TheInfoList

Gottfried Wilhelm (von) Leibniz ; see inscription of the engraving depicted in the " 1666–1676" section. ( – 14 November 1716) was a German
polymath A polymath ( el, πολυμαθής, , "having learned much"; la, homo universalis, "universal human") is an individual whose knowledge spans a substantial number of subjects, known to draw on complex bodies of knowledge to solve specific prob ...

active as a
mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers ( and ), formulas and related structures (), shapes and spaces in which they are contained ( ...

,
philosopher A philosopher is someone who practices philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about Metaphysics, existence, reason, Epistemology, knowledge, Ethics, values, Philosophy of mind, mi ...

,
scientist A scientist is a person who conducts scientific research The scientific method is an Empirical evidence, empirical method of acquiring knowledge that has characterized the development of science since at least the 17th century. It involves ...

, and
diplomat A diplomat (from grc, δίπλωμα; romanized Romanization or romanisation, in linguistics Linguistics is the scientific study of language A language is a structured system of communication used by humans, including speech ( ...
. He is a prominent figure in both the
history of philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about existence Existence is the ability of an entity to interact with physical reality Reality is the sum or aggregate of all that is real or existen ...
and the
history of mathematics The history of mathematics deals with the origin of discoveries in and the . Before the and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales. From 3000 BC the states ...
. He wrote works on
philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about Metaphysics, existence, reason, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and Philosophy of language, language. Such questio ...

,
theology Theology is the systematic study of the nature of the divine Divinity or the divine are things that are either related to, devoted to, or proceeding from a deity A deity or god is a supernatural The supernatural encompasses supposed ...
,
ethics Ethics or moral philosophy is a branch of philosophy that "involves systematizing, defending, and recommending concepts of right and wrong action (philosophy), behavior".''Internet Encyclopedia of Philosophy'"Ethics"/ref> The field of ethics, al ...

,
politics Politics (from , ) is the set of activities that are associated with Decision-making, making decisions in Social group, groups, or other forms of Power (social and political), power relations between individuals, such as the distribution of res ...

,
law Law is a system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by its bounda ...
,
history History (from Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approxima ...

, and
philology Philology is the study of language A language is a structured system of communication used by humans, including speech (spoken language), gestures (Signed language, sign language) and writing. Most languages have a writing system composed o ...
. Leibniz also made major contributions to
physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of eve ...

and
technology Technology ("science of craft", from Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. I ...

, and anticipated notions that surfaced much later in
probability theory Probability theory is the branch of mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are containe ...
,
biology Biology is the natural science that studies life and living organisms, including their anatomy, physical structure, Biochemistry, chemical processes, Molecular biology, molecular interactions, Physiology, physiological mechanisms, Development ...

,
medicine Medicine is the science Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity, awareness, or understanding of someone or something, such as facts ( descriptive knowledge), skills (proced ...

,
geology Geology (from the Ancient Greek Ancient Greek includes the forms of the Greek language Greek ( el, label=Modern Greek Modern Greek (, , or , ''Kiní Neoellinikí Glóssa''), generally referred to by speakers simply as Greek ...

,
psychology Psychology is the scientific Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity or awareness, of someone or something, such as facts A fact is an occurrence in the real world. ...

,
linguistics Linguistics is the scientific study of language, meaning that it is a comprehensive, systematic, objective, and precise study of language. Linguistics encompasses the analysis of every aspect of language, as well as the methods for studying ...

, and
computer science Computer science deals with the theoretical foundations of information, algorithms and the architectures of its computation as well as practical techniques for their application. Computer science is the study of , , and . Computer science ...
. He also contributed to the field of
library science Library science (often termed library studies, bibliothecography, library economy, and informatics) is an or multidisciplinary field that applies the practices, perspectives, and tools of , , , and other areas to ; the collection, organization, , ...
: while serving as overseer of the Wolfenbüttel library in
Germany ) , image_map = , map_caption = , map_width = 250px , capital = Berlin Berlin (; ) is the and by both area and population. Its 3,769,495 inhabitants, as of 31 December 2019 makes it the , according to population within city l ...

, he devised a cataloging system that would have served as a guide for many of Europe's largest libraries. Leibniz's contributions to this vast array of subjects were scattered in various
learned journal An academic or scholarly journal is a periodical publication in which Scholarly method, scholarship relating to a particular list of academic disciplines, academic discipline is published. Academic journals serve as permanent and transparent forums ...
s, in tens of thousands of letters, and in unpublished manuscripts. He wrote in several languages, primarily in
Latin Latin (, or , ) is a classical language A classical language is a language A language is a structured system of communication Communication (from Latin ''communicare'', meaning "to share" or "to be in relation with") is "an appa ...

, and
German German(s) may refer to: Common uses * of or related to Germany * Germans, Germanic ethnic group, citizens of Germany or people of German ancestry * For citizens of Germany, see also German nationality law * German language The German la ...

, but also in
English English usually refers to: * English language English is a West Germanic languages, West Germanic language first spoken in History of Anglo-Saxon England, early medieval England, which has eventually become the World language, leading lan ...

,
Italian Italian may refer to: * Anything of, from, or related to the country and nation of Italy ** Italians, an ethnic group or simply a citizen of the Italian Republic ** Italian language, a Romance language *** Regional Italian, regional variants of the ...

and
Dutch Dutch commonly refers to: * Something of, from, or related to the Netherlands * Dutch people () * Dutch language () *Dutch language , spoken in Belgium (also referred as ''flemish'') Dutch may also refer to:" Castle * Dutch Castle Places * ...
. As a philosopher, he was one of the greatest representatives of 17th-century
rationalism In philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and Philosophy of language, ...
and
idealism In philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and Philosophy of language, l ...

. As a mathematician, his greatest achievement was the development of the main ideas of
differential and integral calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimal In mathematics, infinitesimals or infinitesimal numbers are quantities that are closer to zero than any standard real number, but are not zero. They do not ex ...
, independently of
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics a ...

's contemporaneous developments. Mathematical works have consistently favored
Leibniz's notation In calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimal In mathematics, infinitesimals or infinitesimal numbers are quantities that are closer to zero than any standard real number, but are not zero. ...
as the conventional expression of calculus. However, it was only in the 20th century that Leibniz's
law of continuity The law of continuity is a heuristic principle introduced by Gottfried Leibniz Gottfried Wilhelm (von) Leibniz ; see inscription of the engraving depicted in the " 1666–1676" section. (; or ; – 14 November 1716) was a prominent German p ...
and
transcendental law of homogeneity In mathematics, the transcendental law of homogeneity (TLH) is a heuristic principle enunciated by Gottfried Wilhelm Leibniz Gottfried Wilhelm (von) Leibniz ; see inscription of the engraving depicted in the " 1666–1676" section. (; or ; – ...
found a consistent mathematical formulation by means of
non-standard analysis The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal In mathematics, infinitesimals or infinitesimal numbers are quantities that are closer to zero than any standard ...
. He was also a pioneer in the field of
mechanical calculator A mechanical calculator, or calculating machine, is a mechanical device used to perform the basic operations of arithmetic automatically. Most mechanical calculators were comparable in size to small desktop computers and have been rendered obso ...
s. While working on adding automatic multiplication and division to
Pascal's calculator A Pascaline signed by Pascal in 1652 Top view and overview of the entire mechanism Pascal's calculator (also known as the arithmetic machine or Pascaline) is a mechanical calculator invented by Blaise Pascal in the mid 17th century. Pascal was le ...
, he was the first to describe a
pinwheel calculator A pinwheel calculator was a class of mechanical calculator popular in the 19th and 20th century using, for its calculating engine, a set of wheels that had an adjustable number of teeth. These wheels, also called pinwheels, could be set by using a ...
in 1685 and invented the
Leibniz wheel A Leibniz wheel or stepped drum is a cylinder with a set of teeth of incremental lengths which, when coupled to a counting wheel, can be used in the calculating engine of a class of mechanical calculators. Invented by Leibniz Gottfried Wilhel ...
, used in the
arithmometer The Arithmometer or ''Arithmomètre'' was the first digital Digital usually refers to something using digits, particularly binary digits. Technology and computing Hardware *Digital electronics Digital electronics is a field of electronics ...
, the first mass-produced mechanical calculator. He also refined the
binary number In mathematics and digital electronics Digital electronics is a field of electronics The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons The electr ...
system, which is the foundation of nearly all digital (
electronic Electronic may refer to: *Electronics Electronics comprises the physics, engineering, technology and applications that deal with the emission, flow and control of electrons in vacuum and matter. It uses active devices to control electron flow b ...

, solid-state,
discrete logic A logic gate is an idealized model of computation or physical electronics, electronic device implementing a Boolean function, a logical operation performed on one or more Binary number, binary inputs that produces a single binary output. Depending ...
)
computer A computer is a machine that can be programmed to Execution (computing), carry out sequences of arithmetic or logical operations automatically. Modern computers can perform generic sets of operations known as Computer program, programs. These ...

s, including the
Von Neumann architecture The von Neumann architecture — also known as the von Neumann model or Princeton architecture — is a computer architecture In computer engineering Computer engineering (CoE or CpE) is a branch of engineering Engineering is ...

, which is the standard design paradigm, or "
computer architecture In computer engineering, computer architecture is a set of rules and methods that describe the functionality, organization, and implementation of computer systems. The architecture of a system refers to its structure in terms of separately specifi ...
", followed from the second half of the 20th century, and into the 21st. Leibniz has been called the "founder of computer science". In
philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about Metaphysics, existence, reason, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and Philosophy of language, language. Such questio ...

and
theology Theology is the systematic study of the nature of the divine Divinity or the divine are things that are either related to, devoted to, or proceeding from a deity A deity or god is a supernatural The supernatural encompasses supposed ...
, Leibniz is most noted for his
optimism Optimism is an Attitude (psychology), attitude reflecting a belief or hope that the outcome of some specific endeavor, or outcomes in general, will be positive, favorable, and desirable. A common idiom used to illustrate optimism versus pessimism ...
, i.e. his conclusion that our world is, in a qualified sense, the best possible world that
God In monotheism, monotheistic thought, God is conceived of as the supreme being, creator deity, creator, and principal object of Faith#Religious views, faith.Richard Swinburne, Swinburne, R.G. "God" in Ted Honderich, Honderich, Ted. (ed)''The Oxfo ...

could have created, a view sometimes lampooned by other thinkers, such as
Voltaire François-Marie Arouet (; 21 November 169430 May 1778), known by his ''nom de plume A pen name, also called a ''nom de plume'' () or a literary double, is a pseudonym A pseudonym () or alias () (originally: ψευδώνυμος in Greek) is a ...

in his
satirical Satire is a genre Genre () is any form or type of communication in any mode (written, spoken, digital, artistic, etc.) with socially-agreed-upon conventions developed over time. In popular usage, it normally describes a Category of being, ...
novella A novella is a narrative prose fiction whose length is shorter than that of most novel A novel is a relatively long work of narrative fiction, typically written in prose and published as a book. The present English word for a long work of pr ...

''
Candide ( , ) is a French satire Satire is a genre of the visual arts, visual, literature, literary, and performing arts, usually in the form of fiction and less frequently Nonfiction, non-fiction, in which vices, follies, abuses and shortcoming ...
''. Leibniz, along with
René Descartes René Descartes ( or ; ; Latinisation of names, Latinized: Renatus Cartesius; 31 March 1596 – 11 February 1650) was a French philosopher, Mathematics, mathematician, and scientist who invented analytic geometry, linking the previously sep ...

and
Baruch Spinoza Baruch (de) Spinoza (; ; ; born Baruch Espinosa; later as an author and a correspondent Benedictus de Spinoza, anglicized to Benedict de Spinoza; 24 November 1632 – 21 February 1677) was a Dutch philosopher of Spanish and Portuguese Jews, Por ...

, was one of the three great early modern
rationalists In philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and Philosophy of language, ...
. His philosophy also assimilates elements of the 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 Logic is an interdisciplinary field which studies truth and reasoning. Informal logic seeks to characterize Validity (logic), valid arguments informally, for instance by listing varieties of fallacies. Formal logic represents statements and ar ...

and still influences contemporary
analytic philosophy Analytic philosophy is a branch and tradition of philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about existence Existence is the ability of an entity to interact with physical reality ...
, such as its adopted use of the term "
possible world A possible world is a complete and consistent way the world is or could have been. They are widely used as a formal device in logic Logic is an interdisciplinary field which studies truth and reasoning Reason is the capacity of consciously ...
" to define modal notions.

# Biography

## Early life

Gottfried Leibniz was born on 1 July 1646, toward the end of the
Thirty Years' War The Thirty Years' War was a conflict fought largely within the Holy Roman Empire The Holy Roman Empire ( la, Sacrum Romanum Imperium; german: Heiliges Römisches Reich) was a multi-ethnic complex of territories in Western Europe, Weste ...
, in
Leipzig Leipzig (, ; Upper Saxon: ) is the most populous city in the Germany, German States of Germany, state of Saxony. With a population of 605,407 inhabitants as of 2021 (1.1 million residents in the larger urban zone), it surpasses the Saxon c ...

,
Saxony Saxony (german: Sachsen ; Upper Saxon Upper Saxon (german: Obersächsisch, ; ) is an East Central German East Central German (german: Ostmitteldeutsch) is the eastern, non-Franconian languages, Franconian Central German language, part o ...
, to Friedrich Leibniz and Catharina Schmuck. Friedrich noted in his family journal: In English: Leibniz was baptized on 3 July of that year at
St. Nicholas Church, Leipzig The St. Nicholas Church (german: Nikolaikirche) is one of the major churches of central Leipzig Leipzig (, also , ; Upper Saxon: ) is the most populous city in the Germany, German States of Germany, state of Saxony. With a population of 605 ...
; his godfather was the
Lutheran Lutheranism is one of the largest branches of Protestantism that identifies with the teachings of Jesus Christ and was founded by Martin Luther, a 16th-century German monk and Protestant Reformers, reformer whose efforts to reform the theology ...
theologian . His father died when he was six years old, and from that point on, Leibniz was raised by his mother. Leibniz's father had been a Professor of Moral Philosophy at the
University of Leipzig Leipzig University (german: Universität Leipzig), in Leipzig in the Free State of Saxony, Germany, is one of the world's oldest University, universities and the List of universities in Germany#Universities by years of existence, second-oldest univ ...
, and the boy later inherited his father's personal library. He was given free access to it from the age of seven. While Leibniz's schoolwork was largely confined to the study of a small
canon Canon or Canons may refer to: Places * Canon, Georgia Canon is a city in Franklin County, Georgia, Franklin and Hart County, Georgia, Hart counties in the U.S. state of Georgia (U.S. state), Georgia. The population was 804 at the 2010 census. His ...
of authorities, his father's library enabled him to study a wide variety of advanced philosophical and theological works—ones that he would not have otherwise been able to read until his college years. Access to his father's library, largely written in
Latin Latin (, or , ) is a classical language A classical language is a language A language is a structured system of communication Communication (from Latin ''communicare'', meaning "to share" or "to be in relation with") is "an appa ...

, also led to his proficiency in the Latin language, which he achieved by the age of 12. He also composed 300
hexametersHexameter is a metrical line Line, lines, The Line, or LINE may refer to: Arts, entertainment, and media Films * ''Lines'' (film), a 2016 Greek film * ''The Line'' (2017 film) * ''The Line'' (2009 film) * ''The Line'', a 2009 independent film ...
of
Latin verse The history of Latin poetry can be understood as the adaptation of Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast ...
, in a single morning, for a special event at school at the age of 13. In April 1661 he enrolled in his father's former university at age 14, and completed his
bachelor's degree A bachelor's degree (from Middle Latin Medieval Latin was the form of Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken in the area ...
in Philosophy in December 1662. He defended his ''Disputatio Metaphysica de Principio Individui'' (''Metaphysical Disputation on the Principle of Individuation''),Arthur 2014, p. x. which addressed the principle of individuation, on 9 June 1663. Leibniz earned his
master's degree A master's degree (from Latin ) is an academic degree awarded by University, universities or colleges upon completion of a course of study demonstrating mastery or a high-order overview of a specific field of study or area of Profession, professio ...
in Philosophy on 7 February 1664. He published and defended a dissertation ''Specimen Quaestionum Philosophicarum ex Jure collectarum'' (''An Essay of Collected Philosophical Problems of Right''), arguing for both a theoretical and a pedagogical relationship between philosophy and law, in December 1664. After one year of legal studies, he was awarded his bachelor's degree in Law on 28 September 1665. His dissertation was titled ''De conditionibus'' (''On Conditions''). In early 1666, at age 19, Leibniz wrote his first book, '' De Arte Combinatoria'' (''On the Combinatorial Art''), the first part of which was also his
habilitation Habilitation is the procedure to achieve the highest university degree in many European countries in which the candidate fulfills certain criteria set by the university which require excellence in research, teaching, and further education. Its qua ...
thesis in Philosophy, which he defended in March 1666. ''De Arte Combinatoria'' was inspired by
Ramon Llull Ramon Llull (; c. 1232 – c. 1315/16) was a philosopher A philosopher is someone who practices philosophy Philosophy (from , ) is the study of general and fundamental questions, such as those about reason, Metaphysics, existence, ...

's '' Ars Magna'' and contained a proof of the existence of God, cast in geometrical form, and based on the argument from motion. His next goal was to earn his license and Doctorate in Law, which normally required three years of study. In 1666, the University of Leipzig turned down Leibniz's doctoral application and refused to grant him a Doctorate in Law, most likely due to his relative youth. Leibniz subsequently left Leipzig. Leibniz then enrolled in the
University of Altdorf 400px, The University of Altdorf in 1714 The University of Altdorf () was a university in Altdorf bei Nürnberg, a small town outside the Free Imperial City of Nuremberg. It was founded in 1578 and received university privileges in 1622 and was cl ...
and quickly submitted a thesis, which he had probably been working on earlier in Leipzig. The title of his thesis was ''Disputatio Inauguralis de Casibus Perplexis in Jure'' (''Inaugural Disputation on Ambiguous Legal Cases''). Leibniz earned his license to practice law and his Doctorate in Law in November 1666. He next declined the offer of an academic appointment at Altdorf, saying that "my thoughts were turned in an entirely different direction". As an adult, Leibniz often introduced himself as "Gottfried
von The term ''von'' () is used in German language The German language (, ) is a West Germanic language mainly spoken in Central Europe. It is the most widely spoken and official or co-official language in Germany, Austria, Switzerland, Liech ...
Leibniz". Many posthumously published editions of his writings presented his name on the title page as "
Freiherr (; male, abbreviated as ), (; his wife, abbreviated as , literally "free lord" or "free lady") and (, his unmarried daughters and maiden aunts) are designations used as titles of nobility Traditional rank amongst European royalty, peers ...
G. W. von Leibniz." However, no document has ever been found from any contemporary government that stated his appointment to any form of
nobility Nobility is a social class normally ranked immediately below Royal family, royalty and found in some societies that have a formal aristocracy (class), aristocracy. Nobility has often been an Estates of the realm, estate of the realm that p ...
.

## 1666–1676

Leibniz's first position was as a salaried secretary to an
alchemical File:Aurora consurgens zurich 044 f-21v-44 dragon-pot.jpg, Depiction of Ouroboros from the alchemical treatise ''Aurora consurgens'' (15th century), Zentralbibliothek Zürich, Switzerland Alchemy (from Arabic: ''al-kīmiyā''; from Ancient Gree ...
society in
Nuremberg Nuremberg ( ; german: link=no, Nürnberg ; in the local East Franconian dialect: ''Nämberch'' ) is the second-largest city of the Germany, German States of Germany, state of Bavaria after its capital Munich, and its 518,370 (2019) inhabitants ...

. He knew fairly little about the subject at that time but presented himself as deeply learned. He soon met Johann Christian von Boyneburg (1622–1672), the dismissed chief minister of the Elector of
Mainz Mainz (; ) is the capital and largest city of Rhineland-Palatinate Rhineland-Palatinate (german: Rheinland-Pfalz, ) is a western state State may refer to: Arts, entertainment, and media Literature * ''State Magazine'', a monthly magazine ...

, Johann Philipp von Schönborn. Von Boyneburg 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 the Electorate. In 1669, Leibniz was appointed assessor in the Court of Appeal. Although von Boyneburg died late in 1672, Leibniz remained under the employment of his widow until she dismissed him in 1674. Von Boyneburg did much to promote Leibniz's reputation, and the latter's memoranda and letters began to attract favorable notice. After Leibniz's service to the Elector there soon followed a diplomatic role. He published an essay, under the pseudonym of a fictitious Polish nobleman, arguing (unsuccessfully) for the German candidate for the Polish crown. The main force in European geopolitics during Leibniz's adult life was the ambition of
Louis XIV of France Louis XIV (Louis Dieudonné; 5 September 16381 September 1715), also known as Louis the Great () or the Sun King (), was from 14 May 1643 until his death in 1715. His reign of 72 years and 110 days is the of any monarch of a sovereign country in ...

, backed by French military and economic might. Meanwhile, the
Thirty Years' War The Thirty Years' War was a conflict fought largely within the Holy Roman Empire The Holy Roman Empire ( la, Sacrum Romanum Imperium; german: Heiliges Römisches Reich) was a multi-ethnic complex of territories in Western Europe, Weste ...
German-speaking Europe This article details the geographical distribution of speakers of the German language, regardless of the legislative status within the countries where it is spoken. In addition to the German German(s) may refer to: Common uses * of or related t ...
exhausted, fragmented, and economically backward. Leibniz proposed to protect German-speaking Europe by distracting Louis as follows. France would be invited to take
Egypt Egypt ( ar, مِصر, Miṣr), officially the Arab Republic of Egypt, is a transcontinental country This is a list of countries located on more than one continent A continent is one of several large landmasses. Generally identi ...

as a stepping stone towards an eventual conquest of the
Dutch East Indies The Dutch East Indies (or Netherlands East-Indies; nl, Nederlands(ch)-Indië; ) was a Dutch colony The Dutch colonial empire ( nl, Nederlandse koloniale rijk) comprised the overseas territories and trading posts controlled and administer ...
. 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 the outbreak of the
Franco-Dutch War The 1672 to 1678 Franco-Dutch War, also known as the Dutch War (french: Guerre de Hollande; nl, Hollandse Oorlog), was fought between France France (), officially the French Republic (french: link=no, République française), is a Li ...
and became irrelevant. Napoleon's failed invasion of Egypt in 1798 can be seen as an unwitting, late implementation of Leibniz's plan, after the Eastern hemisphere colonial supremacy in Europe had already passed from the Dutch to the British. Thus Leibniz went to Paris in 1672. Soon after arriving, he met Dutch physicist and mathematician
Christiaan Huygens Christiaan Huygens ( , also , ; la, Hugenius; 14 April 1629 – 8 July 1695), also spelled Huyghens, was a Dutch mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) i ...

## Death

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 that time) nor any fellow courtier other than his personal secretary attended the funeral. Even though Leibniz was a life member of the Royal Society and the Prussian Academy of Sciences, Berlin Academy of Sciences, neither organization saw fit to honor his death. His grave went unmarked for more than 50 years. He was, however, eulogized by Bernard de Fontenelle, Fontenelle, before the French Academy of Sciences in Paris, which had admitted him as a foreign member in 1700. The eulogy was composed at the behest of the Elizabeth Charlotte, Princess Palatine, Duchess of Orleans, a niece of the Electress Sophia.

## Personal life

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 put him in a bad light during the Newton v. Leibniz calculus controversy, calculus controversy. He was charming, well-mannered, and not without humor and imagination. He had many friends and admirers all over Europe. He identified as a Protestant and a philosophical theism, philosophical theist. Leibniz remained committed to Trinitarian Christianity throughout his life.

# Philosopher

Leipzig Leipzig (, ; Upper Saxon: ) is the most populous city in the Germany, German States of Germany, state of Saxony. With a population of 605,407 inhabitants as of 2021 (1.1 million residents in the larger urban zone), it surpasses the Saxon c ...

professor Jakob Thomasius, who also supervised his BA thesis in philosophy.Arthur 2014, p. 13. Leibniz also eagerly read Francisco Suárez, a Spanish Society of Jesus, Jesuit respected even in Lutheranism, Lutheran universities. Leibniz was deeply interested in the new methods and conclusions of Descartes, Huygens, Newton, and Robert Boyle, Boyle, but viewed their work through a lens heavily tinted by scholastic notions. Yet it remains the case that Leibniz's methods and concerns often anticipate the
logic Logic is an interdisciplinary field which studies truth and reasoning. Informal logic seeks to characterize Validity (logic), valid arguments informally, for instance by listing varieties of fallacies. Formal logic represents statements and ar ...

, and analytic philosophy, analytic and linguistic philosophy of the 20th century.

## Principles

Leibniz variously invoked one or another of seven fundamental philosophical Principles: * Identity (mathematics), Identity/contradiction. If a proposition is true, then its negation is false and vice versa. * Identity of indiscernibles. Two distinct things cannot have all their properties in common. If every predicate possessed by x is also possessed by y and vice versa, then entities x and y are identical; to suppose two things indiscernible is to suppose the same thing under two names. Frequently invoked in modern logic and philosophy, the "identity of indiscernibles" is often referred to as Leibniz's Law. It has attracted the most controversy and criticism, especially from corpuscular philosophy and quantum mechanics. * principle of sufficient reason, Sufficient reason. "There must be a sufficient reason for anything to exist, for any event to occur, for any truth to obtain." * Pre-established harmony. "[T]he appropriate nature of each substance brings it about that what happens to one corresponds to what happens to all the others, without, however, their acting upon one another directly." (''Discourse on Metaphysics'', XIV) A dropped glass shatters because it "knows" it has hit the ground, and not because the impact with the ground "compels" the glass to split. * Law of Continuity. ''Natura non facit saltus''Gottfried Leibniz, New Essays on Human Understanding, ''New Essays'', IV, 16: "''la nature ne fait jamais des sauts''". ''Natura non-facit saltus'' is the Latin translation of the phrase (originally put forward by Carolus Linnaeus, Linnaeus' ''Philosophia Botanica'', 1st ed., 1751, Chapter III, § 77, p. 27; see also Stanford Encyclopedia of Philosophy
"Continuity and Infinitesimals"
and Alexander Baumgarten, ''Metaphysics: A Critical Translation with Kant's Elucidations'', Translated and Edited by Courtney D. Fugate and John Hymers, Bloomsbury, 2013, "Preface of the Third Edition (1750)"
p. 79 n.d.
"[Baumgarten] must also have in mind Leibniz's "''natura non-facit saltus'' [nature does not make leaps]" (Nouveaux essais sur l'entendement humain, NE IV, 16)."). A variant translation is "''natura non-saltum facit''" (literally, "Nature does not make a jump")
Extract of page 289
)
(literally, "Nature does not make jumps"). * Philosophical optimism, Optimism. "God assuredly always chooses the best." * Principle of plenitude, Plenitude. Leibniz believed that the best of all possible worlds would actualize every genuine possibility, and argued in ''Théodicée'' that this best of all possible worlds will contain all possibilities, with our finite experience of eternity giving no reason to dispute nature's perfection. Leibniz would on occasion give a rational defense of a specific principle, but more often took them for granted.

## Theodicy and optimism

The ''Théodicée, Theodicy'' tries to justify the apparent imperfections of the world by claiming that it is Best of all possible worlds, optimal among all possible worlds. It must be the best possible and most balanced world, because it was created by an all powerful and all knowing God, who would not choose to create an imperfect world if a better world could be known to him or possible to exist. In effect, apparent flaws that can be identified in this world must exist in every possible world, because otherwise God would have chosen to create the world that excluded those flaws. Leibniz asserted that the truths of theology (religion) and philosophy cannot contradict each other, since reason and faith are both "gifts of God" so that their conflict would imply God contending against himself. The ''Theodicy'' is Leibniz's attempt to reconcile his personal philosophical system with his interpretation of the tenets of Christianity. This project was motivated in part by Leibniz's belief, shared by many philosophers and theologians during the Age of Enlightenment, Enlightenment, in the rational and enlightened nature of the Christian religion. It was also shaped by Leibniz's belief in the perfectibility of human nature (if humanity relied on correct philosophy and religion as a guide), and by his belief that metaphysical necessity must have a rational or logical foundation, even if this metaphysical causality seemed inexplicable in terms of physical necessity (the natural laws identified by science). Because reason and faith must be entirely reconciled, any tenet of faith which could not be defended by reason must be rejected. Leibniz then approached one of the central criticisms of Christian theism: if God is Omnibenevolence, all good, Omniscience, all wise, and Omnipotence, all powerful, then how did Problem of evil, evil come into the world? The answer (according to Leibniz) is that, while God is indeed unlimited in wisdom and power, his human creations, as creations, are limited both in their wisdom and in their will (power to act). This predisposes humans to false beliefs, wrong decisions, and ineffective actions in the exercise of their free will. God does not arbitrarily inflict pain and suffering on humans; rather he permits both ''moral evil'' (sin) and ''physical evil'' (pain and suffering) as the necessary consequences of ''metaphysical evil'' (imperfection), as a means by which humans can identify and correct their erroneous decisions, and as a contrast to true good. Further, although human actions flow from prior causes that ultimately arise in God and therefore are known to God as metaphysical certainties, an individual's free will is exercised within natural laws, where choices are merely contingently necessary and to be decided in the event by a "wonderful spontaneity" that provides individuals with an escape from rigorous predestination.

## ''Discourse on Metaphysics''

For Leibniz, "God is an absolutely perfect being". He describes this perfection later in section VI as the simplest form of something with the most substantial outcome (VI). Along these lines, he declares that every type of perfection "pertains to him (God) in the highest degree" (I). Even though his types of perfections are not specifically drawn out, Leibniz highlights the one thing that, to him, does certify imperfections and proves that God is perfect: "that one acts imperfectly if he acts with less perfection than he is capable of", and since God is a perfect being, he cannot act imperfectly (III). Because God cannot act imperfectly, the decisions he makes pertaining to the world must be perfect. Leibniz also comforts readers, stating that because he has done everything to the most perfect degree; those who love him cannot be injured. However, to love God is a subject of difficulty as Leibniz believes that we are "not disposed to wish for that which God desires" because we have the ability to alter our disposition (IV). In accordance with this, many act as rebels, but Leibniz says that the only way we can truly love God is by being content "with all that comes to us according to his will" (IV). Because God is "an absolutely perfect being" (I), Leibniz argues that God would be acting imperfectly if he acted with any less perfection than what he is able of (III). His syllogism then ends with the statement that God has made the world perfectly in all ways. This also affects how we should view God and his will. Leibniz states that, in lieu of God’s will, we have to understand that God "is the best of all masters" and he will know when his good succeeds, so we, therefore, must act in conformity to his good will—or as much of it as we understand (IV). In our view of God, Leibniz declares that we cannot admire the work solely because of the maker, lest we mar the glory and love God in doing so. Instead, we must admire the maker for the work he has done (II). Effectively, Leibniz states that if we say the earth is good because of the will of God, and not good according to some standards of goodness, then how can we praise God for what he has done if contrary actions are also praiseworthy by this definition (II). Leibniz then asserts that different principles and geometry cannot simply be from the will of God, but must follow from his understanding.

## Fundamental question of metaphysics

Leibniz wrote: "Problem of why there is anything at all, Why is there something rather than nothing? The sufficient reason ... is found in a substance which ... is a necessary being bearing the reason for its existence within itself." Martin Heidegger called this question "the fundamental question of metaphysics".

## 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.
Leibniz's calculus ratiocinator, which resembles Mathematical logic, symbolic logic, can be viewed as a way of making such calculations feasible. Leibniz wrote memoranda that can now be read as groping attempts to get symbolic logic—and thus his ''calculus''—off the ground. These writings remained unpublished until the appearance of a selection edited by Carl Immanuel Gerhardt (1859). Louis Couturat published a selection in 1901; by this time the main developments of modern logic had been created by Charles Sanders Peirce and by Gottlob Frege. Leibniz thought symbols were important for human understanding. He attached so much importance to the development of good notations that he attributed all his discoveries in mathematics to this. His notation for calculus is an example of his skill in this regard. Leibniz's passion for symbols and notation, as well as his belief that these are essential to a well-running logic and mathematics, made him a precursor of semiotics. But Leibniz took his speculations much further. Defining a Grapheme, character as any written sign, he then defined a "real" character as one that represents an idea directly and not simply as the word embodying the idea. Some real characters, such as the notation of logic, serve only to facilitate reasoning. Many characters well known in his day, including Egyptian hieroglyphics, Chinese characters, and the symbols of astronomy and chemistry, he deemed not real. 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:
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.
Complex thoughts would be represented by combining characters for simpler thoughts. Leibniz saw that the uniqueness of prime factorization suggests a central role for prime numbers in the universal characteristic, a striking anticipation of Gödel numbering. Granted, there is no intuitive or mnemonic way to number any set of elementary concepts using the prime numbers. 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 characteristic, universal language or script. Only in 1676 did he conceive of a kind of "algebra of thought", modeled on and including conventional algebra and its notation. The resulting ''characteristic'' included a logical calculus, some combinatorics, algebra, his ''analysis situs'' (geometry of situation), 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 calculus, may never be established. Leibniz's idea of reasoning through a universal language of symbols and calculations remarkably foreshadows great 20th-century developments in formal systems, such as Turing completeness, where computation was used to define equivalent universal languages (see Turing degree).

## Formal logic

Leibniz has been noted as one of the most important logicians between the times of Aristotle and Gottlob Frege. Leibniz enunciated the principal properties of what we now call logical conjunction, conjunction, disjunction, negation, Identity (mathematics), identity, set subset, inclusion, and the empty set. The principles of Leibniz's logic and, arguably, of his whole philosophy, reduce to two: # All our ideas are compounded from a very small number of simple ideas, which form the alphabet of human thought. # Complex ideas proceed from these simple ideas by a uniform and symmetrical combination, analogous to arithmetical multiplication. The formal logic that emerged early in the 20th century also requires, at minimum, unary function, unary negation and Quantification (logic), quantified variable (mathematics), variables ranging over some universe of discourse. Leibniz published nothing on formal logic in his lifetime; most of what he wrote on the subject consists of working drafts. In his ''A History of Western Philosophy, History of Western Philosophy'', Bertrand Russell went so far as to claim that Leibniz had developed logic in his unpublished writings to a level which was reached only 200 years later. Russell's principal work on Leibniz found that many of Leibniz's most startling philosophical ideas and claims (e.g., that each of the fundamental Monad (philosophy), monads mirrors the whole universe) follow logically from Leibniz's conscious choice to reject ''relations'' between things as unreal. He regarded such relations as (real) ''qualities'' of things (Leibniz admitted unary function, unary Predicate (mathematical logic), predicates only): For him, "Mary is the mother of John" describes separate qualities of Mary and of John. This view contrasts with the relational logic of Augustus de Morgan, De Morgan, Charles S. Peirce, Peirce, Ernst Schröder (mathematician), Schröder and Russell himself, now standard in predicate logic. Notably, Leibniz also declared space and time to be inherently relational. Leibniz's 1690 discovery of his algebra of concepts (deductively equivalent to the Boolean algebra) and the associated metaphysics, are of interest in present-day computational metaphysics.

# Mathematician

Although the mathematical notion of Function (mathematics), 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 (geometry), chord, and the Normal (geometry), perpendicular (see History of the function concept). In the 18th century, "function" lost these geometrical associations. Leibniz also believed that the sum of an infinite number of zeros would be equal to one half using the analogy of the creation of the world from nothing. Leibniz was also one of the pioneers in actuarial science, calculating the purchase price of life annuities and the liquidation of a state's debt. Leibniz's research into formal logic, also relevant to mathematics, is discussed in the #Formal logic, preceding section. The best overview of Leibniz's writings on calculus may be found in Bos (1974). Leibniz, who invented one of the earliest mechanical calculators, said of calculation: "For it is unworthy of excellent men to lose hours like slaves in the labor of calculation which could safely be relegated to anyone else if machines were used."

## Linear systems

Leibniz arranged the coefficients of a system of linear equations into an array, now called a Matrix (mathematics), matrix, in order to find a solution to the system if it existed. This method was later called Gaussian elimination. Leibniz laid down the foundations and theory of determinants, although the Japanese mathematician Seki Takakazu also discovered determinants independently of Leibniz. His works show calculating the determinants using cofactors. Calculating the determinant using cofactors is named the Leibniz formula for determinants, Leibniz formula. Finding the determinant of a matrix using this method proves impractical with large ''n'', requiring to calculate ''n!'' products and the number of n-permutations. He also solved systems of linear equations using determinants, which is now called Cramer's rule. This method for solving systems of linear equations based on determinants was found in 1684 by Leibniz (Cramer published his findings in 1750). Although Gaussian elimination requires $O\left(n^3\right)$ arithmetic operations, linear algebra textbooks still teach cofactor expansion before LU factorization.

## Geometry

The Leibniz formula for π, Leibniz formula for states that :$1 \,-\, \frac \,+\, \frac \,-\, \frac \,+\, \cdots \,=\, \frac.$ Leibniz wrote that circles "can most simply be expressed by this series, that is, the aggregate of fractions alternately added and subtracted". However this formula is only accurate with a large number of terms, using 10,000,000 terms to obtain the correct value of to 8 decimal places. Leibniz attempted to create a definition for a straight line while attempting to prove the parallel postulate. While most mathematicians defined a straight line as the shortest line between two points, Leibniz believed that this was merely a property of a straight line rather than the definition.

## Calculus

Leibniz is credited, along with Sir
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician A mathematician is someone who uses an extensive knowledge of mathematics Mathematics (from Greek: ) includes the study of such topics a ...

, with the discovery of calculus (differential and integral calculus). According to Leibniz's notebooks, a critical breakthrough occurred on 11 November 1675, when he employed integral calculus for the first time to find the area under the graph of a function . He introduced several notations used to this day, for instance the integral sign , representing an elongated S, from the Latin word ''summa'', and the used for Differential (infinitesimal), differentials, from the Latin word ''differentia''. Leibniz did not publish anything about his calculus until 1684. Leibniz expressed the inverse relation of integration and differentiation, later called the fundamental theorem of calculus, by means of a figure in his 1693 paper ''Supplementum geometriae dimensoriae...''. However, James Gregory (mathematician), James Gregory is credited for the theorem's discovery in geometric form, Isaac Barrow proved a more generalized geometric version, and Isaac Newton, Newton developed supporting theory. The concept became more transparent as developed through Leibniz's formalism and new notation. The product rule of differential calculus is still called "Leibniz's law". In addition, the theorem that tells how and when to differentiate under the integral sign is called the Leibniz integral rule. Leibniz exploited infinitesimals in developing calculus, manipulating them in ways suggesting that they had paradoxical algebraic properties. George Berkeley, in a tract called ''The Analyst'' and also in ''De Motu'', criticized these. A recent study argues that Leibnizian calculus was free of contradictions, and was better grounded than Berkeley's empiricist criticisms. From 1711 until his death, Leibniz was engaged in a dispute with John Keill, Newton and others, over whether Leibniz had invented calculus independently of Newton. This subject is treated at length in the article Leibniz–Newton calculus controversy. The use of infinitesimals in mathematics was frowned upon by followers of Karl Weierstrass, but survived in science and engineering, and even in rigorous mathematics, via the fundamental computational device known as the Differential (infinitesimal), differential. Beginning in 1960, Abraham Robinson worked out a rigorous foundation for Leibniz's infinitesimals, using model theory, in the context of a field of hyperreal numbers. The resulting
non-standard analysis The history of calculus is fraught with philosophical debates about the meaning and logical validity of fluxions or infinitesimal In mathematics, infinitesimals or infinitesimal numbers are quantities that are closer to zero than any standard ...
can be seen as a belated vindication of Leibniz's mathematical reasoning. Robinson's transfer principle is a mathematical implementation of Leibniz's heuristic
law of continuity The law of continuity is a heuristic principle introduced by Gottfried Leibniz Gottfried Wilhelm (von) Leibniz ; see inscription of the engraving depicted in the " 1666–1676" section. (; or ; – 14 November 1716) was a prominent German p ...
, while the standard part function implements the Leibnizian
transcendental law of homogeneity In mathematics, the transcendental law of homogeneity (TLH) is a heuristic principle enunciated by Gottfried Wilhelm Leibniz Gottfried Wilhelm (von) Leibniz ; see inscription of the engraving depicted in the " 1666–1676" section. (; or ; – ...
.

## Topology

Leibniz was the first to use the term ''analysis situs'', later used in the 19th century to refer to what is now known as topology. There are two takes on this situation. On the one hand, Mates, 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 Seven Bridges of Königsberg, Königsberg Bridge Problem and its generalizations, used the term ''geometria situs'' in such a sense that the situs remains unchanged under topological deformations. He mistakenly credits Leibniz with originating this concept. ... [It] is sometimes not realized that Leibniz used the term in an entirely different sense and hence can hardly be considered the founder of that part of mathematics.
But Hideaki Hirano argues differently, quoting Benoit Mandelbrot, Mandelbrot:
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, 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 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''.

## Physics

Leibniz contributed a fair amount to the statics and dynamics emerging around him, often disagreeing with Descartes and Isaac Newton, Newton. He devised a new theory of Motion (physics), motion (Dynamics (mechanics), dynamics) based on kinetic energy and potential energy, which posited space as relative, whereas Newton was thoroughly convinced that space was absolute. An important example of Leibniz's mature physical thinking is his ''Specimen Dynamicum'' of 1695. Until the discovery of subatomic particles and the quantum mechanics governing them, many of Leibniz's speculative ideas about aspects of nature not reducible to statics and dynamics made little sense. For instance, he anticipated Albert Einstein by arguing, against Newton, that space, time and motion are relative, not absolute: "As for my own opinion, I have said more than once, that I hold space to be something merely relative, as time is, that I hold it to be an order of coexistences, as time is an order of successions." Leibniz held a Relational theory, relationist notion of space and time, against Newton's substantivalist views. According to Newton's substantivalism, space and time are entities in their own right, existing independently of things. Leibniz's relationism, in contrast, describes space and time as systems of relations that exist between objects. The rise of general relativity and subsequent work in the history of physics has put Leibniz's stance in a more favorable light. One of Leibniz's projects was to recast Newton's theory as a Mechanical explanations of gravitation, vortex theory.Arthur 2014, p. 56. However, his project went beyond vortex theory, since at its heart there was an attempt to explain one of the most difficult problems in physics, that of the origin of the Cohesion (chemistry), cohesion of matter. The principle of sufficient reason has been invoked in recent cosmology, and his identity of indiscernibles in quantum mechanics, a field some even credit him with having anticipated in some sense. Those who advocate digital philosophy, a recent direction in cosmology, claim Leibniz as a precursor. In addition to his theories about the nature of reality, Leibniz's contributions to the development of calculus have also had a major impact on physics.

### The ''vis viva''

Leibniz's ''vis viva'' (Latin for "living force") is , twice the modern kinetic energy. He realized that the total energy would be conserved in certain mechanical systems, so he considered it an innate motive characteristic of matter. 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 and Voltaire in France; hence academics in those countries tended to neglect Leibniz's idea. Leibniz knew of the validity of conservation of momentum. In reality, both energy and momentum are conserved, so both approaches are valid.

## Other natural science

By proposing that the earth has a molten core, he anticipated modern geology. In embryology, he was a preformationist, but also proposed that organisms are the outcome of a combination of an infinite number of possible microstructures and of their powers. In the life sciences and paleontology, he revealed an amazing transformist intuition, fueled by his study of comparative anatomy and fossils. One of his principal works on this subject, ''Protogaea'', unpublished in his lifetime, has recently been published in English for the first time. He worked out a primal organismic theory. 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.

## Psychology

Psychology had been a central interest of Leibniz. He appears to be an "underappreciated pioneer of psychology" He wrote on topics which are now regarded as fields of psychology: attention and consciousness, memory, learning (Association (psychology), association), motivation (the act of "striving"), emergent individuality, the general dynamics of development (evolutionary psychology). His discussions in the ''New Essays'' and ''Monadology'' often rely on everyday observations such as the behaviour of a dog or the noise of the sea, and he develops intuitive analogies (the synchronous running of clocks or the balance spring of a clock). He also devised postulates and principles that apply to psychology: the continuum of the unnoticed ''petites perceptions'' to the distinct, self-aware apperception, and psychophysical parallelism from the point of view of causality and of purpose: "Souls act according to the laws of final causes, through aspirations, ends and means. Bodies act according to the laws of efficient causes, i.e. the laws of motion. And these two realms, that of efficient causes and that of final causes, harmonize with one another." This idea refers to the mind-body problem, stating that the mind and brain do not act upon each other, but act alongside each other separately but in harmony. Leibniz, however, did not use the term ''psychologia''. Leibniz’ epistemological position—against John Locke and English empiricism (sensualism)—was made clear: "Nihil est in intellectu quod non fuerit in sensu, nisi intellectu ipse." – "Nothing is in the intellect that was not first in the senses, except the intellect itself." Principles that are not present in sensory impressions can be recognised in human perception and consciousness: logical inferences, categories of thought, the principle of causality and the principle of purpose (teleology). Leibniz found his most important interpreter in Wilhelm Wundt, founder of psychology as a discipline. Wundt used the "… nisi intellectu ipse" quotation 1862 on the title page of his ''Beiträge zur Theorie der Sinneswahrnehmung'' (Contributions on the Theory of Sensory Perception) and published a detailed and aspiring monograph on Leibniz Wundt shaped the term apperception, introduced by Leibniz, into an experimental psychologically based apperception psychology that included neuropsychological modelling – an excellent example of how a concept created by a great philosopher could stimulate a psychological research program. One principle in the thinking of Leibniz played a fundamental role: "the principle of equality of separate but corresponding viewpoints." Wundt characterized this style of thought (perspectivism) in a way that also applied for him—viewpoints that "supplement one another, while also being able to appear as opposites that only resolve themselves when considered more deeply." Much of Leibniz's work went on to have a great impact on the field of psychology. Leibniz thought that there are many petites perceptions, or small perceptions of which we perceive but of which we are unaware. He believed that by the principle that phenomena found in nature were continuous by default, it was likely that the transition between conscious and unconscious states had intermediary steps. For this to be true, there must also be a portion of the mind of which we are unaware at any given time. His theory regarding consciousness in relation to the principle of continuity can be seen as an early theory regarding the stages of sleep. In this way, Leibniz's theory of perception can be viewed as one of many theories leading up to the idea of the The unconscious, unconscious. Leibniz was a direct influence on Ernst Platner, who is credited with originally coining the term Unbewußtseyn (unconscious). Additionally, the idea of subliminal stimuli can be traced back to his theory of small perceptions. Leibniz's ideas regarding music and tonal perception went on to influence the laboratory studies of Wilhelm Wundt.

## Social science

In public health, he advocated establishing a medical administrative authority, with powers over epidemiology and veterinary medicine. He worked to set up a coherent medical training program, oriented towards public health and preventive measures. In economic policy, he proposed tax reforms and a national insurance program, and discussed the balance of trade. He even proposed something akin to what much later emerged as game theory. In sociology he laid the ground for communication theory.

## 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 praxi'', he urged that theory be combined with practical application, and thus has been claimed as the father of applied science. He designed wind-driven propellers and water pumps, mining machines to extract ore, hydraulic presses, lamps, submarines, clocks, etc. With Denis Papin, he created a steam engine. He even proposed a method for desalinating water. From 1680 to 1685, he struggled to overcome the chronic flooding that afflicted the ducal silver mines in the Harz Mountains, but did not succeed.

### Computation

Leibniz may have been the first computer scientist and information theorist. Early in life, he documented the binary numeral system (radix, base 2), then revisited that system throughout his career. While Leibniz was examining other cultures to compare his metaphysical views, he encountered an ancient Chinese book ''I Ching''. Leibniz interpreted a diagram which showed yin and yang and corresponded it to a zero and one. More information can be found in the #Sinophile, Sinophile section. Leibniz may have plagiarized Juan Caramuel y Lobkowitz and Thomas Harriot, who independently developed the binary system, as he was familiar with their works on the binary system. Juan Caramuel y Lobkowitz worked extensively on logarithms including logarithms with base 2. Thomas Harriot's manuscripts contained a table of binary numbers and their notation, which demonstrated that any number could be written on a base 2 system. Regardless, Leibniz simplified the binary system and articulated logical properties such as conjunction, disjunction, negation, identity, inclusion, and the empty set. He anticipated Lagrange polynomial, Lagrangian interpolation and algorithmic information theory. His calculus ratiocinator anticipated aspects of the universal Turing machine. In 1961, Norbert Wiener suggested that Leibniz should be considered the patron saint of cybernetics. Wiener is quoted with "Indeed, the general idea of a computing machine is nothing but a mechanization of Leibniz's Calculus Ratiocinator." In 1671, Leibniz began to invent a machine that could execute all four arithmetic operations, gradually improving it over a number of years. This "stepped reckoner" attracted fair attention and was the basis of his election to the Royal Society in 1673. A number of such machines were made during his years in Hanover by a craftsman working under his supervision. They were not an unambiguous success because they did not fully mechanize the Carry (arithmetic), carry operation. Couturat reported finding an unpublished note by Leibniz, dated 1674, describing a machine capable of performing some algebraic operations. Leibniz also devised a (now reproduced) cipher machine, recovered by Nicholas Rescher in 2010. In 1693, Leibniz described a design of a machine which could, in theory, integrate differential equations, which he called "integraph". Leibniz was groping towards hardware and software concepts worked out much later by Charles Babbage and Ada Lovelace. In 1679, while mulling over his binary arithmetic, Leibniz imagined a machine in which binary numbers were represented by marbles, governed by a rudimentary sort of punched cards. 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.

## Librarian

Later in Leibniz’s career (after the death of von Boyneburg), Leibniz moved to Paris and accepted a position as a librarian in the Hanoverian court of Johann Friedrich, Duke of Brunswick-Luneburg. Leibniz’s predecessor, Tobias Fleischer, had already created a cataloging system for the Duke’s library but it was a clumsy attempt. At this library, Leibniz focused more on advancing the library than on the cataloging. For instance, within a month of taking the new position, he developed a comprehensive plan to expand the library. He was one of the first to consider developing a core collection for a library and felt "that a library for display and ostentation is a luxury and indeed superfluous, but a well-stocked and organized library is important and useful for all areas of human endeavor and is to be regarded on the same level as schools and churches". Unfortunately, Leibniz lacked the funds to develop the library in this manner. After working at this library, by the end of 1690 Leibniz was appointed as privy-councilor and librarian of the Bibliotheca Augusta at Wolfenbüttel. It was an extensive library with at least 25,946 printed volumes. At this library, Leibniz sought to improve the catalog. He was not allowed to make complete changes to the existing closed catalog, but was allowed to improve upon it so he started on that task immediately. He created an alphabetical author catalog and had also created other cataloging methods that were not implemented. While serving as librarian of the ducal libraries in Hanover and Wolfenbüttel, Leibniz effectively became one of the founders of
library science Library science (often termed library studies, bibliothecography, library economy, and informatics) is an or multidisciplinary field that applies the practices, perspectives, and tools of , , , and other areas to ; the collection, organization, , ...
. He also designed a book library classification, indexing system in ignorance of the only other such system then extant, that of the Bodleian Library at Oxford University. He also called on publishers to distribute abstracts of all new titles they produced each year, in a standard form that would facilitate indexing. He hoped that this abstracting project would eventually include everything printed from his day back to Johannes Gutenberg, Gutenberg. Neither proposal met with success at the time, but something like them became standard practice among English language publishers during the 20th century, under the aegis of the Library of Congress and the British Library. He called for the creation of an empirical database as a way to further all sciences. His ''characteristica universalis'', calculus ratiocinator, and a "community of minds"—intended, among other things, to bring political and religious unity to Europe—can be seen as distant unwitting anticipations of artificial languages (e.g., Esperanto and its rivals), Mathematical logic, symbolic logic, even the World Wide Web.

Leibniz emphasized that research was a collaborative endeavor. Hence he warmly advocated the formation of national scientific societies along the lines of the Royal Society, British Royal Society and the French Académie 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 Prussian Academy of Sciences, Berlin Academy of Sciences was created. Leibniz drew up its first statutes, and served as its first President for the remainder of his life. That Academy evolved into the German Academy of Sciences, the publisher of the ongoing critical edition of his works.

# Lawyer and moralist

Leibniz's writings on law, ethics, and politics were long overlooked by English-speaking scholars, but this has changed of late. 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 liberalism, in 18th-century America and later elsewhere. The following excerpt from a 1695 letter to Baron J. C. Boyneburg'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. 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.
In 1677, Leibniz called for a European confederation, governed by a council or senate, whose members would represent entire nations and would be free to vote their consciences; this is sometimes considered an anticipation of the European Union. He believed that Europe would adopt a uniform religion. He reiterated these proposals in 1715. But at the same time, he arrived to propose an interreligious and multicultural project to create a universal system of justice, which required from him a broad interdisciplinary perspective. In order to propose it, he combined linguistics (especially sinology), moral and legal philosophy, management, economics, and politics.

## Ecumenism

Leibniz devoted considerable intellectual and diplomatic effort to what would now be called ecumenism, ecumenical endeavor, seeking to reconcile the Roman Catholic and
Lutheran Lutheranism is one of the largest branches of Protestantism that identifies with the teachings of Jesus Christ and was founded by Martin Luther, a 16th-century German monk and Protestant Reformers, reformer whose efforts to reform the theology ...
churches. In this respect, he followed the example of his early patrons, Baron von Boyneburg and the Duke John Frederick, Duke of Brunswick-Lüneburg, John Frederickboth cradle Lutherans who converted to Catholicism as adultswho did what they could to encourage the reunion of the two faiths, and who warmly welcomed such endeavors by others. (The House of Brunswick-Lüneburg, Brunswick remained Lutheran, because the Duke's children did not follow their father.) These efforts included corresponding with French bishop Jacques-Bénigne Bossuet, and involved Leibniz in some theological controversy. He evidently thought that the thoroughgoing application of reason would suffice to heal the breach caused by the Protestant Reformation, Reformation.

# Philologist

Leibniz the philologist was an avid student of languages, eagerly latching on to any information about vocabulary and grammar that came his way. He refuted the belief, widely held by Christian scholars of the time, that Hebrew language, Hebrew was the primeval language of the human race. He also refuted the argument, advanced by Swedish scholars in his day, that a form of proto-Swedish language, Swedish was the ancestor of the Germanic languages. He puzzled over the origins of the Slavic languages and was fascinated by classical Chinese. Leibniz was also an expert in the Sanskrit language. He published the ''princeps editio'' (first modern edition) of the Late Middle Ages, late medieval ''Chronicon Holtzatiae'', a Latin chronicle of the County of Holstein.

# Sinophile

Leibniz was perhaps the first major European intellectual to take a close interest in Chinese civilization, which he knew by corresponding with, and reading other works by, Jesuit China missions, European Christian missionaries posted in China. He apparently read ''Philippe Couplet, Confucius Sinarum Philosophus'' in the first year of its publication. He came to the conclusion that Europeans could learn much from the Confucianism, Confucian ethical tradition. He mulled over the possibility that the Chinese characters were an unwitting form of his Characteristica universalis, universal characteristic. He noted how the ''I Ching'' hexagrams correspond to the
binary number In mathematics and digital electronics Digital electronics is a field of electronics The field of electronics is a branch of physics and electrical engineering that deals with the emission, behaviour and effects of electrons The electr ...
s from 000000 to 111111, and concluded that this mapping was evidence of major Chinese accomplishments in the sort of philosophical mathematics he admired. Leibniz communicated his ideas of the binary system representing Christianity to the Emperor of China, hoping it would convert him. Leibniz was the only major Western philosopher of the time who attempted to accommodate Confucian ideas to prevailing European beliefs. Leibniz's attraction to Chinese philosophy originates from his perception that Chinese philosophy was similar to his own. The historian E.R. Hughes suggests that Leibniz's ideas of "simple substance" and "pre-established harmony" were directly influenced by Confucianism, pointing to the fact that they were conceived during the period when he was reading ''Confucius Sinarum Philosophus''.

# Polymath

While making his grand tour of European archives to research the Brunswick family history that he never completed, Leibniz stopped in Vienna between May 1688 and February 1689, where he did much legal and diplomatic work for the Brunswicks. He visited mines, talked with mine engineers, and tried to negotiate export contracts for lead from the ducal mines in the Harz mountains. His proposal that the streets of Vienna be lit with lamps burning rapeseed oil was implemented. During a formal audience with the Holy Roman Emperor, 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 Holy See, Vatican, and creating an imperial research library, official archive, and public insurance fund. He wrote and published an important paper on mechanics.

# Posthumous reputation

When Leibniz died, his reputation was in decline. He was remembered for only one book, the ''Théodicée'', whose supposed central argument
Voltaire François-Marie Arouet (; 21 November 169430 May 1778), known by his ''nom de plume A pen name, also called a ''nom de plume'' () or a literary double, is a pseudonym A pseudonym () or alias () (originally: ψευδώνυμος in Greek) is a ...

lampooned in his popular book ''
Candide ( , ) is a French satire Satire is a genre of the visual arts, visual, literature, literary, and performing arts, usually in the form of fiction and less frequently Nonfiction, non-fiction, in which vices, follies, abuses and shortcoming ...
'', which concludes with the character Candide saying, "''Non liquet''" (it is not clear), a term that was applied during the Roman Republic to a legal verdict of "not proven". Voltaire's depiction of Leibniz's ideas was so influential that many believed it to be an accurate description. 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 (philosopher), Christian Wolff, whose dogmatic and facile outlook did Leibniz's reputation much harm. He also influenced David Hume, who read his ''Théodicée'' and used some of his ideas. 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 proponent. 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 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 calculus and Leibniz's charge that Newton's theory of universal gravitation was incorrect. Leibniz's long march to his present glory began with the 1765 publication of the ''Nouveaux Essais'', which Immanuel Kant, Kant read closely. In 1768, Louis Dutens edited the first multi-volume edition of Leibniz's writings, followed in the 19th century by a number of editions, including those edited by Erdmann, Foucher de Careil, Gerhardt, Gerland, Klopp, and Mollat. Publication of Leibniz's correspondence with notables such as Antoine Arnauld, Samuel Clarke, Sophia of Hanover, and her daughter Sophia Charlotte of Hanover, began. In 1900, Bertrand Russell published a critical study of Leibniz's metaphysics. Shortly thereafter, Louis Couturat published an important study of Leibniz, and edited a volume of Leibniz's heretofore unpublished writings, mainly on logic. They made Leibniz somewhat respectable among 20th-century analytic philosophy, analytical and linguistic philosophy, linguistic philosophers in the English-speaking world (Leibniz had already been of great influence to many Germans such as Bernhard Riemann). For example, Leibniz's phrase ''salva veritate'', meaning interchangeability without loss of or compromising the truth, recurs in Willard Quine's writings. Nevertheless, the secondary literature on Leibniz did not really blossom until after World War II. This is especially true of English speaking countries; in Gregory Brown's bibliography fewer than 30 of the English language entries were published before 1946. American Leibniz studies owe much to Leroy Loemker (1904–1985) through his translations and his interpretive essays in LeClerc (1973). Nicholas Jolley has surmised that Leibniz's reputation as a philosopher is now perhaps higher than at any time since he was alive. Analytic and contemporary philosophy continue to invoke his notions of Identity (philosophy), identity, Principle of individuation, individuation, and possible worlds. Work in the history of 17th- and 18th-century history of ideas, ideas has revealed more clearly the 17th-century "Intellectual Revolution" that preceded the better-known industrial revolution, Industrial and commercial revolutions of the 18th and 19th centuries. In 1985, the German government created the Gottfried Wilhelm Leibniz Prize, Leibniz Prize, offering an annual award of 1.55 million euros for experimental results and 770,000 euros for theoretical ones. It was the world's largest prize for scientific achievement prior to the Fundamental Physics Prize. The collection of manuscript papers of Leibniz at the Gottfried Wilhelm Leibniz Bibliothek – Niedersächische Landesbibliothek was inscribed on UNESCO's Memory of the World Register in 2007.

## Cultural references

Leibniz still receives popular attention. The Google Doodle for 1 July 2018 celebrated Leibniz's 372nd birthday. Using a quill, his hand is shown writing "Google" in binary ASCII code. One of the earliest popular but indirect expositions of Leibniz was
Voltaire François-Marie Arouet (; 21 November 169430 May 1778), known by his ''nom de plume A pen name, also called a ''nom de plume'' () or a literary double, is a pseudonym A pseudonym () or alias () (originally: ψευδώνυμος in Greek) is a ...

's satire ''
Candide ( , ) is a French satire Satire is a genre of the visual arts, visual, literature, literary, and performing arts, usually in the form of fiction and less frequently Nonfiction, non-fiction, in which vices, follies, abuses and shortcoming ...
'', published in 1759. Leibniz was lampooned as Professor Pangloss, described as "the greatest philosopher of the Holy Roman Empire". Leibniz also appears as one of the main historical figures in Neal Stephenson's series of novels ''The Baroque Cycle''. Stephenson credits readings and discussions concerning Leibniz for inspiring him to write the series. Leibniz also stars in Adam Ehrlich Sachs's novel ''The Organs of Sense''.

# Writings and publication

Leibniz mainly wrote in three languages: scholastic
Latin Latin (, or , ) is a classical language A classical language is a language A language is a structured system of communication Communication (from Latin ''communicare'', meaning "to share" or "to be in relation with") is "an appa ...

, French and German. During his lifetime, he published many pamphlets and scholarly articles, but only two "philosophical" books, the ''Combinatorial Art'' and the ''Théodicée''. (He published numerous pamphlets, often anonymous, on behalf of the House of Brunswick-Lüneburg, most notably the "De jure suprematum" a major consideration of the nature of sovereignty.) One substantial book appeared posthumously, his ''Nouveaux essais sur l'entendement humain'', which Leibniz had withheld from publication after the death of John Locke. Only in 1895, when Bodemann completed his catalogue 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 1700, remains unpublished, and much of what is published has appeared only in recent decades. The amount, variety, and disorder of Leibniz's writings are a predictable result of a situation he described in a letter 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.Letter to Vincent Placcius, 15 September 1695, in Louis Dutens (ed.), ''Gothofridi Guillemi Leibnitii Opera Omnia'', vol. 6.1, 1768, pp. 59–60.
The extant parts of the critical editionwww.leibniz-edition.de
See photograph there.
of Leibniz's writings are organized as follows: * Series 1. ''Political, Historical, and General Correspondence''. 25 vols., 1666–1706. * Series 2. ''Philosophical Correspondence''. 3 vols., 1663–1700. * Series 3. ''Mathematical, Scientific, and Technical Correspondence''. 8 vols., 1672–1698. * Series 4. ''Political Writings''. 7 vols., 1667–99. * Series 5. ''Historical and Linguistic Writings''. Inactive. * Series 6. ''Philosophical Writings''. 7 vols., 1663–90, and ''Nouveaux essais sur l'entendement humain''. * Series 7. ''Mathematical Writings''. 6 vols., 1672–76. * Series 8. ''Scientific, Medical, and Technical Writings''. 1 vol., 1668–76. The systematic cataloguing of all of Leibniz's ''Nachlass'' began in 1901. It was hampered by two world wars and then by decades of German division into two states with the Cold War's "iron curtain" in between, separating scholars, and also scattering portions of his literary estates. The ambitious project has had to deal with writings in seven languages, contained in some 200,000 written and printed pages. 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, Hanover and Berlin have jointly published 57 volumes of the critical edition, with an average of 870 pages, and prepared index and Concordance (publishing), concordance works.

## Selected works

The year given is usually that in which the work was completed, not of its eventual publication. * 1666 (publ. 1690). '' De Arte Combinatoria'' (''On the Art of Combination''); partially translated in Loemker §1 and Parkinson (1966). * 1667. ''Nova Methodus Discendae Docendaeque Iurisprudentiae'' (''A New Method for Learning and Teaching Jurisprudence''). * 1667. "Dialogus de connexione inter res et verba." * 1671. ''Hypothesis Physica Nova'' (''New Physical Hypothesis''); Loemker §8.I (part). * 1673 ''Confessio philosophi'' (''A Philosopher's Creed''); an English translation i
available
online. * Oct. 1684. "Meditationes de cognitione, veritate et ideis" ("Meditations on Knowledge, Truth, and Ideas"). * Nov. 1684. "Nova methodus pro maximis et minimis" ("New method for maximums and minimums"); translated in Struik, D. J., 1969. ''A Source Book in Mathematics, 1200–1800''. Harvard University Press: 271–81. * 1686. ''Discourse on Metaphysics (book), Discours de métaphysique''; Martin and Brown (1988), Ariew and Garber 35, Loemker §35, Wiener III.3, Woolhouse and Francks 1. * 1686. ''Generales inquisitiones de analysi notionum et veritatum'' (''General Inquiries About the Analysis of Concepts and of Truths''). * 1694. "De prima philosophiae Emendatione, et de Notione Substantiae" ("On the Correction of First Philosophy and the Notion of Substance"). * 1695. ''Système nouveau de la nature et de la communication des substances'' (''New System of Nature''). * 1700. ''Accessiones historicae''.. * 1703. "Explication de l'Arithmétique Binaire" ("Explanation of Binary Arithmetic"); Carl Immanuel Gerhardt, ''Mathematical Writings'' VII.223. An English translation by Lloyd Strickland i
available
online. * 1704 (publ. 1765). ''Nouveaux essais sur l'entendement humain''. Translated in: Remnant, Peter, and Bennett, Jonathan, trans., 1996. ''New Essays on Human Understanding'' Langley translation 1896. Cambridge University Press. Wiener III.6 (part). * 1707–1710. ''Scriptores rerum Brunsvicensium'' (3 Vols.). * 1710. ''Théodicée''; Farrer, A. M., and Huggard, E. M., trans., 1985 (1952). Wiener III.11 (part). An English translation i
available
online at Project Gutenberg. * 1714. "Principes de la nature et de la Grâce fondés en raison." * 1714. ''Monadologie''; translated by Nicholas Rescher, 1991. ''The Monadology: An Edition for Students''. University of Pittsburgh Press. Ariew and Garber 213, Loemker §67, Wiener III.13, Woolhouse and Francks 19. An English translation by Robert Latta i
available
online.

### Posthumous works

* 1717. ''Collectanea Etymologica'', edited by the secretary of Leibniz Johann Georg von Eckhart * 1749. ''Protogaea'' * 1750. ''Origines Guelficae''

## Collections

Six important collections of English translations are Wiener (1951), Parkinson (1966), Loemker (1969), Ariew and Garber (1989), Woolhouse and Francks (1998), and Strickland (2006). The ongoing critical edition of all of Leibniz's writings is ''Sämtliche Schriften und Briefe''.

* General Leibniz rule * Leibniz Association * Leibniz operator * List of German inventors and discoverers * List of pioneers in computer science * List of things named after Gottfried Leibniz * ''Mathesis universalis'' * Scientific revolution * Leibniz University Hannover * Bartholomew Des Bosses * Joachim Bouvet * Outline of Gottfried Wilhelm Leibniz * Gottfried Wilhelm Leibniz bibliography

# References

## Sources

### Bibliographies

* Bodemann, Eduard, ''Die Leibniz-Handschriften der Königlichen öffentlichen Bibliothek zu Hannover'', 1895, (anastatic reprint: Hildesheim, Georg Olms, 1966). * Bodemann, Eduard, ''Der Briefwechsel des Gottfried Wilhelm Leibniz in der Königlichen öffentliche Bibliothek zu Hannover'', 1895, (anastatic reprint: Hildesheim, Georg Olms, 1966). * Ravier, Émile, ''Bibliographie des œuvres de Leibniz'', Paris: Alcan, 1937 (anastatic reprint Hildesheim: Georg Olms, 1966). * Heinekamp, Albert and Mertens, Marlen. ''Leibniz-Bibliographie. Die Literatur über Leibniz bis 1980'', Frankfurt: Vittorio Klostermann, 1984. * Heinekamp, Albert and Mertens, Marlen. ''Leibniz-Bibliographie. Die Literatur über Leibniz. Band II: 1981–1990'', Frankfurt: Vittorio Klostermann, 1996. An updated bibliography of more than 25.000 titles is available a
Leibniz Bibliographie

### Primary literature (chronologically)

* Wiener, Philip, (ed.), 1951. ''Leibniz: Selections''. Scribner. * Schrecker, Paul & Schrecker, Anne Martin, (eds.), 1965. ''Monadology and other Philosophical Essays''. Prentice-Hall. * George Henry Radcliffe Parkinson, Parkinson, G. H. R. (ed.), 1966. ''Logical Papers''. Clarendon Press. * Mason, H. T. & Parkinson, G. H. R. (eds.), 1967. ''The Leibniz-Arnauld Correspondence''. Manchester University Press. * Loemker, Leroy, (ed.), 1969 [1956]. ''Leibniz: Philosophical Papers and Letters''. Reidel. * Morris, Mary & Parkinson, G. H. R. (eds.), 1973. ''Philosophical Writings''. Everyman’s University Library. * Riley, Patrick, (ed.), 1988. ''Leibniz: Political Writings''. Cambridge University Press. * Niall, R. Martin, D. & Brown, Stuart (eds.), 1988. ''Discourse on Metaphysics and Related Writings''. Manchester University Press. * Ariew, Roger and Garber, Daniel. (eds.), 1989. ''Leibniz: Philosophical Essays''. Hackett. * Rescher, Nicholas (ed.), 1991. ''G. W. Leibniz’s Monadology. An Edition for Students'', University of Pittsburgh Press. * Rescher, Nicholas, ''On Leibniz'', (Pittsburgh: University of Pittsburgh Press, 2013). * Parkinson, G. H. R. (ed.) 1992. ''De Summa Rerum. Metaphysical Papers, 1675–1676''. Yale University Press. * Cook, Daniel, & Rosemont, Henry Jr., (eds.), 1994. ''Leibniz: Writings on China''. Open Court. * Farrer, Austin (ed.), 1995. ''Theodicy'', Open Court. * Remnant, Peter, & Bennett, Jonathan, (eds.), 1996 (1981). ''Leibniz: New Essays on Human Understanding''. Cambridge University Press. * Roger Woolhouse, Woolhouse, R. S., and Francks, R., (eds.), 1997. ''Leibniz's 'New System' and Associated Contemporary Texts''. Oxford University Press. * Woolhouse, R. S., and Francks, R., (eds.), 1998. ''Leibniz: Philosophical Texts''. Oxford University Press. * Ariew, Roger, (ed.), 2000. ''G. W. Leibniz and Samuel Clarke: Correspondence''. Hackett. * Richard T. W. Arthur, (ed.), 2001. ''The Labyrinth of the Continuum: Writings on the Continuum Problem, 1672–1686''. Yale University Press. * Richard T. W. Arthur, 2014. ''Leibniz''. John Wiley & Sons. * Robert C. Sleigh Jr., (ed.), 2005. ''Confessio Philosophi: Papers Concerning the Problem of Evil, 1671–1678''. Yale University Press. * Dascal, Marcelo (ed.), 2006. "G. W. Leibniz. The Art of Controversies’’, Springer. * Strickland, Lloyd, 2006 (ed.). ''The Shorter Leibniz Texts: A Collection of New Translations''. Continuum. * Look, Brandon and Rutherford, Donald (eds.), 2007. ''The Leibniz-Des Bosses Correspondence'', Yale University Press. * Cohen, Claudine and Wakefield, Andre, (eds.), 2008. ''Protogaea''. University of Chicago Press. * Murray, Michael, (ed.) 2011. ''Dissertation on Predestination and Grace'', Yale University Press. * Strickand, Lloyd (ed.), 2011. ''Leibniz and the two Sophies. The Philosophical Correspondence'', Toronto. * Lodge, Paul (ed.), 2013. ''The Leibniz-De Volder Correspondence: With Selections from the Correspondence Between Leibniz and Johann Bernoulli'', Yale University Press. * Artosi, Alberto, Pieri, Bernardo, Sartor, Giovanni (eds.), 2014. ''Leibniz: Logico-Philosophical Puzzles in the Law'', Springer. * De Iuliis, Carmelo Massimo, (ed.), 2017. ''Leibniz: The New Method of Learning and Teaching Jurisprudence'', Talbot, Clark NJ.

### Secondary literature up to 1950

* Emil du Bois-Reymond, Du Bois-Reymond, Emil, 1912. ''Leibnizsche Gedanken in der neueren Naturwissenschaft'', Berlin: Dummler, 1871 (reprinted in ''Reden'', Leipzig: Veit, vol. 1). * Louis Couturat, Couturat, Louis, 1901. ''La Logique de Leibniz''. Paris: Felix Alcan. * Martin Heidegger, Heidegger, Martin, 1983. ''The Metaphysical Foundations of Logic''. Indiana University Press (lecture course, 1928). * Lovejoy, Arthur O., 1957 (1936). "Plenitude and Sufficient Reason in Leibniz and Spinoza" in his ''The Great Chain of Being''. Harvard University Press: 144–182. Reprinted in Frankfurt, H. G., (ed.), 1972. ''Leibniz: A Collection of Critical Essays''. Anchor Books 1972. * John Milton Mackie, Mackie, John Milton; Gottschalk Eduard Guhrauer, Guhrauer, Gottschalk Eduard, 1845. ''Life of Godfrey William von ''. Gould, Kendall and Lincoln. * Bertrand Russell, Russell, Bertrand, 1900, ''A Critical Exposition of the Philosophy of Leibniz'', Cambridge: The University Press. * * Friedrich Adolf Trendelenburg, Trendelenburg, F. A., 1857, "Über Leibnizens Entwurf einer allgemeinen Charakteristik," ''Philosophische Abhandlungen der Königlichen Akademie der Wissenschaften zu Berlin. Aus dem Jahr 1856'', Berlin: Commission Dümmler, pp. 36–69. * (lecture)

### Secondary literature post-1950

* Adams, Robert Merrihew. 1994. ''Leibniz: Determinist, Theist, Idealist''. New York: Oxford, Oxford University Press. * Aiton, Eric J., 1985. ''Leibniz: A Biography''. Hilger (UK). * Maria Rosa Antognazza, 2008. ''Leibniz: An Intellectual Biography''. Cambridge Univ. Press. * * * Brown, Stuart (ed.), 1999. ''The Young Leibniz and His Philosophy (1646–76)'', Dordrecht, Kluwer. * Martin Davis (mathematician), Davis, Martin, 2000. ''The Universal Computer: The Road from Leibniz to Turing''. WW Norton. * Gilles Deleuze, Deleuze, Gilles, 1993. ''The Fold: Leibniz and the Baroque''. University of Minnesota Press. * Jochen Fahrenberg, Fahrenberg, Jochen, 2017. PsyDok ZPI
The influence of Gottfried Wilhelm Leibniz on the Psychology, Philosophy, and Ethics of Wilhelm Wundt.
* Jochen Fahrenberg, Fahrenberg, Jochen, 2020. ''Wilhelm Wundt (1832 – 1920). Introduction, Quotations, Reception, Commentaries, Attempts at Reconstruction''. Pabst Science Publishers, Lengerich 2020, . * Finster, Reinhard & van den Heuvel, Gerd 2000. ''Gottfried Wilhelm Leibniz''. Mit Selbstzeugnissen und Bilddokumenten. 4. Auflage. Rowohlt, Reinbek bei Hamburg (Rowohlts Monographien, 50481), . * Ivor Grattan-Guinness, Grattan-Guinness, Ivor, 1997. ''The Norton History of the Mathematical Sciences''. W W Norton. * Hall, A. R., 1980. ''Philosophers at War: The Quarrel between Newton and Leibniz''. Cambridge University Press. * Hamza, Gabor, 2005. "Le développement du droit privé européen". ELTE Eotvos Kiado Budapest. * * Hostler, John, 1975. ''Leibniz's Moral Philosophy''. UK: Duckworth. * Ishiguro, Hidé 1990. ''Leibniz's Philosophy of Logic and Language''. Cambridge University Press. * Jolley, Nicholas, (ed.), 1995. ''The Cambridge Companion to Leibniz''. Cambridge University Press. * Kaldis, Byron, 2011. ''Leibniz' Argument for Innate Ideas'' in Just the Arguments: 100 of the Most Important Arguments in Western Philosophy edited by M Bruce & S Barbone. Blackwell. * * LeClerc, Ivor (ed.), 1973. ''The Philosophy of Leibniz and the Modern World''. Vanderbilt University Press. * * Benson Mates, Mates, Benson, 1986. ''The Philosophy of Leibniz: Metaphysics and Language''. Oxford University Press. * Mercer, Christia, 2001. ''Leibniz's Metaphysics: Its Origins and Development''. Cambridge University Press. * Perkins, Franklin, 2004. ''Leibniz and China: A Commerce of Light''. Cambridge University Press. * Patrick T. Riley, Riley, Patrick, 1996. ''Leibniz's Universal Jurisprudence: Justice as the Charity of the Wise''. Harvard University Press. * Donald Rutherford (philosopher), Rutherford, Donald, 1998. ''Leibniz and the Rational Order of Nature''. Cambridge University Press. * Schulte-Albert, H. G. (1971). Gottfried Wilhelm Leibniz and Library Classification. ''The Journal of Library History'' (1966–1972), (2). 133–152. * Smith, Justin E. H., 2011. ''Divine Machines. Leibniz and the Sciences of Life'', Princeton University Press. * Wilson, Catherine, 1989. ''Leibniz's Metaphysics: A Historical and Comparative Study''. Princeton University Press. *

* * * * * * * * * *
Translations
by Jonathan Bennett (philosopher), Jonathan Bennett, of the ''New Essays'', the exchanges with Bayle, Arnauld and Clarke, and about 15 shorter works.
Gottfried Wilhelm Leibniz: Texts and Translations
compiled by Donald Rutherford, UCSD
Leibnitiana
links and resources edited by Gregory Brown, University of Houston
Philosophical Works of Leibniz translated by G.M. Duncan (1890)

The Best of All Possible Worlds: Nicholas Rescher Talks About Gottfried Wilhelm von Leibniz's "Versatility and Creativity"

"Protogæa"
(1693, Latin, in ''Acta eruditorum'') – Linda Hall Library
''Protogaea''
(1749, German) – full digital facsimile from Linda Hall Library * Leibniz's (1768, 6-volume
''Opera omnia''
– digital facsimile * Leibniz' arithmetical machine, 1710, online and analyzed on
BibNum
' [click 'à télécharger' for English analysis] * Leibniz' binary numeral system, 'De progressione dyadica', 1679, online and analyzed on
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' [click 'à télécharger' for English analysis] {{DEFAULTSORT:Leibniz, Gottfried Gottfried Leibniz, 1646 births 1716 deaths 17th-century German mathematicians 17th-century German philosophers 17th-century German scientists 17th-century German writers 17th-century German male writers 17th-century Latin-language writers 18th-century German mathematicians 18th-century German philosophers 18th-century German scientists 18th-century German writers 18th-century German male writers 18th-century Latin-language writers Age of Enlightenment Analytic philosophy Constructed language creators Determinists Enlightenment philosophers Epistemologists Fellows of the Royal Society 17th-century German inventors German librarians German logicians German Lutherans German philologists 18th-century German physicists German political philosophers German Protestants German writers in French Idealists Leipzig University alumni Mathematical analysts Mathematics of infinitesimals Linear algebraists Members of the Prussian Academy of Sciences Metaphysicians Moral philosophers Ontologists Panpsychism People associated with Baruch Spinoza People educated at the St. Thomas School, Leipzig People from the Electorate of Saxony People involved in plagiarism controversies People of the Age of Enlightenment Philosophers of art Philosophers of culture Philosophers of economics Philosophers of education Philosophers of ethics and morality Philosophers of language Philosophers of law Philosophers of literature Philosophers of logic Philosophers of mathematics Philosophers of mind Philosophers of science Philosophers of technology Philosophers of time Philosophical cosmologists Philosophical theists Philosophy writers Rationalists Scholasticism University of Altdorf alumni Writers about religion and science Giftedness 18th-century German inventors