René Descartes
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René Descartes ( or ; ; 31 March 1596 – 11 February 1650) was a
French philosopher French philosophy, here taken to mean philosophy in the French language, has been extremely diverse and has influenced Western philosophy as a whole for centuries, from the medieval scholasticism of Peter Abelard, through the founding of modern ph ...
, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science. Mathematics was paramount to his method of inquiry, and he connected the previously separate fields of geometry and algebra into
analytic geometry In classical 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 engineerin ...
. Descartes spent much of his working life in the Dutch Republic, initially serving the Dutch States Army, and later becoming a central intellectual of the
Dutch Golden Age The Dutch Golden Age ( nl, Gouden Eeuw ) was a period in the history of the Netherlands, roughly spanning the era from 1588 (the birth of the Dutch Republic) to 1672 (the Rampjaar, "Disaster Year"), in which Dutch trade, science, and Dutch art, ...
. Although he served a Protestant state and was later counted as a deist by critics, Descartes was Roman Catholic. Many elements of Descartes' philosophy have precedents in late Aristotelianism, the revived Stoicism of the 16th century, or in earlier philosophers like Augustine. In his natural philosophy, he differed from the schools on two major points. First, he rejected the splitting of corporeal substance into matter 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 In his final philosophical treatise, ''The Passions of the Soul'' (french: Les Passions de l'âme), completed in 1649 and dedicated to Princess Elisabeth of Bohemia, René Descartes contributes to a long tradition of philosophical inquiry into the ...
'', an early modern 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 " la, link=no, cogito, ergo sum, label=none" ("I think, therefore I am"; french: link=no, Je pense, donc je suis), found in '' Discourse on the Method'' (1637, in French and Latin, 1644) and ''
Principles of Philosophy ''Principles of Philosophy'' ( la, Principia Philosophiae) is a book by René Descartes. In essence, it is a synthesis of the ''Discourse on Method'' and ''Meditations on First Philosophy''.Guy Durandin, ''Les Principes de la Philosophie. Intro ...
'' (1644, in Latin, 1647 in French). The statement has either been interpreted as a logical
syllogism A syllogism ( grc-gre, συλλογισμός, ''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. ...
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 in the 17th century. Bertrand Russell (2004
''History of western philosophy''
pp. 511, 516–17.
He laid the foundation for 17th-century continental rationalism, later advocated by Spinoza and Leibniz, and was later opposed by the
empiricist In philosophy, empiricism is an epistemological theory that holds that knowledge or justification comes only or primarily from sensory experience. It is one of several views within epistemology, along with rationalism and skepticism. Empir ...
school of thought consisting of Hobbes,
Locke Locke may refer to: People *John Locke, English philosopher *Locke (given name) *Locke (surname), information about the surname and list of people Places in the United States *Locke, California, a town in Sacramento County *Locke, Indiana *Locke, ...
,
Berkeley Berkeley most often refers to: *Berkeley, California, a city in the United States **University of California, Berkeley, a public university in Berkeley, California * George Berkeley (1685–1753), Anglo-Irish philosopher Berkeley may also refer ...
, and
Hume Hume most commonly refers to: * David Hume (1711–1776), Scottish philosopher Hume may also refer to: People * Hume (surname) * Hume (given name) * James Hume Nisbet (1849–1923), Scottish-born novelist and artist In fiction * Hume, the ...
. 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 reason, or the Enlightenment, was an intellectual and philosophical movement that dominated the world of ideas in Europe during the 17th to 19th centuries. Age of reason or Age of Reason may also refer to: * Age of reason (canon law), ...
" 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. Descartes' '' Meditations on First Philosophy'' (1641) continues to be a standard text at most university philosophy departments. Descartes' influence in mathematics is equally apparent, being the namesake of the
Cartesian coordinate system A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in t ...
. He is credited as the father of analytic geometry—used in the discovery of infinitesimal calculus and analysis. Descartes was also one of the key figures in the Scientific Revolution.


Life


Early life

René Descartes was born in La Haye en Touraine, Province of Touraine (now Descartes, Indre-et-Loire), France, on 31 March 1596. In May 1597, his mother Jeanne Brochard, died a few days after giving birth to a still-born child. Descartes' father, Joachim, was a member of the
Parlement of Rennes The Parlement of Rennes or Parlement of Brittany (, ) was one of the , a court of justice under the French , with its seat at Rennes. The last building to house the Parlement still stands and now houses the Rennes Court of Appeal (France), Court o ...
at
Rennes Rennes (; br, Roazhon ; Gallo: ''Resnn''; ) is a city in the east of Brittany in northwestern France at the confluence of the Ille and the Vilaine. Rennes is the prefecture of the region of Brittany, as well as the Ille-et-Vilaine department ...
. René lived with his grandmother and with his great-uncle. Although the Descartes family was Roman Catholic, the Poitou region was controlled by the Protestant Huguenots. In 1607, late because of his fragile health, he entered the
Jesuit , image = Ihs-logo.svg , image_size = 175px , caption = ChristogramOfficial seal of the Jesuits , abbreviation = SJ , nickname = Jesuits , formation = , founders ...
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 15. * ''Lycées'' () provide a three-year course of further secondary education for children 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) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...
'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, earning a ''
Baccalauréat The ''baccalauréat'' (; ), often known in France colloquially as the ''bac'', is a French national academic qualification that students can obtain at the completion of their secondary education (at the end of the ''lycée'') by meeting certain ...
'' and ''
Licence A license (or licence) 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 party (licensee) as an element of an agreeme ...
'' 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. In '' Discourse on the Method'', 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, the Protestant Dutch States Army in
Breda Breda () is a city and municipality in the southern part of the Netherlands, located in the province of North Brabant. The name derived from ''brede Aa'' ('wide Aa' or 'broad Aa') and refers to the confluence of the rivers Mark and Aa. Breda has ...
under the command of Maurice of Nassau, and undertook a formal study of
military engineering Military engineering is loosely defined as the art, science, and practice of designing and building military works and maintaining lines of military transport and military communications. Military engineers are also responsible for logistics be ...
, as established by
Simon Stevin Simon Stevin (; 1548–1620), sometimes called Stevinus, was a Flemish mathematician, scientist and music theorist. He made various contributions in many areas of science and engineering, both theoretical and practical. He also translated vario ...
. 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 school, for whom he wrote the ''Compendium of Music'' (written 1618, published 1650). While in the service of the Catholic Duke Maximilian of Bavaria from 1619, Descartes was present at the Battle of the White Mountain near Prague, in November 1620. According to Adrien Baillet, on the night of 10–11 November 1619 (
St. Martin's Day Saint Martin's Day or Martinmas, sometimes historically called Old Halloween or Old Hallowmas Eve, is the feast day of Saint Martin of Tours and is celebrated in the liturgical year on 11 November. In the Middle Ages and early modern period, it ...
), while stationed in Neuburg an der Donau, Descartes shut himself in a room with an "oven" (probably a
cocklestove A masonry heater (also called a masonry stove) is a device for warming an interior space through radiant heating, by capturing the heat from periodic burning of fuel (usually wood), and then radiating the heat at a fairly constant temperature ...
) 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 Exploding head syndrome (EHS) is an abnormal sensory perception during sleep in which a person experiences auditory hallucinations that are loud and of short duration when falling asleep or waking up. The noise may be frightening, typically occ ...
. Upon exiting, he had formulated
analytic geometry In classical 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 engineerin ...
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 discovered 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, Duke of Richelieu (; 9 September 1585 – 4 December 1642), known as Cardinal Richelieu, was a French clergyman and statesman. He was also known as ''l'Éminence rouge'', or "the Red Eminence", a term derived from the ...
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 ( la, nuntius apostolicus; 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 or ...
Guidi di Bagno The House of Guidi di Bagno is an old Italian noble family which moved first into Romagna (Bagno di Romagna) and then into Mantua from the 14th century. History and famous personalities The branch of the family originated from Riccardo count Guid ...
, where he came with
Mersenne Marin Mersenne, OM (also known as Marinus Mersennus or ''le Père'' Mersenne; ; 8 September 1588 – 1 September 1648) was a French polymath whose works touched a wide variety of fields. He is perhaps best known today among mathematicians for ...
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 Dutch Republic 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''; nl, Universiteit Leiden) is a Public university, public research university in Leiden, Netherlands. The university was founded as a Protestant university in 1575 by William the Silent, William, Prince o ...
, 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 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 :''This is a disambiguation page for the common name Francine.'' Francine is a female given name. The name is of French origin. The name Francine was most popular in France itself during the 1940s (Besnard & Desplanques 2003), and was well used i ...
, who was born in 1635 in
Deventer Deventer (; Sallands: ) is a city and municipality in the Salland historical region of the province of Overijssel, Netherlands. In 2020, Deventer had a population of 100,913. The city is largely situated on the east bank of the river IJssel, bu ...
. 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 speculates that the experience of fatherhood and losing a child formed a turning point in Descartes' 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 The Roman Inquisition, formally the Supreme Sacred Congregation of the Roman and Universal Inquisition, was a system of partisan tribunals developed by the Holy See of the Catholic Church, Roman Catholic Church, during the second half of the 16th ...
, and Descartes abandoned plans to publish ''
Treatise on the World A treatise is a formal and systematic written discourse on some subject, generally longer and treating it in greater depth than an essay, and more concerned with investigating or exposing the principles of the subject and its conclusions."Trea ...
'', 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 ''La Géométrie'' was published in 1637 as an appendix to ''Discours de la méthode'' (''Discourse on the Method''), written by René Descartes. In the ''Discourse'', he presents his method for obtaining clarity on any subject. ''La Géométrie ...
'' (''Geometry''), preceded by an introduction, his famous ''Discours de la méthode'' ('' Discourse on the Method''). 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. 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 ''Principles of Philosophy'' ( la, Principia Philosophiae) is a book by René Descartes. In essence, it is a synthesis of the ''Discourse on Method'' and ''Meditations on First Philosophy''.Guy Durandin, ''Les Principes de la Philosophie. Intro ...
''), 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 Egmond-Binnen () is a village in the Dutch province of North Holland. It is a part of the municipality of Bergen, and lies about southwest of Alkmaar. History The village was first mentioned in 922 as Ekmunde. The etymology is unknown. The m ...
. 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 and participated in the design of his mansion and estate. He also met
Dirck Rembrantsz van Nierop Dirck Rembrantsz van Nierop (1610 – 4 November 1682) was a seventeenth-century Dutch cartographer, mathematician, surveyor, astronomer, shoemaker and Mennonite teacher. Life Van Nierop was born and died at Nieuwe Niedorp ("Nierop"), Holland (n ...
, a mathematician and
surveyor Surveying or land surveying is the technique, profession, art, and science of determining the terrestrial two-dimensional or three-dimensional positions of points and the distances and angles between them. A land surveying professional is ca ...
. 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 Christia Mercer is an American philosopher and the Gustave M. Berne Professor in the Department of Philosophy at Columbia University. She is known for her work on the history of early modern philosophy, the history of Platonism, and the history ...
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 ''Philosophical Studies'' is a peer-reviewed academic journal for philosophy in the analytic tradition. The journal is devoted to the publication of papers in exclusively analytic philosophy and welcomes papers applying formal techniques to philo ...
'' 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 In his final philosophical treatise, ''The Passions of the Soul'' (french: Les Passions de l'âme), completed in 1649 and dedicated to Princess Elisabeth of Bohemia, René Descartes contributes to a long tradition of philosophical inquiry into th ...
''), 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

By 1649, Descartes had become one of Europe's most famous philosophers and scientists. That year,
Queen Christina of Sweden Christina ( sv, Kristina, 18 December (New Style) 1626 – 19 April 1689), a member of the House of Vasa, was Queen of Sweden in her own right from 1632 until her abdication in 1654. She succeeded her father Gustavus Adolphus upon his death ...
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 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 Pierre Hector Chanut (February 22, 1601 in Riom – July 3, 1662 in Livry-sur-Seine) was a civil servant in the Auvergne, a French ambassador in Sweden and the Dutch Republic, and state counsellor. Life In 1626 Chanut married Marguerite Cler ...
, living on
Västerlånggatan Västerlånggatan ("the Western Long Street") is a street in Gamla stan, the old town of Stockholm, Sweden. Stretching southward between the squares Mynttorget and Järntorget, it follows the course of the city's now demolished 13th-century def ...
, less than 500 meters from Castle Tre Kronor in
Stockholm Stockholm () is the Capital city, capital and List of urban areas in Sweden by population, largest city of Sweden as well as the List of urban areas in the Nordic countries, largest urban area in Scandinavia. Approximately 980,000 people liv ...
. There, Chanut and Descartes made observations with a Torricellian mercury barometer. Challenging
Blaise Pascal Blaise Pascal ( , , ; ; 19 June 1623 – 19 August 1662) was a French mathematician, physicist, inventor, philosopher, and Catholic Church, Catholic writer. He was a child prodigy who was educated by his father, a tax collector in Rouen. Pa ...
, Descartes took the first set of barometric readings in Stockholm to see if atmospheric pressure could be used in forecasting the weather.


Death

Descartes arranged to give lessons to 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 and literature. On 1 February 1650, he contracted pneumonia 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' 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). 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 Claude Clerselier (1614, in Paris – 1684, in Paris) was a French editor and translator. Clerselier was a lawyer in the Parlement of Paris and resident for the King of France in Sweden. He was the brother-in-law of Pierre Chanut, and served as ...
, 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 placed Descartes' 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 Saint-Étienne-du-Mont is a church in Paris, France, on the Montagne Sainte-Geneviève in the 5th arrondissement, near the Panthéon. It contains the shrine of St. Geneviève, the patron saint of Paris. The church also contains the tombs of Bl ...
. In 1671, Louis XIV prohibited all lectures in Cartesianism. Although the National Convention in 1792 had planned to transfer his remains to the Panthéon, he was reburied in the
Abbey of Saint-Germain-des-Prés An abbey is a type of monastery used by members of a religious order under the governance of an abbot or abbess. Abbeys provide a complex of buildings and land for religious activities, work, and housing of Christian monks and nuns. The conce ...
in 1819, missing a finger and the skull. His skull is in the Musée de l'Homme in Paris.


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: 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 Dictio ...
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" (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' 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. 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 as unreliable and, instead, admitting only deduction as a method.


Mind–body dualism

Descartes, influenced by the automatons 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 ''département'' of Yvelines, about 19 km west of Paris, France. Today, it houses the ''musée d'Archéologie nationale'' (Nati ...
near Paris, investigated the connection between mind and body, and how they interact. His main influences for
dualism Dualism most commonly refers to: * Mind–body dualism, a philosophical view which holds that mental phenomena are, at least in certain respects, not physical phenomena, or that the mind and the body are distinct and separable from one another ** ...
were theology and physics. The theory on the dualism of mind and body is Descartes' 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 and the distinction between the human soul and the body. Humans are a union of mind and body; thus Descartes' 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 ''Principles of Philosophy'' ( la, Principia Philosophiae) is a book by René Descartes. In essence, it is a synthesis of the ''Discourse on Method'' and ''Meditations on First Philosophy''.Guy Durandin, ''Les Principes de la Philosophie. Intro ...
'', 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' 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 Aristotelianism ( ) is a philosophical tradition inspired by the work of Aristotle, usually characterized by deductive logic and an analytic inductive method in the study of natural philosophy and metaphysics. It covers the treatment of the socia ...
of Descartes' days held that the universe was inherently purposeful or teleological. Everything that happened, be it the motion of the
star A star is an astronomical object comprising a luminous spheroid of plasma (physics), plasma held together by its gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many other stars are visible to the naked ...
s or the growth of a tree, 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' theory of dualism supports the distinction between traditional Aristotelian science and the new science of Kepler and Galileo, which denied the role of a divine power and "final causes" in its attempts to explain nature. Descartes' 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 physics, it also held the door open for religious beliefs about the immortality of the soul. Descartes' 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' 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 for many years after Descartes' death. Descartes was also a rationalist and believed in the power of
innate ideas Innatism is a philosophical and epistemological doctrine that the mind is born with ideas, knowledge, and beliefs. Therefore, the mind is not a ''tabula rasa'' (blank slate) at birth, which contrasts with the views of early empiricists such as J ...
. 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 – 28 October 1704) was an English philosopher and physician, widely regarded as one of the most influential of Age of Enlightenment, Enlightenment thinkers and commonly known as the "father of liberalism ...
(1632–1704), an empiricist.
Empiricism In philosophy, empiricism is an epistemological theory that holds that knowledge or justification comes only or primarily from sensory experience. It is one of several views within epistemology, along with rationalism and skepticism. Empir ...
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 The pineal gland, conarium, or epiphysis cerebri, is a small endocrine gland in the brain of most vertebrates. The pineal gland produces melatonin, a serotonin-derived hormone which modulates sleep, sleep patterns in both circadian rhythm, circ ...
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 In biology, a reflex, or reflex action, is an involuntary, unplanned sequence or action and nearly instantaneous response to a stimulus. Reflexes are found with varying levels of complexity in organisms with a nervous system. A reflex occurs ...
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, thus religious authorities regarded his books as dangerous. Descartes' writings went on to form the basis for theories on emotions and how
cognitive Cognition refers to "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 advanced computer 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 the living organisms to investigate the principles that govern the structure, development a ...
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 stimuli. The International Association for the Study of Pain defines pain as "an unpleasant sensory and emotional experience associated with, or resembling that associated with, ...
and anxiety, 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 Suffering, or pain in a broad sense, may be an experience of unpleasantness or aversion, possibly associated with the perception of harm or threat of harm in an individual. Suffering is the basic element that makes up the negative valence of af ...
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 using Power (physics), power to apply Force, forces and control Motion, movement to perform an action. The term is commonly applied to artificial devices, such as those employing engines or motors, but also to na ...
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 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 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. 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 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 A somatic symptom disorder, formerly known as a somatoform disorder,(2013) 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 both identified sovereign goods with virtue. For
Epicurus Epicurus (; grc-gre, Ἐπίκουρος ; 341–270 BC) was an ancient Greek philosopher and sage who founded Epicureanism, a highly influential school of philosophy. He was born on the Greek island of Samos to Athenian parents. Influenced ...
, 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'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 Proof most often refers to: * Proof (truth), argument or sufficient evidence for the truth of a proposition * Alcohol proof, a measure of an alcoholic drink's strength Proof may also refer to: Mathematics and formal logic * Formal proof, a co ...
of a benevolent God (the
trademark argument The trademark argument is an ''a priori'' argument for the existence of God developed by French philosopher and mathematician, René Descartes. In the ''Meditations'' Descartes provides two arguments for the existence of God. In Meditation V he ...
and the
ontological argument An ontological argument is a philosophical argument, made from an ontological basis, that is advanced in support of the existence of God. Such arguments tend to refer to the state of being or existing. More specifically, ontological arguments ...
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 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 epistemology, therefore, Descartes can be said to have contributed such ideas as a conception of foundationalism and the possibility that reason 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 Causality (also referred to as causation, or cause and effect) is influence by which one event, process, state, or object (''a'' ''cause'') contributes to the production of another event, process, state, or object (an ''effect'') where the cau ...
to support his trademark argument for the existence of God, quoting Lucretius in defence: ''"Ex nihilo nihil fit"'', meaning "
Nothing comes from nothing Nothing comes from nothing ( gr, οὐδὲν ἐξ οὐδενός; la, ex nihilo nihil fit) is a philosophical dictum first argued by Parmenides. It is associated with ancient Greek cosmology, such as is presented not just in the works of Homer ...
" ( Lucretius). ''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 Pascal, Pascal's or PASCAL may refer to: People and fictional characters * Pascal (given name), including a list of people with the name * Pascal (surname), including a list of people and fictional characters with the name ** Blaise Pascal, Fren ...
regarded Descartes' views as a rationalist and mechanist, and accused him of
deism Deism ( or ; derived from the Latin ''deus'', meaning "god") is the Philosophy, philosophical position and Rationalism, rationalistic theology that generally rejects revelation as a source of divine knowledge, and asserts that Empirical evi ...
: "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 Martin Schoock (1 April 1614–1669) was a Dutch academic and polymath. Life He was born in Utrecht. His grandfather Anton van Voorst taught him Latin. His parents were Remonstrants and intended him for the law; he studied theology and philosophy ...
, accused him of
atheist Atheism, in the broadest sense, is an absence of belief in the existence of deities. Less broadly, atheism is a rejection of the belief that any deities exist. In an even narrower sense, atheism is specifically the position that there no ...
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 Philosophical skepticism ( UK spelling: scepticism; from Greek σκέψις ''skepsis'', "inquiry") is a family of philosophical views that question the possibility of knowledge. It differs from other forms of skepticism in that it even reject ...
. 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 perceptions come to him involuntarily, and are not willed by him. They are external to his senses, and according to Descartes, this is evidence of the existence of something outside of his mind, and thus, an external world. Descartes goes on to 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 A subscript or superscript is a character (such as a number or letter) that is set slightly below or above the normal line of type, respectively. It is usually smaller than the rest of the text. Subscripts appear at or below the baseline, whil ...
to show the powers or exponents; for example, the 2 used in x2 to indicate x squared.


Analytic geometry

One of Descartes' most enduring legacies was his development of Cartesian or
analytic geometry In classical 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 engineerin ...
, which uses algebra to describe geometry; the
Cartesian coordinate system A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in t ...
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. 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 Fra Luca Bartolomeo de Pacioli (sometimes ''Paccioli'' or ''Paciolo''; 1447 – 19 June 1517) was an Italian mathematician, Franciscan friar, collaborator with Leonardo da Vinci, and an early contributor to the field now known as accounting ...
, Cardano,
Tartaglia Tartaglia may refer to: *Tartaglia (commedia dell'arte), Commedia dell'arte stock character *Angelo Tartaglia (1350 or 1370–1421), Italian condottiero * Niccolò Fontana Tartaglia (1499/1500–1557), Venetian mathematician and engineer *Ivo Tarta ...
and
Ferrari Ferrari S.p.A. (; ) is an Italian luxury sports car manufacturer based in Maranello, Italy. Founded by Enzo Ferrari (1898–1988) in 1939 from the Alfa Romeo racing division as ''Auto Avio Costruzioni'', the company built its first car in ...
. Equations of
degree Degree may refer to: As a unit of measurement * Degree (angle), a unit of angle measurement ** Degree of geographical latitude ** Degree of geographical longitude * Degree symbol (°), a notation used in science, engineering, and mathematics ...
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 in envisioning a more general science of algebra or "universal mathematics", as a precursor to
symbolic logic Mathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal ...
, 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, and this is arguably one of his most important contributions. Descartes' influence extended not directly from his original French edition of ''La Géométrie'', however, but rather from Frans van Schooten's expanded second Latin edition of the work. Newton continued Descartes' work on cubic equations, which freed the subject from fetters of the Greek perspectives. The most important concept was his very modern treatment of single variables.


The basis of calculus

Descartes' work provided the basis for the calculus developed by Leibniz and
Newton Newton most commonly refers to: * Isaac Newton (1642–1726/1727), English scientist * Newton (unit), SI unit of force named after Isaac Newton Newton may also refer to: Arts and entertainment * ''Newton'' (film), a 2017 Indian film * 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 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 review and repeatab ...
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 to Descartes' 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
Galileo Galileo di Vincenzo Bonaiuti de' Galilei (15 February 1564 – 8 January 1642) was an Italian astronomer, physicist and engineer, sometimes described as a polymath. Commonly referred to as Galileo, his name was pronounced (, ). He was ...
's ideas.Harold J. Cook, in ''The Scientific Revolution in National Context'',
Roy Porter Roy Sydney Porter, FBA (31 December 1946 – 3 March 2002) was a British historian known for his work on the history of medicine. He retired in 2001 from the director of the Wellcome Institute for the History of Medicine at University College L ...
, Mikuláš Teich, (eds.), Cambridge University Press, 1992, pages 127–129
Together, they worked on free fall,
catenaries In physics and geometry, a catenary (, ) is the curve that an idealized hanging chain or cable assumes under its own weight when supported only at its ends in a uniform gravitational field. The catenary curve has a U-like shape, superficial ...
, conic sections, and
fluid statics Fluid statics or hydrostatics is the branch of fluid mechanics that studies the condition of the equilibrium of a floating body and submerged body "fluids at hydrostatic equilibrium and the pressure in a fluid, or exerted by a fluid, on an imme ...
. 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 ''Principles of Philosophy'' ( la, Principia Philosophiae) is a book by René Descartes. In essence, it is a synthesis of the ''Discourse on Method'' and ''Meditations on First Philosophy''.Guy Durandin, ''Les Principes de la Philosophie. Intro ...
'' (''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' exposition.) Descartes defined "quantity of motion" ('' Latin: 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. 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' 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

Descartes' vortex theory of planetary motion was later rejected by Newton in favor of his
law of universal gravitation Newton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the square of the distanc ...
, and most of the second book of Newton's '' Principia'' is devoted to his counterargument.


Optics

Descartes also made contributions to the field of optics. He showed by using geometric construction and the law of refraction (also known as Descartes' law, or more commonly
Snell's law Snell's law (also known as Snell–Descartes law and ibn-Sahl law and the law of refraction) is a formula used to describe the relationship between the angles of incidence and refraction, when referring to light or other waves passing through ...
outside France) that the angular radius of a rainbow is 42 degrees (i.e., the angle subtended at the eye by the edge of the rainbow and the ray passing from the sun through the rainbow's centre is 42°). He also independently discovered the law of reflection, and his essay on optics was the first published mention of this law.


Meteorology

Within '' Discourse on the Method'', there is an appendix in which Descartes discusses his theories on Meteorology 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' theory on Meteorology. While rejecting most of Aristotle'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, the thinker whose approaches has profoundly changed the course of Western philosophy and set the basis for modernity. The first two of his ''Meditations on First Philosophy'', those that formulate the famous methodic doubt, represent the portion of Descartes' 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 Emancipation generally means to free a person from a previous restraint or legal disability. More broadly, it is also used for efforts to procure economic and social rights, political rights or equality, often for a specifically disenfranchis ...
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 revelational truth and Church doctrine; humanity making its own law and taking its own stand.
Martin Heidegger Martin Heidegger (; ; 26 September 188926 May 1976) was a German philosopher who is best known for contributions to phenomenology, hermeneutics, and existentialism. He is among the most important and influential philosophers of the 20th centur ...
938 Year 938 ( CMXXXVIII) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. Events By place Europe * Summer – The Hungarian army invades Northern Italy with the permission of King H ...
(2002) ''
The Age of the World Picture "The Age of the World Picture" or "The Age of the World View" (german: Die Zeit des Weltbildes) is a 1938 lecture by Martin Heidegger in which he addresses the metaphysical ground of modern science. It was published in the essay collection ''Holzwe ...
'' 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
Martin Heidegger Martin Heidegger (; ; 26 September 188926 May 1976) was a German philosopher who is best known for contributions to phenomenology, hermeneutics, and existentialism. He is among the most important and influential philosophers of the 20th centur ...
'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' work, establishing human reason as autonomous, provided the basis for the
Enlightenment Enlightenment or enlighten may refer to: Age of Enlightenment * Age of Enlightenment, period in Western intellectual history from the late 17th to late 18th century, centered in France but also encompassing (alphabetically by country or culture): ...
's emancipation from God and the Church. According to
Martin Heidegger Martin Heidegger (; ; 26 September 188926 May 1976) was a German philosopher who is best known for contributions to phenomenology, hermeneutics, and existentialism. He is among the most important and influential philosophers of the 20th centur ...
, the perspective of Descartes' work also provided the basis for all subsequent anthropology.Heidegger
938 Year 938 ( CMXXXVIII) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. Events By place Europe * Summer – The Hungarian army invades Northern Italy with the permission of King H ...
(2002), p. 75 quotation:
Descartes' philosophical revolution is sometimes said to have sparked modern
anthropocentrism Anthropocentrism (; ) is the belief that human beings are the central or most important entity in the universe. The term can be used interchangeably with humanocentrism, and some refer to the concept as human supremacy or human exceptionalism. F ...
and subjectivism.


Contemporary reception

In commercial terms, The ''Discourse'' appeared during Descartes' 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' 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 Gisbertus Voetius ( Latinized version of the Dutch name Gijsbert Voet ; 3 March 1589 – 1 November 1676) was a Dutch Calvinist theologian. Life He was born at Heusden, in the Dutch Republic, studied at Leiden, and in 1611 became Protestant past ...
(Voetius), for teaching Descartes' 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 Anthony John Gottlieb (born 1956) is a British writer, author, historian of ideas, and former Executive Editor of The ''Economist''. He is the author of two major works on the history of philosophy, '' The Dream of Reason'' and '' The Dream of Enli ...
, a former senior editor of '' The Economist'', and the author of ''
The Dream of Reason ''The Dream of Reason: A History of Philosophy from the Greeks to the Renaissance'' is a 2000 nonfiction book by Anthony Gottlieb, the first in a series of three volumes that introduce Western philosophy to a wide audience. The second volume is ...
'' and ''
The Dream of Enlightenment ''The Dream of Enlightenment: The Rise of Modern Philosophy'' is a 2016 nonfiction book by Anthony Gottlieb, a former editor of ''The Economist''. It is a sequel to his 2001 nonfiction, '' The Dream of Reason: A History of Philosophy from the Gr ...
'', one of the reasons Descartes and Thomas Hobbes 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 Agnes Callard (born Agnes Gellen; January 6, 1976) is associate professor of philosophy at the University of Chicago. Her primary areas of specialization are ancient philosophy and ethics. She is also noted for her popular writings and work on pub ...
described Descartes' 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's monologues"meditations on the nature of life and emotion"were similar to Descartes' 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 Bayesian probability is an interpretation of the concept of probability, in which, instead of frequency or propensity of some phenomenon, probability is interpreted as reasonable expectation representing a state of knowledge or as quantification o ...
?" Callard agreed that this argument can be traced to Descartes, who had said that he had refuted it. She clarified that in Descartes' 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 Rosicrucianism is a spiritual and cultural movement that arose in Europe in the early 17th century after the publication of several texts purported to announce the existence of a hitherto unknown esoteric order to the world and made seeking its ...
is debated. The initials of his name have been linked to the R.C. acronym 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 solids and three-dimensional figurate numbers. Said by some scholars to prefigure
Euler's polyhedral formula In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space ...
. Unpublished; discovered in Descartes' 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 The ''Search for Truth by Natural Light'' (') is an unfinished philosophical dialogue by René Descartes “set in the courtly culture of the ‘’ and ‘’.” It was written in French (presumably after the Meditations was completed) but fir ...
'') unfinished dialogue published in 1701. * 1630–1633. ''Le Monde'' (''
The World In its most general sense, the term "world" refers to the totality of entities, to the whole of reality or to everything that is. The nature of the world has been conceptualized differently in different fields. Some conceptions see the worl ...
'') and '' L'Homme'' (''Man''). Descartes' first systematic presentation of his natural philosophy. ''Man'' was published posthumously in Latin translation in 1662; and ''The World'' posthumously in 1664. * 1637. ''Discours de la méthode'' ('' Discourse on the Method''). An introduction to the ''Essais'', which include the '' Dioptrique'', the ''Météores'' and the ''Géométrie''. * 1637. ''
La Géométrie ''La Géométrie'' was published in 1637 as an appendix to ''Discours de la méthode'' (''Discourse on the Method''), written by René Descartes. In the ''Discourse'', he presents his method for obtaining clarity on any subject. ''La Géométrie ...
'' (''Geometry''). Descartes' 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, probably done without Descartes' supervision, was published in 1647. Includes six Objections and Replies. * 1644. ''Principia philosophiae'' (''
Principles of Philosophy ''Principles of Philosophy'' ( la, Principia Philosophiae) is a book by René Descartes. In essence, it is a synthesis of the ''Discourse on Method'' and ''Meditations on First Philosophy''.Guy Durandin, ''Les Principes de la Philosophie. Intro ...
''), 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' one-time disciple Henricus Regius. * 1648. ''La description du corps humain'' (''
The Description of the Human Body The ''Treatise on Man'' (french: L'Homme) is an unfinished treatise by René Descartes written in the 1630s and published posthumously, firstly in 1662 in Latin, then in 1664 in French by Claude Clerselier. The 1664 edition is accompanied by a shor ...
''). 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 In his final philosophical treatise, ''The Passions of the Soul'' (french: Les Passions de l'âme), completed in 1649 and dedicated to Princess Elisabeth of Bohemia, René Descartes contributes to a long tradition of philosophical inquiry into the ...
''). Dedicated to Princess
Elisabeth of the Palatinate Elisabeth of the Palatinate (26 December 1618 – 11 February 1680), also known as Elisabeth of Bohemia, Princess Elisabeth of the Palatinate, or Princess-Abbess of Herford Abbey, was the eldest daughter of Frederick V, Elector Palatine (who was ...
. * 1657. ''Correspondance'' (three volumes: 1657, 1659, 1667). Published by Descartes' literary executor
Claude Clerselier Claude Clerselier (1614, in Paris – 1684, in Paris) was a French editor and translator. Clerselier was a lawyer in the Parlement of Paris and resident for the King of France in Sweden. He was the brother-in-law of Pierre Chanut, and served as ...
. The third edition, in 1667, was the most complete; Clerselier omitted, however, much of the material pertaining to mathematics. In January 2010, a previously unknown letter from Descartes, dated 27 May 1641, was found by the Dutch philosopher Erik-Jan Bos when browsing through Google. Bos found the letter mentioned in a summary of autographs kept by
Haverford College Haverford College ( ) is a private liberal arts college in Haverford, Pennsylvania. It was founded as a men's college in 1833 by members of the Religious Society of Friends (Quakers), began accepting non-Quakers in 1849, and became coeducational ...
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' ''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 Michael Sean Mahoney (June 30, 1939 – July 23, 2008) was a historian of science. Mahoney was born in New York City, and did his undergraduate studies at Harvard University, graduating in 1960. He earned a Ph.D. in history and history of science ...
. * 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 Open or OPEN may refer to: Music * Open (band), Australian pop/rock band * The Open (band), English indie rock band * ''Open'' (Blues Image album), 1969 * ''Open'' (Gotthard album), 1999 * ''Open'' (Cowboy Junkies album), 2001 * ''Open'' (YF ...
, 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: ( Dordrecht/Boston/London: Kluwer Academic Publishers, 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 Elisabeth of the Palatinate (26 December 1618 – 11 February 1680), also known as Elisabeth of Bohemia, Princess Elisabeth of the Palatinate, or Princess-Abbess of Herford Abbey, was the eldest daughter of Frederick V, Elector Palatine (who was ...
. * 1619–1648. ''René Descartes, Isaac Beeckman, Marin Mersenne. Lettere 1619–1648'', ed. by Giulia Beglioioso and Jean Robert-Armogathe, Milano, Bompiani, 2015 pp. 1696.


See also

* 3587 Descartes, asteroid * Bucket argument * Cartesian circle * Cartesian materialism (not a view that was held by or formulated by Descartes) * Cartesian plane *
Cartesian product In mathematics, specifically set theory, the Cartesian product of two sets ''A'' and ''B'', denoted ''A''×''B'', is the set of all ordered pairs where ''a'' is in ''A'' and ''b'' is in ''B''. In terms of set-builder notation, that is : A\ti ...
* Cartesian product of graphs * Cartesian theater * Cartesian tree *
Descartes (crater) Descartes is a heavily worn lunar impact crater that is located in the rugged south-central highlands of the Moon. To the southwest is the crater Abulfeda. It is named after the French philosopher, mathematician and physicist René Descartes. ...
and Highlands on the Moon (
Apollo 16 Apollo 16 (April 1627, 1972) was the tenth crewed mission in the United States Apollo space program, administered by NASA, and the fifth and penultimate to land on the Moon. It was the second of Apollo's " J missions", with an extended sta ...
landing site) *
Descartes number In number theory, a Descartes number is an odd number which would have been an odd perfect number, if one of its composite factors were prime. They are named after René Descartes who observed that the number would be an odd perfect number if onl ...
* Descartes Prize * Descartes' rule of signs * Descartes-Huygens Prize *
Descartes' theorem In geometry, Descartes' theorem states that for every four kissing, or mutually tangent, circles, the radii of the circles satisfy a certain quadratic equation. By solving this equation, one can construct a fourth circle tangent to three given, mu ...
(4 tangent circles) *
Descartes' theorem on total angular defect In geometry, the (angular) defect (or deficit or deficiency) means the failure of some angles to add up to the expected amount of 360° or 180°, when such angles in the Euclidean plane would. The opposite notion is the angle excess, excess. Classi ...
* Folium of Descartes *
List of things named after René Descartes {{unref, date=March 2022 This is the list of things named after René Descartes (1596–1650), a French philosopher, mathematician, and scientist. Computer science * Cartesian genetic programming * Cartesian tree Mathematics *Cartesian closed ca ...
*
Paris Descartes University Paris Descartes University (french: Université Paris 5 René Descartes, links=no), also known as Paris V, was a French public university located in Paris. It was one of the inheritors of the historic University of Paris, which was split into 13 ...


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 Year 938 ( CMXXXVIII) was a common year starting on Monday (link will display the full calendar) of the Julian calendar. Events By place Europe * Summer – The Hungarian army invades Northern Italy with the permission of King H ...
(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' 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 Ivor Owen Grattan-Guinness (23 June 1941 – 12 December 2014) was a historian of mathematics and logic. Life Grattan-Guinness was born in Bakewell, England; his father was a mathematics teacher and educational administrator. He gained his bac ...
, 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


General


The Correspondence of René Descartes
i
EMLO
* * *

*

* ttp://digitalcommons.unl.edu/modlangfrench/20/ René Descartes (1596–1650)Published in ''Encyclopedia of Rhetoric and Composition'' (1996)
A site containing Descartes' main works, including correspondence, slightly modified for easier reading

Descartes Philosophical Writings tr. by Norman Kemp Smith
at archive.org
Studies in the Cartesian philosophy (1902) by Norman Kemp Smith
at archive.org
The Philosophical Works Of Descartes Volume II (1934)
at archive.org

* *
Centro Interdipartimentale di Studi su Descartes e il Seicento
* Livre Premier, ''La Géométrie'', online and analyzed by A. Warusfel
''BibNum''
small> lick "à télécharger" for English analysis/small>


Bibliographies


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


''

Stanford Encyclopedia of Philosophy The ''Stanford Encyclopedia of Philosophy'' (''SEP'') combines an online encyclopedia of philosophy with peer-reviewed publication of original papers in philosophy, freely accessible to Internet users. It is maintained by Stanford University. Eac ...
''


Descartes

Life and works

Epistemology

Mathematics

Physics

Ethics

Modal Metaphysics

Ontological Argument

Theory of Ideas

Pineal Gland



''

Internet Encyclopedia of Philosophy The ''Internet Encyclopedia of Philosophy'' (''IEP'') is a scholarly online encyclopedia, dealing with philosophy, philosophical topics, and philosophers. The IEP combines open access publication with peer reviewed publication of original pape ...
''


Descartes

Descartes: Ethics

Descartes: Mind-Body Distinction

Descartes: Scientific Method


Other


Bernard Williams interviewed about Descartes on ''Men of ideas''
* {{DEFAULTSORT:Descartes, Rene * 1596 births 1650 deaths 17th-century French mathematicians 17th-century French philosophers 17th-century French scientists 17th-century French writers 17th-century writers in Latin 17th-century male writers Age of Enlightenment Aphorists Augustinian philosophers Burials at Saint-Germain-des-Prés (abbey) Catholic philosophers French consciousness researchers and theorists Constructed language creators Critics of animal rights Deaths from pneumonia in Sweden Dualists Enlightenment philosophers French emigrants Immigrants to the Dutch Republic French ethicists French expatriates in Sweden French expatriates in the Dutch Republic French logicians French mercenaries French music theorists French Roman Catholics Leiden University alumni Metaphilosophers Metaphysics writers French military personnel of the Thirty Years' War Natural philosophers Ontologists People from Indre-et-Loire People of the Age of Enlightenment French philosophers of art French philosophers of culture French philosophers of education French philosophers of history Philosophers of logic Philosophers of mathematics Philosophers of mind Philosophers of psychology French philosophers of science Philosophers of social science Philosophers of time Rationalists University of Poitiers alumni Writers about activism and social change Writers about religion and science Writers who illustrated their own writing Critics of atheism