René Descartes

René Descartes

Overview
René Descartes ʁəne dekaʁt; (31 March 1596 – 11 February 1650) (Latinized
Latinisation (literature)
Latinisation is the practice of rendering a non-Latin name in a Latin style. It is commonly met with for historical personal names, with toponyms, or for the standard binomial nomenclature of the life sciences. It goes further than Romanisation, which is the writing of a word in the Latin alphabet...

 form: Renatus Cartesius; adjectival form: "Cartesian") was a French philosopher and writer who spent most of his adult life in the Dutch Republic
Dutch Republic
The Dutch Republic — officially known as the Republic of the Seven United Netherlands , the Republic of the United Netherlands, or the Republic of the Seven United Provinces — was a republic in Europe existing from 1581 to 1795, preceding the Batavian Republic and ultimately...

. He has been dubbed the 'Father of Modern Philosophy', and much subsequent Western philosophy
Western philosophy
Western philosophy is the philosophical thought and work of the Western or Occidental world, as distinct from Eastern or Oriental philosophies and the varieties of indigenous philosophies....

 is a response to his writings, which are studied closely to this day. In particular, his Meditations on First Philosophy
Meditations on First Philosophy
Meditations on First Philosophy is a philosophical treatise written by René Descartes and first published in 1641 . The French translation was published in 1647 as Méditations Metaphysiques...

continues to be a standard text at most university philosophy departments.
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Encyclopedia
René Descartes ʁəne dekaʁt; (31 March 1596 – 11 February 1650) (Latinized
Latinisation (literature)
Latinisation is the practice of rendering a non-Latin name in a Latin style. It is commonly met with for historical personal names, with toponyms, or for the standard binomial nomenclature of the life sciences. It goes further than Romanisation, which is the writing of a word in the Latin alphabet...

 form: Renatus Cartesius; adjectival form: "Cartesian") was a French philosopher and writer who spent most of his adult life in the Dutch Republic
Dutch Republic
The Dutch Republic — officially known as the Republic of the Seven United Netherlands , the Republic of the United Netherlands, or the Republic of the Seven United Provinces — was a republic in Europe existing from 1581 to 1795, preceding the Batavian Republic and ultimately...

. He has been dubbed the 'Father of Modern Philosophy', and much subsequent Western philosophy
Western philosophy
Western philosophy is the philosophical thought and work of the Western or Occidental world, as distinct from Eastern or Oriental philosophies and the varieties of indigenous philosophies....

 is a response to his writings, which are studied closely to this day. In particular, his Meditations on First Philosophy
Meditations on First Philosophy
Meditations on First Philosophy is a philosophical treatise written by René Descartes and first published in 1641 . The French translation was published in 1647 as Méditations Metaphysiques...

continues to be a standard text at most university philosophy departments. Descartes' influence in mathematics is equally apparent; the Cartesian coordinate system
Cartesian coordinate system
A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length...

 — allowing algebraic equations to be expressed as geometric shapes, in a 2D coordinate system — was named after him. He is credited as the father of analytical geometry, the bridge between algebra and geometry, crucial to the discovery of infinitesimal calculus
Infinitesimal calculus
Infinitesimal calculus is the part of mathematics concerned with finding slope of curves, areas under curves, minima and maxima, and other geometric and analytic problems. It was independently developed by Gottfried Leibniz and Isaac Newton starting in the 1660s...

 and analysis
Mathematical analysis
Mathematical analysis, which mathematicians refer to simply as analysis, has its beginnings in the rigorous formulation of infinitesimal calculus. It is a branch of pure mathematics that includes the theories of differentiation, integration and measure, limits, infinite series, and analytic functions...

. Descartes was also one of the key figures in the Scientific Revolution
Scientific revolution
The Scientific Revolution is an era associated primarily with the 16th and 17th centuries during which new ideas and knowledge in physics, astronomy, biology, medicine and chemistry transformed medieval and ancient views of nature and laid the foundations for modern science...

.

Descartes frequently sets his views apart from those of his predecessors. In the opening section of the Passions of the Soul
Passions of the Soul
In the treatise Passions of the Soul , the last of Descartes' published work, completed in 1649 and dedicated to Princess Elizabeth of Bohemia, the author contributes to a long tradition of theorizing "the passions." The passions were experiences often equated with or labeled as precursors to what...

, a treatise on the Early Modern version of what are now commonly called emotions, Descartes goes so far as to assert that he will write on this topic "as if no one had written on these matters before". Many elements of his philosophy have precedents in late Aristotelianism
Aristotelianism
Aristotelianism is a tradition of philosophy that takes its defining inspiration from the work of Aristotle. The works of Aristotle were initially defended by the members of the Peripatetic school, and, later on, by the Neoplatonists, who produced many commentaries on Aristotle's writings...

, the revived Stoicism
Stoicism
Stoicism is a school of Hellenistic philosophy founded in Athens by Zeno of Citium in the early . The Stoics taught that destructive emotions resulted from errors in judgment, and that a sage, or person of "moral and intellectual perfection," would not suffer such emotions.Stoics were concerned...

 of the 16th century, or in earlier philosophers like St. Augustine
Augustine of Hippo
Augustine of Hippo , also known as Augustine, St. Augustine, St. Austin, St. Augoustinos, Blessed Augustine, or St. Augustine the Blessed, was Bishop of Hippo Regius . He was a Latin-speaking philosopher and theologian who lived in the Roman Africa Province...

. In his natural philosophy, he differs from the schools
Scholasticism
Scholasticism is a method of critical thought which dominated teaching by the academics of medieval universities in Europe from about 1100–1500, and a program of employing that method in articulating and defending orthodoxy in an increasingly pluralistic context...

 on two major points: First, he rejects the analysis of corporeal substance into matter and form; second, he rejects any appeal to ends
Teleology
A teleology is any philosophical account which holds that final causes exist in nature, meaning that design and purpose analogous to that found in human actions are inherent also in the rest of nature. The word comes from the Greek τέλος, telos; root: τελε-, "end, purpose...

—divine or natural—in explaining natural phenomena. In his theology
Theology
Theology is the systematic and rational study of religion and its influences and of the nature of religious truths, or the learned profession acquired by completing specialized training in religious studies, usually at a university or school of divinity or seminary.-Definition:Augustine of Hippo...

, he insists on the absolute freedom of God’s act of creation.

Descartes was a major figure in 17th-century continental rationalism
Rationalism
In epistemology and in its modern sense, rationalism is "any view appealing to reason as a source of knowledge or justification" . In more technical terms, it is a method or a theory "in which the criterion of the truth is not sensory but intellectual and deductive"...

, later advocated by Baruch Spinoza
Baruch Spinoza
Baruch de Spinoza and later Benedict de Spinoza was a Dutch Jewish philosopher. Revealing considerable scientific aptitude, the breadth and importance of Spinoza's work was not fully realized until years after his death...

 and Gottfried Leibniz
Gottfried Leibniz
Gottfried Wilhelm Leibniz was a German philosopher and mathematician. He wrote in different languages, primarily in Latin , French and German ....

, and opposed by the empiricist school of thought consisting of Hobbes
Thomas Hobbes
Thomas Hobbes of Malmesbury , in some older texts Thomas Hobbs of Malmsbury, was an English philosopher, best known today for his work on political philosophy...

, Locke
John Locke
John Locke FRS , widely known as the Father of Liberalism, was an English philosopher and physician regarded as one of the most influential of Enlightenment thinkers. Considered one of the first of the British empiricists, following the tradition of Francis Bacon, he is equally important to social...

, Berkeley
George Berkeley
George Berkeley , also known as Bishop Berkeley , was an Irish philosopher whose primary achievement was the advancement of a theory he called "immaterialism"...

, Jean-Jacques Rousseau
Jean-Jacques Rousseau
Jean-Jacques Rousseau was a Genevan philosopher, writer, and composer of 18th-century Romanticism. His political philosophy influenced the French Revolution as well as the overall development of modern political, sociological and educational thought.His novel Émile: or, On Education is a treatise...

, and Hume
David Hume
David Hume was a Scottish philosopher, historian, economist, and essayist, known especially for his philosophical empiricism and skepticism. He was one of the most important figures in the history of Western philosophy and the Scottish Enlightenment...

. Leibniz, Spinoza and Descartes were all well versed in mathematics as well as philosophy, and Descartes and Leibniz contributed greatly to science as well.

He is perhaps best known for the philosophical statement "Cogito ergo sum
Cogito ergo sum
is a philosophical Latin statement proposed by . The simple meaning of the phrase is that someone wondering whether or not they exist is, in and of itself, proof that something, an "I", exists to do the thinking — However this "I" is not the more or less permanent person we call "I"...

" , found in part IV of Discourse on the Method (1637 – written in French but with inclusion of "Cogito ergo sum") and §7 of part I of Principles of Philosophy
Principles of Philosophy
Principles of Philosophy is a book by René Descartes. Written in Latin, it was published in 1644 and dedicated to Elisabeth of Bohemia, with whom Descartes had a long standing friendship. A French version followed in 1647. It set forth the principles of nature—the Laws of Physics--as Descartes...

(1644 – written in Latin).

Biography



Descartes was born in La Haye en Touraine (now Descartes
Descartes, Indre-et-Loire
Descartes is a commune in the Indre-et-Loire department in central France. It is approximately 13 miles east of Richelieu and about 24 miles east of Loudun, on the banks of the Creuze River.-History:...

), Indre-et-Loire
Indre-et-Loire
Indre-et-Loire is a department in west-central France named after the Indre and the Loire rivers.-History:Indre-et-Loire is one of the original 83 départements created during the French Revolution on 4 March 1790...

, France. When he was one year old, his mother Jeanne Brochard died. His father Joachim was a member in the provincial parliament. At the age of eight, he entered the Jesuit
Society of Jesus
The Society of Jesus is a Catholic male religious order that follows the teachings of the Catholic Church. The members are called Jesuits, and are also known colloquially as "God's Army" and as "The Company," these being references to founder Ignatius of Loyola's military background and a...

 Collège Royal Henry-Le-Grand at La Flèche
La Flèche
La Flèche is a municipality located in the French department of Sarthe and the region of Pays de la Loire in the Loire Valley. This is the sub-prefecture of the South-Sarthe, the chief district and the chief city of a canton. This is the second most populous city of the department. The city is part...

. After graduation, he studied at the University of Poitiers
University of Poitiers
The University of Poitiers is a university in Poitiers, France. It is a member of the Coimbra Group.-History:Founded in 1431 by Pope Eugene IV and chartered by King Charles VII, the University of Poitiers was originally composed of five faculties: theology, canon law, civil law, medicine, and...

, earning a Baccalauréat
Baccalauréat
The baccalauréat , often known in France colloquially as le bac, is an academic qualification which French and international students take at the end of the lycée . It was introduced by Napoleon I in 1808. It is the main diploma required to pursue university studies...

and Licence in law in 1616, in accordance with his father's wishes that he should become a lawyer.

"I entirely abandoned the study of letters. Resolving to seek no knowledge other than that of which could be found in myself or else in the great book of the world, I spent the rest of my youth traveling, visiting courts and armies, mixing with people of diverse temperaments and ranks, gathering various experiences, testing myself in the situations which fortune offered me, and at all times reflecting upon whatever came my way so as to derive some profit from it." (Descartes, Discourse on the Method).

In 1618, Descartes was engaged in the army of Maurice of Nassau
Maurice of Nassau, Prince of Orange
Maurice of Nassau, Prince of Orange was sovereign Prince of Orange from 1618, on the death of his eldest half brother, Philip William, Prince of Orange,...

 in the Dutch Republic
Dutch Republic
The Dutch Republic — officially known as the Republic of the Seven United Netherlands , the Republic of the United Netherlands, or the Republic of the Seven United Provinces — was a republic in Europe existing from 1581 to 1795, preceding the Batavian Republic and ultimately...

, but as a truce had been established between Holland and Spain, Descartes used his spare time to study mathematics. In this way he became acquainted with Isaac Beeckman
Isaac Beeckman
Isaac Beeckman was a Dutch philosopher and scientist, who, through his studies and contact with leading natural philosophers, may have "virtually given birth to modern atomism".-Biography:...

, principal of Dordrecht
Dordrecht
Dordrecht , colloquially Dordt, historically in English named Dort, is a city and municipality in the western Netherlands, located in the province of South Holland. It is the fourth largest city of the province, having a population of 118,601 in 2009...

 school. Beeckman had proposed a difficult mathematical problem, and to his astonishment, it was the young Descartes who found the solution. Both believed that it was necessary to create a method that thoroughly linked mathematics and physics. While in the service of the Duke Maximilian of Bavaria, Descartes was present at the Battle of the White Mountain outside Prague
Prague
Prague is the capital and largest city of the Czech Republic. Situated in the north-west of the country on the Vltava river, the city is home to about 1.3 million people, while its metropolitan area is estimated to have a population of over 2.3 million...

, in November 1620.

On the night of 10–11 November 1619, while stationed in Neuburg an der Donau
Neuburg an der Donau
Neuburg an der Donau, literally Neuburg on the Danube River, is a town which is the capital of the Neuburg-Schrobenhausen district in the state of Bavaria in Germany.-Divisions:The municipality has 16 divisions:-History:...

, Germany, Descartes experienced a series of three powerful dreams or visions that he later claimed profoundly influenced his life. He concluded from these visions that the pursuit of science would prove to be, for him, the pursuit of true wisdom and a central part of his life's work.. Descartes also saw very clearly that all truths were linked with one another, so that finding a fundamental truth and proceeding with logic would open the way to all science. This basic truth, Descartes found quite soon: his famous "I think".

In 1622 he returned to France, and during the next few years spent time in Paris and other parts of Europe. It was during a stay in Paris that he composed his first essay on method: Regulae at Directionem Ingenii (Rules for the Direction of the Mind
Rules for the Direction of the Mind
In 1619, René Descartes began work on an unfinished treatise regarding the proper method for scientific and philosophical thinking entitled Regulae ad directionem ingenii, or Rules for the Direction of the Mind. This work outlined the basis for his later work on complex problems of mathematics,...

). He arrived in La Haye in 1623, selling all of his property to invest in bonds
Bond (finance)
In finance, a bond is a debt security, in which the authorized issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay interest to use and/or to repay the principal at a later date, termed maturity...

, which provided a comfortable income for the rest of his life. Descartes was present at the siege of La Rochelle
Siege of La Rochelle
The Siege of La Rochelle was a result of a war between the French royal forces of Louis XIII of France and the Huguenots of La Rochelle in 1627-1628...

 by Cardinal Richelieu
Armand Jean du Plessis, Cardinal Richelieu
Armand Jean du Plessis, Cardinal-Duc de Richelieu et de Fronsac was a French clergyman, noble, and statesman.Consecrated as a bishop in 1608, he later entered politics, becoming a Secretary of State in 1616. Richelieu soon rose in both the Catholic Church and the French government, becoming a...

 in 1627.

He returned to the Dutch Republic
Dutch Republic
The Dutch Republic — officially known as the Republic of the Seven United Netherlands , the Republic of the United Netherlands, or the Republic of the Seven United Provinces — was a republic in Europe existing from 1581 to 1795, preceding the Batavian Republic and ultimately...

 in 1628, where he lived until September 1649. In April 1629 he joined the University of Franeker
University of Franeker
The University of Franeker was a university in Franeker, Friesland, presently part of the Netherlands. It was the second oldest university of the Netherlands, founded shortly after Leiden University....

, living at the Sjaerdemaslot
Sjaerdemaslot
Sjaerdemaslot was a Frisian castle, a so-called "state", in Franeker, the Netherlands. In 1446 the construction of the castle was started and the state was demolished in 1727. Famous residents include the philosopher René Descartes and Duke Albert of Saxony....

, and the next year, under the name "Poitevin", he enrolled at the Leiden University
Leiden University
Leiden University , located in the city of Leiden, is the oldest university in the Netherlands. The university was founded in 1575 by William, Prince of Orange, leader of the Dutch Revolt in the Eighty Years' War. The royal Dutch House of Orange-Nassau and Leiden University still have a close...

 to study mathematics with Jacob Golius and astronomy with Martin Hortensius
Martin van den Hove
Martin van den Hove was a Dutch astronomer and mathematician. His adopted Latin name is a translation of the Dutch hof , in Latin horta.-Early life:...

. In October 1630 he had a falling-out with Beeckman, whom he accused of plagiarizing some of his ideas. In Amsterdam
Amsterdam
Amsterdam is the largest city and the capital of the Netherlands. The current position of Amsterdam as capital city of the Kingdom of the Netherlands is governed by the constitution of August 24, 1815 and its successors. Amsterdam has a population of 783,364 within city limits, an urban population...

, he had a relationship with a servant girl, Helena Jans van der Strom, with whom he had a daughter, Francine
Francine Descartes
Francine Descartes was René Descartes' daughter.Francine was the daughter of Helena Jans van der Strom, a domestic servant of Thomas Sergeant – a bookshop owner and associate of Descartes at whose house in Amsterdam Descartes lodged on 15 October 1634...

, who was born in 1635 in Deventer
Deventer
Deventer is a municipality and city in the Salland region of the Dutch province of Overijssel. Deventer is largely situated on the east bank of the river IJssel, but also has a small part of its territory on the west bank. In 2005 the municipality of Bathmen Deventer is a municipality and city in...

, at which time Descartes taught at the Utrecht University
Utrecht University
Utrecht University is a university in Utrecht, Netherlands. It is one of the oldest universities in the Netherlands and one of the largest in Europe. Established March 26, 1636, it had an enrollment of 29,082 students in 2008, and employed 8,614 faculty and staff, 570 of which are full professors....

. Francine Descartes died in 1640 in Amersfoort
Amersfoort
Amersfoort is a municipality and the second largest city of the province of Utrecht in central Netherlands. The city is growing quickly but has a well-preserved and protected medieval centre. Amersfoort is one of the largest railway junctions in the country, because of its location on two of the...

, from Scarlet Fever
Scarlet fever
Scarlet fever is a disease caused by exotoxin released by Streptococcus pyogenes. Once a major cause of death, it is now effectively treated with antibiotics...

.

While in the Netherlands he changed his address frequently, living among other places in Dordrecht
Dordrecht
Dordrecht , colloquially Dordt, historically in English named Dort, is a city and municipality in the western Netherlands, located in the province of South Holland. It is the fourth largest city of the province, having a population of 118,601 in 2009...

 (1628), Franeker
Franeker
Franeker is one of the eleven historical cities of Friesland and capital of the municipality of Franekeradeel. It is located about 20 km west of Leeuwarden on the Van Harinxma Canal. As of 1 January 2006, it had 12,996 inhabitants. The city is famous for the Eisinga Planetarium from around...

 (1629), Amsterdam (1629–30), Leiden (1630), Amsterdam (1630–32), Deventer
Deventer
Deventer is a municipality and city in the Salland region of the Dutch province of Overijssel. Deventer is largely situated on the east bank of the river IJssel, but also has a small part of its territory on the west bank. In 2005 the municipality of Bathmen Deventer is a municipality and city in...

 (1632–34), Amsterdam (1634–35), Utrecht
Utrecht (city)
Utrecht city and municipality is the capital and most populous city of the Dutch province of Utrecht. It is located in the eastern corner of the Randstad conurbation, and is the fourth largest city of the Netherlands with a population of 312,634 on 1 Jan 2011.Utrecht's ancient city centre features...

 (1635–36), Leiden (1636), Egmond (1636–38), Santpoort (1638–1640), Leiden (1640–41), Endegeest (a castle near Oegstgeest
Oegstgeest
Oegstgeest is a town and municipality in the province of South Holland in the western Netherlands. Its population was 22,576 in 2008.-Location :...

) (1641–43), and finally for an extended time in Egmond-Binnen
Egmond-Binnen
Egmond-Binnen is a village in the Dutch province of North Holland. It is a part of the municipality of Bergen, and lies about southwest of Alkmaar....

 (1643–49).

Despite these frequent moves he wrote all his major work during his 20-plus years in the Netherlands, where he managed to revolutionize mathematics and philosophy. In 1633, Galileo
Galileo Galilei
Galileo Galilei , was an Italian physicist, mathematician, astronomer, and philosopher who played a major role in the Scientific Revolution. His achievements include improvements to the telescope and consequent astronomical observations and support for Copernicanism...

 was condemned by the Roman Catholic Church, and Descartes abandoned plans to publish Treatise on the World
The World (Descartes)
The World, originally titled Le Monde and also called Treatise on the Light, is a book by René Descartes . Written between 1629 and 1633, it contains a relatively complete version of his philosophy, from method, to metaphysics, to physics and biology.Descartes was a follower of the mechanical...

, his work of the previous four years. Nevertheless, in 1637 he published part of this work in three essays: Les Météores (The Meteors), La Dioptrique (Dioptrics) and La Géométrie (Geometry), preceded by an introduction, his famous Discours de la Métode (Discourse on the Method). In it Descartes lays out four rules of thought, meant to ensure that our knowledge rests upon a firm foundation.

Descartes continued to publish works concerning both mathematics and philosophy for the rest of his life. In 1641 he published a metaphysics work, Meditationes de Prima Philosophia (Meditations on First Philosophy
Meditations on First Philosophy
Meditations on First Philosophy is a philosophical treatise written by René Descartes and first published in 1641 . The French translation was published in 1647 as Méditations Metaphysiques...

), written in Latin and thus addressed to the learned. It was followed, in 1644, by Principia Philosophiæ (Principles of Philosophy
Principles of Philosophy
Principles of Philosophy is a book by René Descartes. Written in Latin, it was published in 1644 and dedicated to Elisabeth of Bohemia, with whom Descartes had a long standing friendship. A French version followed in 1647. It set forth the principles of nature—the Laws of Physics--as Descartes...

), a kind of synthesis of the Meditations and the Discourse. In 1643, Cartesian philosophy was condemned at the University of Utrecht
Utrecht University
Utrecht University is a university in Utrecht, Netherlands. It is one of the oldest universities in the Netherlands and one of the largest in Europe. Established March 26, 1636, it had an enrollment of 29,082 students in 2008, and employed 8,614 faculty and staff, 570 of which are full professors....

, and Descartes began his long correspondence with Princess Elisabeth of Bohemia
Elisabeth of Bohemia, Princess Palatine
Elisabeth of the Palatinate , also known as Elisabeth of Bohemia, was the eldest daughter of Frederick V, who was briefly elected King of Bohemia, and Elizabeth Stuart. She ruled the Herford Abbey as Princess-Abbess Elizabeth III...

, devoted mainly to moral and psychological subjects. Connected with this correspondence, in 1649 he published Les Passions de l'âme (Passions of the Soul
Passions of the Soul
In the treatise Passions of the Soul , the last of Descartes' published work, completed in 1649 and dedicated to Princess Elizabeth of Bohemia, the author contributes to a long tradition of theorizing "the passions." The passions were experiences often equated with or labeled as precursors to what...

), that he dedicated to the Princess. In 1647, he was awarded a pension by the King of France. Descartes was interviewed by Frans Burman at Egmond-Binnen
Egmond-Binnen
Egmond-Binnen is a village in the Dutch province of North Holland. It is a part of the municipality of Bergen, and lies about southwest of Alkmaar....

 in 1648.

A French translation of Principia Philosophiæ, prepared by Abbot Claude Picot, was published in 1647. This edition Descartes dedicated to Princess Elisabeth of Bohemia. In the preface Descartes praised true philosophy as a means to attain wisdom. He identifies four ordinary sources to reach wisdom, and finally says that there is a fifth, better and more secure, consisting in the search for first causes.

René Descartes died on 11 February 1650 in Stockholm
Stockholm
Stockholm is the capital and the largest city of Sweden and constitutes the most populated urban area in Scandinavia. Stockholm is the most populous city in Sweden, with a population of 851,155 in the municipality , 1.37 million in the urban area , and around 2.1 million in the metropolitan area...

, Sweden, where he had been invited as a tutor for Queen Christina of Sweden
Christina of Sweden
Christina , later adopted the name Christina Alexandra, was Queen regnant of Swedes, Goths and Vandals, Grand Princess of Finland, and Duchess of Ingria, Estonia, Livonia and Karelia, from 1633 to 1654. She was the only surviving legitimate child of King Gustav II Adolph and his wife Maria Eleonora...

. The cause of death was said to be pneumonia
Pneumonia
Pneumonia is an inflammatory condition of the lung—especially affecting the microscopic air sacs —associated with fever, chest symptoms, and a lack of air space on a chest X-ray. Pneumonia is typically caused by an infection but there are a number of other causes...

; accustomed to working in bed until noon, he may have suffered damage to his health from Christina's demands for early morning study (the lack of sleep could have severely compromised his immune system). Descartes stayed at the French ambassador Pierre Chanut
Pierre Chanut
Pierre Hector Chanut was a civil servant in the Auvergne, a French ambassador and state counsellor....

. In his recent book, Der rätselhafte Tod des René Descartes (The Mysterious Death of René Descartes), the German philosopher Theodor Ebert asserts that Descartes died not through natural causes, but from an arsenic-laced communion wafer given to him by a Catholic priest. He believes that Jacques Viogué, a missionary working in Stockholm, administered the poison because he feared Descartes's radical theological ideas would derail an expected conversion to Roman Catholicism by the monarch of Protestant Lutheran Sweden.

In 1663, the Pope
Pope Alexander VII
Pope Alexander VII , born Fabio Chigi, was Pope from 7 April 1655, until his death.- Early life :Born in Siena, a member of the illustrious banking family of Chigi and a great-nephew of Pope Paul V , he was privately tutored and eventually received doctorates of philosophy, law, and theology from...

 placed his works on the Index of Prohibited Books
Index Librorum Prohibitorum
The Index Librorum Prohibitorum was a list of publications prohibited by the Catholic Church. A first version was promulgated by Pope Paul IV in 1559, and a revised and somewhat relaxed form was authorized at the Council of Trent...

.

As a Roman Catholic in a Protestant nation, he was interred in a graveyard used mainly for unbaptized infants in Adolf Fredriks kyrka
Adolf Fredriks kyrka
Adolf Fredriks kyrka is a church in central Stockholm, Sweden. It was built in 1768-1774, replacing a wooden chapel from 1674, which was dedicated to Saint Olof....

 in Stockholm. Later, his remains were taken to France and buried in the Abbey of Saint-Germain-des-Prés
Abbey of Saint-Germain-des-Prés
The Benedictine Abbey of Saint-Germain-des-Prés, just beyond the outskirts of early medieval Paris, was the burial place of Merovingian kings of Neustria...

 in Paris. Although the National Convention
National Convention
During the French Revolution, the National Convention or Convention, in France, comprised the constitutional and legislative assembly which sat from 20 September 1792 to 26 October 1795 . It held executive power in France during the first years of the French First Republic...

 in 1792 had planned to transfer his remains to the Panthéon, they are, two centuries later, still resting between two other graves — those of the scholarly monks Jean Mabillon
Jean Mabillon
Jean Mabillon was a French Benedictine monk and scholar, considered the founder of palaeography and diplomatics.-Early career:...

 and Bernard de Montfaucon
Bernard de Montfaucon
Bernard de Montfaucon was a French Benedictine monk, a scholar who founded a new discipline, palaeography; an editor of works of the Fathers of the Church; he is also regarded to be one of the founders of modern archaeology.-Early life:Montfaucon was born January 13, 1655 in the castle of...

 — in a chapel of the abbey. His memorial, erected in the 18th century, remains in the Swedish church.

Philosophical work


Descartes is often regarded as the first thinker to provide a philosophical framework for the natural sciences as these began to develop.

In his Discourse on the Method, he attempts to arrive at a fundamental set of principles that one can know as true without any doubt. To achieve this, he employs a method called hyperbolical/metaphysical doubt, also sometimes referred to as methodological skepticism: he rejects any ideas that can be doubted, and then reestablishes them in order to acquire a firm foundation for genuine knowledge.

Initially, Descartes arrives at only a single principle: thought exists. Thought cannot be separated from me, therefore, I exist (Discourse on the Method and Principles of Philosophy). Most famously, this is known as cogito ergo sum
Cogito ergo sum
is a philosophical Latin statement proposed by . The simple meaning of the phrase is that someone wondering whether or not they exist is, in and of itself, proof that something, an "I", exists to do the thinking — However this "I" is not the more or less permanent person we call "I"...

(English: "I think, therefore I am"). Therefore, Descartes concluded, if he doubted, then something or someone must be doing the doubting, therefore the very fact that he doubted proved his existence. "The simple meaning of the phrase is that if one is skeptical of existence, that is in and of itself proof that he does exist."

Descartes concludes that he can be certain that he exists because he thinks. But in what form? He perceives his body through the use of the senses; however, these have previously been unreliable. So Descartes determines that the only indubitable knowledge is that he is a thinking thing. Thinking is what he does, and his power must come from his essence. Descartes defines "thought" (cogitatio) as "what happens in me such that I am immediately conscious of it, insofar as I am conscious of it". Thinking is thus every activity of a person of which he is immediately conscious
Consciousness
Consciousness is a term that refers to the relationship between the mind and the world with which it interacts. It has been defined as: subjectivity, awareness, the ability to experience or to feel, wakefulness, having a sense of selfhood, and the executive control system of the mind...

.

To further demonstrate the limitations of the senses, Descartes proceeds with what is known as the Wax Argument. He considers a piece of wax; his senses inform him that it has certain characteristics, such as shape, texture, size, color, smell, and so forth. When he brings the wax towards a flame, these characteristics change completely. However, it seems that it is still the same thing: it is still the same piece of wax, even though the data of the senses inform him that all of its characteristics are different. Therefore, in order to properly grasp the nature of the wax, he should put aside the senses. He must use his mind. Descartes concludes:
In this manner, Descartes proceeds to construct a system of knowledge, discarding perception
Perception
Perception is the process of attaining awareness or understanding of the environment by organizing and interpreting sensory information. All perception involves signals in the nervous system, which in turn result from physical stimulation of the sense organs...

 as unreliable and instead admitting only deduction
Deductive reasoning
Deductive reasoning, also called deductive logic, is reasoning which constructs or evaluates deductive arguments. Deductive arguments are attempts to show that a conclusion necessarily follows from a set of premises or hypothesis...

 as a method. In the third and fifth Meditation
Meditations on First Philosophy
Meditations on First Philosophy is a philosophical treatise written by René Descartes and first published in 1641 . The French translation was published in 1647 as Méditations Metaphysiques...

, he offers an ontological proof of a benevolent God (through both the ontological argument
Ontological argument
The ontological argument for the existence of God is an a priori argument for the existence of God. The ontological argument was first proposed by the eleventh-century monk Anselm of Canterbury, who defined God as the greatest possible being we can conceive...

 and trademark argument
Trademark argument
The trademark argument is an a priori argument for the existence of God developed by French philosopher and mathematician, René Descartes. The argument, though similar to the ontological argument, differs in some respects, since it seeks to prove the existence of God through the causal adequacy...

). Because God is benevolent, he can have some faith in the account of reality his senses provide him, for God has provided him with a working mind and sensory system
Sensory system
A sensory system is a part of the nervous system responsible for processing sensory information. A sensory system consists of sensory receptors, neural pathways, and parts of the brain involved in sensory perception. Commonly recognized sensory systems are those for vision, hearing, somatic...

 and does not desire to deceive him. From this supposition, however, he finally establishes the possibility of acquiring knowledge about the world based on deduction and perception. In terms of epistemology therefore, he can be said to have contributed such ideas as a rigorous conception of foundationalism
Foundationalism
Foundationalism is any theory in epistemology that holds that beliefs are justified based on what are called basic beliefs . This position is intended to resolve the infinite regress problem in epistemology...

 and the possibility that reason
Reason
Reason is a term that refers to the capacity human beings have to make sense of things, to establish and verify facts, and to change or justify practices, institutions, and beliefs. It is closely associated with such characteristically human activities as philosophy, science, language, ...

 is the only reliable method of attaining knowledge.

Descartes also wrote a response to skepticism about the existence of the external world. He argues that sensory perceptions come to him involuntarily, and are not willed by him. They are external to his senses, and according to Descartes, this is evidence of the existence of something outside of his mind, and thus, an external world. Descartes goes on to show that the things in the external world are material by arguing that God would not deceive him as to the ideas that are being transmitted, and that God has given him the "propensity" to believe that such ideas are caused by material things.

Dualism



Descartes in his Passions of the Soul
Passions of the Soul
In the treatise Passions of the Soul , the last of Descartes' published work, completed in 1649 and dedicated to Princess Elizabeth of Bohemia, the author contributes to a long tradition of theorizing "the passions." The passions were experiences often equated with or labeled as precursors to what...

 and The Description of the Human Body
The Description of the Human Body
The Description of the Human Body is an unfinished treatise written in 1647 by René Descartes. Descartes felt knowing oneself was particularly useful. This for him included medical knowledge. He hoped to cure and prevent disease, even to slow down aging.René Descartes believed the soul caused...

 suggested that the body works like a machine, that it has the material properties of extension and motion, and that it follows the laws of nature. The mind
Mind
The concept of mind is understood in many different ways by many different traditions, ranging from panpsychism and animism to traditional and organized religious views, as well as secular and materialist philosophies. Most agree that minds are constituted by conscious experience and intelligent...

 (or soul), on the other hand, was described as a nonmaterial
Mental world
The mental world is an ontological category in metaphysics, populated by nonmaterial mental objects, without physical extension contrasted with the physical world of space and time populated with physical objects, or Plato's world of ideals populated, in part, with mathematical...

 entity that lacks extension and motion, and does not follow the laws of nature. Descartes argued that only humans have minds, and that the mind interacts with the body at the pineal gland
Pineal gland
The pineal gland is a small endocrine gland in the vertebrate brain. It produces the serotonin derivative melatonin, a hormone that affects the modulation of wake/sleep patterns and seasonal functions...

. This form of dualism
Dualism
Dualism denotes a state of two parts. The term 'dualism' was originally coined to denote co-eternal binary opposition, a meaning that is preserved in metaphysical and philosophical duality discourse but has been diluted in general or common usages. Dualism can refer to moral dualism, Dualism (from...

 or duality proposes that the mind controls the body, but that the body can also influence the otherwise rational mind, such as when people act out of passion. Most of the previous accounts of the relationship between mind and body had been uni-directional.

Descartes suggested that the pineal gland
Pineal gland
The pineal gland is a small endocrine gland in the vertebrate brain. It produces the serotonin derivative melatonin, a hormone that affects the modulation of wake/sleep patterns and seasonal functions...

 is "the seat of the soul" for several reasons. First, the soul is unitary, and unlike many areas of the brain the pineal gland appeared to be unitary (though subsequent microscopic inspection has revealed it is formed of two hemispheres). Second, Descartes observed that the pineal gland was located near the ventricles
Ventricular system
The ventricular system is a set of structures containing cerebrospinal fluid in the brain. It is continuous with the central canal of the spinal cord.-Components:The system comprises four ventricles:* right and left lateral ventricles* third ventricle...

. He believed the cerebrospinal fluid
Cerebrospinal fluid
Cerebrospinal fluid , Liquor cerebrospinalis, is a clear, colorless, bodily fluid, that occupies the subarachnoid space and the ventricular system around and inside the brain and spinal cord...

 of the ventricles acted through the nerves to control the body, and that the pineal gland influenced this process. Finally, although Descartes realized that both humans and animals have pineal glands (see Passions of the Soul Part One, Section 50, AT 369), he believed that only humans have minds. This led him to the belief that animals cannot feel pain, and Descartes's practice of vivisection
Vivisection
Vivisection is defined as surgery conducted for experimental purposes on a living organism, typically animals with a central nervous system, to view living internal structure...

 (the dissection of live animals) became widely used throughout Europe until the Enlightenment
Age of Enlightenment
The Age of Enlightenment was an elite cultural movement of intellectuals in 18th century Europe that sought to mobilize the power of reason in order to reform society and advance knowledge. It promoted intellectual interchange and opposed intolerance and abuses in church and state...

.
Cartesian dualism set the agenda for philosophical discussion of the mind–body problem for many years after Descartes's death.

Mathematical legacy


Descartes's theory provided the basis for the calculus of Newton
Isaac Newton
Sir Isaac Newton PRS was an English physicist, mathematician, astronomer, natural philosopher, alchemist, and theologian, who has been "considered by many to be the greatest and most influential scientist who ever lived."...

 and Leibniz
Gottfried Leibniz
Gottfried Wilhelm Leibniz was a German philosopher and mathematician. He wrote in different languages, primarily in Latin , French and German ....

, by applying infinitesimal calculus
Infinitesimal calculus
Infinitesimal calculus is the part of mathematics concerned with finding slope of curves, areas under curves, minima and maxima, and other geometric and analytic problems. It was independently developed by Gottfried Leibniz and Isaac Newton starting in the 1660s...

 to the tangent line problem, thus permitting the evolution of that branch of modern mathematics. This appears even more astounding considering that the work was just intended as an example to his Discours de la méthode pour bien conduire sa raison, et chercher la verité dans les sciences (Discourse on the Method of Rightly Conducting the Reason, and Searching for Truth in the Sciences, better known under the shortened title Discours de la méthode; English, Discourse on the Method).

Descartes' rule of signs
Descartes' rule of signs
In mathematics, Descartes' rule of signs, first described by René Descartes in his work La Géométrie, is a technique for determining the number of positive or negative real roots of a polynomial....

 is also a commonly used method to determine the number of positive and negative roots of a polynomial.

Descartes created analytic geometry
Analytic geometry
Analytic geometry, or analytical geometry has two different meanings in mathematics. The modern and advanced meaning refers to the geometry of analytic varieties...

, and discovered an early form of the law of conservation of momentum
Momentum
In classical mechanics, linear momentum or translational momentum is the product of the mass and velocity of an object...

 (the term momentum refers to the momentum of a force). He outlined his views on the universe in his Principles of Philosophy
Principles of Philosophy
Principles of Philosophy is a book by René Descartes. Written in Latin, it was published in 1644 and dedicated to Elisabeth of Bohemia, with whom Descartes had a long standing friendship. A French version followed in 1647. It set forth the principles of nature—the Laws of Physics--as Descartes...

.

Descartes also made contributions to the field of optics
Optics
Optics is the branch of physics which involves the behavior and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behavior of visible, ultraviolet, and infrared light...

. He showed by using geometric construction and the law of refraction (also known as Descartes's law or more commonly Snell's law, who discovered it 16 years earlier) that the angular radius of a rainbow is 42 degrees (i.e., the angle subtended at the eye by the edge of the rainbow and the ray passing from the sun through the rainbow's centre is 42°). He also independently discovered the law of reflection, and his essay on optics was the first published mention of this law.

One of Descartes most enduring legacies was his development of Cartesian geometry, which uses algebra to describe geometry. He "invented the convention of representing unknowns in equations by x, y, and z, and knowns by a, b, and c". He also "pioneered the standard notation" that uses superscripts to show the powers or exponents, for example the 4 used in x4 to indicate squaring of squaring.

Contemporary reception


Although Descartes was well known in academic circles towards the end of his life, the teaching of his works in schools was controversial. Henri de Roy (Henricus Regius, 1598–1679), Professor of Medicine at the University of Utrecht, was condemned by the Rector of the University, Gijsbert Voet (Voetius), for teaching Descartes's physics.

Religious beliefs


The religious beliefs of René Descartes have been rigorously debated within scholarly circles. He claimed to be a devout Roman Catholic, claiming that one of the purposes of the Meditations
Meditations on First Philosophy
Meditations on First Philosophy is a philosophical treatise written by René Descartes and first published in 1641 . The French translation was published in 1647 as Méditations Metaphysiques...

was to defend the Christian faith. However, in his own era, Descartes was accused of harboring secret deist or atheist beliefs. Contemporary Blaise Pascal
Blaise Pascal
Blaise Pascal , was a French mathematician, physicist, inventor, writer and Catholic philosopher. He was a child prodigy who was educated by his father, a tax collector in Rouen...

 said that "I cannot forgive Descartes; in all his philosophy, Descartes did his best to dispense with God. But Descartes could not avoid prodding God to set the world in motion with a snap of his lordly fingers; after that, he had no more use for God."

Stephen Gaukroger
Stephen Gaukroger
Stephen Gaukroger is a British philosopher and intellectual historian. He is Professor of History of Philosophy and History of Science at the University of Sydney. Recently he also took up a position as Professor of Philosophy at the University of Aberdeen.-Life:He graduated B.A. from the...

's biography of Descartes reports that "he had a deep religious faith as a Catholic, which he retained to his dying day, along with a resolute, passionate desire to discover the truth." After Descartes died in Sweden
Sweden
Sweden , officially the Kingdom of Sweden , is a Nordic country on the Scandinavian Peninsula in Northern Europe. Sweden borders with Norway and Finland and is connected to Denmark by a bridge-tunnel across the Öresund....

, Queen Christina
Christina of Sweden
Christina , later adopted the name Christina Alexandra, was Queen regnant of Swedes, Goths and Vandals, Grand Princess of Finland, and Duchess of Ingria, Estonia, Livonia and Karelia, from 1633 to 1654. She was the only surviving legitimate child of King Gustav II Adolph and his wife Maria Eleonora...

 abdicated her throne to convert to Roman Catholicism (Swedish law required a Protestant ruler). The only Roman Catholic with whom she had prolonged contact was Descartes, who was her personal tutor.

Writings



  • 1618. Compendium Musicae. A treatise on music theory and the aesthetics of music written for Descartes's early collaborator Isaac Beeckman.
  • 1626–1628. Regulae ad directionem ingenii (Rules for the Direction of the Mind
    Rules for the Direction of the Mind
    In 1619, René Descartes began work on an unfinished treatise regarding the proper method for scientific and philosophical thinking entitled Regulae ad directionem ingenii, or Rules for the Direction of the Mind. This work outlined the basis for his later work on complex problems of mathematics,...

    ). Incomplete. First published posthumously in 1684. The best critical edition, which includes an early Dutch translation, is edited by Giovanni Crapulli (The Hague: Martinus Nijhoff, 1966).
  • 1630–1633. Le Monde (The World
    The World (Descartes)
    The World, originally titled Le Monde and also called Treatise on the Light, is a book by René Descartes . Written between 1629 and 1633, it contains a relatively complete version of his philosophy, from method, to metaphysics, to physics and biology.Descartes was a follower of the mechanical...

    ) and L'Homme (Man). Descartes's first systematic presentation of his natural philosophy. Man was published posthumously in Latin translation in 1662; and The World posthumously in 1664.
  • 1637. Discours de la méthode (Discourse on the Method). An introduction to the Essais, which include the Dioptrique, the Météores and the Géométrie.
  • 1637. La Géométrie
    La Géométrie
    La Géométrie was published in 1637 as an appendix to Discours de la méthode , written by René Descartes. In the Discourse, he presents his method for obtaining clarity on any subject...

    (Geometry). Descartes's major work in mathematics. There is an English translation by Michael Mahoney (New York: Dover, 1979).
  • 1641. Meditationes de prima philosophia (Meditations on First Philosophy
    Meditations on First Philosophy
    Meditations on First Philosophy is a philosophical treatise written by René Descartes and first published in 1641 . The French translation was published in 1647 as Méditations Metaphysiques...

    ), also known as Metaphysical Meditations. In Latin; a French translation, probably done without Descartes's supervision, was published in 1647. Includes six Objections and Replies. A second edition, published the following year, included an additional objection and reply, and a Letter to Dinet.
  • 1644. Principia philosophiae (Principles of Philosophy
    Principles of Philosophy
    Principles of Philosophy is a book by René Descartes. Written in Latin, it was published in 1644 and dedicated to Elisabeth of Bohemia, with whom Descartes had a long standing friendship. A French version followed in 1647. It set forth the principles of nature—the Laws of Physics--as Descartes...

    ), a Latin textbook at first intended by Descartes to replace the Aristotelian textbooks then used in universities. A French translation, Principes de philosophie by Claude Picot, under the supervision of Descartes, appeared in 1647 with a letter-preface to Queen Christina of Sweden.
  • 1647. Notae in programma (Comments on a Certain Broadsheet). A reply to Descartes's one-time disciple Henricus Regius.
  • 1647. The Description of the Human Body
    The Description of the Human Body
    The Description of the Human Body is an unfinished treatise written in 1647 by René Descartes. Descartes felt knowing oneself was particularly useful. This for him included medical knowledge. He hoped to cure and prevent disease, even to slow down aging.René Descartes believed the soul caused...

    . Published posthumously.
  • 1648. Responsiones Renati Des Cartes... (Conversation with Burman). Notes on a Q&A session between Descartes and Frans Burman on 16 April 1648. Rediscovered in 1895 and published for the first time in 1896. An annotated bilingual edition (Latin with French translation), edited by Jean-Marie Beyssade, was published in 1981 (Paris: PUF).
  • 1649. Les passions de l'âme (Passions of the Soul
    Passions of the Soul
    In the treatise Passions of the Soul , the last of Descartes' published work, completed in 1649 and dedicated to Princess Elizabeth of Bohemia, the author contributes to a long tradition of theorizing "the passions." The passions were experiences often equated with or labeled as precursors to what...

    ). Dedicated to Princess Elizabeth of Bohemia.
  • 1656. Musicae Compendium (Instruction in Music). Posth. Publ.: Johannes Janssonius jun., Amsterdam
  • 1657. Correspondence. Published by Descartes's literary executor Claude Clerselier. The third edition, in 1667, was the most complete; Clerselier omitted, however, much of the material pertaining to mathematics.


In January 2010, a previously unknown letter from Descartes, dated 27 May 1641, was found by the Dutch philosopher Erik-Jan Bos when browsing through Google
Google search
Google or Google Web Search is a web search engine owned by Google Inc. Google Search is the most-used search engine on the World Wide Web, receiving several hundred million queries each day through its various services....

. Bos found the letter mentioned in a summary of autographs kept by Haverford College
Haverford College
Haverford College is a private, coeducational liberal arts college located in Haverford, Pennsylvania, United States, a suburb of Philadelphia...

 in Haverford
Haverford, Pennsylvania
Haverford is an unincorporated community located partially in Haverford Township in Delaware County, Pennsylvania, USA, but primarily in Lower Merion Township in Montgomery County, about west of Philadelphia. It is on the Main Line, which is known historically for its wealth. As of August 2009,...

, Pennsylvania. The College was unaware that the letter had never been published. This was the third letter by Descartes found in the last 25 years.

See also


  • 3587 Descartes
    3587 Descartes
    3587 Descartes is a small main belt asteroid. It is 9.35 km in diameter. It was discovered by L. V. Zhuravleva in 1981. It is named after René Descartes, the seventeenth century philosopher....

    , asteroid
  • Analytic geometry
    Analytic geometry
    Analytic geometry, or analytical geometry has two different meanings in mathematics. The modern and advanced meaning refers to the geometry of analytic varieties...

  • Balloonist theory
    Balloonist theory
    Balloonist theory was a theory in early neuroscience that attempted to explain muscle movement by asserting that muscles contract by inflating with air or fluid. The Greek physician Galen believed that muscles contracted due to a fluid flowing into them, and for 1500 years afterward, it was...

  • Baruch Spinoza
    Baruch Spinoza
    Baruch de Spinoza and later Benedict de Spinoza was a Dutch Jewish philosopher. Revealing considerable scientific aptitude, the breadth and importance of Spinoza's work was not fully realized until years after his death...

  • Philosophy of Spinoza
    Philosophy of Spinoza
    One of the three great Rationalists, Spinoza's philosophy encompasses nearly every area of philosophical discourse, including metaphysics, epistemology, political philosophy, ethics, philosophy of mind and philosophy of science....

  • Cartesian circle
    Cartesian circle
    The Cartesian circle is a potential mistake in reasoning attributed to René Descartes.Descartes argues – for example, in the third of his Meditations on First Philosophy – that whatever one clearly and distinctly perceives is true: "I now seem to be able to lay it down as a general rule that...

  • Cartesian coordinate system
    Cartesian coordinate system
    A Cartesian coordinate system specifies each point uniquely in a plane by a pair of numerical coordinates, which are the signed distances from the point to two fixed perpendicular directed lines, measured in the same unit of length...

  • Cartesian diagram
  • Cartesian diver
    Cartesian diver
    A Cartesian diver or Cartesian devil is a classic science experiment, named for René Descartes, which demonstrates the principle of buoyancy and the ideal gas law.-Experiment description:...

  • Cartesian morphism
  • Cartesian product
    Cartesian product
    In mathematics, a Cartesian product is a construction to build a new set out of a number of given sets. Each member of the Cartesian product corresponds to the selection of one element each in every one of those sets...

  • Cartesian product of graphs
    Cartesian product of graphs
    In graph theory, the Cartesian product G \square H of graphs G and H is a graph such that* the vertex set of G \square H is the Cartesian product V × V; and...

  • Cartesian tree
    Cartesian tree
    In computer science, a Cartesian tree is a binary tree derived from a sequence of numbers; it can be uniquely defined from the properties that it is heap-ordered and that a symmetric traversal of the tree returns the original sequence...

  • Defect (geometry)
    Defect (geometry)
    In geometry, the defect means the failure of some angles to add up to the expected amount of 360° or 180°, when such angles in the plane would...

  • Descartes' rule of signs
    Descartes' rule of signs
    In mathematics, Descartes' rule of signs, first described by René Descartes in his work La Géométrie, is a technique for determining the number of positive or negative real roots of a polynomial....

  • Descartes' theorem
    Descartes' theorem
    In geometry, Descartes' theorem, named after René Descartes, establishes a relationship between four kissing, or mutually tangent, circles. The theorem can be used to construct a fourth circle tangent to three given, mutually tangent circles.-History:...

  • Dualistic interactionism
  • Folium of Descartes
    Folium of Descartes
    In geometry, the Folium of Descartes is an algebraic curve defined by the equationx^3 + y^3 - 3 a x y = 0 \,.It forms a loop in the first quadrant with a double point at the origin and asymptotex + y + a = 0 \,.It is symmetrical about y = x....

  • Self-organization
    Self-organization
    Self-organization is the process where a structure or pattern appears in a system without a central authority or external element imposing it through planning...

  • Scientific Revolution
    Scientific revolution
    The Scientific Revolution is an era associated primarily with the 16th and 17th centuries during which new ideas and knowledge in physics, astronomy, biology, medicine and chemistry transformed medieval and ancient views of nature and laid the foundations for modern science...

  • Solipsism


External links



Video

General


Stanford Encyclopedia of Philosophy