Editing Gottfried Wilhelm Leibniz (section)

{{Short description|German polymath (1646–1716)}}
{{Redirect|Leibniz}}
{{CS1 config|mode=cs1}}
{{Use dmy dates|date=July 2017}}
{{Infobox philosopher
| name  = Gottfried Wilhelm Leibniz
| image = Christoph Bernhard Francke - Bildnis des Philosophen Leibniz (ca. 1695).jpg
| caption          = ''Bildnis des Philosophen Leibniz'' (1695), by [[Christoph Bernhard Francke|Christoph Francke]]
| birth_date       = 1 July 1646
| birth_place      = [[Leipzig]], [[Electorate of Saxony]], Holy Roman Empire
| death_date       = {{Death date and age|df=yes|1716|11|14|1646|07|1}}
| death_place      = [[Hanover]], [[Electorate of Hanover]], Holy Roman Empire
| education        = {{plainlist|
* {{Interlanguage link|Alte Nikolaischule|de|3=Alte Nikolaischule (Leipzig)|lt=Alte Nikolaischule}}
* [[Leipzig University]] ([[Bachelor of Arts|BA]], 1662; [[Master of Arts|MA]], 1664; [[LLB]], 1665; [[Dr. phil. hab.]], 1666)
* [[University of Jena]]<br />(1663)<ref name="Arthur p. 16">Arthur 2014, p. 16.</ref>
* [[University of Altdorf]]<br />([[Dr. jur.]], 1666)}}
| era              = [[17th-century philosophy|17th-]]/[[18th-century philosophy]]
| region           = [[Western philosophy]]
| main_interests   = [[Mathematics]], [[physics]], [[geology]], [[medicine]], [[biology]], [[embryology]], [[epidemiology]], [[veterinary medicine]], [[paleontology]], [[psychology]], [[engineering]], [[librarianship]], [[linguistics]], [[philology]], [[sociology]], [[metaphysics]], [[ethics]], [[economics]], [[diplomacy]], [[history]], [[politics]], [[music theory]], [[poetry]], [[logic]], [[theodicy]], [[universal language]], [[universal science]]
|school_tradition = {{ubl|[[Rationalism]]|[[Pluralistic idealism]]<ref>Michael Blamauer (ed.), ''The Mental as Fundamental: New Perspectives on Panpsychism'', Walter de Gruyter, 2013, p. 111.</ref>|[[Foundationalism]]<ref name=SEP-FTJ>{{Cite SEP|url-id=justep-foundational|title=Foundationalist Theories of Epistemic Justification|date=August 5, 2022|edition=Fall 2022|author-last1=Hasan|author-first1=Ali|author-first2=Richard|author-last2=Fumerton}}</ref>|[[Conceptualism]]<ref>Stefano Di Bella, Tad M. Schmaltz (eds.), ''The Problem of Universals in Early Modern Philosophy'', Oxford University Press, 2017, p. 207 n. 25: "Leibniz's conceptualism [is related to] the Ockhamist tradition..."</ref>|[[Optimism]]|[[Indirect realism]]<ref>A. B. Dickerson, ''Kant on Representation and Objectivity'', Cambridge University Press, 2003, p. 85.</ref>|[[Correspondence theory of truth]]<ref>{{Cite SEP|url-id=truth-correspondence|title=The Correspondence Theory of Truth|date=May 28, 2015|edition=Summer 2022|first=Marian|last=David}}</ref>|[[Relational theory|Relationalism]]}}
|notable_ideas    = {{collapsible list|title={{nbsp}}|[[Algebraic logic]]|[[Binary code]]|[[Calculus]]|[[Differential equations]]|[[Mathesis universalis]]|[[Monadology|Monads]]|[[Best of all possible worlds]]|[[Pre-established harmony]]|[[Identity of indiscernibles]]|[[Matrix (mathematics)|Mathematical matrix]]|[[Function (mathematics)|Mathematical function]]|[[Fundamental theorem of calculus#Second part|Newton–Leibniz axiom]]|[[Leibniz's notation]]|[[Leibniz integral rule]]|[[Integral symbol]]|[[Leibniz harmonic triangle]]|[[Leibniz's test]]|[[Leibniz formula for π]]|[[Leibniz formula for determinants]]|[[Fractional calculus|Fractional derivative]]|[[Chain rule]]|[[Quotient rule]]|[[Product rule]]|[[Leibniz wheel]]|[[Leibniz's gap]]|[[Algebra of concepts]]|''[[Vis viva]]'' (principle of [[conservation of energy]])|[[Principle of least action]]|''[[Salva veritate]]''|[[Stepped reckoner]]|[[Symbolic logic]]|''[[Topology|Analysis situs]]''|[[Principle of sufficient reason]]|[[Law of continuity]]|[[Transcendental law of homogeneity]]|''[[De Arte Combinatoria|Ars combinatoria]]'' ([[alphabet of human thought]])|''[[Characteristica universalis]]''|''[[Calculus ratiocinator]]''|[[Compossibility]]|[[Partial fraction decomposition]]|[[Protogaea]]|[[Problem of why there is anything at all]]|[[Pluralistic idealism]]|[[Dynamism (metaphysics)|Metaphysical dynamism]]|[[Relational theory|Relationalism]]|[[Apperception]]|[[A priori and a posteriori|''A priori''/''a posteriori'' distinction]]|[[Deontic logic]]
}}
| signature=Leibnitz signature.svg
| thesis1_title      = De Arte Combinatoria (On the Combinatorial Art)
| thesis1_url        = https://archive.org/details/ita-bnc-mag-00000844-001
| thesis1_year       = March 1666
| thesis2_title      = Disputatio Inauguralis de Casibus Perplexis in Jure (Inaugural Disputation on Ambiguous Legal Cases)
| thesis2_url        = http://digital.slub-dresden.de/werkansicht/dlf/60594/1/
| thesis2_year       = November 1666
| doctoral_advisor   = {{ill|v=ib|Bartholomäus Leonhard von Schwendendörffer|de|3=Bartholomäus Leonhard von Schwendendörffer|lt=B. L. von Schwendendörffer}} (Dr. jur. advisor)<ref>Kurt Huber, ''Leibniz: Der Philosoph der universalen Harmonie'', Severus Verlag, 2014, p. 29.</ref><ref>{{MathGenealogy|id=60985}}.</ref><!--The Mathematics Genealogy Project lists Thomasius as his Dr. phil. supervisor but Arthur 2014, p. 13 lists him as Leibniz's BA advisor-->.
| academic_advisors = {{plainlist|
* [[Erhard Weigel]] (Jena)<ref name="Arthur p. 16" />
* [[Jakob Thomasius]] (B.A. advisor)<ref name="Arthur p. 13" />
* {{ill|v=ib|Johann Friedrich LeBret|de|3=Johann Adam Schertzer|lt=J. A. Schertzer}}<ref>Christia Mercer, ''Leibniz's Metaphysics: Its Origins and Development'', Cambridge University Press, 2001, p. 37.</ref>
* [[Christiaan Huygens]]}}
| notable_students = {{ubl|[[Jacob Bernoulli]] (epistolary correspondent)|[[Christian Wolff (philosopher)|Christian Wolff]] (epistolary correspondent)}}
}}
{{Theodicy}}

'''Gottfried Wilhelm Leibniz''' (or '''Leibnitz''';{{efn|English: {{IPAc-en|ˈ|l|aɪ|b|n|ɪ|t|s}} {{respell|LYBE|nits}};<ref>[http://www.collinsdictionary.com/dictionary/english/leibniz "Leibniz"] entry in ''[[Collins English Dictionary]]''.</ref> {{IPA|de|ˈɡɔtfʁiːt ˈvɪlhɛlm ˈlaɪbnɪts|lang|De-Gottfried Wilhelm Leibniz.ogg|small=no}}<ref>{{cite book |editor-first=Max |editor-last=Mangold |title=Duden-Aussprachewörterbuch (Duden Pronunciation Dictionary) |edition=7th |year=2005 |publisher=Bibliographisches Institut GmbH |location=Mannheim |language=de |isbn=978-3-411-04066-7 }}</ref><ref>{{citation|last=Wells|first=John C.|year=2008|title=Longman Pronunciation Dictionary|edition=3rd|publisher=Longman|isbn=9781405881180}}</ref> {{IPA|de|ˈlaɪpnɪts||De-Leibniz.ogg|label=or|small=no}};<ref>{{cite book |editor=Eva-Maria Krech |display-editors=etal |title=Deutsches Aussprachewörterbuch (German Pronunciation Dictionary) |edition=1st |year=2010 |publisher=Walter de Gruyter GmbH & Co. KG |location=Berlin |language=de |isbn=978-3-11-018203-3 }}</ref> {{langx|fr|Godefroi Guillaume {{notatypo|Leibnitz}}}}<ref>See inscription of the engraving depicted in the "[[#1666–1676|1666–1676]]" section.</ref> {{IPA|fr|ɡɔdfʁwa ɡijom lɛbnits|}}.}} {{OldStyleDateDY|1 July|1646|21 June}} – 14 November 1716) was a German [[polymath]] active as a [[mathematician]], [[philosopher]], [[scientist]] and [[diplomat]] who is credited, alongside [[Isaac Newton|Sir Isaac Newton]], with the creation of [[calculus]] in addition to many other branches of [[mathematics]], such as binary arithmetic and [[statistics]]. Leibniz has been called the "last universal genius" due to his vast expertise across fields, which became a rarity after his lifetime with the coming of the Industrial Revolution and the spread of specialized labor.<ref>{{Cite web |last=Dunne |first=Luke |date=2022-12-21 |title=Gottfried W. Leibniz: The Last True Genius |url=https://www.thecollector.com/leibniz-last-genius-philosopher/ |access-date=2023-10-01 |website=TheCollector |language=en}}</ref> He is a prominent figure in both the [[history of philosophy]] and the [[history of mathematics]]. He wrote works on [[philosophy]], [[theology]], [[ethics]], [[politics]], [[law]], [[history]], [[philology]], [[games]], [[music]], and other studies. Leibniz also made major contributions to [[physics]] and [[technology]], and anticipated notions that surfaced much later in [[probability theory]], [[biology]], [[medicine]], [[geology]], [[psychology]], [[linguistics]] and [[computer science]].

Leibniz contributed to the field of [[library science]], developing a cataloguing system (at the [[Herzog August Library]] in [[Wolfenbüttel]], Germany) that came to serve as a model for many of Europe's largest libraries.<ref>{{cite book |last1=Murray |first1=Stuart A.P. |url=https://archive.org/details/libraryillustrat0000murr/page/122 |title=The Library: An Illustrated History |date=2009 |publisher=[[Skyhorse Pub.]] |isbn=978-1-60239-706-4 |location=New York, NY |pages=122 |url-access=registration}}</ref><ref>Palumbo, Margherita, 'Leibniz as Librarian', in Maria Rosa Antognazza (ed.), ''The Oxford Handbook of Leibniz'', Oxford Handbooks (2018; online edn, Oxford Academic, 28 Jan. 2013), https://doi.org/10.1093/oxfordhb/9780199744725.013.008, accessed 25 Aug. 2024.</ref> His contributions to a wide range of subjects were scattered in various [[learned journal]]s, in tens of thousands of letters and in unpublished manuscripts. He wrote in several languages, primarily in Latin, French and German.<ref>Roughly 40%, 35% and 25%, respectively. [http://www.gwlb.de/Leibniz/Leibniz-Nachlass/index.htm www.gwlb.de]. {{Webarchive|url=https://web.archive.org/web/20110707122856/http://www.gwlb.de/Leibniz/Leibniz-Nachlass/index.htm|date=7 July 2011}}. ''Leibniz-Nachlass'' (i.e. Legacy of Leibniz), ''Gottfried Wilhelm Leibniz Bibliothek'' (one of the three Official Libraries of the German state [[Lower Saxony]]).</ref>{{efn|There is no complete gathering of the writings of Leibniz translated into English.<ref>{{cite book|last1=Baird|first1=Forrest E.|title=From Plato to Derrida|last2=Kaufmann|first2=Walter|publisher=Pearson Prentice Hall|year=2008|isbn=978-0-13-158591-1|location=Upper Saddle River, New Jersey}}</ref>}}

As a philosopher, he was a leading representative of 17th-century [[rationalism]] and [[idealism]]. As a mathematician, his major achievement was the development of differential and integral calculus, [[Leibniz–Newton calculus controversy|independently]] of Newton's contemporaneous developments.<ref>{{Cite book|title = History of Western Philosophy: Collectors Edition|edition=revised|url = https://books.google.com/books?id=Gm_cCZBiOhQC|publisher = Routledge|date = 15 April 2013|isbn = 978-1-135-69284-1|first = Bertrand|last = Russell|page = 469}} [https://books.google.com/books?id=Gm_cCZBiOhQC&pg=PA469 Extract of page 469].</ref> [[Leibniz's notation]] has been favored as the conventional and more exact expression of calculus.<ref>{{cite book |last1=Handley |first1=Lindsey D. |url=https://books.google.com/books?id=l3zWDwAAQBAJ |title=Don't Teach Coding: Until You Read This Book |last2=Foster |first2=Stephen R. |publisher=John Wiley & Sons |year=2020 |isbn=9781119602620 |page=29}} [https://books.google.com/books?id=l3zWDwAAQBAJ&pg=PA29 Extract of page 29].</ref><ref>{{cite book |last1=Apostol |first1=Tom M. |url=https://books.google.com/books?id=o2D4DwAAQBAJ |title=Calculus, Volume 1 |publisher=John Wiley & Sons |year=1991 |isbn=9780471000051 |edition=illustrated |page=172}} [https://books.google.com/books?id=o2D4DwAAQBAJ&pg=PA172 Extract of page 172].</ref><ref>{{cite book |last1=Maor |first1=Eli |url=https://books.google.com/books?id=e1CwvYNfvwgC |title=The Facts on File Calculus Handbook |publisher=The Facts on File Calculus Handbook |year=2003 |isbn=9781438109541 |page=58}} [https://books.google.com/books?id=e1CwvYNfvwgC&pg=PA58 Extract of page 58].</ref> In addition to his work on calculus, he is credited with devising the modern [[binary number]] system, which is the basis of modern communications and digital computing;<ref>{{Cite book |url=https://books.google.com/books?id=N-oEEQAAQBAJ&pg=PA168 |title=Handbook of the History and Philosophy of Mathematical Practice |date=2024 |publisher=Springer |isbn=978-3-031-40845-8 |editor-last=Sriraman |editor-first=Bharath |series= |volume=IV |location=Cham |pages=168}}</ref> however, [[Thomas Harriot]] had devised the same system decades before.<ref>{{cite journal |last1=Strickland |first1=Lloyd |author1-link=Lloyd Strickland |date=2023 |title=Why Did Thomas Harriot Invent Binary? |journal=The Mathematical Intelligencer |volume=46 |pages=57–62 |doi=10.1007/s00283-023-10271-9 |doi-access=free}}</ref> He envisioned the field of [[combinatorial topology]] as early as 1679,<ref name=":2">{{Cite book |last=Przytycki |first=Józef H. |url=https://books.google.com/books?id=22X8EAAAQBAJ&pg=PA5 |title=Lectures in Knot Theory: An Exploration of Contemporary Topics |last2=Bakshi |first2=Rhea Palak |last3=Ibarra |first3=Dionne |last4=Montoya-Vega |first4=Gabriel |last5=Weeks |first5=Deborah |date=2024 |publisher=Springer Nature |isbn=978-3-031-40044-5 |series= |location= |pages=5}}</ref> and helped initiate the field of [[fractional calculus]].<ref name=":12" /><ref name="Derivative" />

In the 20th century, Leibniz's notions of the [[law of continuity]] and the [[transcendental law of homogeneity]] found a consistent mathematical formulation by means of [[non-standard analysis]]. He was also a pioneer in the field of [[mechanical calculator]]s. While working on adding automatic multiplication and division to [[Pascal's calculator]], he was the first to describe a [[pinwheel calculator]] in 1685<ref>[[#SMITH|David Smith]], pp. 173–181 (1929).</ref> and invented the [[Leibniz wheel]], later used in the [[arithmometer]], the first mass-produced mechanical calculator.

In [[philosophy]] and [[theology]], Leibniz is most noted for his [[Philosophical optimism|optimism]], i.e. his conclusion that our world is, in a qualified sense, the [[Best of all possible worlds|best possible world]] that [[God]] could have [[Creatio ex nihilo|created]], a view sometimes lampooned by other thinkers, such as [[Voltaire]] in his [[Satire|satirical]] [[novella]] ''[[Candide]]''. Leibniz, along with [[René Descartes]] and [[Baruch Spinoza]], was one of the three influential early modern [[rationalism|rationalists]]. His philosophy also assimilates elements of the [[Scholasticism|scholastic]] tradition, notably the assumption that some substantive knowledge of reality can be achieved by reasoning from first principles or prior definitions. The work of Leibniz anticipated modern [[logic]] and still influences contemporary [[analytic philosophy]], such as its adopted use of the term "[[possible world]]" to define [[Modality (natural language)|modal]] notions.