"Perfect numbers like perfect men are very rare." -- Rene Descartes
René Descartes (; 31 March 1596 — 11 February 1650) (Latinized form: Renatus Cartesius; adjectival form: "Cartesian"), was a French philosopher, mathematician, physicist, and writer who spent most of his adult life in the Dutch Republic. He has been dubbed the "Father of Modern Philosophy," and much subsequent Western philosophy is a response to his writings, which are studied closely to this day. In particular, his Meditations on First Philosophy continues to be a standard text at most university philosophy departments. Descartes' influence in mathematics is also apparent; the Cartesian coordinate system—allowing geometric shapes to be expressed in algebraic equations—was named after him. He is credited as the father of analytical geometry. Descartes was also one of the key figures in the Scientific Revolution.
Descartes frequently sets his views apart from those of his predecessors. In the opening section of the Passions of the Soul, a treatise on the Early Modern version of what are now commonly called emotions, Descartes goes so far as to assert that he will write on this topic "as if no one had written on these matters before". Many elements of his philosophy have precedents in late Aristotelianism, the revived Stoicism of the 16th century, or in earlier philosophers like St. Augustine. In his natural philosophy, he differs from the Schools on two major points: First, he rejects the analysis of corporeal substance into matter and form; second, he rejects any appeal to ends—divine or natural—in explaining natural phenomena. In his theology, he insists on the absolute freedom of God’s act of creation.
Descartes was a major figure in 17th-century continental rationalism, later advocated by Baruch Spinoza and Gottfried Leibniz, and opposed by the empiricist school of thought consisting of Hobbes, Locke, Berkeley, Jean-Jacques Rousseau, and Hume. Leibniz, Spinoza and Descartes were all well versed in mathematics as well as philosophy, and Descartes and Leibniz contributed greatly to science as well. As the inventor of the Cartesian coordinate system, Descartes founded analytic geometry, the bridge between algebra and geometry, crucial to the discovery of infinitesimal calculus and analysis. He is best known for the philosophical statement "Cogito ergo sum" (; ), found in part IV of Discourse on the Method (1637 – written in French but with inclusion of "Cogito ergo sum") and §7 of part I of Principles of Philosophy (1644 – written in Latin).
"A state is better governed which has few laws, and those laws strictly observed.""An optimist may see a light where there is none, but why must the pessimist always run to blow it out?""Common sense is the most fairly distributed thing in the world, for each one thinks he is so well-endowed with it that even those who are hardest to satisfy in all other matters are not in the habit of desiring more of it than they already have.""Divide each difficulty into as many parts as is feasible and necessary to resolve it.""Each problem that I solved became a rule, which served afterwards to solve other problems.""Everything is self-evident.""Except our own thoughts, there is nothing absolutely in our power.""I am accustomed to sleep and in my dreams to imagine the same things that lunatics imagine when awake.""I am indeed amazed when I consider how weak my mind is and how prone to error.""I hope that posterity will judge me kindly, not only as to the things which I have explained, but also to those which I have intentionally omitted so as to leave to others the pleasure of discovery.""I think; therefore I am.""If you would be a real seeker after truth, it is necessary that at least once in your life you doubt, as far as possible, all things.""Illusory joy is often worth more than genuine sorrow.""In order to improve the mind, we ought less to learn, than to contemplate.""It is not enough to have a good mind; the main thing is to use it well.""It is only prudent never to place complete confidence in that by which we have even once been deceived.""Nothing is more fairly distributed than common sense: no one thinks he needs more of it than he already has.""One cannot conceive anything so strange and so implausible that it has not already been said by one philosopher or another.""The first precept was never to accept a thing as true until I knew it as such without a single doubt.""The greatest minds are capable of the greatest vices as well as of the greatest virtues.""The reading of all good books is like a conversation with the finest minds of past centuries.""The senses deceive from time to time, and it is prudent never to trust wholly those who have deceived us even once.""The two operations of our understanding, intuition and deduction, on which alone we have said we must rely in the acquisition of knowledge.""There is nothing so strange and so unbelievable that it has not been said by one philosopher or another.""Travelling is almost like talking with those of other centuries.""When it is not in our power to follow what is true, we ought to follow what is most probable.""Whenever anyone has offended me, I try to raise my soul so high that the offense cannot reach it.""You just keep pushing. You just keep pushing. I made every mistake that could be made. But I just kept pushing."
Descartes was born in La Haye en Touraine (now Descartes), Indre-et-Loire, France. When he was one year old, his mother Jeanne Brochard died. His father Joachim was a member in the provincial parliament. Around the age of eleven, he entered the Jesuit Collège Royal Henry-Le-Grand at La Flèche. After graduation, he studied at the University of Poitiers, earning a Baccalauréat and Licence in law in 1616, in accordance with his father's wishes that he should become a lawyer.
In 1618, Descartes joined the International College of War of Maurice of Nassau in the Dutch Republic. On 10 November 1618, while walking through Breda, Descartes met Isaac Beeckman, who sparked his interest in mathematics and the new physics, particularly the problem of the fall of heavy bodies. While in the service of the Duke Maximilian of Bavaria, Descartes was present at the Battle of the White Mountain outside Prague, in November 1620.
On the night of 10—11 November 1619, while stationed in Neuburg (near Ulm), Germany, Descartes experienced a series of three powerful dreams or visions that he later claimed profoundly influenced his life. In the first of these dreams, Descartes found himself buffeted and thrown down by a powerful whirlwind while walking near a college. In the second, he was awoken by an inexplicable thunder or explosion-like sound in his head to see sparks coming from the stove in his room. In the third dream, he finds a great dictionary and an anthology of ancient Latin poets on his bedside table. In the latter book, he reads a verse that begins, "What path shall I follow in life?" Descartes 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.
In 1622 he returned to France, and during the next few years spent time in Paris and other parts of Europe. He arrived in La Haye in 1623, selling all of his property to invest in bonds, which provided a comfortable income for the rest of his life. Descartes was present at the siege of La Rochelle by Cardinal Richelieu in 1627.
He returned to the Dutch Republic in 1628, where he lived until September 1649. In April 1629 he joined the University of Franeker, living at the Sjaerdemaslot, and the next year, under the name "Poitevin", he enrolled at the Leiden University to study mathematics with Jacob Golius and astronomy with Martin Hortensius. In October 1630 he had a falling out with Beeckman, whom he accused of plagiarizing some of his ideas. In Amsterdam, he had a relationship with a servant girl, Helena Jans van der Strom, with whom he had a daughter, Francine, who was born in 1635 in Deventer, at which time Descartes taught at the Utrecht University. Francine Descartes died in 1640 in Amersfoort, the cause of death being Scarlet Fever.
While in the Netherlands he changed his address frequently, living among other places in Dordrecht (1628), Franeker (1629), Amsterdam (1629—30), Leiden (1630), Amsterdam (1630—2), Deventer (1632—4), Amsterdam (1634—5), Utrecht (1635—6), Leiden (1636), Egmond (1636—8), Santpoort (1638—1640), Leiden (1640—1), Endegeest (a castle near Oegstgeest) (1641—3), and finally for an extended time in Egmond-Binnen (1643—9).
Despite these frequent moves he wrote all his major work during his 20 plus years in the Netherlands, where he managed to revolutionize mathematics and philosophy. In 1633, Galileo was condemned by the Roman Catholic Church, and Descartes abandoned plans to publish Treatise on the World, his work of the previous four years. "Discourse on the Method" was published in 1637. In it Descartes lays out four rules of thought, meant to ensure that our knowledge rests upon a firm foundation.
Descartes continued to publish works concerning both mathematics and philosophy for the rest of his life. In 1643, Cartesian philosophy was condemned at the University of Utrecht, and Descartes began his long correspondence with Princess Elisabeth of Bohemia. In 1647, he was awarded a pension by the King of France. Descartes was interviewed by Frans Burman at Egmond-Binnen in 1648.
René Descartes died on 11 February 1650 in Stockholm, Sweden, where he had been invited as a teacher for Queen Christina of Sweden. The cause of death was said to be pneumonia...accustomed to working in bed until noon, he may have suffered a detrimental effect on his health due to Christina's demands for early morning study (the lack of sleep could have severely compromised his immune system). Others believe that Descartes may have contracted pneumonia as a result of nursing a French ambassador, Dejion A. Nopeleen, ill with the aforementioned disease, back to health. In his recent book, Der rätselhafte Tod des René Descartes (The Mysterious Death of René Descartes), the German philosopher Theodor Ebert asserts that Descartes died not through natural causes, but from an arsenic-laced communion wafer given to him by a Catholic priest. He believes that Jacques Viogué, a missionary working in Stockholm, administered the poison because he feared Descartes' radical theological ideas would derail an expected conversion to Roman Catholicism by the monarch of Protestant Lutheran Sweden.
In 1663, the Pope placed his works on the Index of Prohibited Books.
As a Roman Catholic in a Protestant nation, he was interred in a graveyard mainly used for unbaptized infants in Adolf Fredriks kyrkan in Stockholm. Later, his remains were taken to France and buried in the Abbey of Saint-Germain-des-Prés in Paris. Although the National Convention in 1792 had planned to transfer his remains to the Panthéon, they are, two centuries later, still resting between two other graves...those of the scholarly monks Jean Mabillon and Bernard de Montfaucon...in a chapel of the abbey. His memorial, erected in the 18th century, remains in the Swedish church.
Descartes is often regarded as the first thinker to provide a philosophical framework for the natural sciences as these began to develop. In his Discourse on the Method, he attempts to arrive at a fundamental set of principles that one can know as true without any doubt. To achieve this, he employs a method called hyperbolical/metaphysical doubt, also sometimes referred to as methodological skepticism: he rejects any ideas that can be doubted, and then reestablishes them in order to acquire a firm foundation for genuine knowledge.
Initially, Descartes arrives at only a single principle: thought exists. Thought cannot be separated from me, therefore, I exist (Discourse on the Method and Principles of Philosophy). Most famously, this is known as cogito ergo sum (English: "I think, therefore I am"). Therefore, Descartes concluded, if he doubted, then something or someone must be doing the doubting, therefore the very fact that he doubted proved his existence. "The simple meaning of the phrase is that if one is skeptical of existence, that is in and of itself proof that he does exist."
Descartes concludes that he can be certain that he exists because he thinks. But in what form? He perceives his body through the use of the senses; however, these have previously been unreliable. So Descartes determines that the only indubitable knowledge is that he is a thinking thing. Thinking is his essence as it is the only thing about him that cannot be doubted. Descartes defines "thought" (cogitatio) as "what happens in me such that I am immediately conscious of it, insofar as I am conscious of it". Thinking is thus every activity of a person of which he is immediately conscious.
To further demonstrate the limitations of the senses, Descartes proceeds with what is known as the Wax Argument. He considers a piece of wax; his senses inform him that it has certain characteristics, such as shape, texture, size, color, smell, and so forth. When he brings the wax towards a flame, these characteristics change completely. However, it seems that it is still the same thing: it is still a piece of wax, even though the data of the senses inform him that all of its characteristics are different. Therefore, in order to properly grasp the nature of the wax, he cannot use the senses. He must use his mind. Descartes concludes:
In this manner, Descartes proceeds to construct a system of knowledge, discarding perception as unreliable and instead admitting only deduction as a method. In the third and fifth Meditation, he offers an ontological proof of a benevolent God (through both the ontological argument and trademark argument). Because God is benevolent, he can have some faith in the account of reality his senses provide him, for God has provided him with a working mind and sensory system and does not desire to deceive him. From this supposition, however, he finally establishes the possibility of acquiring knowledge about the world based on deduction and perception. In terms of epistemology therefore, he can be said to have contributed such ideas as a rigorous conception of foundationalism and the possibility that reason is the only reliable method of attaining knowledge.
In Descartes' system, knowledge takes the form of ideas, and philosophical investigation is the contemplation of these ideas. This concept would influence subsequent internalist movements as Descartes' epistemology requires that a connection made by conscious awareness will distinguish knowledge from falsity. As a result of his Cartesian doubt, he viewed rational knowledge as being "incapable of being destroyed" and sought to construct an unshakable ground upon which all other knowledge can be based. The first item of unshakable knowledge that Descartes argues for is the aforementioned cogito, or thinking thing.
Descartes also wrote a response to skepticism about the existence of the external world. He argues that sensory perceptions come to him involuntarily, and are not willed by him. They are external to his senses, and according to Descartes, this is evidence of the existence of something outside of his mind, and thus, an external world. Descartes goes on to show that the things in the external world are material by arguing that God would not deceive him as to the ideas that are being transmitted, and that God has given him the "propensity" to believe that such ideas are caused by material things.
Descartes was also known for his work in producing the Cartesian Theory of Fallacies. This can be most easily explored using the statement: "This statement is a lie." While it is most commonly referred to as a paradox, the Cartesian Theory of Fallacies states that at any given time a statement can be both true and false simultaneously because of its contradictory nature. The statement is true in its fallacy. Thus, Descartes developed the Cartesian Theory of Fallacies, which greatly influenced the thinking of the time. Many would-be philosophers were trying to develop inexplicable statements of seeming fact, however, this laid rumors of such a proposition impossible. Many philosophers believe that when Descartes formulated his Theory of Fallacies, he intended to be lying, which in and of itself embodies the theory.
Descartes in his Passions of the Soul and The Description of the Human Body suggested that the body works like a machine, that it has the material properties of extension and motion, and that it follows the laws of physics. The mind (or soul), on the other hand, was described as a nonmaterial entity that lacks extension and motion, and does not follow the laws of physics. Descartes argued that only humans have minds, and that the mind interacts with the body at the pineal gland. This form of dualism or duality proposes that the mind controls the body, but that the body can also influence the otherwise rational mind, such as when people act out of passion. Most of the previous accounts of the relationship between mind and body had been uni-directional.
Descartes suggested that the pineal gland is "the seat of the soul" for several reasons. First, the soul is unitary, and unlike many areas of the brain the pineal gland appeared to be unitary (though subsequent microscopic inspection has revealed it is formed of two hemispheres). Second, Descartes observed that the pineal gland was located near the ventricles. He believed the cerebrospinal fluid of the ventricles acted through the nerves to control the body, and that the pineal gland influenced this process. Finally, although Descartes realized that both humans and animals have pineal glands (see Passions of the Soul Part One, Section 50, AT 369), he believed that only humans have minds. This led him to the belief that animals cannot feel pain, and Descartes' practice of vivisection (the dissection of live animals) became widely used throughout Europe until the Enlightenment.Cartesian dualism set the agenda for philosophical discussion of the mind—body problem for many years after Descartes' death.
Descartes' theory provided the basis for the calculus of Newton and Leibniz, by applying infinitesimal calculus to the tangent line problem, thus permitting the evolution of that branch of modern mathematics. This appears even more astounding considering that the work was just intended as an example to his Discours de la méthode pour bien conduire sa raison, et chercher la verité dans les sciences (Discourse on the Method of Rightly Conducting the Reason, and Searching for Truth in the Sciences, better known under the shortened title Discours de la méthode; English, Discourse on the Method).
Descartes' rule of signs is also a commonly used method to determine the number of positive and negative roots of a polynomial.
Descartes created analytic geometry, and discovered an early form of the law of conservation of momentum (the term momentum refers to the momentum of a force). He outlined his views on the universe in his Principles of Philosophy.
Descartes also made contributions to the field of optics. He showed by using geometric construction and the law of refraction (also known as Descartes' law or more commonly Snell's law, who discovered it 16 years earlier) that the angular radius of a rainbow is 42 degrees (i.e., the angle subtended at the eye by the edge of the rainbow and the ray passing from the sun through the rainbow's centre is 42°). He also independently discovered the law of reflection, and his essay on optics was the first published mention of this law.
One of Descartes most enduring legacies was his development of Cartesian geometry, which uses algebra to describe geometry. He also "invented", the notation that uses superscripts to show the powers or exponents, for example the 4 used in x4 to indicate squaring of squaring.
Although Descartes was well known in academic circles towards the end of his life, the teaching of his works in schools was controversial. Henri de Roy (Henricus Regius, 1598—1679), Professor of Medicine at the University of Utrecht, was condemned by the Rector of the University, Gijsbert Voet (Voetius), for teaching Descartes' physics.
The religious beliefs of René Descartes have been rigorously debated within scholarly circles. He claimed to be a devout Roman Catholic, claiming that one of the purposes of the Meditations was to defend the Christian faith. However, in his own era, Descartes was accused of harboring secret deist or atheist beliefs. Contemporary Blaise Pascal said that "I cannot forgive Descartes; in all his philosophy, Descartes did his best to dispense with God. But Descartes could not avoid prodding God to set the world in motion with a snap of his lordly fingers; after that, he had no more use for God."
Stephen Gaukroger's biography of Descartes reports that "he had a deep religious faith as a Catholic, which he retained to his dying day, along with a resolute, passionate desire to discover the truth." After Descartes died in Sweden, Queen Christina abdicated her throne to convert to Roman Catholicism (Swedish law required a Protestant ruler). The only Roman Catholic with whom she had prolonged contact was Descartes, who was her personal tutor.
1618. Compendium Musicae. A treatise on music theory and the aesthetics of music written for Descartes' early collaborator Isaac Beeckman.
1626—1628. Regulae ad directionem ingenii (Rules for the Direction of the Mind). Incomplete. First published posthumously in 1684. The best critical edition, which includes an early Dutch translation, is edited by Giovanni Crapulli (The Hague: Martinus Nijhoff, 1966).
1630—1633. Le Monde (The World) and L'Homme (Man). Descartes' first systematic presentation of his natural philosophy. Man was published posthumously in Latin translation in 1662; and The World posthumously in 1664.
1637. Discours de la méthode (Discourse on the Method). An introduction to the Essais, which include the Dioptrique, the Météores and the Géométrie.
1637. La Géométrie (Geometry). Descartes' major work in mathematics. There is an English translation by Michael Mahoney (New York: Dover, 1979).
1641. Meditationes de prima philosophia (Meditations on First Philosophy), also known as Metaphysical Meditations. In Latin; a French translation, probably done without Descartes' supervision, was published in 1647. Includes six Objections and Replies. A second edition, published the following year, included an additional objection and reply, and a Letter to Dinet.
1644. Principia philosophiae (Principles of Philosophy), a Latin textbook at first intended by Descartes to replace the Aristotelian textbooks then used in universities. A French translation, Principes de philosophie by Claude Picot, under the supervision of Descartes, appeared in 1647 with a letter-preface to Queen Christina of Sweden.
1647. Notae in programma (Comments on a Certain Broadsheet). A reply to Descartes' one-time disciple Henricus Regius.
1647. The Description of the Human Body. Published posthumously.
1648. Responsiones Renati Des Cartes (Conversation with Burman). Notes on a Q&A session between Descartes and Frans Burman on 16 April 1648. Rediscovered in 1895 and published for the first time in 1896. An annotated bilingual edition (Latin with French translation), edited by Jean-Marie Beyssade, was published in 1981 (Paris: PUF).
1649. Les passions de l'âme (Passions of the Soul). Dedicated to Princess Elizabeth of Bohemia.
1656. Musicae Compendium (Instruction in Music). Posth. Publ.: Johannes Janssonius jun., Amsterdam
1657. Correspondence. Published by Descartes' literary executor Claude Clerselier. The third edition, in 1667, was the most complete; Clerselier omitted, however, much of the material pertaining to mathematics.
In January 2010, a previously unknown letter from Descartes, dated May 27, 1641, was found by the Dutch philosopher Erik-Jan Bos when browsing through Google. Bos found the letter mentioned in a summary of autographs kept by Haverford College in Haverford, Pennsylvania. This was the third letter by Descartes found in the last 25 years .
