany
"July 1st" redirects here For the Ayumi Hamasaki song see H (song. This sort of fix restores section edit linkpoints to where they belong Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. Events 1533 - Conquistadors from Spain under the leadership of Francisco Pizarro arrive in Cajamarca, Inca Year 1716 ( MDCCXVI) was a Leap year starting on Wednesday (link will display the full calendar of the Gregorian calendar (or a Hanover (i ( haˈnoːfɐ on the river Leine, is the capital of the federal state of Lower Saxony ( Niedersachsen Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe.
© 2009 citizendia.org; parts available under the terms of GNU Free Documentation License, from http://en.wikipedia.org
 Dapyx Software network: MP3 Explorer | Ebook Manager | Zenithic