Gottfried Leibniz

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Gottfried Wilhelm (von) Leibniz . ( – 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 pro ...
active as a
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...
,
philosopher A philosopher is a person who practices or investigates philosophy Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Suc ...
,
scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, area of the natural sciences. In classical antiquity, there was no real ancient analog of a modern scientist. Instead, ...
and
diplomat A diplomat (from grc, δίπλωμα; romanization, romanized ''diploma'') is a person appointed by a state (polity), state or an intergovernmental institution such as the United Nations or the European Union to conduct diplomacy with one or m ...
. He is one of the most prominent figures in both the
history of philosophy Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, Epistemology, knowledge, Ethics, values, Philosophy of mind, mind, and Philosophy of language, language. Such quest ...
and the
history of mathematics The history of mathematics deals with the origin of discoveries in mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and ...
. He wrote works on
philosophy Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ...
,
theology Theology is the systematic study of the nature of the Divinity, divine and, more broadly, of religious belief. It is taught as an Discipline (academia), academic discipline, typically in universities and seminaries. It occupies itself with the ...
,
ethics Ethics or moral philosophy is a branch of philosophy that "involves systematizing, defending, and recommending concepts of morality, right and wrong action (philosophy), behavior".''Internet Encyclopedia of Philosophy'' The field of ethics, alo ...
,
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 among individuals, such as the distribution of res ...
,
law Law is a set of rules that are created and are law enforcement, enforceable by social or governmental institutions to regulate behavior,Robertson, ''Crimes against humanity'', 90. with its precise definition a matter of longstanding debate. ...
,
history History (derived ) is the systematic study and the documentation of the human activity. The time period of event before the invention of writing systems is considered prehistory. "History" is an umbrella term comprising past events as we ...
and
philology Philology () is the study of language in oral and writing, written historical sources; it is the intersection of textual criticism, literary criticism, history, and linguistics (with especially strong ties to etymology). Philology is also defin ...
. Leibniz also made major contributions to
physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical science is that depar ...
and
technology Technology is the application of knowledge to reach practical goals in a specifiable and Reproducibility, reproducible way. The word ''technology'' may also mean the product of such an endeavor. The use of technology is widely prevalent in me ...
, and anticipated notions that surfaced much later in
probability theory Probability theory is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expressing it through a set o ...
,
biology Biology is the scientific study of life. It is a natural science with a broad scope but has several unifying themes that tie it together as a single, coherent field. For instance, all organisms are made up of Cell (biology), cells that proce ...
,
medicine Medicine is the science and Praxis (process), practice of caring for a patient, managing the diagnosis, prognosis, Preventive medicine, prevention, therapy, treatment, Palliative care, palliation of their injury or disease, and Health promotion ...
,
geology Geology () is a branch of natural science concerned with Earth and other Astronomical object, astronomical objects, the features or rock (geology), rocks of which it is composed, and the processes by which they change over time. Modern geology ...
,
psychology Psychology is the science, scientific study of mind and behavior. Psychology includes the study of consciousness, conscious and Unconscious mind, unconscious phenomena, including feelings and thoughts. It is an academic discipline of immens ...
,
linguistics Linguistics is the scientific study of human language. It is called a scientific study because it entails a comprehensive, systematic, objective, and precise analysis of all aspects of language, particularly its nature and structure. Linguis ...
and
computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...
. In addition, he contributed to the field of
library science Library science (often termed library studies, bibliothecography, and library economy) is an interdisciplinary or multidisciplinary field that applies the practices, perspectives, and tools of management, information technology, education, and ...
: while serving as overseer of the Wolfenbüttel library in Germany, 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 journals, in tens of thousands of letters and in unpublished manuscripts. He wrote in several languages, primarily in Latin, French and German, but also in English, Italian and Dutch. As a philosopher, he was one of the greatest representatives of 17th-century
rationalism In philosophy, rationalism is the epistemology, epistemological view that "regards reason as the chief source and test of knowledge" or "any view appealing to reason as a source of knowledge or justification".Lacey, A.R. (1996), ''A Dictionary o ...
and
idealism In philosophy, the term idealism identifies and describes metaphysics, metaphysical perspectives which assert that reality is indistinguishable and inseparable from perception and understanding; that reality is a mental construct closely con ...
. As a mathematician, his greatest achievement was the development of the main ideas of differential and integral calculus, independently of
Isaac Newton Sir Isaac Newton (25 December 1642 – 20 March 1726/27) was an English mathematician, physicist, astronomer, alchemist, Theology, theologian, and author (described in his time as a "natural philosophy, natural philosopher"), widely ...
's contemporaneous developments, and mathematicians have consistently favored Leibniz's notation as the conventional and more exact expression of calculus. However, it was only in the 20th century that Leibniz's law of continuity and transcendental law of homogeneity found a consistent mathematical formulation by means of non-standard analysis. He was also a pioneer in the field of mechanical calculators. While working on adding automatic multiplication and division to Pascal's calculator, he was the first to describe a pinwheel calculator in 1685 and invented the Leibniz wheel, used in the arithmometer, the first mass-produced mechanical calculator. He also refined the
binary number A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" (one). The base-2 numeral system is a positional notation ...
system, which is the foundation of nearly all digital ( electronic, solid-state, discrete logic)
computer A computer is a machine that can be programmed to carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as Computer program, pr ...
s, including the
Von Neumann architecture The von Neumann architecture — also known as the von Neumann model or Princeton architecture — is a computer architecture based on a 1945 description by John von Neumann, and by others, in the ''First Draft of a Report on the EDVAC''. The ...
, which is the standard design paradigm, or "
computer architecture In computer engineering, computer architecture is a description of the structure of a computer system made from component parts. It can sometimes be a high-level description that ignores details of the implementation. At a more detailed level, the ...
", 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 systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. Some ...
and
theology Theology is the systematic study of the nature of the Divinity, divine and, more broadly, of religious belief. It is taught as an Discipline (academia), academic discipline, typically in universities and seminaries. It occupies itself with the ...
, 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 pessimis ...
, i.e. his conclusion that our world is, in a qualified sense, the best possible world that
God In monotheistic thought, God is usually viewed as the supreme being, creator, and principal object of faith. Swinburne, R.G. "God" in Honderich, Ted. (ed)''The Oxford Companion to Philosophy'', Oxford University Press, 1995. God is typicall ...
could have created, a view sometimes lampooned by other thinkers, such as
Voltaire François-Marie Arouet (; 21 November 169430 May 1778) was a French Age of Enlightenment, Enlightenment writer, historian, and philosopher. Known by his ''Pen name, nom de plume'' M. de Voltaire (; also ; ), he was famous for his wit, and his ...
in his
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novella A novella is a narrative prose fiction whose length is shorter than most novels, but longer than most Short story, short stories. The English word ''novella'' derives from the Italian ''novella'' meaning a short story related to true (or apparen ...
''
Candide ( , ) is a French satire written by Voltaire, a philosopher of the Age of Enlightenment, first published in 1759. The novella has been widely translated, with English versions titled ''Candide: or, All for the Best'' (1759); ''Candide: or, The ...
''. Leibniz, along with
René Descartes René Descartes ( or ; ; Latinisation of names, Latinized: Renatus Cartesius; 31 March 1596 – 11 February 1650) was a French people, French philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of m ...
and
Baruch Spinoza Baruch (de) Spinoza (born Bento de 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 Republic, Dutch philosopher of Spanish and ...
, was one of the three great early modern rationalists. 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 the study of correct reasoning. It includes both Mathematical logic, formal and informal logic. Formal logic is the science of Validity (logic), deductively valid inferences or of logical truths. It is a formal science investigating h ...
and still influences contemporary
analytic philosophy Analytic philosophy is a Academic discipline, branch and Philosophical tradition, tradition of philosophy using philosophical analysis, analysis, popular in the Western world and particularly the Anglosphere, which began around the turn of the 2 ...
, such as its adopted use of the term " possible world" to define modal notions.

# Biography

## Early life

Gottfried Leibniz was born on July 1 1646, toward the end of the
Thirty Years' War The Thirty Years' War was one of the longest and List of wars and anthropogenic disasters by death toll, most destructive conflicts in History of Europe, European history, lasting from 1618 to 1648. Fought primarily in Central Europe, an es ...
, in
Leipzig Leipzig ( , ; Upper Saxon: ) is the most populous city in the Germany, German States of Germany, state of Saxony. Leipzig's population of 605,407 inhabitants (1.1 million in the larger urban zone) as of 2021 places the city as Germany's L ...
,
Saxony Saxony (german: Sachsen ; Upper Saxon German, Upper Saxon: ''Saggsn''; hsb, Sakska), officially the Free State of Saxony (german: Freistaat Sachsen, links=no ; Upper Saxon: ''Freischdaad Saggsn''; hsb, Swobodny stat Sakska, links=no), is a ...
, 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; his godfather was the
Lutheran Lutheranism is one of the largest branches of Protestantism, identifying primarily with the theology of Martin Luther, the 16th-century German monk and Protestant Reformers, reformer whose efforts to reform the theology and practice of the Cathol ...
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 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 university (by conse ...
, 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: Arts and entertainment * Canon (fiction), the conceptual material accepted as official in a fictional universe by its fan base * Literary canon, an accepted body of works considered as high culture ** Western can ...
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 belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through ...
, also led to his proficiency in the Latin language, which he achieved by the age of 12. At the age of 13 he composed 300 hexameters of Latin verse in a single morning for a special event at school. 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 ''baccalaureus'') or baccalaureate (from New Latin, Modern Latin ''baccalaureatus'') is an Undergraduate degree, undergraduate academic degree awarded by colleges and universities upon completion of a course ...
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 Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) arou ...
in Philosophy on 7 February 1664. In December 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. 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 highest academic degree, university degree, or the procedure by which it is achieved, in many European countries. The candidate fulfills a university's set criteria of excellence in research, teaching and further education, us ...
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 a person who practices or investigates philosophy Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about e ...
'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 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 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 title of nobility, titles of nobility in the German-speaking areas of the ...
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 found in many societies that have an aristocracy (class), aristocracy. It is normally ranked immediately below Royal family, royalty. Nobility has often been an Estates of the realm, estate of the realm with many e ...
.

## 1666–1676

Leibniz's first position was as a salaried secretary to an
alchemical Alchemy (from Arabic: ''al-kīmiyā''; from Ancient Greek: χυμεία, ''khumeía'') is an ancient branch of natural philosophy, a philosophical and protoscience, protoscientific tradition that was historically practiced in Chinese alchemy, C ...
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, Germany. Mainz is on the left bank of the Rhine, opposite to the place that the Main (river), Main joins the Rhine. Downstream of the confluence, the Rhine flows to the north-we ...
, 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 List of French monarchs, King of France from 14 May 1643 until his death in 1715. His reign of 72 years and 110 days is the Li ...
, backed by French military and economic might. Meanwhile, the
Thirty Years' War The Thirty Years' War was one of the longest and List of wars and anthropogenic disasters by death toll, most destructive conflicts in History of Europe, European history, lasting from 1618 to 1648. Fought primarily in Central Europe, an es ...
had left
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 language, German-speaking area (german: Deutscher Sprac ...
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, مصر , ), officially the Arab Republic of Egypt, is a List of transcontinental countries, transcontinental country spanning the North Africa, northeast corner of Africa and Western Asia, southwest corner of Asia via a land bridg ...
as a stepping stone towards an eventual conquest of the
Dutch East Indies The Dutch East Indies, also known as the Netherlands East Indies ( nl, Nederlands(ch)-Indië; ), was a Dutch colony consisting of what is now Indonesia. It was formed from the nationalised trading posts of the Dutch East India Company, whic ...
. 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 Franco-Dutch War, also known as the Dutch War (french: Guerre de Hollande; nl, Hollandse Oorlog), was fought between Kingdom of France, France and the Dutch Republic, supported by its allies the Holy Roman Empire, Habsburg Spain, Spain, Br ...
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, Lord of Zeelhem, ( , , ; also spelled Huyghens; la, Hugenius; 14 April 1629 – 8 July 1695) was a Dutch mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typica ...
and realised that his own knowledge of mathematics and physics was patchy. With Huygens as his mentor, he began a program of self-study that soon pushed him to making major contributions to both subjects, including discovering his version of the differential and integral
calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizati ...
. He met
Nicolas Malebranche Nicolas Malebranche ( , ; 6 August 1638 – 13 October 1715) was a French people, French Oratory of Jesus, Oratorian Catholic priest and rationalist philosophy, philosopher. In his works, he sought to synthesize the thought of Augustine of Hip ...
and
Antoine Arnauld Antoine Arnauld (6 February 16128 August 1694) was a French Catholic The Catholic Church, also known as the Roman Catholic Church, is the largest Christian church, with 1.3 billion baptized Catholics worldwide . It is among th ...
, the leading French philosophers of the day, and studied the writings of Descartes and Pascal, unpublished as well as published. He befriended a German mathematician, Ehrenfried Walther von Tschirnhaus; they corresponded for the rest of their lives. When it became clear that France would not implement its part of Leibniz's Egyptian plan, the Elector sent his nephew, escorted by Leibniz, on a related mission to the English government in London, early in 1673. There Leibniz came into acquaintance of
Henry Oldenburg Henry Oldenburg (also Henry Oldenbourg) Fellow of the Royal Society, FRS (c. 1618 as Heinrich Oldenburg – 5 September 1677), was a Germans, German Theology, theologian, diplomat, and Natural philosophy, natural philosopher, known as one of th ...
and John Collins. He met with the
Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, ...
where he demonstrated a calculating machine that he had designed and had been building since 1670. The machine was able to execute all four basic operations (adding, subtracting, multiplying, and dividing), and the society quickly made him an external member. The mission ended abruptly when news of the Elector's death (12 February 1673) reached them. Leibniz promptly returned to Paris and not, as had been planned, to Mainz. The sudden deaths of his two patrons in the same winter meant that Leibniz had to find a new basis for his career. In this regard, a 1669 invitation from Duke John Frederick of Brunswick to visit Hanover proved to have been fateful. Leibniz had declined the invitation, but had begun corresponding with the duke in 1671. In 1673, the duke offered Leibniz the post of counsellor. Leibniz very reluctantly accepted the position two years later, only after it became clear that no employment was forthcoming in Paris, whose intellectual stimulation he relished, or with the
Habsburg The House of Habsburg (), alternatively spelled Hapsburg in Englishgerman: Haus Habsburg, ; es, Casa de Habsburgo; hu, Habsburg család, it, Casa di Asburgo, nl, Huis van Habsburg, pl, dom Habsburgów, pt, Casa de Habsburgo, la, Domus Hab ...
imperial court. In 1675 he tried to get admitted to the
French Academy of Sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV of France, Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific me ...
as a foreign honorary member, but it was considered that there were already enough foreigners there and so no invitation came. He left Paris in October 1676.

## House of Hanover, 1676–1716

Leibniz managed to delay his arrival in Hanover until the end of 1676 after making one more short journey to London, where Newton accused him of having seen his unpublished work on calculus in advance. This was alleged to be evidence supporting the accusation, made decades later, that he had stolen calculus from Newton. On the journey from London to Hanover, Leibniz stopped in
The Hague The Hague ( ; nl, Den Haag or ) is a list of cities in the Netherlands by province, city and municipalities of the Netherlands, municipality of the Netherlands, situated on the west coast facing the North Sea. The Hague is the country's ad ...
where he met van Leeuwenhoek, the discoverer of microorganisms. He also spent several days in intense discussion with
Spinoza Baruch (de) Spinoza (born Bento de 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 Republic, Dutch philosopher of Spanish and ...
, who had just completed his masterwork, the ''
Ethics Ethics or moral philosophy is a branch of philosophy that "involves systematizing, defending, and recommending concepts of morality, right and wrong action (philosophy), behavior".''Internet Encyclopedia of Philosophy'' The field of ethics, alo ...
''. In 1677, he was promoted, at his request, to Privy Counselor of Justice, a post he held for the rest of his life. Leibniz served three consecutive rulers of the House of Brunswick as historian, political adviser, and most consequentially, as librarian of the ducal library. He thenceforth employed his pen on all the various political, historical, and
theological Theology is the systematic study of the nature of the Divinity, divine and, more broadly, of religious belief. It is taught as an Discipline (academia), academic discipline, typically in universities and seminaries. It occupies itself with the ...
matters involving the House of Brunswick; the resulting documents form a valuable part of the historical record for the period. Leibniz began promoting a project to use windmills to improve the mining operations in the Harz Mountains. This project did little to improve mining operations and was shut down by Duke Ernst August in 1685. Among the few people in north Germany to accept Leibniz were the Electress
Sophia of Hanover Sophia of Hanover (born Princess Sophia of the Palatinate; 14 October 1630 – 8 June 1714) was the List of Hanoverian consorts, Electress of Hanover by marriage to Elector Ernest Augustus and later the heiress presumptive to the thrones of King ...
(1630–1714), her daughter Sophia Charlotte of Hanover (1668–1705), the Queen of Prussia and his avowed disciple, and Caroline of Ansbach, the consort of her grandson, the future George II. To each of these women he was correspondent, adviser, and friend. In turn, they all approved of Leibniz more than did their spouses and the future king
George I of Great Britain George I (George Louis; ; 28 May 1660 – 11 June 1727) was King of Great Britain and King of Ireland, Ireland from 1 August 1714 and ruler of the Electorate of Hanover within the Holy Roman Empire from 23 January 1698 until his death in 1727. ...
. The population of Hanover was only about 10,000, and its provinciality eventually grated on Leibniz. Nevertheless, to be a major courtier to the House of Brunswick was quite an honor, especially in light of the meteoric rise in the prestige of that House during Leibniz's association with it. In 1692, the Duke of Brunswick became a hereditary Elector of the
Holy Roman Empire The Holy Roman Empire was a Polity, political entity in Western Europe, Western, Central Europe, Central, and Southern Europe that developed during the Early Middle Ages and continued until its Dissolution of the Holy Roman Empire, dissolution i ...
. The British
Act of Settlement 1701 The Act of Settlement is an Acts of the Parliament of England, Act of the Parliament of England that settled the order of succession, succession to the English Monarchs, English and List of Irish monarchs, Irish crowns to only Protestants, whic ...
designated the Electress Sophia and her descent as the royal family of England, once both King William III and his sister-in-law and successor, Queen Anne, were dead. Leibniz played a role in the initiatives and negotiations leading up to that Act, but not always an effective one. For example, something he published anonymously in England, thinking to promote the Brunswick cause, was formally censured by the
British Parliament The Parliament of the United Kingdom is the Parliamentary sovereignty in the United Kingdom, supreme Legislature, legislative body of the United Kingdom, the Crown Dependencies and the British Overseas Territories. It meets at the Palace of We ...
. The Brunswicks tolerated the enormous effort Leibniz devoted to intellectual pursuits unrelated to his duties as a courtier, pursuits such as perfecting calculus, writing about other mathematics, logic, physics, and philosophy, and keeping up a vast correspondence. He began working on calculus in 1674; the earliest evidence of its use in his surviving notebooks is 1675. By 1677 he had a coherent system in hand, but did not publish it until 1684. Leibniz's most important mathematical papers were published between 1682 and 1692, usually in a journal which he and Otto Mencke founded in 1682, the '' Acta Eruditorum''. That journal played a key role in advancing his mathematical and scientific reputation, which in turn enhanced his eminence in diplomacy, history, theology, and philosophy. The Elector Ernest Augustus commissioned Leibniz to write a history of the House of Brunswick, going back to the time of
Charlemagne Charlemagne ( , ) or Charles the Great ( la, Carolus Magnus; german: Karl der Große; 2 April 747 – 28 January 814), a member of the Carolingian dynasty, was King of the Franks from 768, King of the Lombards from 774, and the first Holy ...
or earlier, hoping that the resulting book would advance his dynastic ambitions. From 1687 to 1690, Leibniz traveled extensively in Germany, Austria, and Italy, seeking and finding archival materials bearing on this project. Decades went by but no history appeared; the next Elector became quite annoyed at Leibniz's apparent dilatoriness. Leibniz never finished the project, in part because of his huge output on many other fronts, but also because he insisted on writing a meticulously researched and erudite book based on archival sources, when his patrons would have been quite happy with a short popular book, one perhaps little more than a
genealogy Genealogy () is the study of families, family history, and the tracing of their Lineage (anthropology), lineages. Genealogists use oral interviews, historical records, genetic analysis, and other records to obtain information about a family a ...
with commentary, to be completed in three years or less. They never knew that he had in fact carried out a fair part of his assigned task: when the material Leibniz had written and collected for his history of the House of Brunswick was finally published in the 19th century, it filled three volumes. Leibniz was appointed Librarian of the Herzog August Library in Wolfenbüttel,
Lower Saxony Lower Saxony (german: Niedersachsen ; nds, Neddersassen; stq, Läichsaksen) is a States of Germany, German state (') in Northern Germany, northwestern Germany. It is the second-largest state by land area, with , and fourth-largest in populati ...
, in 1691. In 1708, John Keill, writing in the journal of the Royal Society and with Newton's presumed blessing, accused Leibniz of having plagiarised Newton's calculus. Thus began the calculus priority dispute which darkened the remainder of Leibniz's life. A formal investigation by the Royal Society (in which Newton was an unacknowledged participant), undertaken in response to Leibniz's demand for a retraction, upheld Keill's charge. Historians of mathematics writing since 1900 or so have tended to acquit Leibniz, pointing to important differences between Leibniz's and Newton's versions of calculus. In 1711, while traveling in northern Europe, the Russian
Tsar Tsar ( or ), also spelled ''czar'', ''tzar'', or ''csar'', is a title used by East Slavs, East and South Slavs, South Slavic monarchs. The term is derived from the Latin word ''Caesar (title), caesar'', which was intended to mean "emperor" i ...
Peter the Great Peter I ( – ), most commonly known as Peter the Great,) or Pyotr Alekséyevich ( rus, Пётр Алексе́евич, p=ˈpʲɵtr ɐlʲɪˈksʲejɪvʲɪtɕ, , group=pron was a List of Russian monarchs, Russian monarch who ruled the ...
stopped in Hanover and met Leibniz, who then took some interest in Russian matters for the rest of his life. In 1712, Leibniz began a two-year residence in
Vienna Vienna ( ; german: Wien ; bar, Wean, label=Bavarian language, Austro-Bavarian ) is the Capital city, capital, largest city, and one of States of Austria, nine states of Austria. Vienna is Austria's List of cities and towns in Austria, most populou ...
, where he was appointed Imperial Court Councillor to the
Habsburg The House of Habsburg (), alternatively spelled Hapsburg in Englishgerman: Haus Habsburg, ; es, Casa de Habsburgo; hu, Habsburg család, it, Casa di Asburgo, nl, Huis van Habsburg, pl, dom Habsburgów, pt, Casa de Habsburgo, la, Domus Hab ...
s. On the death of Queen Anne in 1714, Elector George Louis became King
George I of Great Britain George I (George Louis; ; 28 May 1660 – 11 June 1727) was King of Great Britain and King of Ireland, Ireland from 1 August 1714 and ruler of the Electorate of Hanover within the Holy Roman Empire from 23 January 1698 until his death in 1727. ...
, under the terms of the 1701 Act of Settlement. Even though Leibniz had done much to bring about this happy event, it was not to be his hour of glory. Despite the intercession of the Princess of Wales, Caroline of Ansbach, George I forbade Leibniz to join him in London until he completed at least one volume of the history of the Brunswick family his father had commissioned nearly 30 years earlier. Moreover, for George I to include Leibniz in his London court would have been deemed insulting to Newton, who was seen as having won the calculus priority dispute and whose standing in British official circles could not have been higher. Finally, his dear friend and defender, the Dowager Electress Sophia, died in 1714.

## Death

Leibniz died in
Hanover Hanover (; german: Hannover ; nds, Hannober) is the capital and largest city of the German States of Germany, state of Lower Saxony. Its 535,932 (2021) inhabitants make it the List of cities in Germany by population, 13th-largest city in Germa ...
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 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 Fontenelle, before the
French Academy of Sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV of France, Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific me ...
in Paris, which had admitted him as a foreign member in 1700. The eulogy was composed at the behest of the Duchess of Orleans, a niece of the Electress Sophia.

## 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 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 Protestantism is a branch of Christianity Christianity is an Abrahamic religions, Abrahamic Monotheism, monotheistic religion based on the Life of Jesus in the New Testament, life and Teachings of Jesus, teachings of Jesus, Jesus of Na ...
and a philosophical theist. Leibniz remained committed to Trinitarian Christianity throughout his life.

# Philosopher

Leibniz's philosophical thinking appears fragmented, because his philosophical writings consist mainly of a multitude of short pieces: journal articles, manuscripts published long after his death, and many letters to many correspondents. He wrote only two book-length philosophical treatises, of which only the ''Théodicée'' of 1710 was published in his lifetime. Leibniz dated his beginning as a philosopher to his '' Discourse on Metaphysics'', which he composed in 1686 as a commentary on a running dispute between
Nicolas Malebranche Nicolas Malebranche ( , ; 6 August 1638 – 13 October 1715) was a French people, French Oratory of Jesus, Oratorian Catholic priest and rationalist philosophy, philosopher. In his works, he sought to synthesize the thought of Augustine of Hip ...
and
Antoine Arnauld Antoine Arnauld (6 February 16128 August 1694) was a French Catholic The Catholic Church, also known as the Roman Catholic Church, is the largest Christian church, with 1.3 billion baptized Catholics worldwide . It is among th ...
. This led to an extensive and valuable correspondence with Arnauld; it and the ''Discourse'' were not published until the 19th century. In 1695, Leibniz made his public entrée into European philosophy with a journal article titled "New System of the Nature and Communication of Substances". Between 1695 and 1705, he composed his ''
New Essays on Human Understanding ''New Essays on Human Understanding'' (french: Nouveaux essais sur l'entendement humain) is a chapter-by-chapter rebuttal by Gottfried Leibniz of John Locke's major work ''An Essay Concerning Human Understanding''. It is one of only two full-lengt ...
'', a lengthy commentary on
John Locke John Locke (; 29 August 1632 – 28 October 1704) was an English philosopher and physician, widely regarded as one of the most influential of Age of Enlightenment, Enlightenment thinkers and commonly known as the "father of liberalism ...
's 1690 ''
An Essay Concerning Human Understanding ''An Essay Concerning Human Understanding'' is a work by John Locke concerning the foundation of human knowledge and understanding. It first appeared in 1689 (although dated 1690) with the printed title ''An Essay Concerning Humane Understand ...
'', but upon learning of Locke's 1704 death, lost the desire to publish it, so that the ''New Essays'' were not published until 1765. The '' Monadologie'', composed in 1714 and published posthumously, consists of 90 aphorisms. Leibniz also wrote a short paper, "Primae veritates" ("First Truths"), first published by
Louis Couturat Louis Couturat (; 17 January 1868 – 3 August 1914) was a French people, French logician, mathematician, philosophy, philosopher, and linguistics, linguist. Couturat was a pioneer of the constructed language Ido (language), Ido. Life and educa ...
in 1903 (pp. 518–523) summarizing his views on
metaphysics Metaphysics is the branch of philosophy that studies the fundamental nature of reality, the first principles of being, identity and change, space and time, causality, necessity, and possibility. It includes questions about the nature of conscio ...
. The paper is undated; that he wrote it while in Vienna in 1689 was determined only in 1999, when the ongoing critical edition finally published Leibniz's philosophical writings for the period 1677–90. Couturat's reading of this paper was the launching point for much 20th-century thinking about Leibniz, especially among analytic philosophers. But after a meticulous study of all of Leibniz's philosophical writings up to 1688—a study the 1999 additions to the critical edition made possible—Mercer (2001) begged to differ with Couturat's reading; the jury is still out. Leibniz met
Spinoza Baruch (de) Spinoza (born Bento de 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 Republic, Dutch philosopher of Spanish and ...
in 1676, read some of his unpublished writings, and has since been suspected of appropriating some of Spinoza's ideas. While Leibniz admired Spinoza's powerful intellect, he was also forthrightly dismayed by Spinoza's conclusions, especially when these were inconsistent with Christian orthodoxy. Unlike Descartes and Spinoza, Leibniz had a thorough university education in philosophy. He was influenced by his
Leipzig Leipzig ( , ; Upper Saxon: ) is the most populous city in the Germany, German States of Germany, state of Saxony. Leipzig's population of 605,407 inhabitants (1.1 million in the larger urban zone) as of 2021 places the city as Germany's L ...
professor Jakob Thomasius, who also supervised his BA thesis in philosophy.Arthur 2014, p. 13. Leibniz also eagerly read Francisco Suárez, a Spanish
Jesuit The Society of Jesus ( la, Societas Iesu; abbreviation: SJ), also known as the Jesuits (; la, Iesuitæ), is a religious order (Catholic), religious order of clerics regular of pontifical right for men in the Catholic Church headquartered in Rom ...
respected even in
Lutheran Lutheranism is one of the largest branches of Protestantism, identifying primarily with the theology of Martin Luther, the 16th-century German monk and Protestant Reformers, reformer whose efforts to reform the theology and practice of the Cathol ...
universities. Leibniz was deeply interested in the new methods and conclusions of Descartes, Huygens, Newton, and Boyle, but viewed their work through a lens heavily tinted by scholastic notions. Yet it remains the case that Leibniz's methods and concerns often anticipate the
logic Logic is the study of correct reasoning. It includes both Mathematical logic, formal and informal logic. Formal logic is the science of Validity (logic), deductively valid inferences or of logical truths. It is a formal science investigating h ...
, and analytic and linguistic philosophy of the 20th century.

## Principles

Leibniz variously invoked one or another of seven fundamental philosophical Principles: * Identity/
contradiction In traditional logic, a contradiction occurs when a proposition conflicts either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias. Illustrating a general tendency in applied logic, Aristotle's ...
. If a proposition is true, then its negation is false and vice versa. *
Identity of indiscernibles The identity of indiscernibles is an ontology, ontological principle that states that there cannot be separate object (philosophy), objects or wikt:entity, entities that have all their property (philosophy), properties in common. That is, entities ...
. 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. * 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. " e 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'', IV, 16: "''la nature ne fait jamais des sauts''". ''Natura non-facit saltus'' is the Latin translation of the phrase (originally put forward by
Linnaeus Carl Linnaeus (; 23 May 1707 – 10 January 1778), also known after his Nobility#Ennoblement, ennoblement in 1761 as Carl von Linné#Blunt, Blunt (2004), p. 171. (), was a Swedish botanist, zoologist, taxonomist, and physician who formalise ...
' '' Philosophia Botanica'', 1st ed., 1751, Chapter III, § 77, p. 27; see also
Stanford Encyclopedia of Philosophy The ''Stanford Encyclopedia of Philosophy'' (''SEP'') combines an online encyclopedia of philosophy with scholarly peer review, peer-reviewed publication of original papers in philosophy, freely accessible to Internet users. It is maintained by S ...

"Continuity and Infinitesimals"
and
Alexander Baumgarten Alexander Gottlieb Baumgarten (; ; 17 July 1714 – 27 MayJan LekschasBaumgarten Family'' 1762) was a German philosopher. He was a brother to theologian Siegmund Jakob Baumgarten (1706–1757). Biography Baumgarten was born in Berlin as the ...
, ''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.
" aumgartenmust also have in mind Leibniz's "''natura non-facit saltus'' ature does not make leaps ( 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"). *
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 pessimis ...
. "God assuredly always chooses the best." * 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.

## Monads

Leibniz's best known contribution to
metaphysics Metaphysics is the branch of philosophy that studies the fundamental nature of reality, the first principles of being, identity and change, space and time, causality, necessity, and possibility. It includes questions about the nature of conscio ...
is his theory of monads, as exposited in '' Monadologie''. He proposes his theory that the universe is made of an infinite number of simple substances known as monads. Monads can also be compared to the corpuscles of the
mechanical philosophy The mechanical philosophy is a form of natural philosophy which compares the universe to a large-scale mechanism (i.e. a machine). The mechanical philosophy is associated with the scientific revolution of early modern Europe. One of the first expos ...
of René Descartes and others. These simple substances or monads are the "ultimate units of existence in nature". Monads have no parts but still exist by the qualities that they have. These qualities are continuously changing over time, and each monad is unique. They are also not affected by time and are subject to only creation and annihilation. Monads are centers of
force In physics, a force is an influence that can change the motion of an Physical object, object. A force can cause an object with mass to change its velocity (e.g. moving from a Newton's first law, state of rest), i.e., to accelerate. Force can ...
; substance is force, while
space Space is the boundless Three-dimensional space, three-dimensional extent in which Physical body, objects and events have relative position (geometry), position and direction (geometry), direction. In classical physics, physical space is often ...
,
matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of atoms, which are made up of interacting subatomic partic ...
, and
motion In physics, motion is the phenomenon in which an object changes its Position (geometry), position with respect to time. Motion is mathematically described in terms of Displacement (geometry), displacement, distance, velocity, acceleration, speed ...
are merely phenomenal. It is said that he anticipated
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born Theoretical physics, theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for d ...
by arguing, against Newton, that
space Space is the boundless Three-dimensional space, three-dimensional extent in which Physical body, objects and events have relative position (geometry), position and direction (geometry), direction. In classical physics, physical space is often ...
,
time Time is the continued sequence of existence and event (philosophy), events that occurs in an apparently irreversible process, irreversible succession from the past, through the present, into the future. It is a component quantity of various me ...
, and motion are completely relative as he quipped, "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."See H. G. Alexander, ed., ''The Leibniz-Clarke Correspondence'', Manchester: Manchester University Press, pp. 25–26. Einstein, who called himself a "Leibnizian" even wrote in the introduction to
Max Jammer Max Jammer (מקס ימר; born Moshe Jammer, ; April 13, 1915 – December 18, 2010), was an Israeli physicist and philosophy of physics, philosopher of physics. He was born in Berlin, Germany. He was Rector and Acting President at Bar-Ilan Uni ...
's book ''Concepts of Space'' that Leibnizianism was superior to Newtonianism, and his ideas would have dominated over Newton's had it not been for the poor technological tools of the time; it has been argued that Leibniz paved the way for Einstein's
theory of relativity The theory of relativity usually encompasses two interrelated theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in ...
. Leibniz's proof of God can be summarized in the '' Théodicée''. Reason is governed by the principle of contradiction and the
principle of sufficient reason The principle of sufficient reason states that everything must have a reason Reason is the capacity of Consciousness, consciously applying logic by Logical consequence, drawing conclusions from new or existing information, with the aim of seekin ...
. Using the principle of reasoning, Leibniz concluded that the first reason of all things is God. All that we see and experience is subject to change, and the fact that this world is contingent can be explained by the possibility of the world being arranged differently in space and time. The contingent world must have some necessary reason for its existence. Leibniz uses a geometry book as an example to explain his reasoning. If this book was copied from an infinite chain of copies, there must be some reason for the content of the book. Leibniz concluded that there must be the "''monas monadum''" or God. The
ontological In metaphysics, ontology is the philosophy, philosophical study of being, as well as related concepts such as existence, Becoming (philosophy), becoming, and reality. Ontology addresses questions like how entities are grouped into Category ...
essence of a monad is its irreducible simplicity. Unlike atoms, monads possess no material or spatial character. They also differ from atoms by their complete mutual independence, so that interactions among monads are only apparent. Instead, by virtue of the principle of pre-established harmony, each monad follows a pre-programmed set of "instructions" peculiar to itself, so that a monad "knows" what to do at each moment. By virtue of these intrinsic instructions, each monad is like a little mirror of the universe. Monads need not be "small"; e.g., each human being constitutes a monad, in which case
free will Free will is the capacity of agents to choice, choose between different possible courses of Action (philosophy), action unimpeded. Free will is closely linked to the concepts of moral responsibility, praise, culpability, sin, and other judgemen ...
is problematic. Monads are purported to have gotten rid of the problematic: * interaction between
mind The mind is the set of faculties responsible for all mental Phenomenon, phenomena. Often the term is also identified with the phenomena themselves. These faculties include thought, imagination, memory, Will (philosophy), will, and Sensation (psy ...
and matter arising in the system of Descartes; * lack of
individuation The principle of individuation, or ', describes the manner in which a thing is identified as distinct from other things. The concept appears in numerous fields and is encountered in works of Leibniz, Carl Gustav Jung, Günther Anders, Gunther And ...
inherent to the system of
Spinoza Baruch (de) Spinoza (born Bento de 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 Republic, Dutch philosopher of Spanish and ...
, which represents individual creatures as merely accidental.

## Theodicy and optimism

The ''
Theodicy Theodicy () means vindication of God. It is to answer the question of why a good God permits the manifestation of evil, thus resolving the issue of the problem of evil. Some theodicies also address the problem of evil "to make the existence of ...
'' tries to justify the apparent imperfections of the world by claiming that it is optimal among all possible worlds. It must be the best possible and most balanced world, because it was created by 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 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 all good, all wise, and all powerful, then how did 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 Free will is the capacity of agents to choice, choose between different possible courses of Action (philosophy), action unimpeded. Free will is closely linked to the concepts of moral responsibility, praise, culpability, sin, and other judgemen ...
. 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: " 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 Martin Heidegger (; ; 26 September 188926 May 1976) was a German philosopher who is best known for contributions to Phenomenology (philosophy), phenomenology, hermeneutics, and existentialism. He is among the most important and influential phi ...
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: Leibniz's calculus ratiocinator, which resembles
symbolic logic Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of for ...
, 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 Louis Couturat (; 17 January 1868 – 3 August 1914) was a French people, French logician, mathematician, philosophy, philosopher, and linguistics, linguist. Couturat was a pioneer of the constructed language Ido (language), Ido. Life and educa ...
published a selection in 1901; by this time the main developments of modern logic had been created by
Charles Sanders Peirce Charles Sanders Peirce ( ; September 10, 1839 – April 19, 1914) was an American philosopher, logician, mathematician and scientist who is sometimes known as "the father of pragmatism". Educated as a chemist and employed as a scientist for t ...
and by
Gottlob Frege Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, Mathematical logic, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the fath ...
. Leibniz thought
symbol A symbol is a mark, sign, or word that indicates, signifies, or is understood as representing an idea, object, or relationship. Symbols allow people to go beyond what is known or seen by creating linkages between otherwise very different ...
s 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 Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizati ...
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 Semiotics (also called semiotic studies) is the systematic study of sign processes (semiosis) and meaning making. Semiosis is any activity, conduct, or process that involves Sign (semiotics), signs, where a sign is defined as anything that commun ...
. But Leibniz took his speculations much further. Defining a character as any written sign, he then defined a "real" character as one that represents an idea directly and not simply as the word embodying the idea. Some real characters, such as the notation of logic, serve only to facilitate reasoning. Many characters well known in his day, including
Egyptian hieroglyphics Egyptian hieroglyphs (, ) were the formal writing system used in Ancient Egypt, used for writing the Egyptian language. Hieroglyphs combined logographic, syllabary, syllabic and alphabetic elements, with some 1,000 distinct characters.There were ...
,
Chinese character Chinese characters () are logograms developed for the Written Chinese, writing of Chinese. In addition, they have been adapted to write other East Asian languages, and remain a key component of the Japanese writing system where they are k ...
s, and the symbols of
astronomy Astronomy () is a natural science that studies astronomical object, celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and chronology of the Universe, evolution. Objects of interest ...
and
chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, properties ...
, he deemed not real. Instead, he proposed the creation of a ''
characteristica universalis The Latin term ''characteristica universalis'', commonly interpreted as ''universal characteristic'', or ''universal character'' in English, is a universal language, universal and formal language imagined by Gottfried Leibniz able to express ma ...
'' or "universal characteristic", built on an
alphabet of human thought The alphabet of human thought ( la, alphabetum cogitationum humanarum) is a concept originally proposed by Gottfried Wilhelm Leibniz that provides a universal way to represent and analyze ideas and relationships by breaking down their component piec ...
in which each fundamental concept would be represented by a unique "real" character: Complex thoughts would be represented by combining characters for simpler thoughts. Leibniz saw that the uniqueness of
prime factorization In number theory, integer factorization is the decomposition of a composite number into a Product (mathematics), product of smaller integers. If these Divisor, factors are further restricted to prime numbers, the process is called prime factoriz ...
suggests a central role for
prime numbers A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...
in the universal characteristic, a striking anticipation of Gödel numbering. Granted, there is no intuitive or
mnemonic A mnemonic ( ) device, or memory device, is any learning technique that aids information retention or retrieval (remembering) in the human memory for better understanding. Mnemonics make use of elaborative encoding, retrieval cues, and imagery ...
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 Algebra () is one of the areas of mathematics, broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathem ...
but rather as a
universal language Universal language may refer to a hypothetical or historical language spoken and understood by all or most of the world's people. In some contexts, it refers to a means of communication said to be understood by all humans. It may be the idea of ...
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 In computability theory, a system of data-manipulation rules (such as a computer's instruction set In computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical di ...
, 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 Friedrich Ludwig Gottlob Frege (; ; 8 November 1848 – 26 July 1925) was a German philosopher, Mathematical logic, logician, and mathematician. He was a mathematics professor at the University of Jena, and is understood by many to be the fath ...
. Leibniz enunciated the principal properties of what we now call conjunction,
disjunction In logic, disjunction is a logical connective typically notated as \lor and read aloud as "or". For instance, the English language, English language sentence "it is raining or it is snowing" can be represented in logic using the disjunctive ...
,
negation In logic, negation, also called the logical complement, is an operation (mathematics), operation that takes a Proposition (mathematics), proposition P to another proposition "not P", written \neg P, \mathord P or \overline. It is interpreted ...
, identity, set inclusion, and the
empty set In mathematics Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in ...
. 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 The alphabet of human thought ( la, alphabetum cogitationum humanarum) is a concept originally proposed by Gottfried Wilhelm Leibniz that provides a universal way to represent and analyze ideas and relationships by breaking down their component piec ...
. # 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 negation and quantified 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 ''
History of Western Philosophy Western philosophy encompasses the philosophy, philosophical thought and work of the Western world. Historically, the term refers to the philosophical thinking of Western culture, beginning with the ancient Greek philosophy of the Pre-Socratic p ...
'',
Bertrand Russell Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, ar ...
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 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 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 De Morgan, Peirce, Schröder and Russell himself, now standard in
predicate logic First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science. First-order logic uses Quantifica ...
. 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 In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variable (mathematics), variables are the truth values ''true'' and ''false'', usually denote ...
) and the associated metaphysics, are of interest in present-day computational metaphysics.

# Mathematician

Although the mathematical notion of function was implicit in trigonometric and logarithmic tables, which existed in his day, Leibniz was the first, in 1692 and 1694, to employ it explicitly, to denote any of several geometric concepts derived from a curve, such as abscissa,
ordinate In common usage, the abscissa refers to the (''x'') coordinate and the ordinate refers to the (''y'') coordinate of a standard two-dimensional In mathematics, a plane is a Euclidean space, Euclidean (flatness (mathematics), flat), two-dime ...
,
tangent In geometry, the tangent line (or simply tangent) to a plane curve at a given Point (geometry), point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitesimal, infinitely ...
, chord, and the
perpendicular In elementary geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works i ...
(see
History of the function concept The Mathematics, mathematical concept of a Function (mathematics), function emerged in the 17th century in connection with the development of the calculus; for example, the slope \operatorname\!y/\operatorname\!x of a Graph of a function, graph at ...
). 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 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 A calculation is a deliberate mathematical process that transforms one or more inputs into one or more outputs or ''results''. The term is used in a variety of senses, from the very definite arithmetical calculation of using an algorithm, to th ...
: "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 equation In mathematics, a linear equation is an equation that may be put in the form a_1x_1+\ldots+a_nx_n+b=0, where x_1,\ldots,x_n are the variable (mathematics), variables (or unknown (mathematics), unknowns), and b,a_1,\ldots,a_n are the coefficients, ...
s into an array, now called a matrix, in order to find a solution to the system if it existed. This method was later called
Gaussian elimination In mathematics, Gaussian elimination, also known as row reduction, is an algorithm for solving systems of linear equations. It consists of a sequence of operations performed on the corresponding matrix (mathematics), matrix of coefficients. This me ...
. 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. 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 In linear algebra, Cramer's rule is an explicit formula for the solution of a system of linear equations with as many equations as unknowns, valid whenever the system has a unique solution. It expresses the solution in terms of the determinants of ...
. 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 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 In geometry, the parallel postulate, also called Euclid's fifth postulate because it is the fifth postulate in Euclid's Elements, Euclid's ''Elements'', is a distinctive axiom in Euclidean geometry. It states that, in two-dimensional geometry: ' ...
. 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, physicist, astronomer, alchemist, Theology, theologian, and author (described in his time as a "natural philosophy, natural philosopher"), widely ...
, with the discovery of
calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the study of generalizati ...
(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 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 The fundamental theorem of calculus is a theorem that links the concept of differentiating a function (calculating its slopes, or rate of change at each time) with the concept of integrating a function (calculating the area under its graph, ...
, by means of a figure in his 1693 paper ''Supplementum geometriae dimensoriae...''. However, James Gregory is credited for the theorem's discovery in geometric form,
Isaac Barrow Isaac Barrow (October 1630 – 4 May 1677) was an English Christian theologian and mathematician who is generally given credit for his early role in the development of infinitesimal calculus; in particular, for proof of the fundamental theorem o ...
proved a more generalized geometric version, and Newton developed supporting theory. The concept became more transparent as developed through Leibniz's formalism and new notation. The
product rule In calculus Calculus, originally called infinitesimal calculus or "the calculus of infinitesimals", is the mathematics, mathematical study of continuous change, in the same way that geometry is the study of shape, and algebra is the stu ...
of
differential calculus In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus—the study of the area beneath a curve. ...
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 In calculus, the Leibniz integral rule for differentiation under the integral sign, named after Gottfried Leibniz, states that for an integral of the form \int_^ f(x,t)\,dt, where -\infty < a(x), b(x) < \infty and the integral are Funct ...
. Leibniz exploited
infinitesimal In mathematics, an infinitesimal number is a quantity that is closer to 0, zero than any standard real number, but that is not zero. The word ''infinitesimal'' comes from a 17th-century New Latin, Modern Latin coinage ''infinitesimus'', which ori ...
s in developing calculus, manipulating them in ways suggesting that they had
paradox A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically u ...
ical
algebra Algebra () is one of the areas of mathematics, broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathem ...
ic properties.
George Berkeley George Berkeley (; 12 March 168514 January 1753) – known as Bishop Berkeley (Bishop of Cloyne of the Anglican Church of Ireland) – was an Anglo-Irish philosopher whose primary achievement was the advancement of a theory he called "immateri ...
, 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. The use of infinitesimals in mathematics was frowned upon by followers of
Karl Weierstrass Karl Theodor Wilhelm Weierstrass (german: link=no, Weierstraß ; 31 October 1815 – 19 February 1897) was a German mathematician often cited as the "father of modern mathematical analysis, analysis". Despite leaving university without a degree, ...
, but survived in science and engineering, and even in rigorous mathematics, via the fundamental computational device known as the differential. Beginning in 1960, Abraham Robinson worked out a rigorous foundation for Leibniz's infinitesimals, using
model theory In mathematical logic, model theory is the study of the relationship between theory (mathematical logic), formal theories (a collection of Sentence (mathematical logic), sentences in a formal language expressing statements about a Structure (math ...
, in the context of a field of hyperreal numbers. The resulting non-standard analysis 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, while the
standard part function In nonstandard analysis, the standard part function is a function from the limited (finite) hyperreal numbers to the real numbers. Briefly, the standard part function "rounds off" a finite hyperreal to the nearest real. It associates to every suc ...
implements the Leibnizian transcendental law of homogeneity.

## 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 In mathematics, topology (from the Greek language, Greek words , and ) is concerned with the properties of a mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformations, such ...
. There are two takes on this situation. On the one hand, Mates, citing a 1954 paper in German by Jacob Freudenthal, argues: But Hideaki Hirano argues differently, quoting Mandelbrot: Thus the fractal geometry promoted by Mandelbrot drew on Leibniz's notions of
self-similarity __NOTOC__ In mathematics, a self-similar object is exactly or approximately similarity (geometry), similar to a part of itself (i.e., the whole has the same shape as one or more of the parts). Many objects in the real world, such as coastlines ...
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 Newton. He devised a new theory of
motion In physics, motion is the phenomenon in which an object changes its Position (geometry), position with respect to time. Motion is mathematically described in terms of Displacement (geometry), displacement, distance, velocity, acceleration, speed ...
( dynamics) based on
kinetic energy In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical sci ...
and
potential energy In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Common types of potential energy include the gravitational potentia ...
, 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 Quantum mechanics is a fundamental Scientific theory, theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is the foundation of all quantum physics including qua ...
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 Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born Theoretical physics, theoretical physicist, widely acknowledged to be one of the greatest and most influential physicists of all time. Einstein is best known for d ...
by arguing, against Newton, that
space Space is the boundless Three-dimensional space, three-dimensional extent in which Physical body, objects and events have relative position (geometry), position and direction (geometry), direction. In classical physics, physical space is often ...
, 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 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 Space and Time or Time and Space, or ''variation'', may refer to: * ''Space and time'' or ''time and space'' or ''spacetime'', any mathematical model that combines space and time into a single interwoven continuum * Philosophy of space and time Sp ...
as systems of relations that exist between objects. The rise of
general relativity General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the differential geometry, geometric scientific theory, theory of gravitation published by Albert Einstein in 1915 and is the current descr ...
and subsequent work in the
history of physics Physics is a branch of science whose primary objects of study are matter and energy. Discoveries of physics find applications throughout the natural sciences and in technology. Physics today may be divided loosely into classical physics and mode ...
has put Leibniz's stance in a more favorable light. One of Leibniz's projects was to recast Newton's theory as a 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 of matter. The
principle of sufficient reason The principle of sufficient reason states that everything must have a reason Reason is the capacity of Consciousness, consciously applying logic by Logical consequence, drawing conclusions from new or existing information, with the aim of seekin ...
has been invoked in recent
cosmology Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount (lexicographer), Thomas Blount's ''Glossographia'', and in 1731 taken up in ...
, and his
identity of indiscernibles The identity of indiscernibles is an ontology, ontological principle that states that there cannot be separate object (philosophy), objects or wikt:entity, entities that have all their property (philosophy), properties in common. That is, entities ...
in quantum mechanics, a field some even credit him with having anticipated in some sense. 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 In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical sci ...
. 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 In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the Multiplication, product of the mass and velocity of an object. It is a Euclidean vector, vector quantity, possessing a magnitude and a dire ...
championed by Newton in England and by Descartes and Voltaire in France; hence
academics An academy (Attic Greek: Ἀκαδήμεια; Koine Greek Ἀκαδημία) is an institution of secondary education, secondary or tertiary education, tertiary higher education, higher learning (and generally also research or honorary membershi ...
in those countries tended to neglect Leibniz's idea. Leibniz knew of the validity of conservation of momentum. In reality, both energy and
momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the Multiplication, product of the mass and velocity of an object. It is a Euclidean vector, vector quantity, possessing a magnitude and a dire ...
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 Embryology (from Ancient Greek, Greek ἔμβρυον, ''embryon'', "the unborn, embryo"; and -λογία, ''-logy, -logia'') is the branch of animal biology that studies the Prenatal development (biology), prenatal development of gametes (sex ...
, 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 This list of life sciences comprises the branches of science that involve the scientific study of life – such as microorganisms, plants, and animals including human beings. This science is one of the two major branches of natural science, the ...
and
paleontology Paleontology (), also spelled palaeontology or palæontology, is the scientific study of life that existed prior to, and sometimes including, the start of the Holocene epoch (geology), epoch (roughly 11,700 years before present). It includes t ...
, 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 Attention is the behavioral and cognitive process of selectively concentrating on a discrete aspect of information, whether considered subjective or objective, while ignoring other perceivable information. William James (1890) wrote that "A ...
and
consciousness Consciousness, at its simplest, is sentience and awareness of internal and external existence. However, the lack of definitions has led to millennia of analyses, explanations and debates by philosophers, theologians, linguisticians, and scient ...
,
memory Memory is the faculty of the mind by which data or information is Encoding (memory), encoded, stored, and retrieved when needed. It is the retention of information over time for the purpose of influencing future action. If Foresight (psycholo ...
,
learning Learning is the process of acquiring new understanding, knowledge, behaviors, skills, value (personal and cultural), values, attitudes, and preferences. The ability to learn is possessed by humans, animals, and some machine learning, machines ...
( association),
motivation Motivation is the reason for which humans and other animals initiate, continue, or terminate a behavior at a given time. Motivational states are commonly understood as forces acting within the agent that create a disposition to engage in goal-dire ...
(the act of "striving"), emergent individuality, the general dynamics of development (
evolutionary psychology Evolutionary psychology is a theoretical approach in psychology that examines cognition and behavior from a modern evolutionary perspective. It seeks to identify human psychological adaptations with regards to the ancestral problems they evolv ...
). 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's epistemological position—against
John Locke John Locke (; 29 August 1632 – 28 October 1704) was an English philosopher and physician, widely regarded as one of the most influential of Age of Enlightenment, Enlightenment thinkers and commonly known as the "father of liberalism ...
and English
empiricism In philosophy, empiricism is an Epistemology, epistemological theory that holds that knowledge or justification comes only or primarily from Empirical evidence, sensory experience. It is one of several views within epistemology, along with ra ...
( 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 Causality (also referred to as causation, or cause and effect) is influence by which one event, process, state, or object (''a'' ''cause'') contributes to the production of another event, process, state, or object (an ''effect'') where the ca ...
and the principle of purpose (
teleology Teleology (from and )Partridge, Eric. 1977''Origins: A Short Etymological Dictionary of Modern English'' London: Routledge, p. 4187. or finalityDubray, Charles. 2020 912Teleology" In ''The Catholic Encyclopedia'' 14. New York: Robert Applet ...
). Leibniz found his most important interpreter in
Wilhelm Wundt Wilhelm Maximilian Wundt (; ; 16 August 1832 – 31 August 1920) was a German physiologist, philosopher, and professor, known today as one of the fathers of modern psychology. Wundt, who distinguished psychology as a science from philosophy and ...
, 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 Perspectivism (german: Perspektivismus; also called perspectivalism) is the epistemology, epistemological principle that perception of and knowledge of something are always bound to the interpretive Perspective (philosophy), perspectives of those ...
) 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 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 Subliminal stimuli (; the prefix ' literally means "below" or "less than") are any sensory stimulus (physiology), stimuli below an individual's sensory threshold, threshold for conscious perception, in contrast to stimuli (above threshold). A 201 ...
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 Epidemiology is the study and analysis of the distribution (who, when, and where), patterns and risk factor, determinants of health and disease conditions in a defined population. It is a cornerstone of public health, and shapes policy decision ...
and
veterinary medicine Veterinary medicine is the branch of medicine Medicine is the science and Praxis (process), practice of caring for a patient, managing the diagnosis, prognosis, Preventive medicine, prevention, therapy, treatment, Palliative care, palliatio ...
. 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 The balance of trade, commercial balance, or net exports (sometimes symbolized as NX), is the difference between the monetary value of a nation's exports and imports over a certain time period. Sometimes a distinction is made between a balance ...
. He even proposed something akin to what much later emerged as
game theory Game theory is the study of mathematical models of strategic interactions among rational agents. Myerson, Roger B. (1991). ''Game Theory: Analysis of Conflict,'' Harvard University Press, p.&nbs1 Chapter-preview links, ppvii–xi It has appl ...
. 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 Applied science is the use of the scientific method and knowledge obtained via conclusions from the method to attain practical goals. It includes a broad range of disciplines such as engineering and medicine. Applied science is often contrasted ...
. He designed wind-driven propellers and water pumps, mining machines to extract ore, hydraulic presses, lamps, submarines, clocks, etc. With
Denis Papin Denis Papin Fellow of the Royal Society, FRS (; 22 August 1647 – 26 August 1713) was a French physicist, mathematician and inventor, best known for his pioneering invention of the steam digester, the forerunner of the pressure cooking, press ...
, he created a
steam engine A steam engine is a heat engine that performs mechanical work using steam as its working fluid. The steam engine uses the force produced by steam pressure to push a piston back and forth inside a Cylinder (locomotive), cylinder. This pus ...
. 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 The Harz () is a Mittelgebirge, highland area in northern Germany. It has the highest elevations for that region, and its rugged terrain extends across parts of Lower Saxony, Saxony-Anhalt, and Thuringia. The name ''Harz'' derives from the Middl ...
, 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 A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" (one). The base-2 numeral system is a positional notation ...
( 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 The ''I Ching'' or ''Yi Jing'' (, ), usually translated ''Book of Changes'' or ''Classic of Changes'', is an ancient Chinese divination text that is among the oldest of the Chinese classics. Originally a divination manual in the Western Z ...
''. 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 A Sinophile is a person who demonstrates a strong interest for China, Chinese culture, Chinese language, History of China, Chinese history, and/or Chinese people. Those with professional training and practice in the study of China are refer ...
section. Leibniz may have plagiarized Juan Caramuel y Lobkowitz and
Thomas Harriot Thomas Harriot (; – 2 July 1621), also spelled Harriott, Hariot or Heriot, was an English astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of ...
, 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 Lagrangian interpolation and
algorithmic information theory Algorithmic information theory (AIT) is a branch of theoretical computer science that concerns itself with the relationship between computation and information of computably generated objects (as opposed to stochastically generated), such as ...
. His calculus ratiocinator anticipated aspects of the
universal Turing machine In computer science, a universal Turing machine (UTM) is a Turing machine that can simulate an arbitrary Turing machine on arbitrary input. The universal machine essentially achieves this by reading both the description of the machine to be simu ...
. In 1961,
Norbert Wiener Norbert Wiener (November 26, 1894 – March 18, 1964) was an American mathematician and philosopher. He was a professor of mathematics at the Massachusetts Institute of Technology (MIT). A child prodigy, Wiener later became an early researcher i ...
suggested that Leibniz should be considered the patron saint of
cybernetics Cybernetics is a wide-ranging field concerned with circular causality, such as feedback, in regulatory and purposive systems. Cybernetics is named after an example of circular causal feedback, that of steering a ship, where the helmsperson ma ...
. 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 The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, ...
in 1673. A number of such machines were made during his years in
Hanover Hanover (; german: Hannover ; nds, Hannober) is the capital and largest city of the German States of Germany, state of Lower Saxony. Its 535,932 (2021) inhabitants make it the List of cities in Germany by population, 13th-largest city in Germa ...
by a craftsman working under his supervision. They were not an unambiguous success because they did not fully mechanize the 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 Charles Babbage (; 26 December 1791 – 18 October 1871) was an English polymath. A mathematician, philosopher, inventor and mechanical engineer, Babbage originated the concept of a digital programmable computer. Babbage is considered ...
and
Ada Lovelace Augusta Ada King, Countess of Lovelace (''née'' Byron; 10 December 1815 – 27 November 1852) was an English mathematician and writer, chiefly known for her work on Charles Babbage's proposed mechanical general-purpose computer, the Ana ...
. 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 Hanover (; german: Hannover ; nds, Hannober) is the capital and largest city of the German States of Germany, state of Lower Saxony. Its 535,932 (2021) inhabitants make it the List of cities in Germany by population, 13th-largest city in Germa ...
and Wolfenbüttel, Leibniz effectively became one of the founders of
library science Library science (often termed library studies, bibliothecography, and library economy) is an interdisciplinary or multidisciplinary field that applies the practices, perspectives, and tools of management, information technology, education, and ...
. Seemingly, Leibniz paid a good deal of attention to the classification of subject matter, favoring a well-balance library covering a host of numerous subjects and interests. Leibniz, for example, proposed the following classification system in the Otivm Hanoveranvm Sive Miscellanea (1737). Leibniz's Idea of Arranging a Narrower Library * Theology * Jurisprudence * Medicine * Intellectual Philosophy * Philosophy of the Imagination or Mathematics * Philosophy of Sensible Things or Physics * Philology or Language * Civil History * Literary History and Libraries * General and Miscellaneous He also designed a book indexing system in ignorance of the only other such system then extant, that of the
Bodleian Library The Bodleian Library () is the main research library of the University of Oxford, and is one of the oldest libraries in Europe Europe is a large peninsula conventionally considered a continent in its own right because of its great ph ...
at
Oxford University Oxford () is a city in England. It is the county town and only city of Oxfordshire. In 2020, its population was estimated at 151,584. It is north-west of London, south-east of Birmingham and north-east of Bristol. The city is home to the Un ...
. He also called on publishers to distribute abstracts of all new titles they produced each year, in a standard form that would facilitate indexing. He hoped that this abstracting project would eventually include everything printed from his day back to Gutenberg. Neither proposal met with success at the time, but something like them became standard practice among English language publishers during the 20th century, under the aegis of the
Library of Congress The Library of Congress (LOC) is the research library A library is a collection of materials, books or media that are accessible for use and not just for display purposes. A library provides physical (hard copies) or digital access (so ...
and the
British Library The British Library is the national library of the United Kingdom and is one of the List of largest libraries, largest libraries in the world. It is estimated to contain between 170 and 200 million items from many countries. As a legal de ...
. He called for the creation of an
empirical Empirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure. Empirical evidence is of central importance to the sciences and ...
database In computing, a database is an organized collection of Data (computing), data stored and accessed electronically. Small databases can be stored on a file system, while large databases are hosted on computer clusters or cloud storage. The Databas ...
as a way to further all sciences. His ''
characteristica universalis The Latin term ''characteristica universalis'', commonly interpreted as ''universal characteristic'', or ''universal character'' in English, is a universal language, universal and formal language imagined by Gottfried Leibniz able to express ma ...
'', 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 Esperanto ( or ) is the world's most widely spoken Constructed language, constructed international auxiliary language. Created by the Warsaw-based ophthalmologist L. L. Zamenhof in 1887, it was intended to be a universal second language for in ...
and its rivals),
symbolic logic Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of for ...
, even the
World Wide Web The World Wide Web (WWW), commonly known as the Web, is an information system enabling documents and other web resources to be accessed over the Internet. Documents and downloadable media are made available to the network through web se ...
.

## Advocate of scientific societies

Leibniz emphasized that research was a collaborative endeavor. Hence he warmly advocated the formation of national scientific societies along the lines of the
British Royal Society The Royal Society, formally The Royal Society of London for Improving Natural Knowledge, is a learned society and the United Kingdom's national academy of sciences. The society fulfils a number of roles: promoting science and its benefits, re ...
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 Saint Petersburg ( rus, links=no, Санкт-Петербург, a=Ru-Sankt Peterburg Leningrad Petrograd Piter.ogg, r=Sankt-Peterburg, p=ˈsankt pʲɪtʲɪrˈburk), formerly known as Petrograd (1914–1924) and later Leningrad (1924–1991), i ...
, Vienna, and Berlin. Only one such project came to fruition; in 1700, the Berlin Academy of Sciences was created. Leibniz drew up its first statutes, and served as its first President for the remainder of his life. That Academy evolved into the German Academy of Sciences, the publisher of the ongoing critical edition of his works.

# 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 Absolute monarchy (or Absolutism as a doctrine) is a form of monarchy in which the monarch rules in their own right or power. In an absolute monarchy, the king or queen is by no means limited and has absolute power, though a limited constitut ...
like
Hobbes Thomas Hobbes ( ; 5/15 April 1588 – 4/14 December 1679) was an English people, English philosopher, considered to be one of the founders of modern political philosophy. Hobbes is best known for his 1651 book ''Leviathan (Hobbes book), Levi ...
, or for tyranny in any form, neither did he echo the political and constitutional views of his contemporary
John Locke John Locke (; 29 August 1632 – 28 October 1704) was an English philosopher and physician, widely regarded as one of the most influential of Age of Enlightenment, Enlightenment thinkers and commonly known as the "father of liberalism ...
, 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: 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 The European Union (EU) is a supranational union, supranational political union, political and economic union of Member state of the European Union, member states that are located primarily in Europe, Europe. The union has a total area of ...
. 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.

## Law

Leibniz trained as a legal academic, but under the tutelage of Cartesian-sympathiser Erhard Weigel we already see an attempt to solve legal problems by rationalist mathematical methods (Weigel’s influence being most explicit in the Specimen Quaestionum Philosophicarum ex Jure collectarum (An Essay of Collected Philosophical Problems of Right)). For example, the Inaugural Disputation on Perplexing Cases uses early combinatorics to solve some legal disputes, while the 1666 Dissertation on the Combinatorial Art includes simple legal problems by way of illustration. The use of combinatorial methods to solve legal and moral problems seems, via
Athanasius Kircher Athanasius Kircher (2 May 1602 – 27 November 1680) was a German Jesuit scholar and polymath who published around 40 major works, most notably in the fields of comparative religion, geology, and medicine Medicine is the science an ...
and Daniel Schwenter to be of Llullist inspiration: Ramón Llull attempted to solve ecumenical disputes through recourse to a combinatorial mode of reasoning he regarded as universal (a mathesis universalis). In the late 1660s the enlightened Prince-Bishop of Mainz Johann Philipp von Schönborn announced a review of the legal system and made available a position to support his current law commissioner. Leibniz left Franconia and made for Mainz before even winning the role. On reaching
Frankfurt am Main Frankfurt, officially Frankfurt am Main (; Hessian dialects, Hessian: , "Franks, Frank ford (crossing), ford on the Main (river), Main"), is the most populous city in the States of Germany, German state of Hesse. Its 791,000 inhabitants as o ...
Leibniz penned The New Method of Teaching and Learning the Law, by way of application. The text proposed a reform of legal education and is characteristically syncretic, integrating aspects of Thomism, Hobbesianism, Cartesianism and traditional jurisprudence. Leibniz’s argument that the function of legal teaching was not to impress rules as one might train a dog, but to aid the student in discovering their own public reason, evidently impressed von Schönborn as he secured the job. Leibniz’s next major attempt to find a universal rational core to law and so found a legal “science of right”, came when Leibniz worked in Mainz from 1667-72. Starting initially from Hobbes’ mechanistic doctrine of power, Leibniz reverted to logico-combinatorial methods in an attempt to define justice. As Leibniz’s so-called Elementa Juris Naturalis advanced, he built in modal notions of right (possibility) and obligation (necessity) in which we see perhaps the earliest elaboration of his possible worlds doctrine within a deontic frame. While ultimately the Elementa remained unpublished, Leibniz continued to work on his drafts and promote their ideas to correspondents up until his death.

## Ecumenism

Leibniz devoted considerable intellectual and diplomatic effort to what would now be called an
ecumenical Ecumenism (), also spelled oecumenism, is the concept and principle that Christians who belong to different Christian denominations should work together to develop closer relationships among their churches and promote Christian unity. The adjec ...
endeavor, seeking to reconcile the
Roman Catholic Roman or Romans most often refers to: *Rome , established_title = Founded , established_date = 753 BC , founder = King Romulus (Romulus and Remus, legendary) , image_map = Map of comune of Rome (metropolitan c ...
and
Lutheran Lutheranism is one of the largest branches of Protestantism, identifying primarily with the theology of Martin Luther, the 16th-century German monk and Protestant Reformers, reformer whose efforts to reform the theology and practice of the Cathol ...
churches. In this respect, he followed the example of his early patrons, Baron von Boyneburg and the Duke 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 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
Reformation The Reformation (alternatively named the Protestant Reformation or the European Reformation) was a major movement within Western Christianity in 16th-century Europe that posed a religious and political challenge to the Catholic Church and in ...
.

# Philologist

Leibniz the
philologist Philology () is the study of language in oral and written historical sources; it is the intersection of textual criticism, literary criticism, history, and linguistics Linguistics is the scientific study of human language. It is c ...
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 Hebrew (; ; ) is a Northwest Semitic languages, Northwest Semitic language of the Afroasiatic languages, Afroasiatic language family. Historically, it is one of the spoken languages of the Israelites and their longest-surviving descendants, ...
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 was the ancestor of the
Germanic languages The Germanic languages are a branch of the Indo-European languages, Indo-European language family spoken natively by a population of about 515 million people mainly in Europe, North America, Oceania and Southern Africa. The most widely spoken ...
. He puzzled over the origins of the
Slavic languages The Slavic languages, also known as the Slavonic languages, are Indo-European languages spoken primarily by the Slavs, Slavic peoples and their descendants. They are thought to descend from a proto-language called Proto-Slavic language, Proto ...
and was fascinated by
classical Chinese Classical Chinese, also known as Literary Chinese (古文 ''gǔwén'' "ancient text", or 文言 ''wényán'' "text speak", meaning "literary language/speech"; modern vernacular: 文言文 ''wényánwén'' "text speak text", meaning "literar ...
. Leibniz was also an expert in the
Sanskrit Sanskrit (; attributively , ; nominalization, nominally , , ) is a classical language belonging to the Indo-Aryan languages, Indo-Aryan branch of the Indo-European languages. It arose in South Asia after its predecessor languages had Trans-cul ...
language. He published the ''princeps editio'' (first modern edition) of the
late medieval The Late Middle Ages or Late Medieval Period was the Periodization, period of European history lasting from AD 1300 to 1500. The Late Middle Ages followed the High Middle Ages and preceded the onset of the early modern period (and in much of Eur ...
'' 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, European Christian missionaries posted in China. He apparently read '' Confucius Sinarum Philosophus'' in the first year of its publication. He came to the conclusion that Europeans could learn much from the
Confucian Confucianism, also known as Ruism or Ru classicism, is a system of thought and behavior originating in ancient China. Variously described as tradition, a philosophy, a Religious Confucianism, religion, a humanistic or rationalistic religion, ...
ethical tradition. He mulled over the possibility that the
Chinese characters Chinese characters () are logograms developed for the writing of Chinese. In addition, they have been adapted to write other East Asian languages, and remain a key component of the Japanese writing system where they are known as ''kanji ...
were an unwitting form of his universal characteristic. He noted how the ''
I Ching The ''I Ching'' or ''Yi Jing'' (, ), usually translated ''Book of Changes'' or ''Classic of Changes'', is an ancient Chinese divination text that is among the oldest of the Chinese classics. Originally a divination manual in the Western Z ...
'' hexagrams correspond to the
binary number A binary number is a number expressed in the base-2 numeral system or binary numeral system, a method of mathematical expression which uses only two symbols: typically "0" (zero) and "1" (one). The base-2 numeral system is a positional notation ...
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 Chinese philosophy originates in the Spring and Autumn period () and Warring States period The Warring States period () was an era in History of China#Ancient China, ancient Chinese history characterized by warfare, as wel ...
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 Vienna ( ; german: Wien ; bar, Wean, label=Bavarian language, Austro-Bavarian ) is the Capital city, capital, largest city, and one of States of Austria, nine states of Austria. Vienna is Austria's List of cities and towns in Austria, most populou ...
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 The Harz () is a Mittelgebirge, highland area in northern Germany. It has the highest elevations for that region, and its rugged terrain extends across parts of Lower Saxony, Saxony-Anhalt, and Thuringia. The name ''Harz'' derives from the Middl ...
. His proposal that the streets of Vienna be lit with lamps burning rapeseed oil was implemented. During a formal audience with the Austrian Emperor and in subsequent memoranda, he advocated reorganizing the Austrian economy, reforming the coinage of much of central Europe, negotiating a Concordat between the
Habsburg The House of Habsburg (), alternatively spelled Hapsburg in Englishgerman: Haus Habsburg, ; es, Casa de Habsburgo; hu, Habsburg család, it, Casa di Asburgo, nl, Huis van Habsburg, pl, dom Habsburgów, pt, Casa de Habsburgo, la, Domus Hab ...
s and the Vatican, and creating an imperial research library, official archive, and public insurance fund. He wrote and published an important paper on
mechanics Mechanics (from Ancient Greek: wikt:μηχανική#Ancient_Greek, μηχανική, ''mēkhanikḗ'', "of machine, machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among Ph ...
.

# 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) was a French Age of Enlightenment, Enlightenment writer, historian, and philosopher. Known by his ''Pen name, nom de plume'' M. de Voltaire (; also ; ), he was famous for his wit, and his ...
lampooned in his popular book ''
Candide ( , ) is a French satire written by Voltaire, a philosopher of the Age of Enlightenment, first published in 1759. The novella has been widely translated, with English versions titled ''Candide: or, All for the Best'' (1759); ''Candide: or, The ...
'', 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, whose dogmatic and facile outlook did Leibniz's reputation much harm. He also influenced
David Hume David Hume (; born David Home; 7 May 1711 New Style, NS (26 April 1711 Old Style, OS) – 25 August 1776)Maurice Cranston, Cranston, Maurice, and T. E. Jessop, Thomas Edmund Jessop. 2020 999avid Hume" ''Encyclopædia Britannica''. Retrieve ...
, 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
Kant Immanuel Kant (, , ; 22 April 1724 – 12 February 1804) was a German Philosophy, philosopher and one of the central Age of Enlightenment, Enlightenment thinkers. Born in Königsberg, Kant's comprehensive and systematic works in epistemolo ...
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 Antoine Arnauld (6 February 16128 August 1694) was a French Catholic The Catholic Church, also known as the Roman Catholic Church, is the largest Christian church, with 1.3 billion baptized Catholics worldwide . It is among th ...
,
Samuel Clarke Samuel Clarke (11 October 1675 – 17 May 1729) was an English philosopher and Anglican cleric. He is considered the major British figure in philosophy between John Locke and George Berkeley. Early life and studies Clarke was born in Norwich, t ...
,
Sophia of Hanover Sophia of Hanover (born Princess Sophia of the Palatinate; 14 October 1630 – 8 June 1714) was the List of Hanoverian consorts, Electress of Hanover by marriage to Elector Ernest Augustus and later the heiress presumptive to the thrones of King ...
, and her daughter Sophia Charlotte of Hanover, began. In 1900,
Bertrand Russell Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British mathematician, philosopher, logician, and public intellectual. He had a considerable influence on mathematics, logic, set theory, linguistics, ar ...
published a critical study of Leibniz's
metaphysics Metaphysics is the branch of philosophy that studies the fundamental nature of reality, the first principles of being, identity and change, space and time, causality, necessity, and possibility. It includes questions about the nature of conscio ...
. Shortly thereafter,
Louis Couturat Louis Couturat (; 17 January 1868 – 3 August 1914) was a French people, French logician, mathematician, philosophy, philosopher, and linguistics, linguist. Couturat was a pioneer of the constructed language Ido (language), Ido. Life and educa ...
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 analytical and linguistic philosophers in the English-speaking world (Leibniz had already been of great influence to many Germans such as
Bernhard Riemann Georg Friedrich Bernhard Riemann (; 17 September 1826 – 20 July 1866) was a German mathematician who made contributions to mathematical analysis, analysis, number theory, and differential geometry. In the field of real analysis, he is mostly ...
). 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,
individuation The principle of individuation, or ', describes the manner in which a thing is identified as distinct from other things. The concept appears in numerous fields and is encountered in works of Leibniz, Carl Gustav Jung, Günther Anders, Gunther And ...
, and possible worlds. Work in the history of 17th- and 18th-century ideas has revealed more clearly the 17th-century "Intellectual Revolution" that preceded the better-known Industrial and commercial revolutions of the 18th and 19th centuries. In 1985, the German government created the Leibniz Prize, offering an annual award of 1.55 million
euro The euro (currency symbol, symbol: euro sign, €; ISO 4217, code: EUR) is the official currency of 19 out of the Member state of the European Union, member states of the European Union (EU). This group of states is known as the eurozone o ...
s 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 The United Nations Educational, Scientific and Cultural Organization is a List of specialized agencies of the United Nations, specialized agency of the United Nations (UN) aimed at promoting world peace and security through international coope ...
's
Memory of the World Register Memory is the faculty of the mind by which data or information is Encoding (memory), encoded, stored, and retrieved when needed. It is the retention of information over time for the purpose of influencing future action. If Foresight (psycholo ...
in 2007.

## Cultural references

Leibniz still receives popular attention. The
Google Doodle A Google Doodle is a special, temporary alteration of the Google logo, logo on Google's home page, homepages intended to commemorate holidays, events, achievements, and notable historical figures. The first Google Doodle honored the 1998 edition ...
for 1 July 2018 celebrated Leibniz's 372nd birthday. Using a
quill A quill is a writing tool made from a moulted flight feather (preferably a primary wing-feather) of a large bird. Quills were used for writing with ink before the invention of the dip pen, the metal-Nib (pen), nibbed pen, the fountain pen, and, ...
, his hand is shown writing "Google" in binary
ASCII ASCII ( ), abbreviated from American Standard Code for Information Interchange, is a character encoding standard for electronic communication. ASCII codes represent text in computers, telecommunications equipment, and other devices. Because of ...
code. One of the earliest popular but indirect expositions of Leibniz was
Voltaire François-Marie Arouet (; 21 November 169430 May 1778) was a French Age of Enlightenment, Enlightenment writer, historian, and philosopher. Known by his ''Pen name, nom de plume'' M. de Voltaire (; also ; ), he was famous for his wit, and his ...
's satire ''
Candide ( , ) is a French satire written by Voltaire, a philosopher of the Age of Enlightenment, first published in 1759. The novella has been widely translated, with English versions titled ''Candide: or, All for the Best'' (1759); ''Candide: or, The ...
'', published in 1759. Leibniz was lampooned as Professor Pangloss, described as "the greatest philosopher of the
Holy Roman Empire The Holy Roman Empire was a Polity, political entity in Western Europe, Western, Central Europe, Central, and Southern Europe that developed during the Early Middle Ages and continued until its Dissolution of the Holy Roman Empire, dissolution i ...
". Leibniz also appears as one of the main historical figures in
Neal Stephenson Neal Town Stephenson (born October 31, 1959) is an American writer known for his works of speculative fiction. His novels have been categorized as science fiction, historical fiction, cyberpunk, postcyberpunk, and baroque. Stephenson's work exp ...
's series of novels '' The Baroque Cycle''. Stephenson credits readings and discussions concerning Leibniz for inspiring him to write the series.Stephenson, Neal. "How the Baroque Cycle Began" in P.S. of '' Quicksilver'' Perennial ed. 2004. 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 belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through ...
, 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 Sovereignty is the defining authority within individual consciousness, Social constructionism, social construct, or territory. Sovereignty entails hierarchy within the state, as well as external autonomy for states. In any state, sovereignty i ...
.) One substantial book appeared posthumously, his '' Nouveaux essais sur l'entendement humain'', which Leibniz had withheld from publication after the death of
John Locke John Locke (; 29 August 1632 – 28 October 1704) was an English philosopher and physician, widely regarded as one of the most influential of Age of Enlightenment, Enlightenment thinkers and commonly known as the "father of liberalism ...
. Only in 1895, when Bodemann completed his catalogue of Leibniz's manuscripts and correspondence, did the enormous extent of Leibniz's ''
Nachlass ''Nachlass'' (, older spelling ''Nachlaß'') is a German language, German word, used in academia to describe the collection of manuscripts, notes, correspondence, and so on left behind when a scholar dies. The word is a compound word, compound in ...
'' 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 more than 67,000 records of th
Leibniz Edition's Catalogue
cover almost all of his known writings and the letters from him and to him. The amount, variety, and disorder of Leibniz's writings are a predictable result of a situation he described in a letter as follows: The extant parts of the critical edition 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
'. 9 vols., 1667–1702. * Series 5.
Historical and Linguistic Writings
'. In preparation. * 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 Potsdam () is the capital and, with around 183,000 inhabitants, largest city of the Germany, German States of Germany, state of Brandenburg. It is part of the Berlin/Brandenburg Metropolitan Region. Potsdam sits on the Havel, River Havel, a trib ...
, Münster,
Hanover Hanover (; german: Hannover ; nds, Hannober) is the capital and largest city of the German States of Germany, state of Lower Saxony. Its 535,932 (2021) inhabitants make it the List of cities in Germany by population, 13th-largest city in Germa ...
and
Berlin Berlin ( , ) is the capital and largest city of Germany by both area and population. Its 3.7 million inhabitants make it the European Union's most populous city, according to population within city limits. One of Germany's sixteen constituen ...
have jointly published 57 volumes of the critical edition, with an average of 870 pages, and prepared index and 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. '' 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 primae 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 Project Gutenberg (PG) is a Virtual volunteering, volunteer effort to digitize and archive cultural works, as well as to "encourage the creation and distribution of eBooks." It was founded in 1971 by American writer Michael S. Hart and is the ...
. * 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''.

# See also

* General Leibniz rule * Leibniz Association * Leibniz operator *
List of German inventors and discoverers ---- __NOTOC__ This is a list of German inventors and discoverers. The following list comprises people from Germany or German-speaking Europe, and also people of predominantly German heritage, in alphabetical order of the surname. For the li ...
*
List of pioneers in computer science This is a list of people who made transformative breakthroughs in the creation, development and imagining of what computers could do. Pioneers : ''To arrange the list by date or person (ascending or descending), click that column's small "up-do ...
* List of things named after Gottfried Leibniz * '' Mathesis universalis'' *
Scientific revolution The Scientific Revolution was a series of events that marked the emergence of modern science during the early modern period, when developments in mathematics Mathematics is an area of knowledge that includes the topics of numbers, fo ...
*
Leibniz University Hannover Gottfried Wilhelm Leibniz University Hannover (german: Gottfried Wilhelm Leibniz Universität), also known as the University of Hannover, is a public research university located in Hanover, Germany. Founded on 2 May 1831 as Higher Vocational ...
* Bartholomew Des Bosses *
Joachim Bouvet Joachim Bouvet (, courtesy name: 明远) (July 18, 1656, in Le Mans – June 28, 1730, in Peking) was a French Jesuit China missions, Jesuit who worked in China, and the leading member of the Figurist movement. China Bouvet came to China in 1687, ...
* 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. * 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 956 ''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. * 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

* Du Bois-Reymond, Emil, 1912. ''Leibnizsche Gedanken in der neueren Naturwissenschaft'', Berlin: Dummler, 1871 (reprinted in ''Reden'', Leipzig: Veit, vol. 1). * Couturat, Louis, 1901. ''La Logique de Leibniz''. Paris: Felix Alcan. * 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. * Mackie, John Milton; Guhrauer, Gottschalk Eduard, 1845. ''Life of Godfrey William von ''. Gould, Kendall and Lincoln. * Russell, Bertrand, 1900, ''A Critical Exposition of the Philosophy of Leibniz'', Cambridge: The University Press. * * 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. * Connelly, Stephen, 2021. ‘’Leibniz: A Contribution to the Archaeology of Power’’, Edinburgh University Press . * Davis, Martin, 2000. ''The Universal Computer: The Road from Leibniz to Turing''. WW Norton. * Deleuze, Gilles, 1993. ''The Fold: Leibniz and the Baroque''. University of Minnesota Press. * Fahrenberg, Jochen, 2017. PsyDok ZPI
The influence of Gottfried Wilhelm Leibniz on the Psychology, Philosophy, and Ethics of Wilhelm Wundt.
* 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), . * 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. * * 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. * Riley, Patrick, 1996. ''Leibniz's Universal Jurisprudence: Justice as the Charity of the Wise''. Harvard University Press. * 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 Princeton University Press is an independent Academic publishing, publisher with close connections to Princeton University. Its mission is to disseminate scholarship within academia and society at large. The press was founded by Whitney Darrow, ...
. *

# External links

* * * * * * * * * *
Translations
by 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 The University of California, San Diego (UC San Diego or colloquially, UCSD) is a public university, public Land-grant university, land-grant research university in San Diego, California. Established in 1960 near the pre-existing Scripps Insti ...

Leibnitiana
links and resources edited by Gregory Brown,
University of Houston The University of Houston (UH) is a Public university, public research university in Houston, Texas. Founded in 1927, UH is a member of the University of Houston System and the List of universities in Texas by enrollment, university in Texas ...

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 The Linda Hall Library is a privately Financial endowment, endowed American library of science, engineering and technology located in Kansas City, Missouri, Kansas City, Missouri, sitting "majestically on a urban arboretum." It is the "largest i ...

''Protogaea''
(1749, German) – full digital facsimile from
Linda Hall Library The Linda Hall Library is a privately Financial endowment, endowed American library of science, engineering and technology located in Kansas City, Missouri, Kansas City, Missouri, sitting "majestically on a urban arboretum." It is the "largest i ...
* Leibniz's (1768, 6-volume
''Opera omnia''
– digital facsimile * Leibniz's arithmetical machine, 1710, online and analyzed on
BibNum
' lick 'à télécharger' for English analysis/small> * Leibniz's binary numeral system, 'De progressione dyadica', 1679, online and analyzed on
BibNum
' lick 'à télécharger' for English analysis/small> {{DEFAULTSORT:Leibniz, Gottfried 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 17th-century German inventors 18th-century German mathematicians 18th-century German philosophers 18th-century German physicists 18th-century German scientists 18th-century German writers 18th-century German male writers 18th-century Latin-language writers 18th-century German inventors Age of Enlightenment Analytic philosophy Constructed language creators Determinists Enlightenment philosophers Epistemologists Fellows of the Royal Society German librarians German logicians German Lutherans German philologists 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 from Leipzig Writers about religion and science