René Descartes ( , ; ; 31 March 1596 – 11 February 1650) was a French philosopher,

scientist A scientist is a person who Scientific method, researches 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, philosophers engag ...

, and

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 ...

, widely considered a seminal figure in the emergence of modern philosophy and

science Science is a systematic discipline that builds and organises knowledge in the form of testable hypotheses and predictions about the universe. Modern science is typically divided into twoor threemajor branches: the natural sciences, which stu ...

. Mathematics was paramount to his method of inquiry, and he connected the previously separate fields of

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

and

algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...

into

analytic geometry In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry. Analytic geometry is used in physics and engineering, and als ...

. Descartes spent much of his working life in the

Dutch Republic The United Provinces of the Netherlands, commonly referred to in historiography as the Dutch Republic, was a confederation that existed from 1579 until the Batavian Revolution in 1795. It was a predecessor state of the present-day Netherlands ...

, initially serving the Dutch States Army, and later becoming a central intellectual of the

Dutch Golden Age The Dutch Golden Age ( ) was a period in the history of the Netherlands which roughly lasted from 1588, when the Dutch Republic was established, to 1672, when the '' Rampjaar'' occurred. During this period, Dutch trade, scientific development ...

. Although he served a Protestant state and was later counted as a

deist Deism ( or ; derived from the Latin term '' deus'', meaning "god") is the philosophical position and rationalistic theology that generally rejects revelation as a source of divine knowledge and asserts that empirical reason and observation ...

by critics, Descartes was

Roman Catholic The Catholic Church (), also known as the Roman Catholic Church, is the largest Christian church, with 1.27 to 1.41 billion baptized Catholics worldwide as of 2025. It is among the world's oldest and largest international institut ...

. Many elements of Descartes's philosophy have precedents in late

Aristotelianism Aristotelianism ( ) is a philosophical tradition inspired by the work of Aristotle, usually characterized by Prior Analytics, deductive logic and an Posterior Analytics, analytic inductive method in the study of natural philosophy and metaphysics ...

, the revived Stoicism of the 16th century, or in earlier philosophers like Augustine. In his

natural philosophy Natural philosophy or philosophy of nature (from Latin ''philosophia naturalis'') is the philosophical study of physics, that is, nature and the physical universe, while ignoring any supernatural influence. It was dominant before the develop ...

, he differed from the schools on two major points. First, he rejected the splitting of corporeal substance into

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 pa ...

and form; second, he rejected any appeal to final ends, divine or natural, in explaining natural phenomena. In his theology, he insists on the absolute freedom of God's act of creation. Refusing to accept the authority of previous philosophers, Descartes frequently set his views apart from the philosophers who preceded him. In the opening section of the '' Passions of the Soul'', an

early modern The early modern period is a Periodization, historical period that is defined either as part of or as immediately preceding the modern period, with divisions based primarily on the history of Europe and the broader concept of modernity. There i ...

treatise on 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." His best known philosophical statement is "" ("I think, therefore I am"; ), found in ''

Discourse on the Method ''Discourse on the Method of Rightly Conducting One's Reason and of Seeking Truth in the Sciences'' () is a philosophical and autobiographical treatise published by René Descartes in 1637. It is best known as the source of the famous quotation ...

'' (1637, in French and Latin, 1644) and '' Principles of Philosophy'' (1644, in Latin, 1647 in French). The statement has either been interpreted as a logical

syllogism A syllogism (, ''syllogismos'', 'conclusion, inference') is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two propositions that are asserted or assumed to be true. In its earliest form (defin ...

or as an intuitive thought. Descartes has often been called the father of modern philosophy, and is largely seen as responsible for the increased attention given to

epistemology Epistemology is the branch of philosophy that examines the nature, origin, and limits of knowledge. Also called "the theory of knowledge", it explores different types of knowledge, such as propositional knowledge about facts, practical knowle ...

in the 17th century.

Bertrand Russell Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British philosopher, logician, mathematician, and public intellectual. He had influence on mathematics, logic, set theory, and various areas of analytic ...

(2004
''History of western philosophy''
pp. 511, 516–17. He laid the foundation for 17th-century continental

rationalism In philosophy, rationalism is the Epistemology, epistemological view that "regards reason as the chief source and test of knowledge" or "the position that reason has precedence over other ways of acquiring knowledge", often in contrast to ot ...

, later advocated by Spinoza and Leibniz, and was later opposed by the empiricist school of thought consisting of Hobbes, Locke, Berkeley, and Hume. The rise of early modern rationalism—as a systematic school of philosophy in its own right for the first time in history—exerted an influence on modern Western thought in general, with the birth of two rationalistic philosophical systems of Descartes ( Cartesianism) and Spinoza ( Spinozism). It was the 17th-century arch-rationalists like Descartes, Spinoza, and Leibniz who have given the "

Age of Reason The Age of Enlightenment (also the Age of Reason and the Enlightenment) was a European intellectual and philosophical movement active from the late 17th to early 19th century. Chiefly valuing knowledge gained through rationalism and empiric ...

" its name and place in history. Leibniz, Spinoza, and Descartes were all well-versed in mathematics as well as philosophy, with Descartes and Leibniz additionally contributing to a variety of scientific disciplines. Although only Leibniz is extensively recognized as a

polymath A polymath or polyhistor is an individual whose knowledge spans many different subjects, known to draw on complex bodies of knowledge to solve specific problems. Polymaths often prefer a specific context in which to explain their knowledge, ...

, all three rationalists integrated disparate domains of knowledge into their respective works. Descartes's '' Meditations on First Philosophy'' (1641) continues to be a standard text at most university philosophy departments. Descartes's influence in mathematics is equally apparent, being the namesake of the

Cartesian coordinate system In geometry, a Cartesian coordinate system (, ) in a plane (geometry), plane is a coordinate system that specifies each point (geometry), point uniquely by a pair of real numbers called ''coordinates'', which are the positive and negative number ...

. He is credited as the father of analytic geometry—used in the discovery of infinitesimal

calculus Calculus 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 generalizations of arithmetic operations. Originally called infinitesimal calculus or "the ...

and

analysis Analysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...

. Descartes was also one of the key figures in the

Scientific Revolution The Scientific Revolution was a series of events that marked the emergence of History of science, modern science during the early modern period, when developments in History of mathematics#Mathematics during the Scientific Revolution, mathemati ...

Life

Early life

René Descartes was born in La Haye en Touraine, Province of Touraine (now Descartes,

Indre-et-Loire Indre-et-Loire () is a department in west-central France named after the Indre River and Loire River. In 2019, it had a population of 610,079. In May 1597, his mother Jeanne Brochard, died a few days after giving birth to a still-born child. Descartes's father, Joachim, was a member of the Parlement of Rennes at

Rennes Rennes (; ; Gallo language, Gallo: ''Resnn''; ) is a city in the east of Brittany in Northwestern France at the confluence of the rivers Ille and Vilaine. Rennes is the prefecture of the Brittany (administrative region), Brittany Regions of F ...

. René lived with his grandmother and with his great-uncle. Although the Descartes family was Roman Catholic, the

Poitou Poitou ( , , ; ; Poitevin: ''Poetou'') was a province of west-central France whose capital city was Poitiers. Both Poitou and Poitiers are named after the Pictones Gallic tribe. Geography The main historical cities are Poitiers (historical ...

region was controlled by the Protestant

Huguenots The Huguenots ( , ; ) are a Religious denomination, religious group of French people, French Protestants who held to the Reformed (Calvinist) tradition of Protestantism. The term, which may be derived from the name of a Swiss political leader, ...

. In 1607, late because of his fragile health, he entered the

Jesuit The Society of Jesus (; abbreviation: S.J. or SJ), also known as the Jesuit Order or the Jesuits ( ; ), is a religious order (Catholic), religious order of clerics regular of pontifical right for men in the Catholic Church headquartered in Rom ...

Collège Royal Henry-Le-Grand In France, secondary education is in two stages: * ''Collèges'' () cater for the first four years of secondary education from the ages of 11 to 14. * ''Lycées'' () provide a three-year course of further secondary education for students between ...

at La Flèche, where he was introduced to mathematics and physics, including

Galileo Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642), commonly referred to as Galileo Galilei ( , , ) or mononymously as Galileo, was an Italian astronomer, physicist and engineer, sometimes described as a poly ...

's work. While there, Descartes first encountered hermetic mysticism. After graduation in 1614, he studied for two years (1615–16) at the

University of Poitiers The University of Poitiers (UP; , ) is a public university located in Poitiers, France. It is a member of the Coimbra Group. It is multidisciplinary and contributes to making Poitiers the city with the highest student/inhabitant ratio in France ...

, earning a '' Baccalauréat'' and ''

Licence A license (American English) or licence (Commonwealth English) is an official permission or permit to do, use, or own something (as well as the document of that permission or permit). A license is granted by a party (licensor) to another part ...

'' in canon and civil law in 1616, in accordance with his father's wishes that he should become a lawyer. From there, he moved to Paris. DescartesGraduationRegistry

In ''

'', Descartes recalls:

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 to derive some profit from it.

Army service

In accordance with his ambition to become a professional military officer in 1618, Descartes joined, as a

mercenary A mercenary is a private individual who joins an armed conflict for personal profit, is otherwise an outsider to the conflict, and is not a member of any other official military. Mercenaries fight for money or other forms of payment rather t ...

, the

Protestant Protestantism is a branch of Christianity that emphasizes Justification (theology), justification of sinners Sola fide, through faith alone, the teaching that Salvation in Christianity, salvation comes by unmerited Grace in Christianity, divin ...

Dutch States Army in

Breda Breda ( , , , ) is a List of cities in the Netherlands by province, city and List of municipalities of the Netherlands, municipality in the southern part of the Netherlands, located in the Provinces of the Netherlands, province of North Brabant. ...

under the command of Maurice of Nassau, and undertook a formal study of military engineering, as established by

Simon Stevin Simon Stevin (; 1548–1620), sometimes called Stevinus, was a County_of_Flanders, Flemish mathematician, scientist and music theorist. He made various contributions in many areas of science and engineering, both theoretical and practical. He a ...

. Descartes, therefore, received much encouragement in Breda to advance his knowledge of mathematics. In this way, he became acquainted with Isaac Beeckman, the principal of a

Dordrecht Dordrecht (), historically known in English as Dordt (still colloquially used in Dutch, ) or Dort, is a List of cities in the Netherlands by province, city and List of municipalities of the Netherlands, municipality in the Western Netherlands, lo ...

school, for whom he wrote the ''Compendium of Music'' (written 1618, published 1650). While in the service of the

Catholic The Catholic Church (), also known as the Roman Catholic Church, is the List of Christian denominations by number of members, largest Christian church, with 1.27 to 1.41 billion baptized Catholics Catholic Church by country, worldwid ...

Duke Maximilian of Bavaria from 1619, Descartes was present at the Battle of the White Mountain near

Prague Prague ( ; ) is the capital and List of cities and towns in the Czech Republic, largest city of the Czech Republic and the historical capital of Bohemia. Prague, located on the Vltava River, has a population of about 1.4 million, while its P ...

, in November 1620. According to Adrien Baillet, on the night of 10–11 November 1619 ( St. Martin's Day), while stationed in Neuburg an der Donau, Descartes shut himself in a room with an "oven" (probably a cocklestove) to escape the cold. While within, he had three dreams, and believed that a divine spirit revealed to him a new philosophy. However, it is speculated that what Descartes considered to be his second dream was actually an episode of exploding head syndrome. Upon exiting, he had formulated

and the idea of applying the mathematical method to philosophy. 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. Descartes arrived at this basic truth quite soon: his famous " I think, therefore I am."Durandin, Guy. 1970. ''Les Principes de la Philosophie. Introduction et notes''. Paris: Librairie Philosophique J. Vrin.

Career

France

In 1620, Descartes left the army. He visited Basilica della Santa Casa in Loreto, then visited various countries before returning to France, and during the next few years, he spent time in Paris. It was there that he composed his first essay on method: ''Regulae ad Directionem Ingenii'' ('' Rules for the Direction of the Mind''). He arrived in La Haye in 1623, selling all of his property to invest in bonds, which provided a comfortable income for the rest of his life. Descartes was present at the siege of La Rochelle by

Cardinal Richelieu Armand Jean du Plessis, 1st Duke of Richelieu (9 September 1585 – 4 December 1642), commonly known as Cardinal Richelieu, was a Catholic Church in France, French Catholic prelate and statesman who had an outsized influence in civil and religi ...

in 1627 as an observer.Shea, William R. 1991. ''The Magic of Numbers and Motion''. Science History Publications. There, he was interested in the physical properties of the great dike that Richelieu was building and studied mathematically everything he saw during the siege. He also met French mathematician Girard Desargues. In the autumn of that year, in the residence of the papal

nuncio An apostolic nuncio (; also known as a papal nuncio or simply as a nuncio) is an ecclesiastical diplomat, serving as an envoy or a permanent diplomatic representative of the Holy See to a state or to an international organization. A nuncio is ...

Guidi di Bagno, where he came with Mersenne and many other scholars to listen to a lecture given by the alchemist, Nicolas de Villiers, Sieur de Chandoux, on the principles of a supposed new philosophy, Cardinal Bérulle urged him to write an exposition of his new philosophy in some location beyond the reach of the Inquisition.

Netherlands

Descartes returned to the

in 1628. In April 1629, he joined the University of Franeker, studying under Adriaan Metius, either living with a Catholic family or renting the Sjaerdemaslot. The next year, under the name "Poitevin", he enrolled at

Leiden University Leiden University (abbreviated as ''LEI''; ) is a Public university, public research university in Leiden, Netherlands. Established in 1575 by William the Silent, William, Prince of Orange as a Protestantism, Protestant institution, it holds the d ...

, which at the time was a Protestant University. He studied both mathematics with Jacobus Golius, who confronted him with Pappus's hexagon theorem, and

astronomy Astronomy is a natural science that studies celestial objects and the phenomena that occur in the cosmos. It uses mathematics, physics, and chemistry in order to explain their origin and their overall evolution. Objects of interest includ ...

with Martin Hortensius. In October 1630, he had a falling-out with Beeckman, whom he accused of plagiarizing some of his ideas. In Amsterdam, he had a relationship with a servant girl, Helena Jans van der Strom, with whom he had a daughter, Francine, who was born in 1635 in

Deventer Deventer (; Sallaans dialect, Sallands: ) is a List of cities in the Netherlands by province, city and Municipalities of the Netherlands, municipality in the Salland historical region of the Provinces of the Netherlands, province of Overijssel, ...

. She was baptized a Protestant and died of scarlet fever at the age of 5. Unlike many moralists of the time, Descartes did not deprecate the passions but rather defended them; he wept upon Francine's death in 1640. According to a recent biography by Jason Porterfield, "Descartes said that he did not believe that one must refrain from tears to prove oneself a man."

Russell Shorto Russell Anthony Shorto (born February 8, 1959) is an American author, historian, and journalist. He is is best known for his book on the New Amsterdam, Dutch origins of New York City, ''The Island at the Center of the World''. Shorto's research ...

speculates that the experience of fatherhood and losing a child formed a turning point in Descartes's work, changing its focus from medicine to a quest for universal answers. Despite frequent moves, he wrote all of his major work during his 20-plus years in the Netherlands, initiating a revolution in mathematics and philosophy. In 1633, Galileo was condemned by the Italian Inquisition, and Descartes abandoned plans to publish '' Treatise on the World'', his work of the previous four years. Nevertheless, in 1637, he published parts 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 méthode'' (''

''). In it, Descartes lays out four rules of thought, meant to ensure that our knowledge rests upon a firm foundation: In ''La Géométrie'', Descartes exploited the discoveries he made with

Pierre de Fermat Pierre de Fermat (; ; 17 August 1601 – 12 January 1665) was a French mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality. In particular, he is recognized for his d ...

. This later became known as Cartesian geometry. Descartes continued to publish works concerning both mathematics and philosophy for the rest of his life. In 1641, he published a metaphysics treatise, ''Meditationes de Prima Philosophia'' (''Meditations on First Philosophy''), written in Latin and thus addressed to the learned. It was followed in 1644 by ''Principia Philosophiae'' ('' Principles of Philosophy''), a kind of synthesis of the ''Discourse on the Method'' and ''Meditations on First Philosophy''. In 1643, Cartesian philosophy was condemned at the University of Utrecht, and Descartes was obliged to flee to the Hague, settling in Egmond-Binnen. Between 1643 and 1649 Descartes lived with his girlfriend at Egmond-Binnen in an inn. Descartes became friendly with Anthony Studler van Zurck, lord of

Bergen Bergen (, ) is a city and municipalities of Norway, municipality in Vestland county on the Western Norway, west coast of Norway. Bergen is the list of towns and cities in Norway, second-largest city in Norway after the capital Oslo. By May 20 ...

, and participated in the design of his mansion and estate. He also met Dirck Rembrantsz van Nierop, a mathematician and surveyor. He was so impressed by Van Nierop's knowledge that he even brought him to the attention of Constantijn Huygens and Frans van Schooten. Christia Mercer suggested that Descartes may have been influenced by Spanish author and Roman Catholic nun Teresa of Ávila, who, fifty years earlier, published '' The Interior Castle'', concerning the role of philosophical reflection in intellectual growth.Mercer, C.
"Descartes' debt to Teresa of Ávila, or why we should work on women in the history of philosophy"
, '' Philosophical Studies'' 174, 2017. Descartes began (through Alfonso Polloti, an Italian general in Dutch service) a six-year correspondence with Princess Elisabeth of Bohemia, devoted mainly to moral and psychological subjects. Connected with this correspondence, in 1649 he published ''Les Passions de l'âme'' ('' The Passions of the Soul''), which he dedicated to the Princess. A French translation of ''Principia Philosophiae'', prepared by Abbot Claude Picot, was published in 1647. This edition was also dedicated to Princess Elisabeth. In the preface to the French edition, 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.

Sweden

Dispute-of-queen-cristina-vasa-and-rene-descartes

By 1649, Descartes had become one of Europe's most famous philosophers and scientists. That year, Queen Christina of Sweden invited him to her court to organize a new scientific academy and tutor her in his ideas about love. Descartes accepted, and moved to the

Swedish Empire The Swedish Empire or the Great Power era () was the period in Swedish history spanning much of the 17th and early 18th centuries during which Sweden became a European great power that exercised territorial control over much of the Baltic regi ...

in the middle of winter. Christina was interested in and stimulated Descartes to publish ''The Passions of the Soul''. He was a guest at the house of Pierre Chanut, living on Västerlånggatan, less than 500 meters from Castle Tre Kronor in Stockholm. There, Chanut and Descartes made observations with a Torricellian mercury barometer. Challenging

Blaise Pascal Blaise Pascal (19June 162319August 1662) was a French mathematician, physicist, inventor, philosopher, and Catholic Church, Catholic writer. Pascal was a child prodigy who was educated by his father, a tax collector in Rouen. His earliest ...

, Descartes took the first set of barometric readings in Stockholm to see if

atmospheric pressure Atmospheric pressure, also known as air pressure or barometric pressure (after the barometer), is the pressure within the atmosphere of Earth. The standard atmosphere (symbol: atm) is a unit of pressure defined as , which is equivalent to 1,013. ...

could be used in forecasting the weather.

Death

Descartes arranged to tutor Queen Christina after her birthday, three times a week at 5 am, in her cold and draughty castle. However, by 15 January 1650 the Queen had actually met with Descartes only four or five times. It soon became clear they did not like each other; she did not care for his mechanical philosophy, nor did he share her interest in

Ancient Greek language Ancient Greek (, ; ) includes the forms of the Greek language used in ancient Greece and the classical antiquity, ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Greek ...

and

literature Literature is any collection of Writing, written work, but it is also used more narrowly for writings specifically considered to be an art form, especially novels, Play (theatre), plays, and poetry, poems. It includes both print and Electroni ...

. On 1 February 1650, he contracted

pneumonia Pneumonia is an Inflammation, inflammatory condition of the lung primarily affecting the small air sacs known as Pulmonary alveolus, alveoli. Symptoms typically include some combination of Cough#Classification, productive or dry cough, ches ...

and died on 11 February at Chanut. The cause of death was pneumonia according to Chanut, but peripneumonia according to Christina's physician Johann van Wullen who was not allowed to bleed him. (The winter seems to have been mild, except for the second half of January which was harsh as described by Descartes himself; however, "this remark was probably intended to be as much Descartes's take on the intellectual climate as it was about the weather.") E. Pies has questioned this account, based on a letter by the Doctor van Wullen; however, Descartes had refused his treatment, and more arguments against its veracity have been raised since. In a 2009 book, German philosopher Theodor Ebert argues that Descartes was poisoned by Jacques Viogué, a Catholic missionary who opposed his religious views. As evidence, Ebert suggests that Catherine Descartes, the niece of René Descartes, made a veiled reference to the act of poisoning when her uncle was administered "communion" two days before his death, in her ''Report on the Death of M. Descartes, the Philosopher'' (1693). His last words were reported to have been: As a Catholic in a Protestant nation, he was interred in the churchyard of what was to become Adolf Fredrik Church in Stockholm, where mainly orphans had been buried. His manuscripts came into the possession of Claude Clerselier, Chanut's brother-in-law, and "a devout Catholic who has begun the process of turning Descartes into a saint by cutting, adding and publishing his letters selectively." In 1663, the

Pope The pope is the bishop of Rome and the Head of the Church#Catholic Church, visible head of the worldwide Catholic Church. He is also known as the supreme pontiff, Roman pontiff, or sovereign pontiff. From the 8th century until 1870, the po ...

placed Descartes's works on the ''Index of Prohibited Books''. In 1666, sixteen years after his death, his remains were taken to France and buried in Saint-Étienne-du-Mont. In 1671,

Louis XIV LouisXIV (Louis-Dieudonné; 5 September 16381 September 1715), also known as Louis the Great () or the Sun King (), was King of France from 1643 until his death in 1715. His verified reign of 72 years and 110 days is the List of longest-reign ...

prohibited all lectures in Cartesianism. Although the

National Convention The National Convention () was the constituent assembly of the Kingdom of France for one day and the French First Republic for its first three years during the French Revolution, following the two-year National Constituent Assembly and the ...

in 1792 had planned to transfer his remains to the Panthéon, he was reburied in the Abbey of Saint-Germain-des-Prés in 1819, missing a finger and the skull. His alleged skull is in the Musée de l'Homme in Paris, but some 2020 researches confirm that it may be a forgery. The original skull was probably divided into pieces in Sweden and given to private collectors; one of those pieces arrived at the University of Lund in 1691, where it is still preserved.

Philosophical work

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 or

Cartesian doubt Cartesian doubt is a form of methodological skepticism associated with the writings and methodology of René Descartes (March 31, 1596February 11, 1650). Cartesian doubt is also known as Cartesian skepticism, methodic doubt, methodological skeptic ...

: he rejects any ideas that can be doubted and then re-establishes them in order to acquire a firm foundation for genuine knowledge. Descartes built his ideas from scratch which he does in ''The Meditations on First Philosophy''. He relates this to architecture: the top soil is taken away to create a new building or structure. Descartes calls his doubt the soil and new knowledge the buildings. To Descartes, Aristotle's

foundationalism Foundationalism concerns philosophical theories of knowledge resting upon non-inferential justified belief, or some secure foundation of certainty such as a conclusion inferred from a basis of sound premises.Simon Blackburn, ''The Oxford Dict ...

is incomplete and his method of doubt enhances foundationalism. Initially, Descartes arrives at only a single first principle: he thinks. This is expressed in the Latin phrase in ''the Discourse on Method'' "

Cogito, ergo sum The Latin , usually translated into English as "I think, therefore I am", is the "first principle" of René Descartes's philosophy. He originally published it in French language, French as , in his 1637 ''Discourse on the Method'', so as to re ...

" (English: "I think, therefore I am"). 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." These two first principles—I think and I exist—were later confirmed by Descartes's clear and distinct perception (delineated in his Third Meditation from ''The Meditations''): as he clearly and distinctly perceives these two principles, Descartes reasoned, ensures their indubitability. 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 the person is immediately

conscious Consciousness, at its simplest, is awareness of a state or object, either internal to oneself or in one's external environment. However, its nature has led to millennia of analyses, explanations, and debate among philosophers, scientists, a ...

. He gave reasons for thinking that waking thoughts are distinguishable from dreams, and that one's mind cannot have been "hijacked" by an evil demon placing an illusory external world before one's senses. In this manner, Descartes proceeds to construct a system of knowledge, discarding

perception Perception () is the organization, identification, and interpretation of sensory information in order to represent and understand the presented information or environment. All perception involves signals that go through the nervous syste ...

as unreliable and, instead, admitting only deduction as a method.

Mind–body dualism

Descartes, influenced by the

automaton An automaton (; : automata or automatons) is a relatively self-operating machine, or control mechanism designed to automatically follow a sequence of operations, or respond to predetermined instructions. Some automata, such as bellstrikers i ...

s on display at the

Château de Saint-Germain-en-Laye The Château de Saint-Germain-en-Laye () is a former royal palace in the commune of Saint-Germain-en-Laye, in the department of Yvelines, about 19 km west of Paris, France. Today, it houses the '' Musée d'Archéologie nationale'' (Nationa ...

near Paris, investigated the connection between mind and body, and how they interact. His main influences for dualism were

theology Theology is the study of religious belief from a Religion, religious perspective, with a focus on the nature of divinity. It is taught as an Discipline (academia), academic discipline, typically in universities and seminaries. It occupies itse ...

and

physics Physics is the scientific study of matter, its Elementary particle, fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge whi ...

. The theory on the dualism of mind and body is Descartes's signature doctrine and permeates other theories he advanced. Known as Cartesian dualism (or mind–body dualism), his theory on the separation between the mind and the body went on to influence subsequent Western philosophies. In ''Meditations on First Philosophy'', Descartes attempted to demonstrate the existence of

God In monotheistic belief systems, God is usually viewed as the supreme being, creator, and principal object of faith. In polytheistic belief systems, a god is "a spirit or being believed to have created, or for controlling some part of the un ...

and the distinction between the human soul and the body. Humans are a union of mind and body; thus Descartes's dualism embraced the idea that mind and body are distinct but closely joined. While many contemporary readers of Descartes found the distinction between mind and body difficult to grasp, he thought it was entirely straightforward. Descartes employed the concept of ''modes'', which are the ways in which substances exist. In '' Principles of Philosophy'', Descartes explained, "we can clearly perceive a substance apart from the mode which we say differs from it, whereas we cannot, conversely, understand the mode apart from the substance". To perceive a mode apart from its substance requires an intellectual abstraction, which Descartes explained as follows:

The intellectual abstraction consists in my turning my thought away from one part of the contents of this richer idea the better to apply it to the other part with greater attention. Thus, when I consider a shape without thinking of the substance or the extension whose shape it is, I make a mental abstraction.

According to Descartes, two substances are really distinct when each of them can exist apart from the other. Thus, Descartes reasoned that God is distinct from humans, and the body and mind of a human are also distinct from one another. He argued that the great differences between body (an extended thing) and mind (an un-extended, immaterial thing) make the two ontologically distinct. According to Descartes's indivisibility argument, the mind is utterly indivisible: because "when I consider the mind, or myself in so far as I am merely a thinking thing, I am unable to distinguish any part within myself; I understand myself to be something quite single and complete." Moreover, in The ''Meditations'', Descartes discusses a piece of wax and exposes the single most characteristic doctrine of Cartesian dualism: that the universe contained two radically different kinds of substances—the mind or soul defined as thinking, and the body defined as matter and unthinking. The Aristotelian philosophy of Descartes's day held that the universe was inherently purposeful or teleological. Everything that happened, be it the motion of the

star A star is a luminous spheroid of plasma (physics), plasma held together by Self-gravitation, self-gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked eye at night sk ...

s or the growth of a

tree In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, e.g., including only woody plants with secondary growth, only ...

, was supposedly explainable by a certain purpose, goal or end that worked its way out within nature. Aristotle called this the "final cause", and these final causes were indispensable for explaining the ways nature operated. Descartes's theory of dualism supports the distinction between traditional Aristotelian science and the new science of

Kepler Johannes Kepler (27 December 1571 – 15 November 1630) was a German astronomer, mathematician, astrologer, natural philosopher and writer on music. He is a key figure in the 17th-century Scientific Revolution, best known for his laws of p ...

and Galileo, which denied the role of a divine power and "final causes" in its attempts to explain nature. Descartes's dualism provided the philosophical rationale for the latter by expelling the final cause from the physical universe (or ''res extensa'') in favor of the mind (or ''res cogitans''). Therefore, while Cartesian dualism paved the way for modern

, it also held the door open for religious beliefs about the immortality of the

soul The soul is the purported Mind–body dualism, immaterial aspect or essence of a Outline of life forms, living being. It is typically believed to be Immortality, immortal and to exist apart from the material world. The three main theories that ...

. Descartes's dualism of mind and matter implied a concept of human beings. A human was, according to Descartes, a composite entity of mind and body. Descartes gave priority to the mind and argued that the mind could exist without the body, but the body could not exist without the mind. In The ''Meditations'', Descartes even argues that while the mind is a substance, the body is composed only of "accidents". But he did argue that mind and body are closely joined:

Nature also teaches me, by the sensations of pain, hunger, thirst and so on, that I am not merely present in my body as a pilot in his ship, but that I am very closely joined and, as it were, intermingled with it, so that I and the body form a unit. If this were not so, I, who am nothing but a thinking thing, would not feel pain when the body was hurt, but would perceive the damage purely by the intellect, just as a sailor perceives by sight if anything in his ship is broken.

Descartes's discussion on embodiment raised one of the most perplexing problems of his dualism philosophy: What exactly is the relationship of union between the mind and the body of a person? Therefore, Cartesian dualism set the agenda for philosophical discussion of the

mind–body problem The mind–body problem is a List_of_philosophical_problems#Mind–body_problem, philosophical problem concerning the relationship between thought and consciousness in the human mind and Human body, body. It addresses the nature of consciousness ...

for many years after Descartes's death. Descartes was also a rationalist and believed in the power of

innate ideas In the philosophy of mind, innatism is the view that the mind is born with already-formed ideas, knowledge, and beliefs. The opposing doctrine, that the mind is a '' tabula rasa'' (blank slate) at birth and all knowledge is gained from experience ...

. Descartes argued the theory of innate knowledge and that all humans were born with knowledge through the higher power of God. It was this theory of innate knowledge that was later combated by philosopher

John Locke John Locke (; 29 August 1632 (Old Style and New Style dates, O.S.) – 28 October 1704 (Old Style and New Style dates, O.S.)) was an English philosopher and physician, widely regarded as one of the most influential of the Enlightenment thi ...

(1632–1704), an empiricist.

Empiricism In philosophy, empiricism is an epistemological view which holds that true knowledge or justification comes only or primarily from sensory experience and empirical evidence. It is one of several competing views within epistemology, along ...

holds that all knowledge is acquired through experience.

Physiology and psychology

In ''The Passions of the Soul'', published in 1649, Descartes discussed the common contemporary belief that the human body contained animal spirits. These animal spirits were believed to be light and roaming fluids circulating rapidly around the nervous system between the brain and the muscles. These animal spirits were believed to affect the human soul, or passions of the soul. Descartes distinguished six basic passions: wonder, love, hatred, desire, joy and sadness. All of these passions, he argued, represented different combinations of the original spirit, and influenced the soul to will or want certain actions. He argued, for example, that fear is a passion that moves the soul to generate a response in the body. In line with his dualist teachings on the separation between the soul and the body, he hypothesized that some part of the brain served as a connector between the soul and the body and singled out the pineal gland as connector. Descartes argued that signals passed from the ear and the eye to the pineal gland, through animal spirits. Thus different motions in the gland cause various animal spirits. He argued that these motions in the pineal gland are based on God's will and that humans are supposed to want and like things that are useful to them. But he also argued that the animal spirits that moved around the body could distort the commands from the pineal gland, thus humans had to learn how to control their passions. Descartes advanced a theory on automatic bodily reactions to external events, which influenced 19th-century reflex theory. He argued that external motions, such as touch and sound, reach the endings of the nerves and affect the animal spirits. For example, heat from fire affects a spot on the skin and sets in motion a chain of reactions, with the animal spirits reaching the brain through the central nervous system, and in turn, animal spirits are sent back to the muscles to move the hand away from the fire. Through this chain of reactions, the automatic reactions of the body do not require a thought process. Above all, he was among the first scientists who believed that the soul should be subject to scientific investigation. He challenged the views of his contemporaries that the soul was

divine Divinity (from Latin ) refers to the quality, presence, or nature of that which is divine—a term that, before the rise of monotheism, evoked a broad and dynamic field of sacred power. In the ancient world, divinity was not limited to a singl ...

, thus religious authorities regarded his books as dangerous. Descartes's writings went on to form the basis for theories on

emotion Emotions are physical and mental states brought on by neurophysiology, neurophysiological changes, variously associated with thoughts, feelings, behavior, behavioral responses, and a degree of pleasure or suffering, displeasure. There is ...

s and how

cognitive Cognition is the "mental action or process of acquiring knowledge and understanding through thought, experience, and the senses". It encompasses all aspects of intellectual functions and processes such as: perception, attention, thought, ...

evaluations were translated into affective processes. Descartes believed the brain resembled a working machine and that mathematics, and mechanics could explain complicated processes in it. In the 20th century,

Alan Turing Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher and theoretical biologist. He was highly influential in the development of theoretical computer ...

advanced

computer science Computer science is the study of computation, information, and automation. Computer science spans Theoretical computer science, theoretical disciplines (such as algorithms, theory of computation, and information theory) to Applied science, ...

based on

mathematical biology Mathematical and theoretical biology, or biomathematics, is a branch of biology which employs theoretical analysis, mathematical models and abstractions of living organisms to investigate the principles that govern the structure, development ...

as inspired by Descartes. His theories on reflexes also served as the foundation for advanced physiological theories, more than 200 years after his death. The physiologist Ivan Pavlov was a great admirer of Descartes.

On animals

Descartes denied that animals had reason or intelligence. He argued that animals did not lack sensations or perceptions, but these could be explained mechanistically. Whereas humans had a soul, or mind, and were able to feel

pain Pain is a distressing feeling often caused by intense or damaging Stimulus (physiology), stimuli. The International Association for the Study of Pain defines pain as "an unpleasant sense, sensory and emotional experience associated with, or res ...

and

anxiety Anxiety is an emotion characterised by an unpleasant state of inner wikt:turmoil, turmoil and includes feelings of dread over Anticipation, anticipated events. Anxiety is different from fear in that fear is defined as the emotional response ...

, animals by virtue of not having a soul could not feel pain or anxiety. If animals showed signs of distress then this was to protect the body from damage, but the innate state needed for them to suffer was absent. Although Descartes's views were not universally accepted, they became prominent in Europe and North America, allowing humans to treat animals with impunity. The view that animals were quite separate from humanity and merely

machine A machine is a physical system that uses power to apply forces and control movement to perform an action. The term is commonly applied to artificial devices, such as those employing engines or motors, but also to natural biological macromol ...

s allowed for the maltreatment of animals, and was sanctioned in law and societal norms until the middle of the 19th century. The publications of

Charles Darwin Charles Robert Darwin ( ; 12 February 1809 – 19 April 1882) was an English Natural history#Before 1900, naturalist, geologist, and biologist, widely known for his contributions to evolutionary biology. His proposition that all speci ...

would eventually erode the Cartesian view of animals. Darwin argued that the continuity between humans and other species suggested the possibility of animal suffering.

Moral philosophy

For Descartes,

ethics Ethics is the philosophy, philosophical study of Morality, moral phenomena. Also called moral philosophy, it investigates Normativity, normative questions about what people ought to do or which behavior is morally right. Its main branches inclu ...

was a science, the highest and most perfect of them. Like the rest of the sciences, ethics had its roots in metaphysics. In this way, he argues for the existence of God, investigates the place of man in nature, formulates the theory of mind–body dualism, and defends

free will Free will is generally understood as the capacity or ability of people to (a) choice, choose between different possible courses of Action (philosophy), action, (b) exercise control over their actions in a way that is necessary for moral respon ...

. However, as he was a convinced rationalist, Descartes clearly states that reason is sufficient in the search for the goods that individuals should seek, and

virtue A virtue () is a trait of excellence, including traits that may be morality, moral, social, or intellectual. The cultivation and refinement of virtue is held to be the "good of humanity" and thus is Value (ethics), valued as an Telos, end purpos ...

consists in the correct reasoning that should guide their actions. Nevertheless, the quality of this reasoning depends on knowledge and mental condition. For this reason, he said that a complete moral philosophy should include the study of the body. He discussed this subject in the correspondence with Princess Elisabeth of Bohemia, and as a result wrote his work ''The Passions of the Soul'', that contains a study of the psychosomatic processes and reactions in man, with an emphasis on emotions or passions.Blom, John J., Descartes. His moral philosophy and psychology. New York University Press. 1978. His works about human passion and emotion would be the basis for the philosophy of his followers (see Cartesianism), and would have a lasting impact on ideas concerning what literature and art should be, specifically how it should invoke emotion. Descartes and

Zeno Zeno may refer to: People * Zeno (name), including a list of people and characters with the given name * Zeno (surname) Philosophers * Zeno of Elea (), philosopher, follower of Parmenides, known for his paradoxes * Zeno of Citium (333 – 264 B ...

both identified sovereign goods with virtue. For

Epicurus Epicurus (, ; ; 341–270 BC) was an Greek philosophy, ancient Greek philosopher who founded Epicureanism, a highly influential school of philosophy that asserted that philosophy's purpose is to attain as well as to help others attain tranqui ...

, the sovereign good was pleasure, and Descartes says that, in fact, this is not in contradiction with Zeno's teaching, because virtue produces a spiritual pleasure that is better than bodily pleasure. Regarding

Aristotle Aristotle (; 384–322 BC) was an Ancient Greek philosophy, Ancient Greek philosopher and polymath. His writings cover a broad range of subjects spanning the natural sciences, philosophy, linguistics, economics, politics, psychology, a ...

's opinion that happiness (eudaimonia) depends on both moral virtue and also on the goods of fortune such as a moderate degree of wealth, Descartes does not deny that fortunes contributes to happiness, but remarks that they are in great proportion outside one's own control, whereas one's mind is under one's complete control. The moral writings of Descartes came at the last part of his life, but earlier, in his ''Discourse on the Method'', he adopted three maxims to be able to act while he put all his ideas into doubt. Those maxims are known as his "Provisional Morals".

Religion

In the third and fifth ''Meditation'', Descartes offers proofs of a benevolent God (the trademark argument and the ontological argument respectively). Descartes has faith in the account of reality his senses provide him, since he believed that God provided him with a working mind and

sensory system The sensory nervous system is a part of the nervous system responsible for processing sensory information. A sensory system consists of sensory neurons (including the sensory receptor cells), neural pathways, and parts of the brain involved ...

and does not desire to deceive him. From this supposition, however, Descartes finally establishes the possibility of acquiring knowledge about the world based on deduction and perception. Regarding

, therefore, Descartes can be said to have contributed such ideas as a conception of foundationalism and the possibility that

reason Reason is the capacity of consciously applying logic by drawing valid conclusions from new or existing information, with the aim of seeking the truth. It is associated with such characteristically human activities as philosophy, religion, scien ...

is the only reliable method of attaining knowledge. Descartes, however, was very much aware that experimentation was necessary to verify and validate theories. Descartes invokes his causal adequacy principle to support his trademark argument for the existence of God, quoting Lucretius in defence: ''"Ex nihilo nihil fit"'', meaning " Nothing comes from nothing" (

Lucretius Titus Lucretius Carus ( ; ; – October 15, 55 BC) was a Roman poet and philosopher. His only known work is the philosophical poem '' De rerum natura'', a didactic work about the tenets and philosophy of Epicureanism, which usually is t ...

). ''Oxford Reference'' summarises the argument, as follows, "that our idea of perfection is related to its perfect origin (God), just as a stamp or trademark is left in an article of workmanship by its maker." In the fifth Meditation, Descartes presents a version of the ontological argument which is founded on the possibility of thinking the "idea of a being that is supremely perfect and infinite," and suggests that "of all the ideas that are in me, the idea that I have of God is the most true, the most clear and distinct." Descartes considered himself to be a devout Catholic, and one of the purposes of the ''Meditations'' was to defend the Catholic faith. His attempt to ground theological beliefs on reason encountered intense opposition in his time. Pascal regarded Descartes's views as a rationalist and mechanist, and accused him of deism: "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," while a powerful contemporary, Martin Schoock, accused him of atheist beliefs, though Descartes had provided an explicit critique of atheism in his ''Meditations''. The Catholic Church prohibited his books in 1663.Descartes, René. (2009). ''Encyclopædia Britannica 2009 Deluxe Edition''. Chicago: Encyclopædia Britannica. Descartes also wrote a response to external world skepticism. Through this method of skepticism, he does not doubt for the sake of doubting but to achieve concrete and reliable information. In other words, certainty. He argues that sensory

s 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 argue 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. Descartes also believes a substance is something that does not need any assistance to function or exist. Descartes further explains how only God can be a true "substance". But minds are substances, meaning they need only God for it to function. The mind is a thinking substance. The means for a thinking substance stem from ideas. Descartes steered clear of theological questions, restricting his attention to showing that there is no incompatibility between his metaphysics and theological orthodoxy. He avoided trying to demonstrate theological dogmas metaphysically. When challenged that he had not established the immortality of the soul merely in showing that the soul and the body are distinct substances, he replied, "I do not take it upon myself to try to use the power of human reason to settle any of those matters which depend on the free will of God."

Mathematics

''x'' for unknown; exponential notation

Descartes "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 2 used in x² to indicate x squared.

Analytic geometry

One of Descartes's most enduring legacies was his development - together with

- of Cartesian or

, which uses algebra to describe geometry; the

is named after him. He was first to assign a fundamental place for algebra in the system of knowledge, using it as a method to automate or mechanize reasoning, particularly about abstract, unknown quantities. Both Descartes and Fermat were in their versions of analytic geometry inspired by the works of the Ancient Greek mathematicians

Pappus of Alexandria Pappus of Alexandria (; ; AD) was a Greek mathematics, Greek mathematician of late antiquity known for his ''Synagoge'' (Συναγωγή) or ''Collection'' (), and for Pappus's hexagon theorem in projective geometry. Almost nothing is known a ...

and Apollonius of Perga; especially by their techniques of analysis. Crucial for their work was also the symbolic algebra of François Viète and the results of Islamic mathematicians such as Sharaf al-Din al-Tusi and

Omar Khayyam Ghiyāth al-Dīn Abū al-Fatḥ ʿUmar ibn Ibrāhīm Nīshābūrī (18 May 1048 – 4 December 1131) (Persian language, Persian: غیاث الدین ابوالفتح عمر بن ابراهیم خیام نیشابورﻯ), commonly known as Omar ...

. The crucial step that their predecessors failed to take was using coordinates to study the relationship between geometry and algebra. European mathematicians had previously viewed geometry as a more fundamental form of mathematics, serving as the foundation of algebra. Algebraic rules were given geometric proofs by mathematicians such as

Pacioli Luca Bartolomeo de Pacioli, Order of Friars Minor, O.F.M. (sometimes ''Paccioli'' or ''Paciolo''; 1447 – 19 June 1517) was an Italian mathematician, Order of Friars Minor, Franciscan friar, collaborator with Leonardo da Vinci, and an early c ...

, Cardano, Tartaglia and

Ferrari Ferrari S.p.A. (; ) is an Italian luxury sports car manufacturer based in Maranello. Founded in 1939 by Enzo Ferrari (1898–1988), the company built Auto Avio Costruzioni 815, its first car in 1940, adopted its current name in 1945, and be ...

. Equations of degree higher than the third were regarded as unreal, because a three-dimensional form, such as a cube, occupied the largest dimension of reality. Descartes professed that the abstract quantity ''a²'' could represent length as well as an area. This was in opposition to the teachings of mathematicians such as François Viète, who insisted that a second power must represent an area. Although Descartes did not pursue the subject, he preceded

Gottfried Wilhelm Leibniz Gottfried Wilhelm Leibniz (or Leibnitz; – 14 November 1716) was a German polymath active as a mathematician, philosopher, scientist and diplomat who is credited, alongside Sir Isaac Newton, with the creation of calculus in addition to ...

in envisioning a more general science of algebra or "universal mathematics", as a precursor to

symbolic logic Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow from premises based on the structure o ...

, that could encompass logical principles and methods symbolically, and mechanize general reasoning.

Influence on Newton's mathematics

Current popular opinion holds that Descartes had the most influence of anyone on the young

Isaac Newton Sir Isaac Newton () was an English polymath active as a mathematician, physicist, astronomer, alchemist, theologian, and author. Newton was a key figure in the Scientific Revolution and the Age of Enlightenment, Enlightenment that followed ...

. Descartes's influence extended not directly from his original French edition of ''La Géométrie'', however, but rather from

Frans van Schooten Frans van Schooten Jr. also rendered as Franciscus van Schooten (15 May 1615 – 29 May 1660) was a Dutch mathematician who is most known for popularizing the analytic geometry of René Descartes. He translated La Géométrie in Latin and wrote c ...

's expanded second Latin edition of the work. Newton continued Descartes's work on

cubic equation In algebra, a cubic equation in one variable is an equation of the form ax^3+bx^2+cx+d=0 in which is not zero. The solutions of this equation are called roots of the cubic function defined by the left-hand side of the equation. If all of th ...

s, which freed the subject from the fetters of the Greek perspectives. The most important concept was his very modern treatment of single variables.

The basis of calculus

Descartes's work provided the basis for the

developed by Leibniz and Newton, who applied the infinitesimal calculus to the tangent line problem, thus permitting the evolution of that branch of modern mathematics. His rule of signs is also a commonly used method to determine the number of positive and negative roots of a polynomial.

Physics

Philosophy, metaphysics, and physics

Descartes is often regarded as the first thinker to emphasize the use of reason to develop the

natural science Natural science or empirical science is one of the branches of science concerned with the description, understanding and prediction of natural phenomena, based on empirical evidence from observation and experimentation. Mechanisms such as peer ...

s. For him, philosophy was a thinking system that embodied all knowledge, as he related in a letter to a French translator:

Mechanics

Mechanical philosophy

The beginning of Descartes's interest in physics is accredited to the amateur scientist and mathematician Isaac Beeckman, whom he met in 1618, and who was at the forefront of a new school of thought known as mechanical philosophy. With this foundation of reasoning, Descartes formulated many of his theories on mechanical and geometric physics. It is said that they met when both were looking at a placard that was set up in the Breda marketplace, detailing a mathematical problem to be solved. Descartes asked Beeckman to translate the problem from Dutch to French. In their following meetings Beeckman interested Descartes in his corpuscularian approach to mechanical theory, and convinced him to devote his studies to a mathematical approach to nature. In 1628, Beeckman also introduced him to many of

's ideas.Harold J. Cook, in ''The Scientific Revolution in National Context'',

Roy Porter Roy Sydney Porter (31 December 1946 – 3 March 2002) was a British historian known for his work on the history of medicine. He retired in 2001 as the director of the Wellcome Institute for the History of Medicine at University College London ...

, Mikuláš Teich, (eds.), Cambridge University Press, 1992, pages 127–129 Together, they worked on

free fall In classical mechanics, free fall is any motion of a physical object, body where gravity is the only force acting upon it. A freely falling object may not necessarily be falling down in the vertical direction. If the common definition of the word ...

, catenaries,

conic section A conic section, conic or a quadratic curve is a curve obtained from a cone's surface intersecting a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a special case of the ellipse, tho ...

s, and

fluid statics In physics, a fluid is a liquid, gas, or other material that may continuously move and deform (''flow'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot r ...

. Both believed that it was necessary to create a method that thoroughly linked mathematics and physics.

Anticipating the concept of work

Although the concept of work (in physics) was not formally used until 1826, similar concepts existed before then. In 1637, Descartes wrote:

Conservation of motion

In '' Principles of Philosophy'' (''Principia Philosophiae'') from 1644 Descartes outlined his views on the universe. In it he describes his three laws of motion. ( Newton's own laws of motion would later be modeled on Descartes's exposition.) Descartes defined "quantity of motion" (''

Latin Latin ( or ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European languages. Latin was originally spoken by the Latins (Italic tribe), Latins in Latium (now known as Lazio), the lower Tiber area aroun ...

: quantitas motus'') as the product of size and speed, and claimed that the total quantity of motion in the universe is conserved.Descartes had discovered an early form of the law of

conservation of momentum In Newtonian mechanics, momentum (: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction. ...

. He envisioned quantity of motion as pertaining to motion in a straight line, as opposed to perfect circular motion, as Galileo had envisioned it.Alexander Afriat
"Cartesian and Lagrangian Momentum"
(2004). Descartes's discovery should not be seen as the modern law of conservation of momentum, since it had no concept of mass as distinct from weight or size, and since he believed that it is speed rather than velocity that is conserved.

Planetary motion and gravity

Descartes's vortex theory of planetary motion was later rejected by Newton in favor of his law of universal gravitation, and most of the second book of Newton's '' Principia'' is devoted to his counterargument.

Magnetism

Descartes proposed a theory to explain magnetism and explain the observation in ''De Magnete'' by William Gilbert. Descartes considered that 'effluvia' were emitted by a magnet, the effluvia rarefied the air creating pressure differences, and thus forces.

Glass science

In 1644, Descartes provides one of the earliest microscopic theories of

glass Glass is an amorphous (non-crystalline solid, non-crystalline) solid. Because it is often transparency and translucency, transparent and chemically inert, glass has found widespread practical, technological, and decorative use in window pane ...

. He considered that glass was formed by particles frozen in motion after heated. He also provides one of the earliest understanding of the role of stress and its relief by annealing.

Optics

Descartes also made contributions to the field of

optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of optical instruments, instruments that use or Photodetector, detect it. Optics usually describes t ...

. He showed by using geometric construction and the law of refraction (also known as Descartes's law in France, or more commonly Snell's law elsewhere) that the angular radius of a

rainbow A rainbow is an optical phenomenon caused by refraction, internal reflection and dispersion of light in water droplets resulting in a continuous spectrum of light appearing in the sky. The rainbow takes the form of a multicoloured circular ...

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.

Meteorology

Within ''

'', there is an appendix in which Descartes discusses his theories on

Meteorology Meteorology is the scientific study of the Earth's atmosphere and short-term atmospheric phenomena (i.e. weather), with a focus on weather forecasting. It has applications in the military, aviation, energy production, transport, agricultur ...

known as ''Les Météores''. He first proposed the idea that the elements were made up of small particles that join together imperfectly, thus leaving small spaces in between. These spaces were then filled with smaller much quicker "subtile matter". These particles were different based on what element they constructed, for example, Descartes believed that particles of water were "like little eels, which, though they join and twist around each other, do not, for all that, ever knot or hook together in such a way that they cannot easily be separated." In contrast, the particles that made up the more solid material, were constructed in a way that generated irregular shapes. The size of the particle also matters; if the particle was smaller, not only was it faster and constantly moving, it was more easily agitated by the larger particles, which were slow but had more force. The different qualities, such as combinations and shapes, gave rise to different secondary qualities of materials, such as temperature. This first idea is the basis for the rest of Descartes's theory on meteorology. While rejecting most of

's theories on meteorology, he still kept some of the terminology that Aristotle used such as vapors and exhalations. These "vapors" would be drawn into the sky by the sun from "terrestrial substances" and would generate wind. Descartes also theorized that falling clouds would displace the air below them, also generating wind. Falling clouds could also generate thunder. He theorized that when a cloud rests above another cloud and the air around the top cloud is hot, it condenses the vapor around the top cloud, and causes the particles to fall. When the particles falling from the top cloud collided with the bottom cloud's particles it would create thunder. He compared his theory on thunder to his theory on avalanches. Descartes believed that the booming sound that avalanches created, was due to snow that was heated, and therefore heavier, falling onto the snow that was below it. This theory was supported by experience "It follows that one can understand why it thunders more rarely in winter than in summer; for then not enough heat reaches the highest clouds, in order to break them up." Another theory that Descartes had was on the production of lightning. Descartes believed that lightning was caused by exhalations trapped between the two colliding clouds. He believed that in order to make these exhalations viable to produce lightning, they had to be made "fine and inflammable" by hot and dry weather. Whenever the clouds would collide, it would cause them to ignite, creating lightning; if the cloud above was heavier than the bottom cloud, it would also produce thunder. Descartes also believed that clouds were made up of drops of water and ice, and believed that rain would fall whenever the air could no longer support them. It would fall as snow if the air was not warm enough to melt the raindrops. And hail was when the cloud drops would melt, and then freeze again because cold air would refreeze them. Descartes did not use mathematics or instruments (as there were not any at the time) to back up his theories on Meteorology and instead used qualitative reasoning in order to deduce his hypothesis.

Historical impact

Emancipation from Church doctrine

Descartes has often been dubbed the father of modern

Western philosophy Western philosophy refers to the Philosophy, philosophical thought, traditions and works of the Western world. Historically, the term refers to the philosophical thinking of Western culture, beginning with the ancient Greek philosophy of the Pre ...

, the thinker whose approaches have profoundly changed the course of Western philosophy and set the basis for

modernity Modernity, a topic in the humanities and social sciences, is both a historical period (the modern era) and the ensemble of particular Society, socio-Culture, cultural Norm (social), norms, attitudes and practices that arose in the wake of the ...

. The first two of his ''Meditations on First Philosophy'', those that formulate the famous methodic doubt, represent the portion of Descartes's writings that most influenced modern thinking. It has been argued that Descartes himself did not realize the extent of this revolutionary move. In shifting the debate from "what is true" to "of what can I be certain?", Descartes arguably shifted the authoritative guarantor of truth from God to humanity (even though Descartes himself claimed he received his visions from God)—while the traditional concept of "truth" implies an external authority, "certainty" instead relies on the judgment of the individual. In an anthropocentric revolution, the human being is now raised to the level of a subject, an agent, an emancipated being equipped with autonomous reason. This was a revolutionary step that established the basis of modernity, the repercussions of which are still being felt: the emancipation of humanity from Christian

revelation Revelation, or divine revelation, is the disclosing of some form of Religious views on truth, truth or Knowledge#Religion, knowledge through communication with a deity (god) or other supernatural entity or entities in the view of religion and t ...

al truth and Church doctrine; humanity making its own law and taking its own stand.

Martin Heidegger Martin Heidegger (; 26 September 1889 – 26 May 1976) was a German philosopher known for contributions to Phenomenology (philosophy), phenomenology, hermeneutics, and existentialism. His work covers a range of topics including metaphysics, art ...

938(2002) '' The Age of the World Picture'' quotation: Ingraffia, Brian D. (1995
''Postmodern theory and biblical theology: vanquishing God's shadow''
p. 126 In modernity, the guarantor of truth is not God anymore but human beings, each of whom is a "self-conscious shaper and guarantor" of their own reality. In that way, each person is turned into a reasoning adult, a subject and agent,Lovitt, Tom (1977) introduction to

's ''The question concerning technology, and other essays'', pp. xxv–xxvi as opposed to a child obedient to God. This change in perspective was characteristic of the shift from the Christian medieval period to the modern period, a shift that had been anticipated in other fields, and which was now being formulated in the field of philosophy by Descartes. This anthropocentric perspective of Descartes's work, establishing human reason as autonomous, provided the basis for the Enlightenment's emancipation from God and the Church. According to

, the perspective of Descartes's work also provided the basis for all subsequent

anthropology Anthropology is the scientific study of humanity, concerned with human behavior, human biology, cultures, society, societies, and linguistics, in both the present and past, including archaic humans. Social anthropology studies patterns of behav ...

.Heidegger 938(2002), p. 75 quotation: Descartes's philosophical revolution is sometimes said to have sparked modern

anthropocentrism Anthropocentrism ( ) is the belief that human beings are the central or most important entity on the planet. The term can be used interchangeably with humanocentrism, and some refer to the concept as human supremacy or human exceptionalism. From a ...

and

subjectivism Subjectivism is the doctrine that "our own mental activity is the only unquestionable fact of our experience", instead of shared or communal, and that there is no external or objective truth. While Thomas Hobbes was an early proponent of subjecti ...

Contemporary reception

In commercial terms, The ''Discourse'' appeared during Descartes's lifetime in a single edition of 500 copies, 200 of which were set aside for the author. Sharing a similar fate was the only French edition of The ''Meditations'', which had not managed to sell out by the time of Descartes's death. A concomitant Latin edition of the latter was, however, eagerly sought out by Europe's scholarly community and proved a commercial success for Descartes. 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. According to philosophy professor John Cottingham, Descartes's ''Meditations on First Philosophy'' is considered to be "one of the key texts of Western philosophy". Cottingham said that the ''Meditations'' is the "most widely studied of all Descartes' writings". According to Anthony Gottlieb, a former senior editor of ''

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'', and the author of '' The Dream of Reason'' and '' The Dream of Enlightenment'', one of the reasons Descartes and

Thomas Hobbes Thomas Hobbes ( ; 5 April 1588 – 4 December 1679) was an English philosopher, best known for his 1651 book ''Leviathan (Hobbes book), Leviathan'', in which he expounds an influential formulation of social contract theory. He is considered t ...

continue to be debated in the second decade of the twenty-first century, is that they still have something to say to us that remains relevant on questions such as, "What does the advance of science entail for our understanding of ourselves and our ideas of God?" and "How is government to deal with religious diversity." In her 2018 interview with Tyler Cowen, Agnes Callard described Descartes's thought experiment in the ''Meditations'', where he encouraged a complete, systematic doubting of everything that you believe, to "see what you come to". She said, "What Descartes comes to is a kind of real truth that he can build upon inside of his own mind." She said that

Hamlet ''The Tragedy of Hamlet, Prince of Denmark'', often shortened to ''Hamlet'' (), is a Shakespearean tragedy, tragedy written by William Shakespeare sometime between 1599 and 1601. It is Shakespeare's longest play. Set in Denmark, the play (the ...

's monologues"meditations on the nature of life and emotion"were similar to Descartes's thought experiment. Hamlet/Descartes were "apart from the world", as if they were "trapped" in their own heads. Cowen asked Callard if Descartes actually found any truths through his thought experiment or was it just "an earlier version of the contemporary argument that we're living in a simulation, where the evil demon is the simulation rather than Bayesian reasoning?" Callard agreed that this argument can be traced to Descartes, who had said that he had refuted it. She clarified that in Descartes's reasoning, you do "end up back in the mind of God"in a "universe God has created" that is the "real world"...The whole question is about being connected to reality as opposed to being a figment. If you're living in the world God created, God can create real things. So you're living in a real world."

Purported Rosicrucianism

The membership of Descartes to the Rosicrucians is debated. The initials of his name have been linked to the R.C.

acronym An acronym is a type of abbreviation consisting of a phrase whose only pronounced elements are the initial letters or initial sounds of words inside that phrase. Acronyms are often spelled with the initial Letter (alphabet), letter of each wor ...

widely used by Rosicrucians. Furthermore, in 1619 Descartes moved to Ulm which was a well renowned international center of the Rosicrucian movement. During his journey in Germany, he met Johannes Faulhaber who had previously expressed his personal commitment to join the brotherhood. Descartes dedicated the work titled ''The Mathematical Treasure Trove of Polybius, Citizen of the World'' to "learned men throughout the world and especially to the distinguished B.R.C. (Brothers of the Rosy Cross) in Germany". The work was not completed and its publication is uncertain.

Bibliography

Writings

* 1618
''Musicae Compendium''
A treatise on music theory and the aesthetics of music, which Descartes dedicated to early collaborator Isaac Beeckman (written in 1618, first published—posthumously—in 1650). * 1626–1628. ''Regulae ad directionem ingenii'' ('' Rules for the Direction of the Mind''). Incomplete. First published posthumously in Dutch translation in 1684 and in the original Latin at Amsterdam in 1701 (''R. Des-Cartes Opuscula Posthuma Physica et Mathematica''). The best critical edition, which includes the Dutch translation of 1684, is edited by Giovanni Crapulli (The Hague: Martinus Nijhoff, 1966). * c. 1630. ''De solidorum elementis''. Concerns the classification of

Platonic solid In geometry, a Platonic solid is a Convex polytope, convex, regular polyhedron in three-dimensional space, three-dimensional Euclidean space. Being a regular polyhedron means that the face (geometry), faces are congruence (geometry), congruent (id ...

s and three-dimensional figurate numbers. Said by some scholars to prefigure Euler's polyhedral formula. Unpublished; discovered in Descartes's estate in Stockholm 1650, soaked for three days in the Seine in a shipwreck while being shipped back to Paris, copied in 1676 by Leibniz, and lost. Leibniz's copy, also lost, was rediscovered circa 1860 in Hannover. * 1630–1631. ''La recherche de la vérité par la lumière naturelle'' ('' The Search for Truth by Natural Light'') unfinished dialogue published in 1701. * 1630–1633. ''Le Monde'' ('' The World'') 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'' (''

''). An introduction to the ''Essais'', which include the '' Dioptrique'', the ''Météores'' and the ''Géométrie''. * 1637. '' La Géométrie'' (''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''), also known as ''Metaphysical Meditations''. In Latin; a second edition, published the following year, included an additional objection and reply, and a ''Letter to Dinet''. A French translation by the

Duke of Luynes The Duke of Luynes ( ) is a territorial name belonging to the noble France, French house d'Albert. Luynes, Indre-et-Loire, Luynes is, today, a commune in France, commune of the Indre-et-Loire ''département in France, département'' in France. The ...

, probably done without Descartes's supervision, was published in 1647. Includes six Objections and Replies. * 1644. ''Principia philosophiae'' ('' Principles of Philosophy''), 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 Princess Elisabeth of Bohemia. * 1647. ''Notae in programma'' (''Comments on a Certain Broadsheet''). A reply to Descartes's one-time disciple Henricus Regius. * 1648. ''La description du corps humain'' ('' The Description of the Human Body''). Published posthumously by Clerselier in 1667. * 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''). Dedicated to Princess Elisabeth of the Palatinate. * 1657. ''Correspondance'' (three volumes: 1657, 1659, 1667). 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

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. Bos found the letter mentioned in a summary of autographs kept by

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in Haverford, 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. File:Handwritten letter by Descartes December 1638.jpg, Handwritten letter by Descartes, December 1638 File:René Descartes 1644 Principia philosophiae.jpg, ''Principia philosophiae'', 1644

Collected editions

* ''Oeuvres de Descartes'' edited by Charles Adam and Paul Tannery, Paris: Léopold Cerf, 1897–1913, 13 volumes; new revised edition, Paris: Vrin-CNRS, 1964–1974, 11 volumes (the first five volumes contain the correspondence). his edition is traditionally cited with the initials ''AT'' (for Adam and Tannery) followed by a volume number in Roman numerals; thus ''AT'' VII refers to ''Oeuvres de Descartes'' volume 7.* ''Étude du bon sens, La recherche de la vérité et autres écrits de jeunesse (1616–1631)'' edited by Vincent Carraud and Gilles Olivo, Paris: PUF, 2013. * Descartes, ''Œuvres complètes'', new edition by Jean-Marie Beyssade and Denis Kambouchner, Paris: Gallimard, published volumes: ** I: ''Premiers écrits. Règles pour la direction de l'esprit'', 2016. ** III: ''Discours de la Méthode et Essais'', 2009. ** VIII.1: ''Correspondance, 1'' edited by Jean-Robert Armogathe, 2013. ** VIII.2: ''Correspondance, 2'' edited by Jean-Robert Armogathe, 2013. * ''René Descartes. Opere 1637–1649'', Milano, Bompiani, 2009, pp. 2531. Edizione integrale (di prime edizioni) e traduzione italiana a fronte, a cura di G. Belgioioso con la collaborazione di I. Agostini, M. Marrone, M. Savini . * ''René Descartes. Opere 1650–2009'', Milano, Bompiani, 2009, pp. 1723. Edizione integrale delle opere postume e traduzione italiana a fronte, a cura di G. Belgioioso con la collaborazione di I. Agostini, M. Marrone, M. Savini . * ''René Descartes. Tutte le lettere 1619–1650'', Milano, Bompiani, 2009 IIa ed., pp. 3104. Nuova edizione integrale dell'epistolario cartesiano con traduzione italiana a fronte, a cura di G. Belgioioso con la collaborazione di I. Agostini, M. Marrone, F.A. Meschini, M. Savini e J.-R. Armogathe . * ''René Descartes, Isaac Beeckman, Marin Mersenne. Lettere 1619–1648'', Milano, Bompiani, 2015 pp. 1696. Edizione integrale con traduzione italiana a fronte, a cura di Giulia Beglioioso e Jean Robert-Armogathe .

Early editions of specific works

''Discours de la methode''
, 1637
''Renati Des-Cartes Principia philosophiæ''
, 1644
''Le monde de Mr. Descartes ou le traité de la lumiere''
, 1664
''Geometria''
, 1659
''Meditationes de prima philosophia''
, 1670
''Opera philosophica''
, 1672

Collected English translations

* 1955. ''The Philosophical Works'', E.S. Haldane and G.R.T. Ross, trans. Dover Publications. This work is traditionally cited with the initials ''HR'' (for Haldane and Ross) followed by a volume number in Roman numerals; thus ''HR'' II refers to volume 2 of this edition. * 1988. ''The Philosophical Writings of Descartes'' in 3 vols. Cottingham, J., Stoothoff, R., Kenny, A., and Murdoch, D., trans. Cambridge University Press. This work is traditionally cited with the initials ''CSM'' (for Cottingham, Stoothoff, and Murdoch) or ''CSMK'' (for Cottingham, Stoothoff, Murdoch, and Kenny) followed by a volume number in Roman numeral; thus ''CSM'' II refers to volume 2 of this edition. * 1998. ''René Descartes: The World and Other Writings.'' Translated and edited by Stephen Gaukroger. Cambridge University Press. (This consists mainly of scientific writings, on physics, biology, astronomy, optics, etc., which were very influential in the 17th and 18th centuries, but which are routinely omitted or much abridged in modern collections of Descartes's ''philosophical'' works.)

Translation of single works

* 1628
''Regulae ad directionem ingenii. Rules for the Direction of the Natural Intelligence. A Bilingual Edition of the Cartesian Treatise on Method''
, ed. & trans. G. Heffernan (Amsterdam/Atlanta: Rodopi, 1998). * 1633

, tr. by Michael S. Mahoney. * 1633. ''Treatise of Man'', tr. by T. S. Hall. Cambridge, MA: Harvard University Press, 1972. * 1637. ''Discourse on the Method, Optics, Geometry and Meteorology'', trans. P. J. Olscamp, Revised edition (Indianapolis: Hackett, 2001). * 1637
''The Geometry of René Descartes''
, trans. D. E. Smith & Marcia Latham (Chicago: Open Court, 1925). * 1641. ''Meditations on First Philosophy'', tr. by J. Cottingham, Cambridge: Cambridge University Press, 1996. Latin original. Alternative English title: ''Metaphysical Meditations''. Includes six ''Objections and Replies''. A second edition published the following year, includes an additional ''Objection and Reply'' and a ''Letter to Dinet''
HTML Online Latin-French-English Edition
. * 1644
''Principles of Philosophy''
, trans. V. R. Miller & R. P. Miller: (

/Boston/London:

Kluwer Academic Publishers Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing. Originally founded in 1842 in ...

, 1982). * 1648. ''Descartes' Conversation with Burman'', tr. by J. Cottingham, Oxford: Clarendon Press, 1989. * 1649
''Passions of the Soul''
, trans. S. H. Voss (Indianapolis: Hackett, 1989). Dedicated to Elisabeth of the Palatinate. * 1619–1648. ''René Descartes, Isaac Beeckman, Marin Mersenne. Lettere 1619–1648'', ed. by Giulia Beglioioso and Jean Robert-Armogathe, Milano, Bompiani, 2015 pp. 1696.

Notes

References

Citations

Sources

* * * * Farrell, John. "Demons of Descartes and Hobbes." ''Paranoia and Modernity: Cervantes to Rousseau'' (Cornell UP, 2006), chapter 7. * * Gillespie, A. (2006)
Descartes' Demon: A Dialogical Analysis of 'Meditations on First Philosophy.'
''Theory & Psychology'', 16, 761–781. * * Grayling, A. C. (2005). ''Descartes: The Life of René Descartes and Its Place in His Times'', The Free Press, London. . * Heidegger, Martin 938(2002) ''The Age of the World Picture'' i
''Off the Beaten Track''
pp. 57–85 * Monnoyeur, Françoise (November 2017), ''Matière et espace dans le système cartésien'', Paris, Harmattan, 266 pp. . * Moreno Romo, Juan Carlos, ''Vindicación del cartesianismo radical'', Anthropos, Barcelona, 2010. * Moreno Romo, Juan Carlos (Coord.), ''Descartes vivo. Ejercicios de hermenéutica cartesiana'', Anthropos, Barcelona, 2007. * Negri, Antonio (2007) ''The Political Descartes'', Verso. * Sasaki Chikara (2003)
''Descartes's Mathematical Thought''
. (Boston Studies in the Philosophy of Science, 237.) xiv + 496 pp., bibl., indexes. Dordrecht/Boston/London: Kluwer Academic Publishers. * Serfati, Michel, 2005, "Géometrie" in Ivor Grattan-Guinness, ed., ''Landmark Writings in Western Mathematics''. Elsevier: 1–22. * Watson, Richard A. (2007). Cogito, Ergo Sum: a life of René Descartes. David R Godine. 2002, reprint 2007. . Was chosen by the New York Public library as one of "25 Books to Remember from 2002" * Frisinger, H. Howard. “Chapter 3 .” The History of Meteorology: To 1800, American Meteorological Society, Boston, MA, 1983, pp. 37–40. * Martin, Craig. “Chapter 6.” Renaissance Meteorology: Pomponazzi to Descartes, Johns Hopkins University Press, Baltimore, MD, 2011.

External links

Digital collections

* * * *
EarlyModernTexts.com
A site containing Descartes's main works, including correspondence, slightly modified for easier reading

Physical collections

The Correspondence of René Descartes
i
Early Modern Letters Online

Biographical links

at MacTutor *
René Descartes (1596–1650)
Published in ''Encyclopedia of Rhetoric and Composition'' (1996) *

Bibliographies and works

''Bibliografia cartesiana/Bibliographie cartésienne on-line (1997–2012)''
*

''
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Descartes

Life and works

Epistemology

Mathematics

Physics

Ethics

Modal Metaphysics

Ontological Argument

Theory of Ideas

Pineal Gland

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Descartes

Descartes: Ethics

Descartes: Mind-Body Distinction

Descartes: Scientific Method

Other

* Video: Bryan Magee interviews Bernard Williams about Descartes on ''Men of ideas''
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from Physicist Jacob Bourjaily's collection of Banknotes featuring Scientists and Mathematicians
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