René Descartes

René Descartes
Portrait after Frans Hals note 1
Born	31 March 1596 La Haye-en-Touraine, France
Died	11 February 1650 (aged 53) Stockholm, Sweden
Children	Francine
Education
Education	Jesuit College of La Flèche (1607–1614) University of Poitiers (LL.B., 1616) University of Franeker (attended) Leiden University (attended)
Thesis	Theses ex utroque iure de Testamentis ordinandis (1616)
Academic advisors	Isaac Beeckman Jacobus Golius Adriaan Metius Étienne Noël
Philosophical work
Era	17th-century philosophy Age of Enlightenment
Region	Western philosophy Dutch philosophy French philosophy
School	Foundationalism Innatism Mechanism Rationalism
Main interests	Epistemology, metaphysics, mathematics, physics, cosmology, ethics
Notable ideas	See list Cogito ergo sum Method of doubt Subjectivity Method of normals Analytic geometry Cartesian coordinate system Imaginary number Mind–body problem Cartesian dualism Interactionism Trialism Cartesian circle Foundationalism Mathesis universalis Folium of Descartes Deus deceptor Dream argument Conservation of momentum (quantitas motus) Balloonist theory Descartes' Rule of Signs Wax argument Trademark argument Causal adequacy principle Res cogitans/res extensa distinction Conatus
Signature

René Descartes (/deɪˈkɑːrt/ day-KART, also /ˈdeɪkɑːrt/ DAY-kart; French: [ʁəne dekaʁt] ^ⓘ; 31 March 1596 – 11 February 1650) was a French polymath, active across philosophy, including metaphysics, epistemology, ethics, and the philosophy of science; theology; mathematics, in which he connected the previously separate fields of geometry and algebra into analytic geometry; science, including physics, optics, mechanics, cosmology, and meteorology; physiology; and medicine. He has been credited as the father of modern philosophy, particularly due to his transformation of methodology by introducing a systematic, method-based approach to pursuing knowledge.

Refusing to accept the authority of previous philosophers, Descartes frequently set his views apart from the philosophers who preceded him. In the opening section of the Passions of the Soul, an early modern treatise on emotions, Descartes goes so far as to assert that he will write on this topic "as if no one had written on these matters before." His best-known philosophical statement is "cogito, ergo sum" ("I think, therefore I am", French: "Je pense, donc je suis").

He was one of the key figures in the Scientific Revolution, and his Meditations on First Philosophy and other philosophical works continue to be studied. His influence in mathematics is equally apparent: the Cartesian coordinate system is named after him. Descartes is also credited as the father of analytic geometry, which facilitated the discovery of infinitesimal calculus and analysis.

Biography

Early life

René Descartes was born in La Haye en Touraine, Province of Touraine (now Descartes, Indre-et-Loire), France, on 31 March 1596. In May 1597, his mother, Jeanne Brochard, died a few days after giving birth to a still-born child. Descartes's father, Joachim, was a member of the Parlement of Rennes at Rennes.^{: 22} René lived with his grandmother and with his great-uncle. Although the Descartes family was Roman Catholic, the Poitou region was controlled by the Protestant Huguenots. In 1607, late because of his fragile health, he entered the Jesuit College of La Flèche, where he was introduced to mathematics and physics.

After graduation in 1614, he studied for two years (1615–16) at the University of Poitiers, earning a Baccalauréat and Licence in canon and civil law in 1616, in accordance with his father's wishes that he should become a lawyer. From there, he moved to Paris.

Army service

In accordance with his ambition to become a professional military officer in 1618, Descartes joined, as a mercenary, the Protestant Dutch States Army in Breda under the command of Maurice of Nassau, and undertook a formal study of military engineering, as established by Simon Stevin. Descartes, therefore, received much encouragement in Breda to advance his knowledge of mathematics. In this way, he became acquainted with Isaac Beeckman, the principal of a Dordrecht school, for whom he wrote the Compendium of Music (written 1618, published 1650).

While in the service of the Catholic Duke Maximilian of Bavaria from 1619, Descartes was present at the Battle of the White Mountain near Prague, in November 1620.

According to Adrien Baillet, on the night of 10–11 November 1619 (St. Martin's Day), while stationed in Neuburg an der Donau, Descartes shut himself in a room with an "oven" (probably a cocklestove) to escape the cold. While within, he had three dreams, and believed that a divine spirit revealed to him a new philosophy. The second dream may have been an episode of exploding head syndrome, in which loud noise is imagined. By the time he exited the room, Descartes had formulated analytic geometry and the idea of applying the mathematical method to philosophy. He concluded from these dreams 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.

Career

France

In 1620, Descartes left the army. He visited Basilica della Santa Casa in Loreto, then visited various countries before returning to France, and during the next few years, he spent time in Paris. It was there that he composed his first essay on method: Regulae ad Directionem Ingenii (Rules for the Direction of the Mind). He arrived in La Haye in 1623, selling all of his property to invest in bonds, which provided a comfortable income for the rest of his life.^{: 94} Descartes was present at the siege of La Rochelle by Cardinal Richelieu in 1627 as an observer.^{: 128} There, he was interested in the physical properties of the great dike that Richelieu was building and studied mathematically everything he saw during the siege. He also met French mathematician Girard Desargues. In the autumn of that year, in the residence of the papal nuncio Guidi di Bagno, where he came with Mersenne and many other scholars to listen to a lecture given by the alchemist, Nicolas de Villiers, sieur de Chandoux, on the principles of a supposed new philosophy, Cardinal Bérulle urged him to write an exposition of his new philosophy in some location beyond the reach of the Inquisition.

Netherlands

Descartes returned to the Dutch Republic in 1628. In April 1629, he joined the University of Franeker, studying under Adriaan Metius, either living with a Catholic family or renting the Sjaerdemaslot. The next year, under the name "Poitevin", he enrolled at Leiden University, which at the time was a Protestant University. He studied both mathematics with Jacobus Golius, who confronted him with Pappus's hexagon theorem, and astronomy with Martin Hortensius. In October 1630, he had a falling-out with Beeckman, whom he accused of plagiarizing some of his ideas. In Amsterdam, he had a relationship with a servant girl, Helena Jans van der Strom, with whom he had a daughter, Francine, who was born in 1635 in Deventer. She was baptized a Protestant and died of scarlet fever at the age of 5.

Unlike many moralists of the time, Descartes did not deprecate the passions but instead defended them; he wept upon Francine's death in 1640. According to a 2018 biography by Jason Porterfield, "Descartes said that he did not believe that one must refrain from tears to prove oneself a man." Russell Shorto speculates that the experience of fatherhood and losing a child formed a turning point in Descartes's work, changing its focus from medicine to a quest for universal answers.

Despite frequent moves, he wrote all of his major work during his 20-plus years in the Netherlands, initiating a revolution in mathematics and philosophy. In 1633, Galileo was condemned by the Italian Inquisition, and Descartes abandoned plans to publish Treatise on the World, his work of the previous four years. Nevertheless, in 1637, he published parts of this work in three essays: "Les Météores" (The Meteors), "La Dioptrique" (Dioptrics) and La Géométrie (Geometry), preceded by an introduction, his famous Discours de la méthode (Discourse on the Method). In it, Descartes lays out four rules of thought, meant to ensure that our knowledge rests upon a firm foundation:

The first was never to accept anything for true which I did not know to be such; that is to say, carefully to avoid precipitancy and prejudice, and to comprise nothing more in my judgment than what was presented to my mind so clearly and distinctly as to exclude all ground of doubt.

In La Géométrie, Descartes exploited the discoveries he made with Pierre de Fermat. This later became known as Cartesian geometry.

Descartes continued to publish works concerning both mathematics and philosophy for the rest of his life. In 1641, he published a metaphysics treatise, Meditationes de Prima Philosophia (Meditations on First Philosophy), written in Latin and thus addressed to the learned. It was followed in 1644 by Principia Philosophiae (Principles of Philosophy), which was dedicated to Princess Elisabeth of Bohemia, a kind of synthesis of the Discourse on the Method and Meditations on First Philosophy.

In 1643, Cartesian philosophy was condemned at the University of Utrecht, and Descartes was obliged to flee to the Hague, then eventually to the north of Amsterdam, ultimately settling in Egmond-Binnen.

Between 1643 and 1649 Descartes lived with his girlfriend at Egmond-Binnen in an inn. Descartes became friendly with Anthony Studler van Zurck, lord of Bergen, and participated in the design of his mansion and estate. He also met Dirck Rembrantsz van Nierop, a mathematician and surveyor. He was so impressed by Van Nierop's knowledge that he even brought him to the attention of Constantijn Huygens and Frans van Schooten.

Descartes began (through Alfonso Polloti, an Italian general in Dutch service) a six-year correspondence with Princess Elisabeth of Bohemia, devoted mainly to moral and psychological subjects. Connected with this correspondence, in 1649 he published Les Passions de l'âme (The Passions of the Soul), which he dedicated to the Princess. A French translation of Principia Philosophiae, prepared by Abbot Claude Picot, was published in 1647. This edition was also dedicated to Princess Elisabeth. In the preface to the French edition, Descartes praised true philosophy as a means to attain wisdom. He identifies four ordinary sources to reach wisdom and finally says that there is a fifth, better and more secure, consisting in the search for first causes.

Sweden

By 1649, Descartes had become one of Europe's most famous philosophers and scientists. That year, Queen Christina of Sweden invited him to her court to organize a new scientific academy and tutor her in his ideas about love. Descartes accepted, and moved to the Swedish Empire in the middle of winter. Christina was interested in and stimulated Descartes to publish The Passions of the Soul.

He was a guest at the house of Pierre Chanut, living on Västerlånggatan, less than 500 meters from Castle Tre Kronor in Stockholm. There, Chanut and Descartes made observations with a Torricellian mercury barometer. Challenging Blaise Pascal, Descartes took the first set of barometric readings in Stockholm to see if atmospheric pressure could be used in forecasting the weather.

Death

Descartes arranged to tutor Queen Christina after her birthday, three times weekly at 5 a.m. in her cold and draughty castle. However, by 15 January 1650 the Queen had actually met with Descartes only four or five times. It soon became clear they did not like each other, as she did not care for his mechanical philosophy, nor did he share her interest in Ancient Greek language and literature. On 1 February 1650, he contracted pneumonia and died on 11 February at Chanut.

According to Chanut, the cause of death was not pneumonia, but peripneumonia according to Christina's physician Johann van Wullen, who was not allowed to bleed him. (The winter seems to have been mild, except for the second half of January which was harsh as described by Descartes himself; however, "this remark was probably intended to be as much Descartes's take on the intellectual climate as it was about the weather.")

E. Pies has questioned this account, based on a letter by the Doctor van Wullen; however, Descartes had refused his treatment, and more arguments against its veracity have been raised since.

His last words were reported to have been:

My soul, though has long been held captive. The hour has now come for thee to quit thy prison, to leave the trammels of this body. Then to this separation with joy and courage!

As a Catholic in a Protestant nation, he was interred in the churchyard of what was to become Adolf Fredrik Church in Stockholm, where mainly orphans had been buried. His manuscripts came into the possession of Claude Clerselier, Chanut's brother-in-law, and "a devout Catholic who has begun the process of turning Descartes into a saint by cutting, adding and publishing his letters selectively."^{: 137–154} In 1663, the Pope placed Descartes's works on the Index of Prohibited Books. In 1666, sixteen years after his death, his remains were taken to France and buried in Saint-Étienne-du-Mont. In 1671, Louis XIV prohibited all lectures in Cartesianism. Although the National Convention in 1792 had planned to transfer his remains to the Panthéon, he was reburied in the Abbey of Saint-Germain-des-Prés in 1819, missing a finger and the skull. His alleged skull is in the Musée de l'Homme in Paris, but some 2020 researches confirm that it may be a forgery. The original skull was probably divided into pieces in Sweden and given to private collectors; one of those pieces arrived at the University of Lund in 1691, where it is still preserved.

Philosophy

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 employed a method called hyperbolic or metaphysical doubt, also sometimes referred to as methodological skepticism or Cartesian doubt: he rejected any ideas that can be doubted and then re-established them in order to acquire a firm foundation for genuine knowledge. He relates this to architecture: the top soil is taken away to create a new building or structure. Descartes calls his doubt the soil and new knowledge the buildings. To Descartes, Aristotle's foundationalism was incomplete and his method of doubt enhances foundationalism.

Initially, Descartes arrives at only a single first principle: he thinks. This is expressed in the Latin phrase in the Discourse on the Method "Cogito, ergo sum" (English: "I think, therefore I am"), originally written in French, "Je pense, donc je suis." Descartes concluded, if he doubted, then something or someone must be doing the doubting; therefore, the very fact that he doubted proved his existence. "The simple meaning of the phrase is that if one is skeptical of existence, that is in and of itself proof that he does exist." These two first principles—I think and I exist—were later confirmed by Descartes's clear and distinct perception (delineated in his Third Meditation from The Meditations): as he clearly and distinctly perceives these two principles, Descartes reasoned, ensures their indubitability.

Descartes concludes that he can be certain that he exists because he thinks, but perceiving his body through the use of the senses is an unreliable evidence. So Descartes determines that the only indubitable knowledge is that he is a thinking thing. Thinking is what he does, and his power must come from his essence. Descartes defines "thought" (cogitatio) as "what happens in me such that I am immediately conscious of it, insofar as I am conscious of it". Thinking is thus every activity of a person of which the person is immediately conscious. He gave reasons for thinking that waking thoughts are distinguishable from dreams, and that one's mind cannot have been "hijacked" by an evil demon placing an illusory external world before one's senses.

And so something that I thought I was seeing with my eyes is grasped solely by the faculty of judgment which is in my mind.^{: 109}

In this manner, Descartes proceeds to construct a system of knowledge, discarding perception as unreliable and, instead, admitting only deduction as a method.

Mind–body dualism

Descartes, influenced by the automatons on display at the Château de Saint-Germain-en-Laye near Paris, investigated the connection between mind and body, and how they interact. His main influences for dualism were theology and physics. The theory on the dualism of mind and body is Descartes's signature doctrine and permeates other theories he advanced. Known as Cartesian dualism (or mind–body dualism), his theory on the separation between the mind and the body went on to influence subsequent Western philosophies. In Meditations on First Philosophy, Descartes attempted to demonstrate the existence of God and the distinction between the human soul and the body. Humans are a union of mind and body; thus Descartes's dualism embraced the idea that mind and body are distinct but closely joined. While many contemporary readers of Descartes found the distinction between mind and body difficult to grasp, he thought it was entirely straightforward. Descartes employed the concept of modes, which are the ways in which substances exist. In Principles of Philosophy, Descartes explained, "we can clearly perceive a substance apart from the mode which we say differs from it, whereas we cannot, conversely, understand the mode apart from the substance". To perceive a mode apart from its substance requires an intellectual abstraction, which Descartes explained as follows:

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

According to Descartes, two substances are really distinct when each of them can exist apart from the other. Thus, Descartes reasoned that God is distinct from humans, and the body and mind of a human are also distinct from one another. He argued that the great differences between body (an extended thing) and mind (an un-extended, immaterial thing) make the two ontologically distinct. According to Descartes's indivisibility argument, the mind is utterly indivisible: because "when I consider the mind, or myself in so far as I am merely a thinking thing, I am unable to distinguish any part within myself; I understand myself to be something quite single and complete."

Moreover, in the Meditations, Descartes discusses a piece of wax and exposes the single most characteristic doctrine of Cartesian dualism: that the universe contained two radically different kinds of substances—the mind or soul defined as thinking, and the body defined as matter and unthinking. The Aristotelian philosophy of Descartes's day held that the universe was inherently purposeful or teleological. Everything that happened, be it the motion of the stars or the growth of a tree, was supposedly explainable by a certain purpose, goal or end that worked its way out within nature. Aristotle called this the "final cause", and these final causes were indispensable for explaining the ways nature operated. Descartes'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. Descartes's dualism provided the philosophical rationale for the latter by expelling the final cause from the physical universe (or res extensa) in favor of the mind (or res cogitans). Therefore, while Cartesian dualism paved the way for modern physics, it also held the door open for religious beliefs about the immortality of the soul.

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

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

Descartes's discussion on embodiment raised one of the most perplexing problems of his dualism philosophy: What exactly is the relationship of union between the mind and the body of a person? Therefore, Cartesian dualism set the agenda for philosophical discussion of the mind–body problem for many years after Descartes's death. Descartes argued the theory of innate knowledge and that all humans were born with knowledge through the higher power of God. It was this theory of innate knowledge that was later combated by philosopher John Locke (1632–1704), an empiricist.

Physiology and psychology

In The Passions of the Soul, published in 1649, Descartes discussed the common contemporary belief that the human body contained animal spirits. These animal spirits were believed to be light and roaming fluids circulating rapidly around the nervous system between the brain and the muscles. These animal spirits were believed to affect the human soul, or the passions of the soul. Descartes distinguished six basic passions: wonder, love, hatred, desire, joy and sadness. All of these passions, he argued, represented different combinations of the original spirit and influenced the soul to will or want certain actions. He argued, for example, that fear is a passion that moves the soul to generate a response in the body. In line with his dualist teachings on the separation between the soul and the body, he hypothesized that some part of the brain served as a connector between the soul and the body and singled out the pineal gland as connector. Descartes argued that signals passed from the ear and the eye to the pineal gland, through animal spirits. Thus, different motions in the gland cause various animal spirits. He argued that these motions in the pineal gland are based on God's will and that humans are supposed to want and like things that are useful to them. But he also argued that the animal spirits that moved around the body could distort the commands from the pineal gland, thus humans had to learn how to control their passions.

Descartes advanced a theory on automatic bodily reactions to external events, which influenced 19th-century reflex theory. He argued that external motions, such as touch and sound, reach the endings of the nerves and affect the animal spirits. For example, heat from fire affects a spot on the skin and sets in motion a chain of reactions, with the animal spirits reaching the brain through the central nervous system, and in turn, animal spirits are sent back to the muscles to move the hand away from the fire. Through this chain of reactions, the automatic reactions of the body do not require a thought process.

Above all, he was among the first scientists who believed that the soul should be subject to scientific investigation. He challenged the views of his contemporaries that the soul was divine, thus religious authorities regarded his books as dangerous. Descartes's writings went on to form the basis for theories on emotions and how cognitive evaluations were translated into affective processes. Descartes believed the brain resembled a working machine and that mathematics and mechanics could explain complicated processes in it.

On animals

It is generally accepted that Descartes denied that animals had reason or intelligence, as historians have generally reduced Descartes's interpretation of animals to a comparison to machines. At a deeper reading, however, questions surface and his interpretation appears more complex: he argued that animals did not lack sensations or perceptions, but these could be explained mechanistically, that is, without any appeals to souls. A more attentive investigation of Descartes's study of animals, and their variety, reveals his attention to animal behaviour, an unexpected outcome of his mechanical interpretation. 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. If animals showed signs of distress, then this was to protect the body from damage, but the innate state needed for them to suffer was absent. Although Descartes's views were not universally accepted, they became prominent in Europe and North America, allowing humans to treat animals with impunity.

The view that animals were quite separate from humanity and merely machines allowed for the maltreatment of animals, and was sanctioned in law and societal norms until the middle of the 19th century.^{: 180–214} The publications of Charles Darwin would eventually erode the Cartesian view of animals.^{: 37} Darwin argued that the continuity between humans and other species suggested the possibility of animal suffering.^{: 177}

Moral philosophy

For Descartes, ethics was a science, the highest and most perfect of them. Like the rest of the sciences, ethics had its roots in metaphysics. In this way, he argues for the existence of God, investigates the place of man in nature, formulates the theory of mind–body dualism, and defends free will. However, as he was a convinced rationalist, Descartes clearly states that reason is sufficient in the search for the goods that individuals should seek, and virtue consists in the correct reasoning that should guide their actions. Nevertheless, the quality of this reasoning depends on knowledge and mental condition. For this reason, he said that a complete moral philosophy should include the study of the body.^{: 189} 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. His works about human passion and emotion would be the basis for the philosophy of his followers, and would have a lasting impact on ideas concerning what literature and art should be, specifically how it should invoke emotion.

The moral writings of Descartes came at the last part of his life, but earlier, in his Discourse on the Method, he adopted three maxims to be able to act while he put all his ideas into doubt. Those maxims are known as his "Provisional Morals".

God

In the third and fifth Meditation, Descartes offers proofs of a benevolent God (the trademark argument and the ontological argument respectively). Descartes has faith in the account of reality his senses provide him, since he believed that God provided him with a working mind and sensory system and does not desire to deceive him. From this supposition, however, Descartes finally establishes the possibility of acquiring knowledge about the world based on deduction and perception. Regarding epistemology, therefore, Descartes can be said to have contributed such ideas as a conception of foundationalism and the possibility that reason is the only reliable method of attaining knowledge. Descartes, however, was very much aware that experimentation was necessary to verify and validate theories.

Descartes invokes his causal adequacy principle to support his trademark argument for the existence of God, quoting Lucretius in defence: "Ex nihilo nihil fit", meaning "Nothing comes from nothing" (Lucretius). The argument is "that our idea of perfection is related to its perfect origin (God), just as a stamp or trademark is left in an article of workmanship by its maker." In the fifth Meditation, Descartes presents a version of the ontological argument which is founded on the possibility of thinking the "idea of a being that is supremely perfect and infinite," and suggests that "of all the ideas that are in me, the idea that I have of God is the most true, the most clear and distinct."

Descartes' attempt to ground theological beliefs on reason encountered intense opposition in his time. Pascal regarded Descartes's views as a rationalist and mechanist, and accused him of deism: "I cannot forgive Descartes; in all his philosophy, Descartes did his best to dispense with God. But Descartes could not avoid prodding God to set the world in motion with a snap of his lordly fingers; after that, he had no more use for God," while a contemporary, Martin Schoock, accused him of atheist beliefs, though Descartes had provided an explicit critique of atheism in his Meditations. The Catholic Church prohibited his books in 1663.^{: 274}

Descartes also wrote a response to external world skepticism. Through this method of skepticism, he does not doubt for the sake of doubting but to achieve concrete and reliable information. In other words, certainty. He argues that sensory perceptions come to him involuntarily, and are not willed by him. They are external to his senses, and according to Descartes, this is evidence of the existence of something outside of his mind, and thus, an external world. Descartes goes on to argue that the things in the external world are material by arguing that God would not deceive him as to the ideas that are being transmitted, and that God has given him the "propensity" to believe that such ideas are caused by material things. Descartes also believes a substance is something that does not need any assistance to function or exist. Descartes further explains how only God can be a true "substance". But minds are substances, meaning they need only God for them to function. The mind is a thinking substance. The means for a thinking substance stem from ideas.

Descartes steered clear of theological questions, restricting his attention to showing that there is no incompatibility between his metaphysics and theological orthodoxy. He avoided trying to demonstrate theological dogmas metaphysically. When challenged that he had not established the immortality of the soul merely in showing that the soul and the body are distinct substances, he replied, "I do not take it upon myself to try to use the power of human reason to settle any of those matters which depend on the free will of God."

Mathematics

x for unknown; exponential notation

Descartes "invented the convention of representing unknowns in equations by x, y, and z, and knowns by a, b, and c". He also "pioneered the standard notation" that uses superscripts to show the powers or exponents; for example, the 2 used in x² to indicate x squared.^{: 19}

Analytic geometry

One of Descartes's most enduring legacies was his development – together with Pierre de Fermat – of Cartesian or analytic geometry, which uses algebra to describe geometry; the Cartesian coordinate system is named after him. Descartes' work on geometry was written to demonstrate its application to correct reasoning he discussed in the Discourse on the Method, which consists of reasoning based on self-evident principles. He was the first to assign a fundamental place for algebra in the system of knowledge, using it as a method to automate or mechanize reasoning, particularly about abstract, unknown quantities.^{: 91–114}

Both Descartes and Fermat were inspired by the works of the Ancient Greek mathematicians Pappus of Alexandria and Apollonius of Perga, especially by their techniques of analysis. Crucial for their work was also the symbolic algebra of François Viète. The step that their predecessors failed to take was using coordinates to study the relationship between geometry and algebra.

European mathematicians had previously viewed geometry as a more fundamental form of mathematics, serving as the foundation of algebra. Algebraic rules were given geometric proofs by mathematicians such as Pacioli, Cardano, Tartaglia and Ferrari. Equations of degree higher than the third were regarded as unreal, because a three-dimensional form, such as a cube, occupied the largest dimension of reality. Descartes professed that the abstract quantity a² could represent length as well as an area. This was in opposition to the teachings of mathematicians such as François Viète, who insisted that a second power must represent an area.

Although Descartes did not pursue the subject, he preceded Gottfried Wilhelm Leibniz in envisioning a more general science of algebra or "universal mathematics", as a precursor to symbolic logic, that could encompass logical principles and methods symbolically, and mechanize general reasoning.^{: 280–281}

Influence on Newton's mathematics

It is often said that Descartes had the most influence of anyone on the young Isaac Newton. Descartes's influence extended not directly from his original French edition of La Géométrie, however, but rather from Frans van Schooten's expanded second Latin edition of the work.^{: 100} Newton continued Descartes's work on cubic equations, which freed the subject from the fetters of the Greek perspectives. The most important concept was his very modern treatment of single variables.^{: 109–129}

The basis of calculus

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

Physics

Mechanics

Mechanical philosophy

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

Descartes's mechanical attempt to study nature reveals success and shortcomings. He managed to explain rather well the functioning of so-called inert phenomena, such as the rainbow, the phenomenon of mock suns, the movement of planets and comets, as well as the differentiation of metals, stones and minerals. This experimental work with metals and inert bodies reveals a different Descartes, investigating nature by means of observations and the uses of microscopes. But there is more, as Descartes tried to explain in the mechanical terms of his philosophy living nature too - namely, plants and animals. This part shows the complexity of his philosophical programme, but also the most fascinating. On the one hand, Descartes managed to lay the ground for a modern medicine, while on the other hand he failed to establish an overall science of nature. Recently, historians have recognized the importance of Descartes's scientific enterprise in his philosophical work.

Anticipating the concept of work

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

Lifting 100 lb one foot twice over is the same as lifting 200 lb one foot, or 100 lb two feet.

Conservation of motion

In Principles of Philosophy (Principia Philosophiae) from 1644, Descartes outlined his views on the universe. In it he describes his three laws of motion. (Newton's own laws of motion would later be modeled on Descartes's exposition.) Descartes defined "quantity of motion" (Latin: quantitas motus) as the product of size and speed, and claimed that the total quantity of motion in the universe is conserved.

If x is twice the size of y, and is moving half as fast, then there's the same amount of motion in each.

[God] created matter, along with its motion... merely by letting things run their course, he preserves the same amount of motion... as he put there in the beginning.

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

Plenism

Descartes was also a devoted "plenist" who believed that no empty space can exist and that space must consequently be filled with matter. The parts of this matter tend to move in straight paths, but because they lie close together, they cannot move freely, which according to Descartes implies that every motion is circular, so the aether is filled with vortices. Descartes also distinguishes between different forms and sizes of matter, in which rough matter resists the circular movement more strongly than fine matter. Due to centrifugal force, matter tends towards the outer edges of the vortex, which causes a condensation of this matter there. The rough matter cannot follow this movement due to its greater inertia—so due to the pressure of the condensed outer matter, those parts will be pushed into the centre of the vortex. According to Descartes, this inward pressure is nothing other than gravity. He compared this mechanism with the fact that if a rotating, liquid-filled vessel is stopped, the liquid goes on to rotate. Now, if one drops small pieces of light matter (e.g. wood) into the vessel, the pieces move to the middle of the vessel.

Magnetism

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

Glass science

In 1644, Descartes provided one of the earliest microscopic theories of glass. He considered that glass was formed by particles frozen in motion after heated. He also provides one of the earliest understanding of the role of stress and its relief by annealing.

Optics

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

Meteorology

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

While rejecting most of Aristotle's theories on meteorology, he still kept some of the terminology that Aristotle used such as vapors and exhalations. These "vapors" would be drawn into the sky by the sun from "terrestrial substances" and would generate wind. Descartes also theorized that falling clouds would displace the air below them, also generating wind. Falling clouds could also generate thunder. He theorized that when a cloud rests above another cloud and the air around the top cloud is hot, it condenses the vapor around the top cloud, and causes the particles to fall. When the particles falling from the top cloud collided with the bottom cloud's particles it would create thunder. He compared his theory on thunder to his theory on avalanches. Descartes believed that the booming sound that avalanches created, was due to snow that was heated, and therefore heavier, falling onto the snow that was below it. This theory was supported by experience: "It follows that one can understand why it thunders more rarely in winter than in summer; for then not enough heat reaches the highest clouds, in order to break them up."

Another theory that Descartes had was on the production of lightning. Descartes believed that lightning was caused by exhalations trapped between the two colliding clouds. He believed that in order to make these exhalations viable to produce lightning, they had to be made "fine and inflammable" by hot and dry weather. Whenever the clouds would collide, it would cause them to ignite, creating lightning; if the cloud above was heavier than the bottom cloud, it would also produce thunder.

Descartes also believed that clouds were made up of drops of water and ice, and believed that rain would fall whenever the air could no longer support them. It would fall as snow if the air was not warm enough to melt the raindrops. And hail was when the cloud drops would melt, and then freeze again because cold air would refreeze them.

Descartes did not use mathematics or instruments (as there were not any at the time) to back up his theories on Meteorology and instead used qualitative reasoning in order to deduce his hypothesis.

Historical impact

Emancipation from Church doctrine

Descartes has often been dubbed the father of modern Western philosophy, the thinker whose approaches have profoundly changed the course of Western philosophy and set the basis for modernity. The first two of his Meditations on First Philosophy, those that formulate the famous methodic doubt, represent the portion of Descartes's writings that most influenced modern thinking. It has been argued that Descartes himself did not realize the extent of this revolutionary move. In shifting the debate from "what is true" to "of what can I be certain?", Descartes arguably shifted the authoritative guarantor of truth from God to humanity—while the traditional concept of "truth" implies an external authority, "certainty" instead relies on the judgment of the individual.

In an anthropocentric revolution, the human being is now raised to the level of a subject, an agent, an emancipated being equipped with autonomous reason. This was a revolutionary step that contributed to the basis of the Modern Era, 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. In modernity, the guarantor of truth is not God anymore but human beings, each of whom is a "self-conscious shaper and guarantor" of their own reality. In that way, each person is turned into a reasoning adult, a subject and agent, as opposed to a child obedient to God. This change in perspective was characteristic of the shift from the Christian medieval period to the modern period, a shift that had been anticipated in other fields, and which was now being formulated in the field of philosophy by Descartes.

This anthropocentric perspective of Descartes's work, establishing human reason as autonomous, provided the basis for the Enlightenment's emancipation from God and the Church. According to Martin Heidegger, the perspective of Descartes's work also provided the basis for all subsequent anthropology. Descartes's philosophical revolution is sometimes said to have sparked modern anthropocentrism and subjectivism.

Reception

The Discourse appeared during Descartes's lifetime in a single edition of 500 copies, 200 of which were set aside for the author. Sharing a similar fate was the only French edition of the Meditations, which had not managed to sell out by the time of Descartes's death. A concomitant Latin edition of the latter was, however, eagerly sought out by Europe's scholarly community and proved a commercial success for Descartes.^{: xliii–xliv}

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

According to philosophy professor John Cottingham, Descartes's Meditations on First Philosophy is considered to be "one of the key texts of Western philosophy". Cottingham said that the Meditations is the "most widely studied of all Descartes' writings".^{: 50} According to author Anthony Gottlieb, one of the reasons Descartes and Thomas Hobbes continue to be debated in the second decade of the twenty-first century, is that they still have something to say to us that remains relevant on questions such as, "What does the advance of science entail for our understanding of ourselves and our ideas of God?" and "How is government to deal with religious diversity?"

Works

Writings

• 1618. Musicae Compendium. A treatise on music theory and the aesthetics of music, which Descartes dedicated to early collaborator Isaac Beeckman (written in 1618, first published—posthumously—in 1650).^{: 127–129}
• 1626–1628. Regulae ad directionem ingenii (Rules for the Direction of the Mind). Incomplete. First published posthumously in Dutch translation in 1684 and in the original Latin at Amsterdam in 1701 (R. Des-Cartes Opuscula Posthuma Physica et Mathematica). The best critical edition, which includes the Dutch translation of 1684, is edited by Giovanni Crapulli (The Hague: Martinus Nijhoff, 1966).
• c. 1630. De solidorum elementis. Concerns the classification of Platonic solids and three-dimensional figurate numbers. Said by some scholars to prefigure Euler's polyhedral formula. Unpublished; discovered in Descartes's estate in Stockholm in 1650, soaked for three days in the Seine in a shipwreck while being shipped back to Paris, copied in 1676 by Leibniz, and lost. Leibniz's copy, also lost, was rediscovered circa 1860 in Hannover.
• 1630–1631. La recherche de la vérité par la lumière naturelle (The Search for Truth by Natural Light) unfinished dialogue published in 1701.^{: 264ff}
• 1630–1633. Le Monde (The World) and L'Homme (Man). Descartes's first systematic presentation of his natural philosophy. Man was published posthumously in Latin translation in 1662; and The World posthumously in 1664.
• 1637. Discours de la méthode (Discourse on the Method). An introduction to the Essais, which include La Dioptrique, Les Météores and La Géométrie.
• 1637. La Géométrie (Geometry). Descartes's major work in mathematics. There is an English translation by Michael Mahoney (New York: Dover, 1979).
• 1641. Meditationes de prima philosophia (Meditations on First Philosophy), also known as Metaphysical Meditations. In Latin; a second edition, published the following year, included an additional objection and reply, and a Letter to Dinet. A French translation by the Duke of Luynes, probably done without Descartes's supervision, was published in 1647. Includes six Objections and Replies.
• 1644. Principia philosophiae (Principles of Philosophy), a Latin textbook at first intended by Descartes to replace the Aristotelian textbooks then used in universities. A French translation, Principes de philosophie by Claude Picot, under the supervision of Descartes, appeared in 1647 with a letter-preface to Princess Elisabeth of Bohemia.
• 1647. Notae in programma (Comments on a Certain Broadsheet). A reply to Descartes's one-time disciple Henricus Regius.
• 1648. La description du corps humain (The Description of the Human Body). Published posthumously by Clerselier in 1664.
• 1648. Responsiones Renati Des Cartes... (Conversation with Burman). Notes on a Q&A session between Descartes and Frans Burman on 16 April 1648. Rediscovered in 1895 and published for the first time in 1896. An annotated bilingual edition (Latin with French translation), edited by Jean-Marie Beyssade, was published in 1981 (Paris: PUF).
• 1649. Les passions de l'âme (Passions of the Soul). Dedicated to Princess Elisabeth of the Palatinate.
• 1657. Correspondance (three volumes: 1657, 1659, 1667). Published by Descartes's literary executor Claude Clerselier. The third edition, in 1667, was the most complete; Clerselier omitted, however, much of the material pertaining to mathematics.

In January 2010, a previously unknown letter from Descartes, dated 27 May 1641, was found by the Dutch philosopher Erik-Jan Bos when browsing through Google. Bos found the letter mentioned in a summary of autographs kept by Haverford College in Haverford, Pennsylvania. The college was unaware that the letter had never been published. This was the third letter by Descartes found in the last 25 years.

Collected editions

• Oeuvres de Descartes edited by Charles Adam and Paul Tannery, Paris: Léopold Cerf, 1897–1913, 13 volumes; new revised edition, Paris: Vrin-CNRS, 1964–1974, 11 volumes (the first five volumes contain the correspondence). [This edition is traditionally cited with the initials AT (for Adam and Tannery) followed by a volume number in Roman numerals; thus AT VII refers to Oeuvres de Descartes volume 7.]
• Étude du bon sens, La recherche de la vérité et autres écrits de jeunesse (1616–1631) edited by Vincent Carraud and Gilles Olivo, Paris: PUF, 2013.
• Descartes, Œuvres complètes, new edition by Jean-Marie Beyssade and Denis Kambouchner, Paris: Gallimard, published volumes:
  • I: Premiers écrits. Règles pour la direction de l'esprit, 2016.
  • III: Discours de la Méthode et Essais, 2009.
  • VIII.1: Correspondance, 1 edited by Jean-Robert Armogathe, 2013.
  • VIII.2: Correspondance, 2 edited by Jean-Robert Armogathe, 2013.
• René Descartes. Opere 1637–1649, Milano, Bompiani, 2009, pp. 2531. Edizione integrale (di prime edizioni) e traduzione italiana a fronte, a cura di G. Belgioioso con la collaborazione di I. Agostini, M. Marrone, M. Savini ISBN 978-88-452-6332-3.
• René Descartes. Opere 1650–2009, Milano, Bompiani, 2009, pp. 1723. Edizione integrale delle opere postume e traduzione italiana a fronte, a cura di G. Belgioioso con la collaborazione di I. Agostini, M. Marrone, M. Savini ISBN 978-88-452-6333-0.
• René Descartes. Tutte le lettere 1619–1650, Milano, Bompiani, 2009 IIa ed., pp. 3104. Nuova edizione integrale dell'epistolario cartesiano con traduzione italiana a fronte, a cura di G. Belgioioso con la collaborazione di I. Agostini, M. Marrone, F.A. Meschini, M. Savini e J.-R. Armogathe ISBN 978-88-452-3422-4.
• René Descartes, Isaac Beeckman, Marin Mersenne. Lettere 1619–1648, Milano, Bompiani, 2015 pp. 1696. Edizione integrale con traduzione italiana a fronte, a cura di Giulia Beglioioso e Jean Robert-Armogathe ISBN 978-88-452-8071-9.

Collected English translations

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

Translation of single works

• 1628. Regulae ad directionem ingenii. Rules for the Direction of the Natural Intelligence. A Bilingual Edition of the Cartesian Treatise on Method Archived 16 August 2021 at the Wayback Machine, ed. & trans. G. Heffernan (Amsterdam/Atlanta: Rodopi, 1998).
• 1633. The World, or Treatise on Light Archived 21 June 2021 at the Wayback Machine, tr. by Michael S. Mahoney.
• 1633. Treatise of Man, tr. by T. S. Hall. Cambridge, MA: Harvard University Press, 1972.
• 1637. Discourse on the Method, Optics, Geometry and Meteorology, trans. P. J. Olscamp, Revised edition (Indianapolis: Hackett, 2001).
• 1637. The Geometry of René Descartes Archived 16 August 2021 at the Wayback Machine, trans. D. E. Smith & Marcia Latham (Chicago: Open Court, 1925).
• 1641. Meditations on First Philosophy, tr. by J. Cottingham, Cambridge: Cambridge University Press, 1996. Latin original. Alternative English title: Metaphysical Meditations. Includes six Objections and Replies. A second edition published the following year, includes an additional Objection and Reply and a Letter to Dinet. HTML Online Latin-French-English Edition Archived 27 August 2006 at the Wayback Machine.
• 1644. Principles of Philosophy Archived 30 September 2020 at the Wayback Machine, trans. V. R. Miller & R. P. Miller: (Dordrecht/Boston/London: Kluwer Academic Publishers, 1982).
• 1648. Descartes' Conversation with Burman, tr. by J. Cottingham, Oxford: Clarendon Press, 1989.
• 1649. Passions of the Soul Archived 16 August 2021 at the Wayback Machine, trans. S. H. Voss (Indianapolis: Hackett, 1989). Dedicated to Elisabeth of the Palatinate.
• 1619–1648. René Descartes, Isaac Beeckman, Marin Mersenne. Lettere 1619–1648, ed. by Giulia Beglioioso and Jean Robert-Armogathe, Milano, Bompiani, 2015 pp. 1696. ISBN 978-88-452-8071-9

See also

• Bucket argument
• Cartesian circle
• Cartesian plane
• Cartesian product
• Cartesian product of graphs
• Cartesian theater
• Cartesian tree
• Descartes number
• Descartes' rule of signs
• Descartes' theorem (4 tangent circles)
• Descartes's theorem on total angular defect
• Folium of Descartes
• List of things named after René Descartes

From the 1913 Catholic Encyclopedia

René Descartes — (Renatus Cartesius), philosopher and scientist, born at La Haye France, 31 March, 1596; died at Stockholm, Sweden, 11 February 1650. He studied at the Jesuit college of La Flèche, one of the most famous schools of the time. In 1613 he went to Paris, where he formed a lasting friendship with Father Mersenne, O. F. M., and made the acquaintance of the mathematician Mydorge. He afterwards enlisted in the armies of Maurice of Nassau, and of the Duke of Bavaria. On 10 November, 1619, he felt a strong impulse to set aside the prejudices of his childhood and of his environment, and to devote his life to the restoration of human knowledge, which was then in a state of decadence; and for him this mission took on quite a mystical character. He had a dream which he interpreted as a revelation, and he became convinced that "it was the Spirit of Truth that willed to open for him all the treasures of knowledge". After much journeying in Brittany, Poitou, Switzerland, and Italy, he returned to Paris in 1625. There he remained for two years during which it was his fortune to meet Cardinal Bérulle who encouraged him in his scientific vocation. But as Paris offered neither the peace nor the independence his work demanded, he set out in 1629 for Holland, and there in the midst of a commercial people he enjoyed the advantage of living as quietly as in a desert. From this retreat he gave to the world his "Discours de la méthode" (1637), "Méditations" (1641), "Principes" (1644), and "Passions"(l649). "Le Monde" had been completed in 1633, but the condemnation of Galileo frightened Descartes who preferred to avoid all collision with ecclesiastical authority. He deferred the publication of this clever work without, however, losing hope of eventually bringing it out. In 1649, yielding to the entreaties of Queen Christina, he went to Sweden, and died at Stockholm of inflammation of the lungs.

Descartes' work is important rather because of its quality than of its quantity. Let us see first of all wherein his method is new. He observed, as Bacon had already done before him, that there is no question on which men agree. "There is nothing", he says "so evident or so certain that it may not be controverted. Whence then this widespread and deep-rooted anarchy? From the fact that our inquiries are haphazard" (Règles pour la direction de l'esprit, 4e Règle). The first problem, then, is to discover a scientific method. How is success in this difficult task to be assured? To begin with, we must cease to rely on authority; and for two principal reasons. "In whom can we trust" when "there is hardly a statement made by one man, of which the opposite is not loudly supported by some other?" And even "if all were agreed, the knowledge of their teaching would not suffice us." "Had we by rote all the arguments of Plato and Aristotle, we should not be any the more philosophers unless we were able to bring to bear on any given question a solid judgment of our own. We should have indeed learned history but not mastered a science" (3e Règle) Philosophy presupposes the understanding of problems—and consequently its method cannot be external, it must be essentially immanent. The true method is to seek for reasonable evidence and the norm of such evidence is to be found in the science of mathematics (Discours de la méthode, 2e partie). "It is not that arithmetic and geometry are the only sciences to be learned, but that he who would progress on the road to truth must not delay over any object about which he cannot have a certainty equal to that given by arithmetical and geometrical demonstrations" (2e Règle).

Is everything, then, capable of being known in this way, and consequently can human knowledge become the complete counterpart of reality? Descartes says so over and over again; it is his controlling idea; and he endeavours to prove it both from the nature of our thought and from the universal connexion of things. The mind is equally intelligent however diverse the objects it considers; and those objects because of their perfect enchainment are always equally intelligible. There is, therefore, no question "so far removed from us as to be beyond our reach or so deeply hidden that we cannot discover it", provided only that we persevere and follow the right method (Disc. de la méth. 2e partie; 4e Règle). Such is the rationalism of Descartes, surpassing even that of Plato, in which under the name of "the Infinite" three-fourths of reality remains for ever unknowable. How then is this mathematical evidence to be obtained. Two methods, dangerous at once and sterile, must be avoided. We cannot build on the experience of our senses; "for they are often deceptive", and consequently need a control which they have not in themselves. Bacon was misled on this point (2e Règle). Neither can we adopt the syllogistic method; for this is not, as was formerly thought, a means of discovery. It is simply a process in which, two terms being given, we find by means of a third that the former two are linked together, i. e. that they have some common characteristic. Now if they have this common characteristic it is useless to search for it with any light other than their own. Let them pass under direct scrutiny; let their natures be studied, and in time the common trait will reveal itself. This is the mind's straight road to discovery, passing on from one idea to another without the aid of a third. The syllogism is of no use until the discovery has been made; it simply serves the purpose of exposition (14e Règle). There are but two ways leading to mathematical evidence: intuition and deduction (3e Règle). Intuition "is the conception formed by an attentive mind so clear and distinct that it admits of no doubt: or what amounts to the same thing, it is the clear conception of a sound and attentive mind, the product of unaided reason" (3e Règle). Intuition is not, therefore, perception by the senses—it is an act of the understanding brought to bear on an idea. The senses do not supply the object but merely the occasion. A movement, for instance, awakens in us the idea of motion, and it is that idea we must regard as the object of intuition. In very simple matters intuition acts quickly; thus "everyone can know intuitively that he exists; that a triangle is terminated by three angles, neither more nor less, and that a globe has but one surface" (3e Règle; 12e Règle; Rép. aux deux objections). In the case of objects more or less complex, intuition proceeds by way of analysis. Since it deals with ideas, and ideas are but one aspect of thought, everything must be reduced to clear and distinct elements, to ultimate or "indecomposable" parts. These ultimate parts must be inspected one after another, until the object is exhausted, "by passing from those that are easily known to those that are less easily known" (6e Règle). In the long run everything will be spread out in full light.

Deduction is the process in which by a continuous movement of thought we draw from a thing that we certainly know the conclusions that of necessity flow from it. This procedure may be carried on in two ways. "If, for instance, after various calculations I discover the relation between the quantities A and B, between B and C, between C and D, and lastly between D and E, I do not yet know the relation between A and E"; but I can infer it by retracting the several steps of the series. This is the first form of deduction (7e Règle). There is a second form in which, the connecting links of the series being too numerous to enter the mental field of vision all at once, we are content to draw conclusions from the general impression we have of the series (7e Règle). Deduction is an intellectual process, but it differs from intuition by bringing in memory as a factor. And this is noteworthy in view of the important role that memory plays in the Cartesian explanation of certitude, and the desperate effort he makes to defend this procedure. From the conspicuous place that reason holds in the Cartesian method, one might infer that there was no room for experience. Nothing could be less true. For Descartes, as for Bacon, the one purpose of science is utility. He also expects from it a continual betterment of the conditions of human life, and his hopes in that direction go very far, as, for instance, when he says of medicine that in the end it would procure us the boon of immortality (Disc. de la méth. 6e partie). And as he who wills the end wills the means also, Descartes accepts in its entirety the experimental part of the Baconian method (letter to Mersenne, 1631), and acts accordingly. He put himself in touch with all the experimental work of his day (letter, April, 1632), urged others to take up research (letter to Mersenne, 1632), and carried on experiments of his own that covered a wide range of subjects: the weight of air (letter, 2 June, 1631), the laws of sound and light (letter, 1633); the essential differences between oils, spirits, eaux-de-vie, common waters, aquafortis, and salts. He dissected the heads of various animals to show the workings of memory and imagination (cf. letters to Mersenne, 1633 April, 1637; 13 November, 1639; 4 January, 1643, ed. Cousin, Paris, 1826). There was hardly a fact that escaped this apologist of Reason nor anything into whose hidden nature he did not inquire; even the "Chasse de Pan" he followed with his accustomed ardour.

But if the mind, moving as it does in the realm of intelligible objects, have a power of intuition sufficient to master them all, why these researches? Are they not a hindrance rather than a help? Let deduction but go on to the end, and it must assuredly attain that exhaustive knowledge which is the goal of investigation, but such is not the case. Experiment helps reasoning in more ways than one. It supplies the fact that calls forth in our intelligence the idea of the problem to be solved. That idea once aroused, the intelligence takes hold of it, and may produce many others, according to the nature of which experience and reason play reciprocal, yet different, roles. The idea of a problem may be so simple as to allow a mathematical deduction of the properties of the object in question and nothing more. In this case experiment is called in only by way of illustration, as happens, for instance, in the study of the laws of motion. (Cf. Principes, 2e partie.) But again the idea of a problem may be so complex as to suggest various hypotheses, since principles as a rule are so fruitful that we can draw from them more than we see in the world around us. We must then choose from among the hypotheses presented by the intellect that which corresponds most nearly to the facts: and experiment is our only resource. It acts as a sort of guide to rational deduction. It sets up, so to say, a number of sign-posts which point out, at the cross-roads of logic the right direction to the world of facts. Finally, we may be confronted with two or more hypotheses equally applicable to the known facts, observations must then be multiplied until we discover some peculiarity which determines our choice: and thus experiment becomes a real means of verification (Principes, 4e partie.) In every case experiment is, as it were, the matter, while calculation becomes the form. In the physical world there is nothing but motion and extension, nothing but quantity. Everything can be reduced to numerical proportions, and this reduction is the final object of science. To understand means to know in terms of mathematics. When this final stage is reached, intelligence and experience unite in closest bonds: the intellect setting its seal on experience and endowing it with intelligibility.

Such is the method of Descartes. There remains to be seen what use he makes of it. Recourse must be had to provisional doubt as the only means of distinguishing the true from the false in the labyrinth of contradictory opinions which are held in the schools and in the world at large. We must needs imitate those builders who, in order to erect a lofty structure, begin by digging deep, so that the foundations may be laid on the rock and solid ground (Remarques sur les 7es objections, ed. Charpentier, Paris; cf. Disc. de la m´thode, 3e partie.) And this provisional doubt goes very deep indeed. We may reject the evidence of the senses for they are deceptive, "and it is but the part of prudence never to trust absolutely what has once deceived us" (1re Méditation). We may even question whether there be "any earth or sky or other extended body"; for, supposing that nothing of the sort exist, I can still have the impression of their existence as I had before; this is plain from the phenomena of madness and dreams. What is more, the very simplest and clearest truths are not free from suspicion." How do I know that God has not so arranged it that I am deceived each time I add two and three together, or number the sides of a square, or form some judgment still more simple, if indeed anything more simple can be imagined" (3e Méditation). What then remains intact? One thing only, the fact of my thought itself. But if I think it is because I exist, for from the one to the other of these terms we pass by simple inspection— Cogito, ergo sum: Behold the long-sought rock on which the edifice of knowledge must be built (Disc. de la méth., 4e partie, 2e Méd.). But how is this to be done? how are we to make our way out of the abyss into which we have descended? By analysing the basic fact, i. e. the content of our thought. I observe that, since my thought gropes amid doubt, I must be imperfect: and this idea calls forth this other, viz. of a being that is not imperfect, and therefore is perfect and infinite (Disc. de la méth., 4e partie.) Let us consider this other idea. It must necessarily include existence otherwise something would be wanting to it; it would not be perfect or infinite. Therefore, God exists, and "I know no less clearly and distinctly that an actual and eternal existence belongs to His nature than I know that whatever I can demonstrate of any figure or number belongs truly to the nature of that figure or number " (Disc. de la méth., 4e partie; 5e Médit.; Rép. aux premières obj.).

God, therefore, is known to us at the outset, the moment we take the trouble to look into the nature of our own minds; and this is enough to eliminate the hypothesis of an evil genius that would take pleasure in deceiving us; it is enough also to secure the validity of all our deductions, whatever be their length, for "I recognize that it is impossible that He should ever deceive me, since in all fraud and deceit there is a certain imperfection" (4e Méd.). Otherwise how would this idea of God be anything more than an idle fancy? It has immensity; it has infinity, and therefore it must of itself be capable of existing. Spinoza, and after him Hegel, will teach that the possible infolds, as it were, an essential tendency to existence, and that this tendency is greater in proportion as the possible is perfect. It is on this principle that they will build their vast synthetic systems. Descartes anticipates them and when closely pressed he replies just as do these later philosophers. (Rép. aux premières objections.) It is a fact worth noting with reference to the genesis of modern systems.

The presence in us of this idea of God must also be explained; and here we find a new ray of light. The objective reality of our ideas must have some cause, and this is readily found when there is question of secondary qualities; these may be illusory or they may result from the imperfection of our nature. The question also can be solved without too much difficulty when it concerns primary qualities. May not these arise perchance from some depth of my own mental being that is beyond the control of my will? But such explanations are of no avail when we try to account for the idea of a being infinite and perfect. I myself am limited, finite; and from the finite, turn it about as we may, we can never derive the infinite the lesser never gives us the greater (3e Méd. cf. Princ., 7e partie). Considered from any and every point of view, the idea of God enlightens us as to His existence. Whatever the manner of our questioning it gives us always from the depth of its fulness the one reply, Ego sum qui sum. Since then the veracity of God Himself guarantees our faculties in their natural exercise, we may go forward in our inquiry; and the first question that meets us concerns the subject in which the process of thought takes place, i.e. the soul. Understanding, conceiving, doubting, affirming, denying, willing, refusing, imagining, feeling, desiring—these are the activities of what I call my soul. Now all these activities have one common quality: they cannot take place without thought or perception, without consciousness or knowledge. Thought then is the essential attribute of the soul. The soul is "a thing that thinks" (2e Méd., Princ., 1re partie) and it is nothing else. There is no substratum underlying and supporting its various states; its whole being issues in each of its activities; thought and soul are equivalent (12e Règle).

Is thought, then, always in some mode of activity? Descartes leans to the belief that it is. "I exist", he says, "but for how long? Just as long as I am thinking; for perhaps if I should wholly cease to think, I should at the same time altogether cease to be" (2e Méd.). It is only with reluctance and under the pressure of objections that he concedes to the soul a simple potentia or power of thinking (5es Obj.); and, as may be easily seen, the concession is quite illogical. Thought, though in itself a unitary process, takes on different forms; it begins with confused ideas or perceptions which require the co-operation of the body; such are the feelings of pleasure and pain, sensations imagination, and local memory. Then the soul has clear and distinct ideas, which it begets and develops within itself as immanent activities. Under this head come the ideas of substance, duration, number, order extension, figure, motion, thought, intelligence, and will (6e Méd.; Princ., I).

These clear and distinct notions constitute of themselves the object of the understanding, and one may say that they are all involved in the idea of perfect being. Whether I understand, or pass judgment or reason, it is always that idea which I perceive and my understanding could have no other object, seeing that its sphere of action is always the infinite, the eternal and the necessary. To advance in knowledge is to progress in the knowledge of God Himself. (Rep. aux 2es obj.) But thought has another dominant form, viz. freedom. For Descartes this function of the mind is a fact "of which reason can never convince us", but one which "we experience in ourselves", and this fact is so evident" that it may be considered one of the most generally known ideas" (Rep. aux 3es obj.; Rep. aux 5es obj.- Princ., 1re partie). Not only is this freedom a primordial and undeniable datum of consciousness: it is, in a way, infinite like God, "since there is no object to which it cannot turn". (4e Méd.; Princ., 1re partie.) It does not creep round in a sort of semi-ignorance, as St. Thomas Aquinas holds, but it grows as the influencing motives become clearer; indifference is but its lowest stage (letter to Mersenne, 20 May, 1630). The part it plays in our lives is considerable: it enters into each of our judgments, and it is the formal cause of all our errors. It makes itself felt in every part of our organism, and through this it influences the external world. Nevertheless, the sum total of motion in the world is always constant; for while our wills may change the direction of movement they do not affect its quantity. (Letter to Regius.) Confronting the soul is the external world: but the soul does not see it as it really is. Heat, odour taste, light, sound, resistance, weight are qualities which we attribute to bodies but which are really in ourselves, since we only conceive them in relation to ourselves. In reality there is nothing in the physical world but motion and extension. Motion imitates as far as possible the immutability of God who is its first cause; hence its principal laws, viz. that the sum of motion in the world is always constant; that a body will continue in its actual state unless disturbed by some other body outside itself; that "once a body is in motion we have no reason for thinking its present velocity will ever cease provided it impinges on no other body which would slacken or destroy its motion". All movement is primarily rectilinear (on this point Aristotle was mistaken). When two bodies moving in different directions collide, a change takes place in their directions, but "such change is always the least possible". When two moving bodies impinge on each other, one cannot transmit any motion to the other without losing what it transmits (Princ., 2e partie). Extension is not infinite in duration but it is infinite in space. "It seems to me that one cannot prove or even conceive that there are limits to the matter of which the world is composed, for I find it is composed of nothing but extension in length, breadth, and depth. So that whatever possesses these three dimensions is a portion of such matter": and however far back in imagination we push the limits of space we still find these three dimensions; they are bounded by no limits (letter to Chanut; letter to Marus). Extension is therefore one block, continuous from end to end; and this proves at the same time that there is no such thing as a vacuum, either in bodies or between them. Moreover extension is divisible ad infinitum since the divided particles, however small, are still extended. It is everywhere homogeneous, since it is made up of spatial dimensions only, and these of themselves give rise to no qualitative differences. And this brilliant idea suggested to Descartes many hypotheses that were to prove fruitful. In his view the matter of the earth and of the stars was the same; and spectrum analysis subsequently proved that he was correct. He held that the primordial state of the sun and planets was nebulous, that under the influence of a cooling process the heavenly bodies formed their crusts, and to changes in these crusts is due the variation in brilliance of the stars and the emergence of the continents on our earth. (Cf. Traité du Monde; Princ., 3e and 4e p.) It does not follow that the world is self-sufficient; but the finality, of which so much is said, leads to nothing. God gave matter a first impulse and the rest followed in the course of nature's laws. "Even if the chaos of the poets be granted, one could always show that, thanks to the laws of nature, this confusion would eventually work itself out to our present order"; the laws of nature being such that "matter is constrained to pass through all the forms of which it is capable".

The older Descartes grew, the more he busied himself with morals, and his aim was to end up with a treatise on ethics. As a matter of fact, we have his treatise on the passions, and a few brief disquisitions scattered among his letters to Chanut and to the Princess Elizabeth. The passions are perceptions generated and nurtured in the soul "through the medium of the nerves" (Passions, 1re partie, art. 3-22). The nerves are bundles of fine threads: these threads contain the animal spirits which are the subtlest parts of the blood: and they all meet at the pineal gland which is the seat of the soul. By means of this mechanism the thinking subject receives impressions from the world without, perceives them, and transforms them into passions (Pass., 1re p, art. 31). And though our organism thus contains the cause of our passions, it is not their subject either entirely or partially; on this point also Aristotle was mistaken. There are perceptions arising from the body and localizing themselves in one or other portion of it—such as hunger, thirst, pain—but the passions are different. They originate in the body, but belong to the soul alone; they are purely psychological facts (Passions, 1re p., art.25). There are as many passions as there are ways in which objects capable of affecting our senses may be hurtful or profitable to us. The primary passions to which all others may be reduced are the six following:

• admiration or surprise, produced by an object as to which we are as yet ignorant whether it is useful or hurtful;

• love and hate, caused by the impression produced on our organs of sense by objects which are already known to us as beneficial or harmful;

• desire, which is but the love or the hate we bear an object considered as future;

• joy and sadness, which result from the presence of an object that is loved or hated (Passions, 2e partie, art. 52).

Perhaps on the whole St. Thomas and Bossuet will be found to have surpassed Descartes, by reducing all the passions to love. In the Cartesian teaching the passions are good in themselves, but they must be kept in subjection to the law of moral order. What this law is he does not clearly indicate; he gives only some scattered precepts in which one may discern a noble effort to build up a Stoico-Christian system of ethics. The foregoing account may perhaps give the impression that Descartes was a great savant rather than a great philosopher; but the significance of his scientific work should be properly understood. What remains of value is not so much his theories, but the impetus given by his genius, his method, his discoveries. His quantitative conception of the world is being gradually abandoned, and today men's minds are turning to a philosophy of nature wherein quality plays a controlling part.

Bibliography

Sources

• Clarke, Desmond (2006). Descartes: A Biography. Cambridge, England: Cambridge University Press. ISBN 978-0-521-82301-2.
• Cottingham, John; Williams, B., eds. (1996). "Sixth Meditation: The existence of material things, and the real distinction between mind and body". Descartes: Meditations on First Philosophy: With Selections from the Objections and Replies. Cambridge Texts in the History of Philosophy. Cambridge: Cambridge University Press. pp. 50–62. doi:10.1017/CBO9780511805028.012. ISBN 978-0521558181.
• Farrell, John. "Demons of Descartes and Hobbes." Paranoia and Modernity: Cervantes to Rousseau (Cornell UP, 2006), chapter 7.
• Gaukroger, Stephen (1995). Descartes: An Intellectual Biography. Oxford, England: Oxford University Press. ISBN 978-0-19-823994-9.
• Gillespie, A. (2006). Descartes' Demon: A Dialogical Analysis of 'Meditations on First Philosophy.' Theory & Psychology, 16, 761–781.
• Gottlieb, Anthony (2016). The Dream of Enlightenment: The Rise of Modern Philosophy. Allen Lane. p. 301. ISBN 978-0871404435.
• Grayling, A. C. (2005). Descartes: The Life of René Descartes and Its Place in His Times, The Free Press, London. ISBN 978-0-74323-147-3.
• Heidegger, Martin [1938] (2002) The Age of the World Picture in Off the Beaten Track Archived 21 November 2020 at the Wayback Machine pp. 57–85
• Monnoyeur, Françoise (November 2017), Matière et espace dans le système cartésien, Paris, Harmattan, 266 pp. ISBN 978-2-343-13394-2.
• Moreno Romo, Juan Carlos, Vindicación del cartesianismo radical, Anthropos, Barcelona, 2010.
• Moreno Romo, Juan Carlos (Coord.), Descartes vivo. Ejercicios de hermenéutica cartesiana, Anthropos, Barcelona, 2007.
• Negri, Antonio (2007) The Political Descartes, Verso.
• Sasaki Chikara (2003). Descartes's Mathematical Thought Archived 5 March 2021 at the Wayback Machine. (Boston Studies in the Philosophy of Science, 237.) xiv + 496 pp., bibl., indexes. Dordrecht/Boston/London: Kluwer Academic Publishers.
• Serfati, Michel, 2005, "Géometrie" in Ivor Grattan-Guinness, ed., Landmark Writings in Western Mathematics. Elsevier: 1–22.
• Watson, Richard A. (2007). Cogito, Ergo Sum: a life of René Descartes. David R Godine. 2002, reprint 2007. ISBN 978-1-56792-335-3. Was chosen by the New York Public library as one of "25 Books to Remember from 2002"
• Frisinger, H. Howard. "Chapter 3." The History of Meteorology: To 1800, American Meteorological Society, Boston, MA, 1983, pp. 37–40. ISBN 978-0882020365
• Martin, Craig. "Chapter 6." Renaissance Meteorology: Pomponazzi to Descartes, Johns Hopkins University Press, Baltimore, MD, 2011. ISBN 978-1421401874

External links

Digital collections

• Works by René Descartes in eBook form at Standard Ebooks
• Works by René Descartes at Project Gutenberg
• Works by or about René Descartes at the Internet Archive
• Works by René Descartes at LibriVox (public domain audiobooks)
• EarlyModernTexts.com — A site containing Descartes's main works, including correspondence, slightly modified for easier reading

Physical collections

• The Correspondence of René Descartes in Early Modern Letters Online

Biographical links

• Detailed biography of Descartes at MacTutor
• Herbermann, Charles, ed. (1913). "René Descartes". Catholic Encyclopedia. New York: Robert Appleton Company.
• René Descartes (1596–1650) Published in Encyclopedia of Rhetoric and Composition (1996)
• René Descartes at the Mathematics Genealogy Project

Bibliographies and works

• Bibliografia cartesiana/Bibliographie cartésienne on-line (1997–2012)^[]
• Free scores by René Descartes at the International Music Score Library Project (IMSLP)

Stanford Encyclopedia of Philosophy

• Descartes
• Life and works
• Epistemology
• Mathematics
• Physics
• Ethics
• Emotions (Passions)
• Method
• Modal Metaphysics
• Ontological Argument
• Theory of Ideas
• Pineal Gland
• Law Thesis

Internet Encyclopedia of Philosophy

• Descartes
• Descartes: Ethics
• Descartes: Mind-Body Distinction
• Descartes: Scientific Method

Other

• Video: Bryan Magee interviewing Bernard Williams about Descartes on Men of Ideas: Section 1, Section 2