René Descartes

Figure 1 Rene Descartes 1596-1650

Contents

Illustrations

Early Life

Birthplace

Family

Schooldays at La Flèche

Poitiers University 1615-16

1616-18

Military Career 1618-28

Isaac Beeckman

Revelation in the Stove-heated room

In France 1622-3

Influence of Cardinal Berulle

In the Dutch Republic 1628-49

Personal Life

Francine

And Rosicrucianism

Withholds publication of ‘The World’, 1633

Discourse on Method 1637

Scientific Method

His choice of language for his publications

Descartes and Mathematics

Geometry 1637

Algebraic Notation

Analytic Geometry

Fermat and Descartes

Calculus

Descartes and Science

Physics

Astronomy

Optics

Biology

Reflexes

Animal suffering

Theology

Voetius 1638-43

Philosophy

Philosophical antecedents

Scepticism

Problems with Scepticism

Defects in sense impression not insuperable

Scepticism and Rationalism

Rationalism

Rationalism and Empiricism

Meditations on First Philosophy 1641

Principles of Philosophy 1644

Physics in the ‘Principles’:

Can there be a vacuum?

Mind/body dualism

Dualism and the brain

Other works

And Morality

Emotions

Move to Sweden 1649

Death

Post Mortem

On the Index, 1663

Estimates

And solipsism

Bibliography

Illustrations

Figure 1 Rene Descartes 1596-1650

Figure 2 La Haye Descartes today

Figure 3 Collège Royal Henry-Le-Grand

Figure 4 Poitiers University

Figure 5: Battle of the White Mountain, 1620, which Descartes witnessed

Figure 6 Neuburg an der Donau – ‘a dreary village’

Figure 7 Deventer, birthplace of Francine

Figure 8: ‘more popular ones in French’

Figure 9: ‘Cartesian co-ordinates’

Figure 10: Princess Elisabeth of Bohemia

Figure 11 Descartes with Queen Christina

Figure 12 The Abbey of St. Germain des Pres

Early Life

Birthplace

René Descartes (1,2) (also known (2,6) in Latin (12) as Renatus (2,6) Cartesius. (1,2)) was a highly influential French (1,2) rationalist (2,9) philosopher, mathematician, (1,2) physicist, (1,3) writer (1) and scientist. (3,6) was born on March 31st, (1,6) 1596, (1,2) in a small town (7,10) called (7,10) La Haye, (2,10) [OR] La Haye en Touraine, (10,12) now renamed (10,12) La Haye Descartes (5,7) [OR] Descartes, (14) after him to honour its most famous son. (10,12) It is in the Loire Valley in central France (14) in the Department of Indre-et-Loire, (12) near Tours (2,7) [OR] in Vienne1. (5)His family connections lay south, across the Creuse River in Poitou, where his father, Joachim, owned farms and houses in Châtellerault and Poitiers. (11) Although the Descartes family was Roman Catholic, the Poitou region was controlled by the Protestant Huguenots, and Châtellerault, a Protestant stronghold, was the site of negotiations over the Edict of Nantes in 1598, which gave Protestants freedom of worship in France following the intermittent Wars of Religion between Protestant and Catholic forces in France. (11) At this time, Huguenot Poitiers was in virtual revolt against the young King Louis XIII (reigned 1610–43). (11) René returned to Poitou regularly until 1628. (11) He used ‘Poitevin’ as a pen name later in life. (16)

Figure 2 La Haye Descartes today

Family

His was a well-educated, upper-class family (12) His father, Joachim, (10,12) was a busy (14,15) lawyer (5,12) and magistrate (14,15) [OR] a local politician. (13) He was a council member in the provincial (10,11) parliament (10) [OR] Parlement (11) [OR] High (14) Court of Justice (12) of Brittany (11,12)[OR] Joachim worked six months of the year a lawyer at Brittany’s Court of Justice (12) in Rennes, (11,12) about 200 miles (300 km) from their home. (12) René therefore inherited a modest rank of nobility. (11) He was the youngest of three (10,12) [OR] five (two siblings and two half-siblings). (15) children. (10,12) His mother (10,11) Jeanne Brochard, (10,12) was the daughter of the Lieutenant General of Poitiers. (12) She died (10,11) in May of the year following his birth (15) [OR] within his first year of life, (10,11) of tuberculosis (14) [OR] giving birth to her fourth child. (12) Joachim remarried a few years later (10,11)when René was four and (12) began living in Rennes permanently. (11,12) His work apparently left little time for family, (15) and he sent the children to live with their maternal grandmother (10,11) in La Haye (11,15)where they remained (10)[OR] later (11) they moved in with his great-uncle (11,12) in Châtellerault. (11) From birth René suffered poor health and had a permanent cough. (12) Local doctors thought he would not survive infancy. (12) His father employed a nurse who devoted herself to René’s care. (12) Descartes’ mother died, and he, his full brother and sister, Pierre and Jeanne, were left to be raised by their grandmother in La Haye. (15)

Schooldays at La Flèche

His father was very concerned with their education, and (10,13) in 1604 (5,14)[OR]1606 (11,15)[OR] in 1607, late because of his fragile health, (16) at the age of 8 (10) [OR] when he was ten (15) [OR]about ten (12,15) or eleven, (12) he was finally considered healthy enough to begin school. (12,16) Hewas sent to the (5,7) new (5) Jesuit (5,7)boarding (10,12) school (5,12)[OR]college (7,10)of Henri IV (10) [OR]Collège Royal Henry-Le-Grand (14,15)at La Flèche, (5,7)several miles to the north, (10)in Anjou. (12,14)

Figure 3 Collège Royal Henry-Le-Grad

At La Flèche, 1,200 young men were trained for careers in m ilitary engineering, the judiciary, and government administration. (11) It had been established in 1604 by Henry IV (reigned 1589–1610). (11) René attended La Flèche (7,14) until 1614 (7) [OR] 1612, (14) for seven (10,12)[OR] eight (12) years. (10,12)He was (5,12)a good student, (19) but he was (5,12)[OR]might have been (10) a delicate child, (5,12) He was a boy of prodigious curiosity, asking questions endlessly, (12) and his intelligence was remarked upon. (5) In a concession to his delicate health (10,12) he didn’t have to abide by the school’s rigorous schedule. (10) He was allowed (10,12) to rise later in the morning than other students (12) and to rest in bed until midmorning. (10) His father encouraged René to follow in his footsteps and study law. (12) He did this. (5,7) Like many well-educated young men at the time, (13) Descartes studied (13,14) classics, (12,14) logic (10,12)and traditional Aristotelian (14) philosophy (10,12)[OR]music, scienceandmetaphysics (10,11) [OR]acting, poetry, classical studies, dancing, riding, and fencing, (11) [OR] a wide range of topics, but he focused on law so that he could follow his father’s profession. (13)Besides law (13)rhetoric (10) natural philosophy,ethics (10) theology, (12) and astronomy. (10,12) In 1610 he participated in an imposing ceremony in which the heart of Henry IV, whose assassination that year had destroyed the hope of religious tolerance in France and Germany, was placed in the cathedral at La Flèche. (11) In his final two years (12) he also learned mathematics (10,11)and physics, (12,15) which was that of Aristotle (12) learned from Scholastic commentaries (11) and almost entirely wrong. (12) [OR]René learned something of Galileo’s work (12,15) At this time, Galileo had still not published his greatest works overturning Aristotle’s physics; his trouble with the Catholic Church lay in the future. (12) All this equipped René well for his future as a philosopher. (10) Looking back he said of Mathematics “I took pleasure, above all, in mathematics, because of the certainty and the absoluteness of its reasons; but I had not yet discovered its true use… I was astonished that with such solid foundations nothing more eminent had ever been built upon them.” (12) He fiercely believed in independent thinking and resented any attempt to corral his mind. (5,13) His schooling left him dissatisfied, disappointed and full of doubts”. (5) At the age of 18, (12) in 1614, (12,15) René Descartes left La Flèche. (12) Of Philosophy he said “Seeing it had been cultivated by the most powerful minds… but nevertheless there is not in it one single thing which is not disputed, and therefore open to doubt, I had not the presumption to hope that I should succeed better than others. (12) Considering how many different opinions there are… while it was impossible that more than one of them could be true, I regarded as little better than false everything that was merely probable.” (12) Of Science he thought “Since they all borrow their principles from philosophy, I judged that nothing solid could have been built on such insecure foundations.” (12) So he left formal education. (13)

Poitiers University 1615-16

Figure 4 Poitiers University

He then spent some time in Paris studying mathematics, before (14) entering the University of Poitiers, (14,15) In 1615 (15), studying law at the University of Poitiers, in accordance with his father’s wishes that he should become a lawyer, obtaining his law degree in 1616. (14) His health was poor and he was granted permission to remain in bed until 11 o’clock in the morning, a custom he maintained for the rest of his life. (14) As a young law student, Descartes was frustrated by the authoritative, dogmatic style of his professors (13) and later claimed that his formal education provided little of substance. (14) In 1616 (5,7) at the age of 22, (10) [OR] 20 (12) he took a degree (5,7) [OR] Baccalaureate (15) [OR] diploma (12) and License in Canon & Civil (12,15) law (7,10) at Poitiers University, (5,7) later adding theology and medicine to his studies. (10) However, he then abandoned his education: (13,14) “as soon as I was old enough to pass from under the control of my instructors, I entirely abandoned the study of letters, and resolved no longer to seek any knowledge that could not be found in myself, or (13) in the great book of the world.” (11,13)He then spent several years traveling and experiencing the world. (13,14)

1616-18

René’s father probably expected him to enter Parlement, but the minimum age for doing so was 27, and René was only 20. (11) Instead of becoming a lawyer, Descartes started a life of travel. (12,13) For about two years (12) he visited cities all over Europe. (13) He spent some time in Paris. (12) In 1617 (10) [OR] 1619 (7,9) René credited a series of three (10) very powerful dreams or visions (8,10) with determining the course of his study for the rest of his life, (10) Some scholars speculate that he may have had a nervous breakdown during this time. (10)

Military Career 1618-28

Descartes was wealthy enough to pursue his own interests. (12) In 1618 (5,7) at the age of twenty-two (15) when the 30 Years’ War began, (5) in accordance with his ambition to become a professional military officer, (15) he became involved in military affairs (5,6) and took up the life of a (7,8) mercenary (7,8) soldier (7,8) [OR] he may have been a soldier, but the majority of biographers suggest that it is more likely that his duties were oriented more toward engineering or education. (15), He went to Breda in the Netherlands, (11,12) and enlisted (7,15) at his own expense [OR] found employment (8)for15 months (11) as a mercenary (7,8)in the peacetime (11) Dutch States (6,12) army of the Protestant stadholder (6,11) of the United Provinces (6) Maurice (6,11) of Nassau, (6,15) Prince (6,11) of Orange (ruled 1585–1625). (11) It’s ironic that a man so obsessed with self-knowledge and inner reflection would have taken up a life of so much outward adventure. (13) Compare that to Immanuel Kant, who argued strenuously for the importance of sensory experience, yet never left his home town! (13) It is not known what his duties were exactly (15) [OR] Baillet suggests that he would have very likely been drawn to what would now be called the Corps of Engineers. (15) [OR] He became a military engineer. (13)In its military academy (12) [OR] there is no definitive evidence that speaks for there being a full-fledged “academy”, and Sorell notes that in Breda, where Descartes was stationed, the army “doubled as military academy for young noblemen on the Continent”. (15) There he studied (11,12) applied (15) mathematics, (11,15)military (15) engineering (12,13) as established by Simon Stevin, (16) and military architecture (11,15He designed a variety of structures and machines aimed at protecting and assisting soldiers in battle. (15) Gaukroger notes that the education of the young noblemen was structured around the educational model of Lipsius (1547–1606), a highly respected Dutch political theorist who received a Jesuit education at Cologne. (15) Afterwards he continued in the pay of various forces, both Catholic and Protestant: (6,7,8)he travelled (7,10) widely in northern and southern Europe, (7,11) which gave him the leisure to think. (7) [OR] Descartes left the army in 1619, and his whereabouts for the next few years are unknown. (15) He visited Holland, (7,11) Italy (11,15) and Germany, (7,15) spending some of the time in the army of the Catholic Duke of Bavaria. (7) Based on what he says in the Discours de la Methode (Discourse on the Method), published in 1637, there is speculation that he also spent time near Ulm. (15) He attended the coronation of Ferdinand II in Frankfurt in 1619. (15) He was in Bohemia (11,12a) in 1619 (11) and 1620. (12a) He saw some battles. (10) While in the service of the Catholic Duke Maximilian of Bavaria, Descartes (16) was present at the Battle of the White Mountain (12a,16) near Prague, in November 1620, (16) though he probably did no fighting. (5) There he invented analytic geometry, a method of solving geometric problems algebraically and algebraic problems geometrically. (11) He also devised a universal method of deductive reasoning, based on mathematics, that is applicable to all the sciences. (11) He visited France (7,11) moving to Paris in 1622. (11,15)

Figure 5: Battle of the White Mountain, 1620, which Descartes witnessed

Isaac Beeckman

In 1618, while walking (14) in Breda, in Holland René (11,14) met (14) [OR] was introduced to (8,10) the Dutch (8,14)amateur (16) scientist, (8,10) physicist (11) and philosopher Isaac Beeckman (8,10) (1588–1637), (11,14) the principal of a Dordrecht school, who was at the forefront of a new school of thought known as mechanical philosophy. (16) Beeckman rekindled in Descartes an intense interest in (15,16) in his studies of science and mathematics, setting him on a course to apply mathematics and logic to understanding the natural world. (10,11) Beeckman proved an influential teacher, (10,11) sparking off his interest (8,9)in mathematics and the New Physics. (8,14)Together they worked on free fall, catenary, conic section, and fluid statics. (16) Both believed that it was necessary to create a method that thoroughly linked mathematics and physics. (16) This work led him to conclude that his real path in life was the pursuit of true wisdom and science. (8) In 1619 he wrote to him: “To tell you the truth, it was really you who got me out of my idleness and made me remember things I once learned and had nearly forgotten: when my mind wandered from serious [mathematical] matters, you put me back on the right path.” (12) [OR] Descartes would later downplay Beeckman’s influence. (15) In October 1630 he had a falling-out with Beeckman, whom he accused of plagiarizing some of his ideas. (16) Questions posed by Beeckman compelled (15) Descartes to write the Compendium Musicae. (11,15) in 1618, (11) [OR] he did not meet him until after Nov 10th 1619. (9)In this Descartes attempted to work out a theory of harmony rooted in the concepts of proportion or ratio, by expressing it in mathematical terms. (15) It would not be published during Descartes’ lifetime. (15) The Compendium was published in the year Descartes died, in 1650; it was his first surviving work. (11)

Revelation in the Stove-heated room

He had visions (7,12) in the form of a series of dreams that would ultimately change the way scientists work. (12) He believed a spirit sent by God gave him new ideas about scientific method, analytical geometry and philosophy. (12) Two days after the Battle of the White Mountain, (12a) on November 10th (9,12) 1619 (7,9) [OR] 1916, (13) when he was 23 (1,2) [OR] a young soldier in his mid-twenties, Descartes had an experience that would change not only his own life but the whole history of European philosophy. (13) He was in Germany (7,12) in the German town [OR] dreary village (13) of Neuburg an der Donau (12,16) with the army of the Duke of Bavaria. (7) On the cold (13,15) night of 10–11 November 1619 (St. Martin’s Day) (16) he found himself with no campfire to keep warm, (13)

Figure 6 Neuburg an der Donau – ‘a dreary village’

so to escape the cold, (13,16) he shut himself into someone’s furnace (13) [OR] a warm, (12) stove-heated room. (7,12) The heater may have been a cocklestove. (16) He stayed there for hours in the darkness, (13) and there he had (9,13) [OR] said that he had (13) his famous intellectual revelation (9,13) in the form of visions: dreams, or possibly hallucinations, that revealed the possibility of a philosophy. (13) 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. (16) All truths were linked with one another, so that finding a fundamental truth and proceeding with logic would open the way to all science (16) via a school of thought that would encompass philosophy, science, maths, indeed all knowledge, and place that knowledge on a foundation so firm that no scepticism could ever shake it. (13) After emerging from the ‘furnace’, Descartes began his writings. (13) It was small stuff at first. (13)

In France 1622-3

He was still living the life of a wandering soldier. (13) He took great precautions to conceal his address and regularly hid from his friends to work, writing treatises, now lost, on fencing and metals. (11) His father had gifted him (12) [OR] he inherited (15) a number of (12) properties which he sold (12,14) in 1620 (12) [OR] in 1622. (14,15) [OR] He arrived in La Haye in 1623, selling all of his property and (16) investing the proceeds in bonds (14,16) which provided him with a comfortable (12,14) [OR] simple (15) income for the rest of his life. (12,14) Among his friends were the poets Jean-Louis Guez de Balzac (1597–1654), who dedicated his Le Socrate chrétien (1652; “Christian Socrates”) to Descartes, and Théophile de Viau (1590–1626), who was burned in effigy and imprisoned in 1623 for writing verses mocking religious themes. (11) Descartes also befriended the mathematician Claude Mydorge (1585–1647) and Father Marin Mersenne (1588–1648), a man of universal learning who corresponded with hundreds of scholars, writers, mathematicians, and scientists and who became Descartes’s main contact with the larger intellectual world. (11)

Influence of Cardinal Berulle

In 1623, (14) [OR] In April 1629 (16) he joined the University of Franeker; (14) In 1624 he was at Leiden University. (14) Descartes was present at the siege of La Rochelle by Cardinal Richelieu in 1627. (16) At a talk in 1628, (11) [OR] in the fall of the same year, (16) Descartes denied (11) the alchemist Chandoux’s (11,16) claim that probabilities are as good as certainties in science and demonstrated his own method for attaining certainty. (11) The Cardinal Pierre de Bérulle (1575–1629)—who had founded the Oratorian teaching congregation in 1611 as a rival to the Jesuits—was present at the talk. (11) Many commentators speculate that (11) Bérulle urged Descartes to write (11,16)an exposition of his new philosophy (16) a metaphysics based on the philosophy of St. Augustine as a replacement for Jesuit teaching. (11) This should be done in some location beyond the reach of the Inquisition. (16)

In the Dutch Republic 1628-49

Be that as it may, within weeks Descartes left for the Netherlands, which was Protestant. (11)Descartes returned to the Dutch Republic in 1628. (16)This was to complete his work (5) [OR] to pursue his rather heretical ideas further, (8) [OR] or because his meeting with Cardinal de Bérulle had shown him that his ideas would be regarded as heretical (11) because life in France was too bustling for him to concentrate on his work (10,12) [OR] he found he needed more peace and quiet (5,12) than military service would allow. (5) Whatever the reason, he resigned his Commission and, (5) in 1628, (5,7) [OR] 1629 (6) and moved (5,8) from the restrictions of Catholic France to the more liberal environment of (8,11)the Protestant (11) Netherlands (5,8) [OR] to Holland [OR] to the Dutch Republic. (6) He stayed there for the next (5,6) 16 (11) [OR] 20 (6,12) [OR] more than 20 (10,11) [OR] 21 (5) [OR] 22 (11) years, (5,6) He spent most of his adult life there, and (8) and acquired a considerable reputation long before he published anything. (11) He became “one of the most notable intellectual figures of the Dutch Golden Age”. (6)

Personal Life

Few details are known of his personal life. (7,10) While in France selling his property in 1622, (14,15) he gambled, rode, fenced, and went to the court, concerts, and the theatre. (11) [OR] He lived quietly (7) single, (11,12)alone and in seclusion, like a Rosicrucian. (11) He habitually spent mornings in bed, where he continued to honour his dream life, incorporating it into his waking methodologies in conscious meditation, (10) working on his dream of merging algebra and geometry. (8) [OR] teaching mathematics. (12) He changed his residence often (11,12) (18 times) (11) [OR] 14 separate addresses in 10 different Dutch cities. (14) During his 20 year period of frequent moves Descartes wrote almost all of his major works on philosophy, mathematics and science. (14) In 1630 he was in Amsterdam, where he worked on drafts of the Dioptrique (the Optics) and the Meteors (the Meteorology), which were very likely intended to be a part of a larger work, Le Monde (The World). (15) In 1632 he moved again, this time to Deventer, to apparently teach Henry Reneri (1593–1639) his physics. (15) Constantijn Huygens received what Descartes refers to as “three sheets” of The World, along with a letter dated 5 October 1637. (15) These “sheets” deal primarily with mechanics. (15) Around 1635, Reneri began teaching “Cartesian” physics at the University of Utrecht. (15) It is also during his stay in Deventer that Descartes probably worked on a final draft of the Traite de l’homme (Treatise on Man), which in connection to the Optics and the Meteorology was probably originally intended to be a part of The World. (15) In 1635, he was at Utrecht University, (14) and in about March of 1636, at the age of forty, Descartes moved to Leiden to work out the publishing of the Discourse. (15) In 1636 Reneri acquired an official chair in Philosophy at the University of Utrecht, and continued to build a following of students interested in Cartesian science. (15)

Francine

With the Discourse out and a following of students building in Utrecht, Descartes seems to have turned his attention from career to family, because on 19th June (15) 1635 (11,15) he had had an illegitimate daughter called Francine (7,10) after a relationship in Amsterdam with (14,15) Helena (10,11) [OR] Helene (15) Jans van der Strom, a maid in his house. (10,11) She was born in Deventer. (16)

Figure 7 Deventer, birthplace of Francine

According to a baptismal record, dated 28th July 1635, Descartes is named the father. (15) However, Gaukroger claims that the baptismal date was 7th August 1635. (15) In a letter dated 30 August 1637 we find him apparently working out an arrangement for Francine, but strangely (15) refers to her as his “niece” (12,15) which suggests that he did not want certain people to know that he was a father (or that Francine had been born out of wedlock). (15) Gaukroger suggests that despite this apparent denial of paternity, Descartes not only corresponds with Francine, but in 1637 (15) brings her and Helene to his new home (12,15) at Santpoort or Egmond-Binnen. (15) He had planned to have Francine educated in France, (10,12) and had arranged for her to live with relatives, (10) but she died of (10,12)scarlet (11) fever (10,11) in 1640 at the age of five. (7,10)Her death was apparently a terrible blow for him. (7) Descartes wrote, “I am not one of those philosophers who think a man should not cry.” (11) Helena later got married, with Descartes playing a fatherly role by paying the wedding dowry. (12) He also supported the nurse who had saved his life by nursing him through his schoolday illnesses, paying her a permanent pension. (12) There is evidence suggesting that he was called away from Leiden around the time of her death, returning soon after. (15) Some have speculated that he left Leiden to be at her side. (15) His father and sister died in the same year. (15) There was always affection between René and his father. (12) [OR] Descartes’ relationship with his father (and brother) was of the sort that Pierre, his brother, failed to even bother him with the news of their father’s death. (15) Rather, it seems to have been in a letter from Mersenne that Descartes first learns of it. (15) In a follow up letter to Mersenne, dated 3 December 1640, Descartes expresses regret in not having been able to see his father before his death. (15) But, he refuses to leave Leiden to attend his father’s funeral, and instead stays to complete the publishing of the Meditations. (15)

And Rosicrucianism

Some scholars claim that Descartes adopted Bérulle as director of his conscience, but this is unlikely, given Descartes’s background and beliefs (he came from a Huguenot province, he was not a Catholic enthusiast). (11) He investigated reports of esoteric knowledge, such as the claims of the practitioners of theosophy to be able to command nature. (11) Although disappointed with the followers of the Catalan mystic Ramon Llull (1232/33–1315/16) and the German alchemist Heinrich Cornelius Agrippa von Nettesheim (1486–1535), he was impressed by the German mathematician Johann Faulhaber (1580–1635), a member of the mystical society of the Rosicrucians. (11) Descartes shared a number of Rosicrucian goals and habits. (11) Like the Rosicrucians, he lived alone and in seclusion, practiced medicine without charge, attempted to increase human longevity, and took an optimistic view of the capacity of science to improve the human condition. (11) He advocated religious tolerance and championed the use of reason. (11) At the end of his life, he left a chest of personal papers (none of which has survived) with a Rosicrucian physician—his close friend Corneille van Hogelande, who handled his affairs in the Netherlands. (11) Despite these affinities, Descartes rejected the Rosicrucians’ magical and mystical beliefs. (11)

Withholds publication of ‘The World’, 1633

By 1633 his ‘The World’ had become ready for publication. (15) It seems to have consisted of several smaller, but related, works: a treatise on physics, a treatise on mechanics (machines), a treatise on animals, and a treatise on man. (15) Like Galileo, Descartes believed the sun sits at the centre of the solar system, and he had intended publishing The World, containing this assertion. (12,14) In June, 1633, (12) however, he learned that the Catholic Church had tried Galileo (12,15) and Nicolaus Copernicus (14) for heresy. (12) Galileo might have been burned at the stake if his trial had gone worse than it did. (12) The sentence was reduced to permanent house arrest because Galileo was rather elderly. (12) The Church also prohibited Galileo’s works. (12) In a letter to Mersenne, dated November (15) 1633, (14,15) Descartes expresses his fear that were he to publish The World, the same fate that befell Galileo would befall him. (15) Unwilling to suffer the same fate as Galileo, (13,15) Descartes decided not to risk the Church’s wrath (12,15) and held off publication of his first work, “Le Monde” (“The World”), (12,14) And, although this is something that he would understandably want to avoid, some scholars question Descartes’ expressed concern, for his living in the Netherlands would have kept him out of reach of Catholic authorities. (15) Although much of ‘The World’ has been lost, some of it seems to have survived in the form of essays attached to the Discourse which, as was mentioned earlier, would be published four years later, in 1637. (15) Some of it was published posthumously. (15)

Discourse on Method 1637

It was, therefore, only years later that he began publishing his ideas. (13) 18 years after his revelation in the stove-heated room at Neuberg (12) in 1637, (4,8) he published (8,12) his ground-breaking philosophical and mathematical treatise (8) ‘Discourse on Method’ (3,4) [OR] Discussion of the Method (12) [OR]Discourse on the Method of Rightly Conducting the Reason and Seeking Truth in the Sciences. (10) It introduced his philosophy (3) in French and Latin. (6) It was his first published work, coming some four years after he had abandoned The World. (15) The Discourse is important for many reasons. (15) For instance, it tells us what Descartes himself seems to have thought of his early education, and in particular, his early exposure to mathematics. (15) Roger Ariew suggests that these reflections are not so much those of the historical Descartes, as much as they are those of a persona Descartes adopts in telling the story of the Discourse. (15) Uncontested, however, is the view that the Discourse sketches out the metaphysical underpinnings of the Cartesian system. (15)

Scientific Method

He proposed a new universal method of deductive reasoning, based on mathematics, that is applicable to all the sciences, (11) to reconstruct knowledge (piece by piece, such that at no stage was the possibility of doubt allowed to creep back in) in order to acquire a firm foundation for genuine knowledge and to dispel any Scepticism. (14) It was his first rationalist vision of the progress of human knowledge. (14)His scientific method contained four (11,12) [OR] five (11) main ideas for scientific progress, (11,12) borrowing from mathematical procedures, (11) were: (11,12) Never accept anything except clear and distinct ideas (11,14) (1)clearly defined and limited. (11) Never accept anything as true until all reasons for doubt can be ruled out; (11,12) a process often referred to as methodological scepticism or Cartesian doubt or hyperbolic doubt. (14) Divide each problem into as many parts are needed to solve it. (12,14) [OR] into their simplest parts; (11,12) Arrange the elements starting with the simplest and easiest to know, (12,14) ascending little by little, and, step by step, to more complex knowledge; (11,12) recheck the reasoning (11,12)making enumerations so complete, and reviews so general, that nothing is omitted. (12) It is ironic that Descartes’ own method might lead us to doubt that a dream 18 years earlier could have been the true source of his ideas! (12) To demonstrate the attainability of certainty, (4) to prove that one cannot doubt one’s own existence as a thinking being: he said (2) probably the most famous three words in all of philosophy: (13) ‘cogito ergo sum’ – ‘I think therefore I am.’ (2,4) In French: ‘Je pense, donc je suis’. (6,11) He stated it in his Discourse on Method, (4) [OR] in ‘Meditationes de prima Philosophia’, (1641) (2) [OR] in ‘Principles of Philosophy’ a more formal exposition of his central tenets (14) (1644) (6) in Latin). (6,14) ‘Cogito ergo sum’ (2,4) is an enigmatic phrase and doesn’t make much sense out of context. (13) It was what he regarded as the first indubitably true proposition: (7) Descartes asserted that a human would still be a human without hands or hair or a face. (9) He also asserted that other things that are not human may have hair, hands, or faces, but a human would not be a human without reason, and only humans possessed the ability to reason. (9) Along with the ‘Discourse’, (7) the ‘Meditationes’ of 1641 (7,14) and the Principia philosophiae’ of 1644, (7,14) set out the fundamental Cartesian doctrines; (7) the method of systematic doubt (7,8) rebuilding knowledge from the ground (8); the ‘indubitably true proposition’; (7) and rationalism. (8,9)Reason was a native gift of humans and true knowledge could not be gleaned from books but only through the methodical application of reason. (9) It was this stress on reason which made Descartes a ‘Rationalist’. (9) Descartes attempted to narrow down, by what is sometimes called the method of doubt, what was certain and what contained even a shadow of a doubt. (14) For example, he realized that he could doubt even something as apparently fundamental as whether he had a body (it could be that he was just dreaming of it or that it was an illusion created by an evil demon), but he could not, under any circumstances, doubt whether he had a mind or that he could think. (14)It also led him to define the idea of (10) the dualism of mind and matter, (7,8) matter meeting non-matter. (10) He identified the point of contact for the body with the soul at the pineal gland. (10)

His choice of language for his publications

Figure 8: ‘more popular ones in French’

He published most of his major works while in Holland. (7) He wrote beautiful, engaging books that proved extremely popular with European nobility. (13) the more popular ones in French, (7,9) the language of his countrymen, so that people without a formal education could understand him, (9) and the more scholarly ones in Latin, (7,9) the language of scholars. (9) The expressed aim of many of his books was to present complex scientific and philosophical matters in such a way that the least sophisticated readers could understand them. (9) Because Descartes believed that every human possesses the “natural light” of reason, he believed that if he presented all his arguments as logical trains of thought, then anyone could understand them and nobody could help but be swayed. (9) In the original edition of Discourse on the Method, in fact, Descartes declares his aim with the subtitle “In which the Author… explains the most abstruse Topics he could choose, and does so in such a way that even persons who have never studied can understand them.” (9) Queens and princesses wrote to him personally, requesting answers to their philosophical questions, and for his remaining years Descartes made a good living as a tutor to Europe’s most powerful women. (13)

Descartes and Mathematics

Geometry 1637

His most important contributions were in the field of mathematics, (13) where his influence in mathematics is equally apparent. (6,7) His ‘Geometry’ followed on from early movements towards the use of symbolic expressions in mathematics by Diophantus, Al-Khwarizmi and François Viète. (8) He also invented the notation which uses superscripts to indicate powers or exponents, and his rule of signs is also a commonly used method to determine the number of positive and negative zeros of a polynomial. (14) It can be argued that his reflections on mind and mechanism, impelled by the invention of the electronic computer and by the possibility of machine intelligence, blossomed into the Turing test of a machine’s capability to demonstrate intelligence. (14)

Algebraic Notation

He reformed algebraic notation. (7,8) “In 1637 he published ‘Geometry’. (3,15) as one of the appendices to ‘Discourse on Method’. (3,8) It was perhaps the first book to look like a modern mathematics textbook, full of a‘s and b‘s, x2‘s, etc. and it is now considered a landmark in the history of mathematics. (8) La Géométrie” introduced what has become known as the standard algebraic notation, using lowercase a, b and c for known quantities and x, y and z for unknown quantities. (8) He also developed a “rule of signs” technique for determining the number of positive or negative real roots of a polynomial (8); and ‘invented’ (or at least popularized) the superscript notation for showing powers or exponents (e.g. 24 to show 2 x 2 x 2 x 2) and a3 rather than a.a.a. (8,12) He re-discovered Thabit ibn Qurra’s general formula for amicable numbers, as well as the amicable pair 9,363,584 and 9,437,056 (which had also been discovered by another Islamic mathematician, Yazdi, almost a century earlier). (8)

Analytic Geometry

Figure 9: ‘Cartesian co-ordinates’

Descartes created a bridge between (6,8) the previously separate (12,13) fields of algebra and geometry. (9,12)Descartes’ ground-breaking work, is usually referred to as (8) analytic geometry, (3,6) or Cartesian geometry (8), and the ‘Cartesian coordinate system’ was named after him. (6,13)[OR] The claim that Descartes is the originator of analytic geometry, at least as we understand it today, overstates the case. (15) Although the Geometry would seem to have come out of nowhere, there is evidence in Descartes’s notes to himself, from which Clerselier reconstructed some of Descartes’s correspondence, that he had been working on some version of it as early as 1619. (15) In a letter to Beeckman, dated 26 March 1619, for example, Descartes discusses the subject matter that is found in the Geometry, and in a letter dated 23rd April 1619, he explicitly mentions the book’s title. (15) It is in this work that Descartes shows how certain geometrical problems can be solved by way of algebraic equations. (15) Descartes showed that algebraic variables (like x and y) could be represented as points along a number line. (13) Any two variables, therefore, could be defined in relationship to one another using a two-dimensional plot. (13) By enabling a representation of geometric figures by algebraic equations and algebraic equations by geometric figures, (3,8)he could solve problems in geometry by converting them into problems in algebra. (8,12) He arrived at this via ‘coordinate geometry’, (7) an application of the principle of relying on reason rather than sense impression. (9) It was in “La Géométrie” that Descartes first proposed that each point in two dimensions can be described by two numbers on a plane, one giving the point’s horizontal location and the other the vertical location, which have come to be known as Cartesian coordinates. (8,12) By creating a two-dimensional graph on which problems could be plotted, he developed a visual vocabulary for arithmetic and algebraic ideas. (9) He used perpendicular lines (or axes), crossing at a point called the origin, to measure the horizontal (x) and vertical (y) locations, (11,12) both positive and negative, thus effectively dividing the plane up into four quadrants. (8) [OR] It’s hard to imagine science and maths without the concept of an x axis and a y axis, (13) although Descartes never actually drew an x- or y-axis in his work. (12) These were assumed in his diagrams. (12) The axes were formally introduced by the mathematician Frans van Schooten and other mathematicians in Leiden who translated La Gèomètrie from French into Latin, while developing it further. (12) Latin editions of La Gèomètrie were released in 1649, 1659 and 1661. (12) By this means curves could be expressed in terms of x and y on a two-dimensional plane and hence as equations in algebra: (12) he made it possible to express mathematics and algebra in geometric forms, (9) allowing the conversion of geometry into algebra (and vice versa). (8) Any equation can be represented on the plane by plotting on it the solution set of the equation. (8) For example, the simple equation y = x yields a straight line linking together the points (0,0), (1,1), (2,2), (3,3), etc. (8) The equation y = 2x yields a straight line linking together the points (0,0), (1,2), (2,4), (3,6), etc. (8) More complex equations involving x2, x3, etc, plot various types of curves on the plane. (8) As a point moves along a curve, then, its coordinates change, but an equation can be written to describe the change in the value of the coordinates at any point in the figure. (8) Using this novel approach, it soon became clear that an equation like x2 + y2 = 4, for example, describes a circle; y2 – 16x a curve called a parabola; x2⁄a2 + y2⁄b2 = 1 an ellipse; x2⁄a2 – y2⁄b2 = 1 a hyperbola; etc. (8) By this means he could solve previously unsolvable problems in geometry by converting them into simpler problems in algebra. (12) A pair of simultaneous equations could now be solved either algebraically or graphically (at the intersection of two lines). (8) Unleashing the mathematical power of algebra to tackle problems in geometry, (12,13) was a tremendous conceptual breakthrough. (8,13)Every scatter plot you’ve ever seen, every line graph showing changes in the stock market, every bell curve and parabola – they all come back to the Cartesian coordinate system. (13) [OR] It should be noted, however, that as groundbreaking as this work may have been, contrary to the claims of many, nowhere in the Geometry is a “Cartesian Coordinate System” ever developed (that is, the x-y coordinate system taught to today’s students of algebra) (15) Simple as it may seem in hindsight, (13) it was far and away Descartes’ most important contribution to mathematics. (8,13)It was the most revolutionary mathematical idea since the invention of zero. (13) He had single-handedly invented the modern field of analytic geometry. (13) Descartes surpassed the expertise of Ancient Greece’s brilliant geometers: he could now solve problems that had defeated them. (12) and is now indispensable in mathematics and other sciences. (12,13)He also developed a method to understanding the properties of objects in the real world by reducing their shapes to formulae and approaching them through reason rather than sense perception. (9)

Fermat and Descartes

Analytical geometry was independently invented (3,12) earlier (12) [OR] simultaneously (3) by Pierre de Fermat, who lived in France at the same time as Descartes. (3,12) Fermat worked on mathematics for his own pleasure and often kept his results private. (12) He did, however, enjoy issuing challenges to other mathematicians to solve problems. (12) In 1638 Fermat sent a work entitled Introduction to Plane and Solid Loci to the mathematician, Marin Mersenne, to show how problems he had posed at an earlier date could be solved. (12) Fermat’s approach was different from Descartes’. (12) Descartes showed how geometry could be expressed as algebra; Fermat showed how algebra could be expressed as geometry. (12)

Calculus

Both Fermat and (12) Descartes helped guide Newton and Leibniz’s development of calculus. (12,14) Calculus has been crucial to the progress of mathematics and the sciences. (12,13) The significance of the sort of connection that Descartes made between geometry and algebra was great indeed, for without it the mathematization of the physics and the development of the calculus might not have happened when they did (15) in the 1660s by Isaac Newton, (12,13) and independently in the 1670s (12) by Gottfried Leibniz (12,15) (1646–1716). (15) It opened up limitless possibilities for physics (13) Analytical geometry was used in the discovery of infinitesimal calculus and analysis. (6,8) In La Gèomètrie, Descartes showed how he could find tangents to curves, a vital part of differential calculus. (12) Both Descartes and Fermat applied analytic geometry to the finding of tangents to curves. (3,12) Fermat’s methods were actually simpler than Descartes’. (12) He was not the originator of other mathematical concepts that bear his name, for example, the “Cartesian Product”. (15) Carl Boyer notes that various concepts that lead to analytic geometry are found for the first time in the Geometry, and that the Geometry’s mathematical notation is still used today. (15) But, he argues, although Cartesian geometry is taken by many to be synonymous with analytic geometry, the fact is that the fundamental aim of Descartes’ system is quite different from that of contemporary analytic geometry. (15)

Descartes and Science

The Aristotelian philosophy of Descartes’s days held that the universe was inherently purposeful or teleological. (16) Everything that happened, be it the motion of the stars or the growth of a tree, was supposedly explainable by a certain purpose, goal or end that worked its way out within nature. (16) Aristotle called this the “final cause,” and these final causes were indispensable for explaining the ways nature operated. (16) Descartes’s 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. (16) By “thinking”, Descartes did not just mean conceptual thought, but all forms of consciousness, experience, feelings, etc. (14) Furthermore, he asserted that the essence of this physical world was extension (that it takes up space), contrary to the extensionless world of the mind. (14) Paradoxically, this was an essential step forward in 17th Century science as it established a physical world which was of a mathematical character and permitted mathematical physics to be used to explain it. (14) Also important is that, as we have seen, although God was indispensable to Descartes’ method of arriving at a physical world, once such a world was accepted, it was no longer necessary to involve God in the description and measurement and explanation of how things work. (14) Thus, the process of science was freed from theological constraints and interference. (14) Cartesian geometry unlocked the possibility of navigating geometries of higher dimensions, impossible to physically visualize – a concept which was to become central to modern technology and physics – thus transforming mathematics forever. (8) Descartes was also, therefore, one of the key figures in the Scientific Revolution. (6) In his ‘Principles of Philosophy’ of 1644 he said that he hoped to deduce the laws of nature from first principles. (12) Although the book had much to commend it to philosophers, its science was incorrect. (12) He argued that action at a distance is impossible: in 1662 Robert Boyle demonstrated that the magnetic force can travel through a vacuum, establishing that action at a distance is possible. (12) He agreed with Aristotle that there could be no vacuum. (12) In 1654 Otto von Guericke constructed the first vacuum pump. (12) His power as a philosopher would be defeated by such scientific experiments, but he did not live long enough to learn of these developments. (12)

Physics

The ‘Discourse’ served as a preface to his works on dioptrics and meteorology (3,15) which, with ‘Optics’ are apparently added so as to exemplify the method of inquiry it develops (though admittedly it is unclear how the method is applied in these essays). (15) It should be stressed that the three attached essays are important independent of the Discourse, for they contain much worth studying. (15) The Optics and Meteorology were very likely versions of works originally intended for The World. (15) From this he had an influential rôle in the development of modern physics, a rôle which has been, until quite recently, generally under-appreciated and under-investigated. (8) He provided mechanistic explanations in terms of matter and motion of a wide variety of physical chemical and biological phenomena. (3) In physics, Descartes introduced (before Newton) the concept of momentum of a moving body (what he termed the “amount of motion”), which he defined as the product of the mass of the body and its velocity or speed. (14) His three (14) “laws of nature” (8,14) were the first distinctly modern formulation of laws of nature. (8) became the basis of Newton’s later laws of motion and the modern theory of dynamics: that each thing tries to remain in the same state and, once moved, continues to move; that all movement is along straight lines; and that when a body comes into contact with another body the combined “quantity of motion” remain the same. (14) This was his ‘conservation of motion principle’. (8,14) According to Thomas Kuhn, he and Newton held the teleological principle that God conserved the amount of motion in the universe. (12a)

Astronomy

In an attempt to explain the orbits of planets, (14) he made important contributions in astronomy, for example with his theory of vortices. (7,14)He constructed a (3,8) vortex (3,14) theory of planetary motion (3,8)which would become the most popular theory of planetary motion of the late 17th Century (8,14)(although subsequently discredited). (14) He proposed a naturalistic account of the formation of the solar system, although he felt he had to suppress much of that due to Galileo’s fate at the hands of the Inquisition. (10,12)

Optics

Descartes also made (2,16) major (2) contributions to optics. (2,16)Willebrord Snellius (1580–1626) had found the mathematical law of refraction, (12a) now known as Snell’s law, (12a,15) [OR] (in France) (16) Descartes’ law (14,16) in 1621. (12a) in relation to the reflection and refraction of light. (8) Descartes first published this (12a) in his essay on optics, (12a,15) attached as a bonus to the ‘Discourse’ (15) in 1632. (12a) Through his laws of refraction, Descartes developed an empirical understanding of rainbows. (10,12) Descartes showed, by using geometric construction and the law of refraction (also known as Descartes’ law), that the angular radius of a rainbow is 42° (i.e. the angle subtended at the eye by the edge of the rainbow and the rainbow’s centre is 42°) (12a,14) He also independently discovered the law of reflection, (12a,14) (that the angle of incidence equals the angle of reflection). (14)

Biology

Reflexes

Descartes advanced a theory on automatic bodily reactions to external events which influenced 19th-century reflex theory. (16) He argued that external motions such as touch and sound reach the endings of the nerves and affect the animal spirits. (16) 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. (16) Through this chain of reactions the automatic reactions of the body do not require a thought process. (16)

Animal suffering

Descartes denied that animals had reason or intelligence. (16) He argued that animals did not lack sensations or perceptions, but these could be explained mechanistically. (16) Whereas humans had a soul, or mind, and were able to feel pain and anxiety, animals by virtue of not having a soul could not feel pain or anxiety. (16) If animals showed signs of distress then this was to protect the body from damage, but the innate state needed for them to suffer was absent. (16) Although Descartes’s views were not universally accepted they became prominent in Europe and North America, allowing humans to treat animals without regard to their feelings. (16) The view that animals were quite separate from humanity and merely machines allowed for the maltreatment of animals, and was sanctioned in law and societal norms until the middle of the 19th century. (16) The publications of Charles Darwin would eventually erode the Cartesian view of animals. (16)

Theology

Descartes’ approach of combining mathematics and logic with philosophy to explain the physical world turned metaphysical when confronted with questions of theology; (10) It led him to a contemplation of the nature of existence. (10) It should be noted, however, that for all Descartes’ innovation and boldness, he does not abandon the traditional idea of God. (14) While Cartesian dualism paved the way for modern physics, it also held the door open for religious beliefs about the immortality of the soul. (16) Descartes’s dualism of mind and matter implied a concept of human beings. (16) A human was according to Descartes a composite entity of mind and body. (16) 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. (16) He defined “substance” (essentially meaning what the world really consists of) as “that which requires nothing other than itself in order to exist”, but he concluded that the only true substance was God himself, because everything else (from souls to material objects like the human body) was dependent on God for its existence. (14) He used his own variations of the causal argument, the ontological argument and the cosmological argument for the existence of God in his “Meditations”, and the existence of God played a major role in his validation of reason and in other parts of Descartes’ system. (14) He remained a Catholic all his life, and he was careful to modify or even suppress some of some of his latest scientific views, for example his sympathy with Copernicus, mindful no doubt of Galileo’s condemnation by the inquisition In 1634. (7) Given the important rôle God plays in his work, suggestions that Descartes was really a closet atheist, and that he includes the arguments for the existence of God as window dressing, appear extremely unlikely. (14) In his theology, he promoted the idea of God as the absolutely perfect being (7) and insisted on the absolute freedom of God’s act of creation. (6) Having dispelled all doubt by the application of his ‘scientific method’, Descartes then worked to build up, or reconstitute, the world again. (14) But he was careful not to do this willy-nilly, but only according to his own very strict rules, so that the “reconstituted world” was not the same as the original one which he had dismantled piece by piece due to doubts. (14) The way he achieved this (which, it must be said, appears from a modern viewpoint like something of a conjuring trick) was to argue that among the contents of our (certain) consciousness was the idea of God, which in itself he saw as proof of the existence of God. (14) He then argued that, if we have the overwhelming impression of the existence of a concrete world around us, as we do, then an omnipotent, omniscient and omnibenevolent God would ensure that such a world does in fact exist for us. (14) His rationalism was controversial, because it sought to dethrone what had been the centre of truth in Europe for centuries: Christianity. (13) 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. (16) In that way, each person is turned into a reasoning adult, a subject and agent, as opposed to a child obedient to God. (16) 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. (16) This anthropocentric perspective of Descartes’s work, establishing human reason as autonomous, provided the basis for the Enlightenment’s emancipation from God and the Church. (16) Descartes called himself a Christian and made arguments for the existence of God, but his view was that God had to be the end of the argument, not the beginning. (13) You couldn’t say “God exists, therefore x is true” – you had to say “x is true, therefore God exists.” This put him in conflict with some Christians who wanted to base their religion on faith rather than rationality. (13) It has been argued that Descartes himself did not realize the extent of this revolutionary move. (16) 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. (16) In an anthropocentric revolution, the human being is now raised to the level of a subject, an agent, an emancipated being equipped with autonomous reason. (16) 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. (16)

Voetius 1638-43

In about 1638, soon after his encounter with the Sorbonne, Descartes’ public life was further complicated by the Dutch theologian, Gisbert Voetius (1588–1676). (15) Voetius had attacked Regius, a Dutch physician who taught medicine at the University of Utrecht, for his having taught certain “Cartesian” ideas that conflicted with traditional theological doctrine. (15) Regius was friend to both Reneri and Descartes, and was a strong adherent to Descartes’s philosophical views. (15) Voetius tried to have Regius removed from his position as professor, and attacked not only Descartes’ work but his character. (15) In his defence Descartes entered into the debate. (15) The controversy would leave Regius confined to teaching medicine, and his published defence of (his conception of) Cartesian thought would be officially condemned by Voetius, who in five years time would rise to the position of University rector. (15) At the end of the debate, which off and on lasted about five years, the situation ultimately became desperate for Descartes. (15) He feared being expelled from the country and of seeing his books burned. (15) He even sought protection by asking the Prince of Orange to intervene and quell Voetius’ attack. (15) In 1643, Cartesian philosophy was condemned at the University of Utrecht, (14,16) and at the age of forty-seven (15) Descartes was obliged to flee to the Hague, (15) settling in Egmond (15,16) Binnen. (16) [OR] du Hoef. (15

Philosophy

He embarked on mathematical research and decided to set about constructing a general theory of knowledge. (5) The great mathematician didn’t stop with the study of numbers – he wanted the same logical, step-by-step thinking to apply in philosophy, indeed in all of life. (13) Descartes is regarded as one of the greatest philosophers of all time. (12)

Philosophical antecedents

Bala proposes that the changes involved in the Scientific Revolution—the mathematical realist turn, the mechanical philosophy, the atomism, the central role assigned to the Sun in Copernican heliocentrism—have to be seen as rooted in multicultural influences on Europe. (12a) He sees specific influences in Alhazen’s physical optical theory, Chinese mechanical technologies leading to the perception of the world as a machine, the Hindu-Arabic numeral system, which carried implicitly a new mode of mathematical atomic thinking, and the heliocentrism rooted in ancient Egyptian religious ideas associated with Hermeticism. (12a) Many elements of Descartes’s philosophy have precedents in late Aristotelianism, the revived Stoicism of the 16th century, or in earlier philosophers like Augustine. (6) His ‘Geometry’ followed on from early movements towards the use of symbolic expressions in mathematics by Diophantus, Al-Khwarizmi and François Viète. (8) Bala argues that by ignoring such multicultural impacts we have been led to a Eurocentric conception of the Scientific Revolution. However, he clearly states: “The makers of the revolution—Copernicus, Kepler, Galileo, Descartes, Newton, and many others—had to selectively appropriate relevant ideas, transform them, and create new auxiliary concepts in order to complete their task… (12a) In the ultimate analysis, even if the revolution was rooted upon a multicultural base it is the accomplishment of Europeans in Europe.” (12a) Christia Mercer posits that the most influential ideas in Meditations on First Philosophy were lifted from 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. (16) [OR] Refusing to accept the authority of previous philosophers, (6,14) in a stubborn rejection of authority (13) Descartes frequently set his views apart from the philosophers who preceded him. (6) For him, this period was a time of hope for a revolution in science. (11) The view of the universe adopted by Galileo had been based on observation, experiment and a liberal application of mathematics. (5,12a) He said that “philosophy [i.e., physics] is written in this grand book—I mean the universe—which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. (12a) It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth. (12a) Descartes took a somewhat different attitude. (5) He set about formulating a new philosophical approach to the universe that broke completely with the old mediaeval scholastic outlook. (5) In his natural philosophy, he differed from the schoolmen 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. (6) Descartes believed in basically clearing all preconceived and inherited notions off the table. (10) He wouldwrite “as if no one had written on these matters before.” (6) Starting afresh, (10) he would put back one by one the things that were certain, (7,10) thus reconstructing the whole of philosophy, and indeed of knowledge, into a unified system of certain truth modelled on mathematics and supported by a rigorous rationalism. (7) Since Descartes believed that all truths were ultimately linked, he sought to uncover the meaning of the natural world with a rational approach, through science and mathematics. (10) The English philosopher (11) Sir (10) Francis Bacon (10,11) (1561–1626), in Advancement of Learning (1605), had earlier proposed a new science of observation and experiment to replace the traditional Aristotelian science, (11) as Descartes himself did later. (10,11) dismissing apparent knowledge derived from authority, the senses, and reason and erected new epistemic foundations. (11) This process for him began with the statement “I exist.” (10) From this sprang his most famous quote: (10) ‘cogito ergo sum’ – ‘I think therefore I am.’ (2,4) In French: ‘Je pense, donc je suis’. (6,11)

Scepticism

Descartes lived during a very sceptical period, at a time before science as we know it existed, and after a long period of relative stagnation in philosophical thought during the Church-dominated and Aristotle-influenced late Middle Ages. (14) One of his main lines of thought was scepticism – that everything should be doubted until it could be proved. (12) He had been impressed, in both his academic work and in his experience of the world at large, by the realization that there appeared to be no certain way of acquiring knowledge, and he saw his main task as the epistemological one of establishing what might be certain knowledge as a stepping stone towards the ultimate pursuit of truth. (14) His more immediate aim in this was to put scientific inquiry in (14) a position where it was no longer subject to attack by Sceptics, (13,14) and he tried to do this by a kind of pre-emptive Scepticism, (14) essentially by being more sceptical than the Sceptics. (14) Applying an original system of methodical doubt, (11) He aimed to re found human knowledge on a basis secure from scepticism. (2,4) [OR] His first step was to throw out everything he thought he knew, (9) seeking “no knowledge other than that which could be found in myself or else in the great book of the world,” (10) on the basis that we should throw out any idea that wasn’t based on absolute certainty. (13) He refused to believe in even the most basic premises before proving them to himself satisfactorily, (9,10)He would only reason from principles that he knew for sure to be the case. (13) In this act of demolishing and reconstructing knowledge, René felt it would be a waste of time to tear down each idea individually. (9) He was sceptical of his own senses, (9,13 attacking the idea that sense perception is necessarily accurate. (9)

Problems with Scepticism

Scepticism sounds nice in theory, but it quickly gets you into trouble. (13) You can be sceptical about the things your teachers say, or sceptical about a tenet of your religion. (13) After all, you could be hallucinating or dreaming. (13) What if the things you see and hear are just illusions? (13) Worse, what if your whole existence is an illusion? (13) We look around and experience the world, but how can we be sure that our experiences are real? (13) What if you were really just a brain in a vat, being stimulated by electrodes but not really experiencing anything? (13) It’s a disturbing thought, but disproving it isn’t easy! (13) Likewise, Descartes suggests that, for all he knows, he may be under the control of an all-powerful being bent on deceiving him. (4,9) In that case, he does not have a body at all but is merely a brain fed information and illusions by the all-powerful being, (as in the Matrix films). (9) In this situation ‘I think therefore I am’ was secure, because even if an all-powerful demon were to try to deceive him into thinking that he exists when he does not, he would have to exist in order for the demon to deceive him. (4,14) His conclusion was the act of thinking, that the demon could never make him believe that he was thinking when he was not (because, after all, even a false thought is still a thought). (14) Therefore, whenever he thinks, he exists. (4) Furthermore, as he argued in his replies to critics in the second edition (1642) of the Meditations, the statement “I am” (sum) expresses an immediate intuition, not the conclusion of a piece of reasoning (regarding the steps of which he could be deceived), and is thus indubitable. (4) Having identified this single indubitable principle, that thought exists, he then argued that, if someone was wondering whether or not he existed, then the very act of thinking was, in and of itself, proof that he did in fact exist: the famous “Je pense, donc je suis” (“I think, therefore I am”) – the similar statement in Latin, “Cogito ergo sum” is found in his later “Principles of Philosophy”. (14)

Defects in sense impression not insuperable

He sought to demonstrate that the senses can be deceived. (9,14) He pointed out that he dreamed of things that seemed real to him while he was asleep. (9) He had, of course, some personal experience with hallucinations. (13) A wax object, having certain properties of size, color, smell, temperature, etc, appears to change almost all of these properties when it is melted, to the extent that it appears to our senses to be a completely different thing. (14) However, we know that it is in fact still the same piece of wax. (14) Descartes concluded from this that the senses can be misleading and that reason and deduction is the only reliable method of attaining knowledge, which is the essence of Rationalism. (14) If we cannot trust our senses to convey true information about the world around us, then we also can’t trust deductions we’ve made on the grounds of sense perception. (9,14) Dreaming that he sits by a fire in his room, he seems to be able to feel the warmth of the fire, just as he feels it in his waking life, even though there is no fire. (9) The fact that he feels the fire doesn’t really allow him to tell when he is awake and when he is dreaming. (9) Moreover, if his senses can convey to him the heat of the fire when he does not really feel it, he can’t trust that the fire exists when he feels it in his waking life. (9) OR] He argues that sensory perceptions come to him involuntarily, and are not willed by him. (16) 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. (14,16) Descartes goes on to show that the things in the external world are material by arguing that God is benevolent (14) 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. (14,16) He can therefore have some faith in the account of reality his senses provide him. (14,16) In addition he had an intuition that, when he was thinking, he existed. (9,11)This was proof of individual human existence. (9) Because thoughts must have a source, there must be an “I” that exists to do the thinking. (9) In arguments that follow from this premise, Descartes pointed out that although he could be sure of nothing else about his existence—he couldn’t prove beyond a doubt that he had hands or hair or a body—he was certain that he had thoughts and the ability to use reason. (9) Descartes believed that the human body works like a machine, that it has the material properties of extension and motion, and that it follows the laws of physics. (14) The pieces of the human machine, he argued, are like clockwork mechanisms, and that the machine could be understood by taking its pieces apart, studying them, and then putting them back together to see the larger picture (an idea referred to as Reductionism). (14) Descartes asserts that these facts come to him as “clear and distinct perceptions.” (9) He argued that anything that could be observed through clear and distinct perceptions was part of the essence of what is observed. (9) Thought and reason, because they are clearly perceived, must be the essence of humanity. (9)

Scepticism and Rationalism

For Descartes, absolute rationality meant we had to take the Matrix problem seriously. (13) We had to find firmer foundations for our reasoning. (13) After years of intense thought, Descartes finally arrived at one principle that could never be doubted: I think. (13) No sceptic could ever argue the contrary – the very act of doubting your own thoughts is an act of thinking! (13) And that realization led to a second: if I think, then I must exist. (13) A non-existent non-being can’t think, Descartes argued, so we thinkers must be real. (13) Once he had found a solid proof for his own existence, Descartes felt he had a real foundation for developing other philosophical ideas about human nature and the nature of God. (13) He does not doubt for the sake of doubting but to achieve concrete and reliable information, in other words, certainty. (16)

Rationalism

The ideal philosophy, Descartes reasoned, would be one founded on truths as clear and unassailable as 1+1=2. (13) This idea sparked the modern school of Rationalism. (13) For generations, philosophers would be captivated by the idea of a perfectly rational system of thought, one with no room for doubt or error. (13) It was a compelling idea. (13) Following his meeting with Beeckman in 1619, René (9) now aged 23, was profoundly serious in his desire to make new discoveries in mathematics (12) which might lead to discoveries about the nature of existence and of knowledge itself. (10) He returned to France, and soon came to the conclusion that the key to philosophy, with all its uncertainties and ambiguity, was to build it (8) not on sense perception (9) but on the indisputable facts of mathematics. (8) He developed a metaphysical dualism that distinguishes radically between mind, the essence of which is thinking, and matter, the essence of which is extension in three dimensions. (11) René Descartes was the first modern rationalist, and one of the greatest practitioners of that school of thought. (13)

Rationalism and Empiricism

Descartes’s metaphysics is rationalist, (11,13) based on the postulation of innate ideas of mind, (11,16) matter, (11) and God, (11,16) but his physics and physiology, based on sensory experience, are mechanistic and empiricist. (11) Cartesianism or 17th Century Continental Rationalism (14) was a radical position setting him against the proponents of the British ‘empiricist’ movement. (9,13) and opposed by the British Empiricist school of thought of (14) Thomas Hobbes, George Berkeley, David Hume (12a,14) and John Locke. (12) [OR] It was Descartes’ theory of innate knowledge that later led philosopher John Locke (1632–1704) to combat the theory of empiricism, which held that all knowledge is acquired through experience. (16) These men developed a sophisticated empirical tradition as the basis of human knowledge. (12a) They believed that all knowledge comes to us through the senses. (9) ‘Empiricist’ was a term coined to distinguish between Francis Bacon, described as empiricist, and Descartes, described as a rationalist. (12a) Descartes was proposing that scientific observation had to be an interpretive act requiring careful monitoring. (9) He argued that true knowledge comes only through the application of pure reason. (9) Descartes mistrusted the information received through the senses, he did believe that certain knowledge can be acquired by other means, arguing that the strict application of reason to all problems is the only way to achieve certainty in science. (9) Descartes shared the view of “mechanical philosophy” that no ‘action at a distance’ is possible, (12,12a) because particles or corpuscles of matter are fundamentally inert. (12a) Motion can only be caused by direct physical collision. (12a) Where natural substances had previously been understood organically, the mechanical philosophers viewed them as machines. (12a) In 1662 Robert Boyle disproved this by demonstrating that a magnetic force can travel through a vacuum, establishing that action at a distance is possible. (12) [OR] Isaac Newton’s theory seemed like some kind of throwback to “spooky action at a distance”. (12a) Cartesianism or 17th Century Continental Rationalism was later supported by Baruch (14) Spinoza (6,14) and Gottfried (14) Leibniz. (6,14) who were, like Descartes, well-versed in mathematics as well as philosophy. (6)

Meditations on First Philosophy 1641

In 1639 Descartes began writing the Meditations, and in 1640 he returned to Leiden to help work out its publication. (15) [OR]Meditationes de prima Philosophia’, it was written in 1641. (2,6) Descartes considered himself to be a devout Catholic, and one of the purposes of the Meditations was to defend the Catholic faith. (16) [OR] Nothing that follows indicates a defence of the Catholic faith. (15) It was written in Latin and thus addressed to the learned. (16) Today, the Meditations is by far Descartes’s most popular work (15) and it continues to be a standard text at most university philosophy departments. (6) This would not have been the case in Descartes’ day. (15) In establishing the ground for science, Descartes was at the same time overthrowing a system of natural philosophy that had been established for centuries—a qualitative, Aristotelian physics. (15) Unlike his earlier work, The World, the Meditations parts ways with the “old” science without explicitly forwarding controversial views, like that of the Copernican heliocentric model of the solar system. (15) Specifically, the Cartesian view denies that physics is grounded in hot, cold, wet, and dry. (15) It argues that contrary to Aristotle’s view, such “qualities” are not properties of bodies at all. (15) Rather, the only properties of bodies with which the physicist can concern him or herself are size, shape, motion, position, and so on—those modifications that conceptually (or logically) entail extension in length, breadth, and depth. (15) In contrast to Aristotle’s “qualities,” the properties (or modes) of bodies dealt with in Cartesian physics are measurable specifically on ratio scales (as opposed to intensive scales), and hence are subject in all the right ways to mathematics. (15) This conception of matter, conjoined with the sort of mathematics found in the Geometry, allies itself with the work of such Italian natural philosophers as Tartaglia, Ubaldo, and Galileo, and helps further the movement of early thinkers in their attempts to establish a mathematical physics. (15) In a letter to Mersenne, dated 28th January 1641, Descartes says “these six meditations contain all the foundations of my physics. (15) But please do not tell people, for that might make it harder for supporters of Aristotle to approve them. (15) I hope that readers will gradually get used to my principles, and recognize their truth, before they notice that they destroy the principles of Aristotle.” (15) Descartes regarded ‘Cogito ergo sum’ as the unshakeable foundation that all other philosophy could be built upon. (4,12) This work is important to today’s scholar for many reasons, not the least of which is its including as an attached text written objections from some of the best minds living in Paris. (15) Mersenne sent the Meditations to philosophers and theologians for criticism. (15) The list of critics includes: Caterus, Hobbes, Arnauld, Gassendi, and Mersenne himself, with several other unnamed readers who raised their objections through Mersenne. (15) A later edition would include an objection from Bordin. (15) Descartes replied to each critic, and the result was an appended text referred to as “The Objections and Replies.” The second edition contains seven sets in all. (15) The Meditations opens by developing sceptical questions concerning the possibility of knowledge. (15) Through a series of several carefully thought out meditations, the reader establishes (along with the author) the groundwork for the possibility of knowledge (scientia). (15) Descartes is not a sceptic, as some have insisted, but uses scepticism as a vehicle to motivate his reader to “discover” by way of philosophical investigation what constitutes this ground. (15) In the Second Replies, Descartes refers to this style of presentation as the “analytic” style. (15) There were two styles of presentation: analytic and synthetic. (15) It is important not to confuse these terms with those, say, used by Kant. (15) For Descartes the analytic style of presentation (and inquiry) proceeds by beginning with what is commonly taken to be known and discovering what is necessary for such knowledge. (15) Thus, the inquiry moves from what is commonly known to first principles. (15) The “discovery” moves in such a way that each discovery is based on what was discovered before. (15) By contrast, the synthetic style of presentation begins by asserting first principles and then to determining what follows. (15) Prompted by Mersenne, Descartes sketches out in the Second Replies a synthetic rendering of the Meditations. (15) Descartes’ letter to the “learned and distinguished men” of the Sorbonne, which is appended to the Meditations, suggests that he was trying to pitch the Meditations as a textbook for the university. (15) Though the endorsement of the Learned Men would not have guaranteed that the Meditations would be accepted or used as a textbook, it could certainly be viewed as an important step to getting it accepted. (15) Unlike today’s notion of a textbook, in Descartes’ day “textbooks” were intended mostly for teachers, not students. (15) Typically, at the close of a teacher’s career, his notes would be published for the benefit of those who would go on to teach such course material. (15) The awkwardness of Descartes’s seeking the acceptance and use of his Meditations by teachers is amplified by the fact that he was not a teacher himself. (15) Consequently, his seeking “textbook” status would have very likely been viewed by those Learned Men as being a bit pretentious. (15) He was, it could be said, a freelancer with no academic or political ties to the university (outside of his connection to Mersenne). (15) And, he certainly lacked the credentials and reputation of someone like a Eustachius, whose widely used textbook of the period is of the sort the Meditations was in all likelihood aimed at replacing. (15) Although the Meditations seems to have been endorsed by the Sorbonne, it was never adopted as a text for the university. (15)

Principles of Philosophy 1644

Figure 10: Princess Elisabeth of Bohemia

With the Voetius controversy seemingly behind him (though, as mentioned above, it would again raise its head and climax five years down the road), Descartes and Princess Elisabeth of Bohemia began to correspond. (15) In this exchange, Princess Elisabeth probed Descartes on the implications of his commitment to mind-body dualism. (15) During this time, he completed a final draft of a new textbook, which he had begun three years earlier, (15) Principles of Philosophy (1644), (3,4) (Principia Philosophiae), and in 1644 it was published. (15) He dedicated it to Princess Elisabeth. (15) Descartes suggested that the cogito is indeed the conclusion of a syllogism whose premises include the propositions that he is thinking and that whatever thinks must exist. (4) The Principles is an important text. (15) The work is divided into four Parts, with five hundred and four articles. (15) Part One develops Descartes’ metaphysics. (15) Although it would appear to be a quick run through of the Meditations, there are a number of dissimilarities. (15) For example, the order of presentation of the proofs for God’s existence, which some have argued is significant, found in the Third and Fifth Meditations, is reversed in the Principles. (15) The principles introduced in Part Two are based on the metaphysics of Part One. (15) The physics developed in Parts Three and Four is based upon the principles of Part Two. (15) A French translation of Principia Philosophiæ, prepared by Abbot Claude Picot, was published in 1647. (16) This edition was also dedicated to Princess Elisabeth. (16) In the preface to the French edition, Descartes praised true philosophy as a means to attain wisdom. (16) 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. (16)

Physics in the ‘Principles’:

Although the physics turns out to be unsound, the Principles nevertheless inspired such great thinkers as Robert Boyle (1627–1691), Edmond Halley (1656–1742), and Isaac Newton. (15) As an important side note, it must be stressed that even though Descartes had throughout his career put a great deal of emphasis on mathematics, the physics developed in the Principles does not appear to be a mathematical physics. (15) Rather, it is traditionally taken to be a conceptual project with only a hint of empirical overtones—a physics rooted entirely in metaphysics. (15) Arguably, however, Descartes’ work on enumeration, order, and measure in the Rules provides the conceptual machinery necessary for establishing a ‘mathematical’ physics—a conceptual machinery that is carried over to the Principles (Smith 2003, 2010). (15) Two parts, never completed, were originally intended to deal with plants, animals, and man. (15) In light of this and what Descartes says in a 31st January 1642 letter to the mathematician Constantijn Huygens, it is plausible to think that the Principles would have looked something like The World had it been completed as planned. (15)

Can there be a vacuum?

One of the more controversial positions the Principles forwarded, at least according to Newton, was that (15) a vacuum was impossible. (14,15) Descartes continued to cling to the traditional mechanical philosophy of the 17th Century, which held that everything physical in the universe was made of tiny “corpuscles” of matter; there could therefore be no vacuum, just a mass of swirling matter. (14) Descartes’ rejection of the possibility of a vacuum followed from his commitment to the view that the essence of body was extension. (15) Given that extension is an attribute, and that nothing cannot possess any attributes, it follows that “nothingness cannot possess any extension”. (15) So, any instance of extension would entail the presence of some substance. (15) In other words, vacuum, taken as an extended nothing, is a flat contradiction. (15) The corporeal universe is thus a plenum, individual bodies separated only by their surfaces. (15) Newton argued in his De Gravitatione and Principia that the concept of motion becomes problematic if the universe is taken to be a plenum. (15) Another controversial position was Descartes’ insistence that matter is infinitely divisible. (15) Gassendi, and later Cordemoy, argued that there must be a bottom, a ‘substance,’ to the physical universe upon which the being of all corporeal things depend. (15) In line with the ancient atomist Epicurus, they argued that if matter was infinitely divisible, so dividing it would show that there was no bottom—and so, corporeality would not be substantial. (15) So, if corporeality is substantial, as Descartes himself had claimed, there must be a minimum measure of extension that could not be divided (by natural means, anyway). (15) And so, there are atoms. (15) This conclusion is something that Descartes explicitly rejects in the Principles, (15) although later Atomism maintained that there could be a vacuum. (14)

Mind/body dualism

He was one of the first to abandon Scholastic Aristotelianism. (11) Within philosophy, psychology, and neuroscience circles, Descartes’ most controversial idea is not analytic geometry or cogito ergo sum. (13) It’s an idea now known as mind-body dualism. (11,13) [OR] substance dualism, (1) saying that mind and body have distinct essences, (1,2) one being characterized by thought, the other by spatial extension. (1,14) the dualism of mind (7,8) the essence of which is thinking, (11) and matter, (7,8) The universe contained two radically different kinds of substances—the mind or soul defined as thinking, and the body defined as matter and unthinking. (16) He said that the mind or soul is a non-material entity that lacks extension and motion. (14) An idea has no physical substance, and is an ethereal or spiritual thing that floats above the physical world of body and matter (13) and does not follow the laws of physics. (14) Descartes believed that the brain resembled a working machine and unlike many of his contemporaries believed that mathematics and mechanics could explain the most complicated processes of the mind. (16) He was the first to formulate the mind-body problem in the form in which it exists today, and the first to clearly identify the mind with consciousness and self-awareness, and to distinguish this from the brain, which was the physical seat of intelligence. (14) the essence of which is extension in three dimensions. (11) For Descartes, mind and body were not only separate entities but totally separate kinds of entities. (13) [OR] He admitted 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. (16) 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”. (16) Because this was the first modern version of mind-body dualism, from which stems the mind-body problem, and because he promoted the development of a new science grounded in observation and experiment, he has been called the father of modern philosophy. (11) In his epistemological work in the “Discourse on the Method”, he had realized that, although he could doubt that he possessed a body, he could not under any circumstances doubt that he possessed a mind, which led him to conclude that the mind and the body were two very different and separate things. (14) His particular form of Dualism (known as Cartesian Dualism) proposed that the mind controls the body, but that the body also influences the otherwise rational mind (such as when people act out of passion) in a kind of two-way interaction, which he claimed, without much evidence, occurred in the pineal gland. (14) Gilbert Ryle later described this kind of Dualism (where mental activity carries on in parallel to physical action, but where their means of interaction are unknown or, at best, speculative) as the “ghost in the machine”. (14) Although his own solution was far from convincing, this kind of Cartesian Dualism set the agenda for philosophical discussion of the mind-body problem for many years after Descartes’ death. (14) Descartes realised that there was a serious problem in the theory of mind-body dualism, (13) arising out of matter meeting non-matter. (10) One view concerning causation, a view that Descartes’s critics seemed to have attributed to him, is that one thing causes another to move, for example, by way of contact. (15) Contact, in this context, seems to be possible only by way of surfaces. (15) Now, bodies, since they are extended and thus have surfaces, can come into contact with one another and thus can cause one another to move. (15) However, if minds are not extended, they lack surfaces. (15) And, if they lack surfaces, there is no way in principle for bodies to come into contact with them. (15) How can my mental experience of a good meal physically cause me to go back and order it again? (13) And how can the smells of my grandmother’s living room physically evoke feelings and memories from childhood? (13) If mind and body are separate (13) there is no way in principle for bodies to move minds, and vice versa. (13,15) That is, minds and bodies cannot in principle causally interact. (13,15) And so, if the view expounded in the Passions requires that bodies and minds be capable of causal interaction, and Descartes’ metaphysical commitments make such interaction impossible, Descartes’ metaphysics puts a great deal of pressure on the view expounded in the Passions. (15)

Dualism and the brain

Because of his mind-body dualism, a lot of people assume that Descartes was uninterested in the physical organ of the brain. (13) Not true! Descartes was intensely interested in the study of the human brain – what we would now call neuroanatomy. (13) This interest arose from Descartes speculated that the answer lay in the structure of the human brain. (13) He argued that there was a special organ in the brain that enabled communication between the mental world and spiritual world. (13) That organ, he believed, was the small nub of grey matter now known as the pineal gland. (10,13) Nearly every brain structure is bilateral, meaning there’s one on each side of the brain. (13) But the pineal gland is a unitary structure found right around the centre of the brain. (13) Descartes reasoned that because the pineal gland is unitary, and consciousness is unitary, that the pineal gland must be the seat of consciousness. (13) We now know that the pineal gland is a relatively simple structure involved in regulating sleep cycles. (13) Moreover, we have a pretty good sense that mental ideas actually do have physical structure – they reside in the electrical activity of the brain and nervous system, and need not be seen as separate entities. (13) Against Descartes’s mind-body dualism, modern science is based on an assumption of monism, in which the mind and the body are really one. (13) The mind, according to this view, is a pattern of physical activity, not a radically separate kind of entity as Descartes argued. (13) But for others, the physical world of atoms and neurotransmitters is just not enough to account for the richness of human consciousness. (13) Cartesian dualism is still influential with those who find monism unsatisfactory, and the debate between dualists and non-dualists is still one of the major controversies gripping philosophy departments all over the world. (13) At the time, though, the problem was different: because his previous philosophical system had given man the tools to define knowledge of what is true, the concept of mind/body dualism led to controversy. (10) His concern about the likely attitude of the church towards that wasn’t misplaced: (10)

Other works

In the later 1620s (9,15) he seems to have been working on the(15) ‘Regulae ad directionem ingenii’ (7,9) (Rules for the Direction of the Mind), (9,15) a work that he would abandon, (7,15) in 1628, (15) at around the time of the move from Paris. (15) In this he argued that all problems should be broken up into their simplest parts and that problems can be expressed as abstract equations. (9) Descartes hoped to minimize or remove the role of unreliable sense perception in the sciences. (9) If all problems were reduced to their least sense-dependent and most abstract elements, then objective reason could be put to work to solve the problem. (9) It is worth noting that relatively recently a copy of the Rules was discovered in a library at Cambridge University. (15) Scholars are unsure how it got there. (15) Currently, based on what it includes, it is thought that this manuscript represents the work as it stood when Descartes had abandoned (15) It was published after his death in 1700. (9,15) The later Amsterdam printing (1701) and a copy that Leibniz acquired from Clerselier (c. 1670) make certain advancements over what is found in the Cambridge manuscript. (15) So, it appears that Descartes picked up the work again. (15) This may have happened after a visit in 1635 from John Dury (1596–1680) and Samuel Hartlib (1600–1662). (15) Hartlib reports that Dury had returned to England with copies of some of Descartes’ works; the speculation being that the recently discovered manuscript is related to something brought back by Dury. (15) The meeting took place in The Hague. (15) Dury and Hartlib were friends of the Cambridge philosopher Henry More (1614–1687), with whom Descartes had corresponded, and of others in More’s circle, including John Milton (1608–1674). (15) Perhaps the copy was made during the visit and brought back to Cambridge. (15) This is a new and interesting development in Descartes scholarship. (15)

And Morality

Humans should seek the sovereign good that Descartes, following Zeno, identifies with virtue, as this produces a solid blessedness or pleasure. (16) For Epicurus 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. (16) As a convinced rationalist, Descartes states that reason is sufficient in the search for the goods that we should seek, and virtue consists in the correct reasoning that should guide our actions. (16) Nevertheless, the quality of this reasoning depends on knowledge, because a well-informed mind will be more capable of making good choices, and it also depends on mental condition. (16) For this reason, he said that a complete moral philosophy should include the study of the body. (16) He discussed this subject in the correspondence with Princess Elisabeth of Bohemia, and as a result wrote his work The Passions of the Soul, that contains a study of the psychosomatic processes and reactions in man, with an emphasis on emotions or passions. (16)

Emotions

Above all he was among the first scientists who believed that the soul should be subject to scientific investigation. (16) He challenged the views of his contemporaries that the soul was divine, thus religious authorities regarded his books as dangerous. (16) Descartes’s writings went on to form the basis for theories on emotions and how cognitive evaluations were translated into affective processes. (16) As a result of the probings of Princess Elisabeth, Descartes completed a working draft of (15) Passions de l’ame (7,15) opening up the issue of emotions. (7,15) between 1645 and 1646 (16) [OR] In 1646, (15) [OR] In 1649, (7,16) during his time in Sweden (15,16) Descartes published the Passions, (15,16) of the Soul (16) dedicating it to the Princess. (15,16) Descartes distinguished six basic passions: wonder, love, hatred, desire, joy and sadness. (16) He discussed the common contemporary belief that the human body contained animal spirits. (16) These animal spirits were believed to be light and roaming fluids circulating rapidly around the nervous system between the brain and the muscles, and served as a metaphor for feelings, like being in high or bad spirit. (16) These animal spirits were believed to affect the human soul, or passions of the soul. (16) All of these passions, he argued, represented different combinations of the original spirit, and influenced the soul to will or want certain actions. (16) He argued, for example, that fear is a passion that moves the soul to generate a response in the body. (16) In line with his dualist teachings on the separation between the soul and the body, he hypothesized that some part of the brain served as a connector between the soul and the body and singled out the pineal gland as connector. (16) Descartes argued that signals passed from the ear and the eye to the pineal gland, through animal spirits. (16) Thus different motions in the gland cause various animal spirits. (16) 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. (16) 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. (16) Like many great philosophers in nearly all traditions, Descartes understood that inner peace begins with letting go of desire. (13) One of his most famous books was an analysis of the passions, or emotions, and their effect on human thought and behavior. (13) Descartes argued that the passions were not an enemy to be subdued through rigid discipline, but a natural force to be mastered through understanding. (13) In this he borrowed from ancient Greek philosophers like Diogenes and Pyrrho, who, in turn, got their ideas from Indian mystics at the time of Alexander the Great. (13) Diogenes and Pyrrho brought back ideas from the growing religion that would become Buddhism and integrated those ideas into classical Greek philosophy. (13) “The ancient philosophers acquired over their thoughts a sway so absolute that they could esteem themselves more rich and happy than other men who, whatever be the favours heaped on them by nature and fortune, if destitute of this philosophy, can never command the realization of all their desires.” (1637) If Descartes’ quote sounds a lot like Buddhism, it’s not by accident! (13) During 1644 he began to correspond with Queen Christina of Sweden (15) and, (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. (16) An aim of this early modern treatise on emotions (6) was to explain how the emotional (and thus moral) life of a human being was connected to the soul’s being essentially united to a body. (15) Simply put, a ’passion of the soul’ is a mental state (or thought) that arises as a direct result of brain activity. (15) Such passions can move us to action. (15) Since this is so, Descartes suggests that one needs to learn to control one’s passions, for they can move one to perform vicious acts. (15) Critics of Descartes, including Elisabeth, argued that Descartes’ metaphysical commitments put real pressure on the view expounded in the Passions. (15) For, according to Descartes’ metaphysics, the nature of mind is to think and the nature of body is to be extended in length, breadth, and depth. (15)

Move to Sweden 1649

Figure 11 Descartes with Queen Christina

In 1647, he was awarded a pension by King Louis XIV of France. (16) It was never paid. (16) By 1649, Descartes had become one of Europe’s most famous philosophers and scientists, (16) but his revolutionary ideas made him a centre of controversy. (8) His commitment to the scientific method was met with strident opposition by the church officials of the day, (8,10)as he anticipated, (10)And, Regius published what he took to be a new and improved version of Cartesian science, which as we now know would draw the wrath of Voetius. (15) But Regius did not stop there, for he seemed to have found important differences between his “Cartesian” view and that of Descartes’, and attempted to separate the two, publishing a broadsheet that listed twenty-one anti-Cartesian theses (which his version of “Cartesian” science rejected). (15) In response to this, Descartes wrote a single-page printed defence that was posted on public kiosks for all to read. (15) Published in 1648, the Notae in Programma Quoddam (also referred to as Comments on a Certain Broadsheet) is Descartes’ public defence. (15) However, as mentioned earlier, tensions mounted as a result of the public exchange and Descartes felt his way of life in the Netherlands to be threatened. (15) As luck would have it, an admirer and friend of Descartes’—Chanut, who worked for Queen Christina’s court—and Queen Christina herself began probing Descartes about the possibility of coming to Sweden. (15) And, after a not too lengthy correspondence, Queen Christina offered Descartes a position in her court. (15) For many reasons, which would certainly include those related to his concerns about Voetius, (15) Descartes accepted the offer, (6,15) and in 1649 he moved to (6,7)Stockholm in (7,10) Sweden (5,7) in the middle of winter, (16) at the invitation of the young Queen Christina (5,7) Ist, a passionate patron of the arts and an ardent collection of learned men for her court. (5) He was a guest at the house of Pierre Chanut, living on Västerlånggatan, less than 500 meters from Tre Kronor in Stockholm. (16) There, Chanut and Descartes made observations with a Torricellian mercury barometer. (16) Challenging Blaise Pascal, Descartes took the first set of barometric readings in Stockholm to see if atmospheric pressure could be used in forecasting the weather. (16) Queen Christina at first required very little from Descartes. (15) But after he had some time to settle in, she ordered him to do two things: first, to put all of his papers in order (15) [OR]to give her tuition in philosophy. (7,10)and secondly, to put together designs for an academy. (12,15) Descartes probably had some idea of how the latter might be done by way of his experience in Breda. (15) In January of 1650, the Queen began to require Descartes to give her lessons in philosophy (15) [OR] in his ideas about love. (16) Descartes arranged to give the Queen lessons after her birthday, (16) three times a week (7,15) at 5:00 a.m.,(7,10) Each would last for about five hours (15) in her cold and draughty castle. (16) By 15th January 1650, Descartes had seen Christina only four or five times. (16) The lessons were especially taxing for Descartes, whose habit of a lifetime was to stay in bed meditating and reading until about 11:00 a.m. (7,10) 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. (16)

Death

His health deteriorated: (8,10) The fragile health indicated in his early life persisted. (10) In a letter to Bregy, for instance, dated 15th January 1650, Descartes expresses reservations about his decision to come to Sweden. (15) The winter seems to have been mild, except for the second half of January which was harsh as described by Descartes himself: (16) he sees himself to be “out of his element,” the winter so harsh that “men’s thoughts are frozen here, like the water”. (15) Given the sentiment expressed in the letter, this remark was probably intended to be as much Descartes’s take on the intellectual climate as it was about the weather. (15) On 1st February (16) he contracted pneumonia, (5,7) a serious respiratory infection, (15) though Christina’s physician Johann van Wullen said it was peripneumonia; he was not allowed to bleed him. (16) Although at the end of a week he appeared to have made some movement towards recovery, things took a turn for the worse and he (15) died (1,5) far from home in Stockholm, (8,10) in the early morning of (15) February 11th, (1,6) 1650. (1,2) He was fifty-three years old. (15) Descartes might have been assassinated. (16) His last words were supposedly ‘Ca, mon ame, il faut partir’ – “so my soul, a time for parting”. (7)

Post Mortem


Figure 12 The Abbey of St. Germain des Pres

He was buried (7,10) at the Adolf Fredriks Church (12,16) in Stockholm. (7,10) Sweden was a Protestant country, so Descartes, a Catholic, was buried in a graveyard primarily for unbaptized babies. (10,16) In death, as in life, Descartes was mobile. (12,14) 16 years after his first burial (12,16) his body was later removed to Paris (7,10) and buried in the (12,14) Saint-Ètienne-du-Mont (12,16) [OR] Sainte-Geneviève-du-Mont (14) church in Paris, France. (12,14) During the French Revolution, (14,16) in 1792, the National Convention planned to transfer [OR] his remains WERE disinterred (10,14) for burial in the Panthéon among the other great thinkers of France. (14,16) In 1819 his remains, minus skull and finger, (12,16) were moved again, to (7,10) the abbey of (10,12) Saint Germain des Prés, (7,10) the oldest church in Paris. (10) where he now rests. (12)[OR] His remains were moved during the French Revolution, and were put back later—although urban legend has it that only his heart is there and the rest is buried in the Panthéon (10) [OR] His skull (16) [OR] his brain (14) is in the Musée de l’Homme (14,16) in Paris. (16)

On the Index, 1663

Because his previous philosophical system had given man the tools to define knowledge of what is true, the concept of mind/body dualism led to controversy. (10) His concern about the likely attitude of the church towards that and his astronomical work wasn’t misplaced: (10) His manuscripts came into the possession of Claude Clerselier, a devout Catholic who began the process of turning Descartes into a saint by cutting, adding and publishing his letters selectively. (16) A powerful contemporary, Martin Schoock, accused him of atheist beliefs, though Descartes had provided an explicit critique of atheism in his Meditations. (16) Despite efforts to avoid the fate of Galileo – Descartes regarded himself as a devout Catholic (12) – Pope Alexander VII (10) later added (8,10) a number of (12) Descartes’ works (8,10) and Galileo’s (12) to the Index of Prohibited Books (8,10) in 1663, (8,12)and they remained there until the Index was finally discontinued, 300 years later in 1966. (12) In 1664, his work ‘Man’ which expounded a mechanistic interpretation of the animal body, was published. (3) In 1671 Louis XIV prohibited all the lectures in Cartesianism. (16)

Estimates

He represents a major break with the Aristotelianism and Scholasticism of the Medieval period, (11,14) He was “one of the most notable intellectual figures of the Dutch Golden Age”. (6) He was one of the great figures in the history of western thought, (7) the “Father of Modern Philosophy”. (1,2) He defined a starting point for existence, “I think; therefore I am”: his ideas departed widely from current understanding in the early 17th century, which was more feeling-based. (10) He formulated the first modern version of mind-body dualism, from which stems the mind-body problem, and because he promoted the development of a new science grounded in observation and experiment, he has been called the father of modern philosophy. (11) Pascal regarded Descartes’s views as a rationalist and mechanist, and accused him of deism: “I cannot forgive Descartes; in all his philosophy, Descartes did his best to dispense with God. But Descartes could not avoid prodding God to set the world in motion with a snap of his lordly fingers; after that, he had no more use for God,” (16) Although philosophy is largely where the 20th century deposited Descartes—each century has focused on different aspects of his work—his investigations in theoretical physics led many scholars to consider him a mathematician first. (10) He is seen as responsible for the increased attention given to epistemology in the 17th century. (6) he was also called the “Father of Modern (1) [OR] the first of the modern school (8) of Mathematics,” (1,8) for having virtually founded coordinate or analytic geometry. (2) He laid the foundation for 17th-century continental rationalism, later advocated by Spinoza and Leibniz, and was later opposed by the empiricist school of thought consisting of Hobbes, Locke, Berkeley, and Hume. (6) Leibniz, Spinoza, and Descartes were all well-versed in mathematics as well as philosophy, and Leibniz and (6) Descartes contributed greatly to science as well (6,8) as one of the key figures in the Scientific Revolution of the 17th Century. (8) In inventing methodological scepticism, or Cartesian doubt, (10,12) he made philosophers of us all. (10) In the 20th century Alan Turing advanced computer science based on mathematical biology as inspired by Descartes. (16) His theories on reflexes also served as the foundation for advanced physiological theories more than 200 years after his death. (16) The physiologist Ivan Pavlov was a great admirer of Descartes. (16)

And solipsism

In ‘The Matrix’, the hero discovers early on that his entire reality is just a computer simulation. (13) All of his sensory experiences are being dictated by evil robots in order to keep his physical body under control. (13) The concept is lifted directly from Descartes, who famously struggled to prove that this was not the case, but that it was nonetheless a possibility that philosophy had to account for. (13) The creators of the Matrix deliberately based their world on a sci-fi rendition of Descartes’ thought experiment. (13) Sid Meier’s Alpha Centauri In in the video game Alpha Centauri, you can encounter this message: We are all aware that the senses can be deceived, the eyes fooled. (13) But how can we be sure our senses are not being deceived at any particular time, or even all the time? (13) Might I just be a brain in a tank somewhere, tricked all my life into believing in the events of this world by some insane computer? (13) And does my life gain or lose meaning based on my reaction to such solipsism? The message itself reads exactly like a student encountering Descartes for the first time – grappling with the possibility that our sensory experiences are an illusion, and pondering the ramifications of that possibility. (13)

Bibliography

12a History of Europe by N. Davies published by Pimlico 1996

Note: sources 16-20 not used

1 Possibly intended to say ‘on the River Vienne’

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