|Died||11 February 1650 (aged 53)|
|Education||Collège Royal Henry-Le-Grand (1607–1614)|
University of Poitiers (LL.B., 1616)
University of Franeker
Correspondence theory of truth
|Metaphysics, epistemology, mathematics, physics, cosmology|
|Cogito ergo sum|
Method of doubt
Method of normals
Cartesian coordinate system
Cartesian dualism (interactionism)
Folium of Descartes
Conservation of momentum (quantitas motus)
Causal adequacy principle
Res cogitans/res extensa distinction
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René Descartes (//, UK also //; French: [ʁəne dekaʁt]; Latinized: Renatus Cartesius; adjectival form: "Cartesian"; 31 March 1596 – 11 February 1650) was a French philosopher, mathematician, and scientist. A native of the Kingdom of France, he spent about 20 years (1629–49) of his life in the Dutch Republic after serving for a while in the Dutch States Army of Maurice of Nassau, Prince of Orange and the Stadtholder of the United Provinces. He is generally considered one of the most notable intellectual figures of the Dutch Golden Age.
Descartes' Meditations on First Philosophy (1641) continues to be a standard text at most university philosophy departments. Descartes' influence in mathematics is equally apparent; the Cartesian coordinate system (see below) was named after him. He is credited as the father of analytical geometry, the bridge between algebra and geometry, used in the discovery of infinitesimal calculus and analysis. Descartes was also one of the key figures in the Scientific Revolution.
Descartes refused to accept the authority of previous philosophers. He frequently set his views apart from those of his predecessors. 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 "I think, therefore I am" (French: Je pense, donc je suis; Latin: Ego cogito, ergo sum), found in Discourse on the Method (1637; written in French and Latin) and Principles of Philosophy (1644; written in Latin).
Many elements of his philosophy have precedents in late Aristotelianism, the revived Stoicism of the 16th century, or in earlier philosophers like Augustine. In his natural philosophy, he differed from the schools on two major points: first, he rejected the splitting of corporeal substance into matter and form; second, he rejected any appeal to final ends, divine or natural, in explaining natural phenomena. In his theology, he insists on the absolute freedom of God's act of creation.
Descartes laid the foundation for 17th-century continental rationalism, later advocated by Spinoza and Leibniz, and opposed by the empiricist school of thought consisting of Hobbes, Locke, Berkeley, 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.
René Descartes was born in La Haye en Touraine (now Descartes, Indre-et-Loire), France, on 31 March 1596. His mother, Jeanne Brochard, died soon after giving birth to him, and so he was not expected to survive. Descartes' father, Joachim, was a member of the Parlement of Brittany at Rennes. 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 Collège Royal Henry-Le-Grand at La Flèche, where he was introduced to mathematics and physics, including Galileo's work. 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.
In Discourse on the Method, Descartes recalls,
I entirely abandoned the study of letters. Resolving to seek no knowledge other than that of which could be found in myself or else in the great book of the world, I spent the rest of my youth traveling, visiting courts and armies, mixing with people of diverse temperaments and ranks, gathering various experiences, testing myself in the situations which fortune offered me, and at all times reflecting upon whatever came my way so as to derive some profit from it.
Given 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). Together they worked on free fall, catenary, conic section, and fluid statics. Both believed that it was necessary to create a method that thoroughly linked mathematics and physics.
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 Kachelofen or masonry heater) to escape the cold. While within, he had three dreams and believed that a divine spirit revealed to him a new philosophy. However, it is likely that what Descartes considered to be his second dream was actually an episode of exploding head syndrome. Upon exiting, he had formulated analytical geometry and the idea of applying the mathematical method to philosophy. He concluded from these visions that the pursuit of science would prove to be, for him, the pursuit of true wisdom and a central part of his life's work. Descartes also saw very clearly that all truths were linked with one another so that finding a fundamental truth and proceeding with logic would open the way to all science. Descartes discovered this basic truth quite soon: his famous "I think, therefore I am".
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 spent time in Paris. It was there that he composed his first essay on method: Regulae ad Directionem Ingenii (Rules for the Direction of the Mind). He arrived in La Haye in 1623, selling all of his property to invest in bonds, which provided a comfortable income for the rest of his life. Descartes was present at the siege of La Rochelle by Cardinal Richelieu in 1627. In the fall of the same 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 own new philosophy in some location beyond the reach of the inquisition.
Descartes returned to the Dutch Republic in 1628. In April 1629 he joined the University of Franeker, studying under Adriaan Metius, living either with a Catholic family, or renting the Sjaerdemaslot, where he invited in vain a French cook and an optician. The next year, under the name "Poitevin", he enrolled at the Leiden University to study 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 died of scarlet fever at the age of 5.
Unlike many moralists of the time, Descartes was not devoid of passions but rather defended them; he wept upon Francine's death in 1640. "Descartes said that he did not believe that one must refrain from tears to prove oneself a man." Russell Shorto postulated that the experience of fatherhood and losing a child formed a turning point in Descartes' work, changing its focus from medicine to a quest for universal answers.
Despite frequent moves, he wrote all 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 Italian Inquisition, and Descartes abandoned plans to publish Treatise on the World, his work of the previous four years. Nevertheless, in 1637 he published part 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 clearly 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, having been able to do so because his paper, Introduction to Loci, was published posthumously in 1679. 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 work, Meditationes de Prima Philosophia (Meditations on First Philosophy), written in Latin and thus addressed to the learned. It was followed, in 1644, by Principia Philosophiæ (Principles of Philosophy), a kind of synthesis of the Discourse on the Method and Meditations on First Philosophy. In 1643, Cartesian philosophy was condemned at the University of Utrecht, and Descartes was obliged to flee to the Hague, and settled in Egmond-Binnen.
Descartes began (through Alfonso Polloti, an Italian general in Dutch service) a long 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 (Passions of the Soul), that he dedicated to the Princess. In 1647, he was awarded a pension by King Louis XIV of France, though it was never paid. A French translation of Principia Philosophiæ, prepared by Abbot Claude Picot, was published in 1647. This edition Descartes 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.
By 1649, Descartes had become famous throughout Europe for being one of the continent's greatest philosophers and scientists. That year, Queen Christina of Sweden invited Descartes to her court to organize a new scientific academy and tutor her in his ideas about love. She was interested in and stimulated Descartes to publish the "Passions of the Soul", a work based on his correspondence with Princess Elisabeth. Descartes accepted, and moved to Sweden in the middle of winter.
He was a guest at the house of Pierre Chanut, living on Västerlånggatan, less than 500 meters from Tre Kronor in Stockholm. There, Chanut and Descartes made observations with a Torricellian barometer, a tube with mercury. 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.
Descartes apparently started giving lessons to Queen Christina after her birthday, three times a week, at 5 a.m, in her cold and draughty castle. Soon it became clear they did not like each other; she did not like his mechanical philosophy, nor did he appreciate her interest in Ancient Greek. By 15 January 1650, Descartes had seen Christina only four or five times. On 1 February he contracted pneumonia and died on 11 February. The cause of death was pneumonia according to Chanut, but peripneumonia according to the doctor Van Wullen who was not allowed to bleed him. (The winter seems to have been mild, except for the second half of January which was harsh as described by Descartes himself; however, "this remark was probably intended to be as much Descartes' take on the intellectual climate as it was about the weather.")
In 1996 E. Pies, a German scholar, published a book questioning this account, based on a letter by Johann van Wullen, who had been sent by Christina to treat him, something Descartes refused, and more arguments against its veracity have been raised since. Descartes might have been assassinated as he asked for an emetic: wine mixed with tobacco.[dubious ]
As a Catholic in a Protestant nation, he was interred in a graveyard used mainly for orphans in Adolf Fredriks kyrka in Stockholm. His manuscripts came into the possession of Claude Clerselier, Chanut's brother-in-law, and "a devout Catholic who has begun the process of turning Descartes into a saint by cutting, adding and publishing his letters selectively." In 1663, the Pope placed his works on the Index of Prohibited Books. In 1666 his remains were taken to France and buried in the Saint-Étienne-du-Mont. In 1671 Louis XIV prohibited all the 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 skull. His skull is on display in the Musée de l'Homme in Paris.
Initially, Descartes arrives at only a single first principle: I think. 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." These two first principles—I think and I exist—were later confirmed by Descartes's clear and distinct perception (delineated in his Third Meditation): that I clearly and distinctly perceive these two principles, Descartes reasoned, ensures their indubitability.
Descartes concludes that he can be certain that he exists because he thinks. But in what form? He perceives his body through the use of the senses; however, these have previously been unreliable. So Descartes determines that the only indubitable knowledge is that he is a thinking thing. Thinking is what he does, and his power must come from his essence. Descartes defines "thought" (cogitatio) as "what happens in me such that I am immediately conscious of it, insofar as I am conscious of it". Thinking is thus every activity of a person of which the person is immediately conscious. He gave reasons for thinking that waking thoughts are distinguishable from dreams, and that one's mind cannot have been "hijacked" by an evil demon placing an illusory external world before one's senses.
And so something that I thought I was seeing with my eyes is in fact grasped solely by the faculty of judgment which is in my mind.
Descartes, influenced by the automatons on display throughout the city of Paris, began to investigate the connection between the mind and body, and how the two interact. His main influences for dualism were theology and physics. The theory on the dualism of mind and body is Descartes' signature doctrine and permeates other theories he advanced. Known as Cartesian dualism (or Mind-Body Dualism), his theory on the separation between the mind and the body went on to influence subsequent Western philosophies. In Meditations on First Philosophy, Descartes attempted to demonstrate the existence of God and the distinction between the human soul and the body. Humans are a union of mind and body; thus Descartes' dualism embraced the idea that mind and body are distinct but closely joined. While many contemporary readers of Descartes found the distinction between mind and body difficult to grasp, he thought it was entirely straightforward. Descartes employed the concept of modes, which are the ways in which substances exist. In Principles of Philosophy, 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. But that the mind was 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."
In Meditations Descartes discussed a piece of wax and exposed 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' days held that the universe was inherently purposeful or theological. 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. With his theory on dualism Descartes fired the opening shot for the battle between the traditional Aristotelian science and the new science of Kepler and Galileo which denied the final cause for explaining nature. Descartes' dualism provided the philosophical rationale for the latter and he expelled the final cause from the physical universe (or res extensa). For Descartes the only place left for the final cause was the mind (or res cogitans). Therefore, while Cartesian dualism paved the way for modern physics, it also held the door open for religious beliefs about the immortality of the soul.
Descartes' dualism of mind and matter implied a concept of human beings. A human was according to Descartes a composite entity of mind and body. Descartes gave priority to the mind and argued that the mind could exist without the body, but the body could not exist without the mind. In Meditations Descartes even argues that while the mind is a substance, the body is composed only of "accidents". But he did argue that mind and body are closely joined:
Nature also teaches me, by the sensations of pain, hunger, thirst and so on, that I am not merely present in my body as a pilot in his ship, but that I am very closely joined and, as it were, intermingled with it, so that I and the body form a unit. If this were not so, I, who am nothing but a thinking thing, would not feel pain when the body was hurt, but would perceive the damage purely by the intellect, just as a sailor perceives by sight if anything in his ship is broken.
Descartes' discussion on embodiment raised one of the most perplexing problems of his dualism philosophy: What exactly is the relationship of union between the mind and the body of a person? Therefore, Cartesian dualism set the agenda for philosophical discussion of the mind–body problem for many years after Descartes' death. Descartes was also a rationalist and believed in the power of innate ideas. 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 later led philosopher John Locke (1632–1704) to combat the theory of empiricism, which held that all knowledge is acquired through experience.
Descartes on physiology and psychology
In The Passions of the Soul written between 1645 and 1646 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, and served as a metaphor for feelings, like being in high or bad spirit. These animal spirits were believed to affect the human soul, or passions of the soul. Descartes distinguished six basic passions: wonder, love, hatred, desire, joy and sadness. All of these passions, he argued, represented different combinations of the original spirit, and influenced the soul to will or want certain actions. He argued, for example, that fear is a passion that moves the soul to generate a response in the body. In line with his dualist teachings on the separation between the soul and the body, he hypothesized that some part of the brain served as a connector between the soul and the body and singled out the pineal gland as connector. Descartes argued that signals passed from the ear and the eye to the pineal gland, through animal spirits. Thus different motions in the gland cause various animal spirits. He argued that these motions in the pineal gland are based on God's will and that humans are supposed to want and like things that are useful to them. But he also argued that the animal spirits that moved around the body could distort the commands from the pineal gland, thus humans had to learn how to control their passions.
Descartes advanced a theory on automatic bodily reactions to external events which influenced 19th-century reflex theory. He argued that external motions such as touch and sound reach the endings of the nerves and affect the animal spirits. Heat from fire affects a spot on the skin and sets in motion a chain of reactions, with the animal spirits reaching the brain through the central nervous system, and in turn animal spirits are sent back to the muscles to move the hand away from the fire. Through this chain of reactions the automatic reactions of the body do not require a thought process.
Above all he was among the first scientists who believed that the soul should be subject to scientific investigation. He challenged the views of his contemporaries that the soul was divine, thus religious authorities regarded his books as dangerous. Descartes' writings went on to form the basis for theories on emotions and how cognitive evaluations were translated into affective processes. Descartes believed that the brain resembled a working machine and unlike many of his contemporaries believed that mathematics and mechanics could explain the most complicated processes of the mind. In the 20th century Alan Turing advanced computer science based on mathematical biology as inspired by Descartes. His theories on reflexes also served as the foundation for advanced physiological theories more than 200 years after his death. The physiologist Ivan Pavlov was a great admirer of Descartes.
Descartes' 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 we should seek, and virtue consists in the correct reasoning that should guide our actions. Nevertheless, the quality of this reasoning depends on knowledge, because a well-informed mind will be more capable of making good choices, and it also depends on mental condition. For this reason, he said that a complete moral philosophy should include the study of the body. He discussed this subject in the correspondence with Princess Elisabeth of Bohemia, and as a result wrote his work The Passions of the Soul, that contains a study of the psychosomatic processes and reactions in man, with an emphasis on emotions or passions. His works about human passion and emotion would be the basis for the philosophy of his followers (see Cartesianism), and would have a lasting impact on ideas concerning what literature and art should be, specifically how it should invoke emotion.
Humans should seek the sovereign good that Descartes, following Zeno, identifies with virtue, as this produces a solid blessedness or pleasure. For Epicurus the sovereign good was pleasure, and Descartes says that, in fact, this is not in contradiction with Zeno's teaching, because virtue produces a spiritual pleasure, that is better than bodily pleasure. Regarding Aristotle's opinion that happiness depends on the goods of fortune, Descartes does not deny that this good contributes to happiness but remarks that they are in great proportion outside one's own control, whereas one's mind is under one's complete control. The moral writings of Descartes came at the last part of his life, but earlier, in his Discourse on the Method he adopted three maxims to be able to act while he put all his ideas into doubt. This is known as his "Provisional Morals".
Descartes on religious beliefs
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. Regarding 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. He, nevertheless, was very much aware that experimentation was necessary to verify and validate theories.
In his Meditations on First Philosophy Descartes sets forth two proofs for God's existence. One of these is founded upon the possibility of thinking the "idea of a being that is supremely perfect and infinite," and suggests that "of all the ideas that are in me, the idea that I have of God is the most true, the most clear and distinct." Descartes considered himself to be a devout Catholic and one of the purposes of the Meditations was to defend the Catholic faith. His attempt to ground theological beliefs on reason encountered intense opposition in his time, however: Pascal regarded Descartes' views as rationalist and mechanist, and accused him of deism: "I cannot forgive Descartes; in all his philosophy, Descartes did his best to dispense with God. But Descartes could not avoid prodding God to set the world in motion with a snap of his lordly fingers; after that, he had no more use for God," while a powerful contemporary, Martin Schoock, accused him of atheist beliefs, though Descartes had provided an explicit critique of atheism in his Meditations. The Catholic Church prohibited his books in 1663. [check quotation syntax]
Descartes also wrote a response to external world scepticism. Through this method of scepticism, 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 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 also believes a substance is something that does not need any assistance to function or exist. Descartes further explains how only God can be a true “substance”. But minds are substances, meaning they need only God for it to function. The mind is a thinking substance. The means for a thinking substance stem from ideas.
Descartes and natural science
Descartes is often regarded as the first thinker to emphasize the use of reason to develop the natural sciences. For him the philosophy was a thinking system that embodied all knowledge, and expressed it in this way:
Thus, all Philosophy is like a tree, of which Metaphysics is the root, Physics the trunk, and all the other sciences the branches that grow out of this trunk, which are reduced to three principals, namely, Medicine, Mechanics, and Ethics. By the science of Morals, I understand the highest and most perfect which, presupposing an entire knowledge of the other sciences, is the last degree of wisdom.
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 scepticism: he rejects any ideas that can be doubted and then re-establishes them in order to acquire a firm foundation for genuine knowledge. Descartes built his ideas from scratch. 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 is incomplete and his method of doubt enhances foundationalism.
Descartes on animals
Descartes denied that animals had reason or intelligence. He argued that animals did not lack sensations or perceptions, but these could be explained mechanistically. Whereas humans had a soul, or mind, and were able to feel pain 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' 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. The publications of Charles Darwin would eventually erode the Cartesian view of animals. Darwin argued that the continuity between humans and other species opened the possibilities that animals did not have dissimilar properties to suffer.
Emancipation from Church doctrine
Descartes has often been dubbed the father of modern Western philosophy, the thinker whose approach has profoundly changed the course of Western philosophy and set the basis for modernity. The first two of his Meditations on First Philosophy, those that formulate the famous methodic doubt, represent the portion of Descartes' writings that most influenced modern thinking. It has been argued that Descartes himself didn't realize the extent of this revolutionary move. In shifting the debate from "what is true" to "of what can I be certain?," Descartes arguably shifted the authoritative guarantor of truth from God to humanity (even though Descartes himself claimed he received his visions from God)—while the traditional concept of "truth" implies an external authority, "certainty" instead relies on the judgment of the individual.
In an anthropocentric revolution, the human being is now raised to the level of a subject, an agent, an emancipated being equipped with autonomous reason. This was a revolutionary step that established the basis of modernity, the repercussions of which are still being felt: the emancipation of humanity from Christian 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' 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' work also provided the basis for all subsequent anthropology. Descartes' philosophical revolution is sometimes said to have sparked modern anthropocentrism and subjectivism.
One of Descartes' most enduring legacies was his development of Cartesian or analytic geometry, which uses algebra to describe geometry. He "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. He was first to assign a fundamental place for algebra in our system of knowledge, using it as a method to automate or mechanize reasoning, particularly about abstract, unknown quantities. European mathematicians had previously viewed geometry as a more fundamental form of mathematics, serving as the foundation of algebra. Algebraic rules were given geometric proofs by mathematicians such as Pacioli, Cardan, 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 Vieta, who argued that it could represent only 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.
Descartes' work provided the basis for the calculus developed by Newton and Leibniz, who applied 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.
The beginning to Descartes' interest in physics is accredited to the amateur scientist and mathematician Isaac Beeckman, 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 geometrical physics. Descartes discovered an early form of the law of conservation of mechanical momentum (a measure of the motion of an object), and envisioned it as pertaining to motion in a straight line, as opposed to perfect circular motion, as Galileo had envisioned it. 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) 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.
Influence on Newton's mathematics
Current opinion is that Descartes had the most influence of anyone on the young Newton, and this is arguably one of Descartes' most important contributions. Newton continued Descartes' work on cubic equations, which will free the subject from fetters of the Greek perspectives. The most important concept was his very modern treatment of single variables.
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.
- Mathematical concepts named after Descartes
- Cartesian circle
- Cartesian coordinate system
- Cartesian diagram
- Cartesian diver
- Cartesian morphism
- Cartesian plane
- Cartesian product
- Cartesian product of graphs
- Cartesian theater
- Cartesian tree
- Descartes' rule of signs
- Descartes' theorem (4 tangent circles)
- Descartes' theorem on total angular defect
- Folium of Descartes
- Cartesian doubt
- 3587 Descartes, asteroid
- Cartesian materialism (not a view that was held by or formulated by Descartes)
- Paris Descartes University
- 1618. Musicae Compendium. A treatise on music theory and the aesthetics of music written for Descartes' early collaborator, Isaac Beeckman (first posthumous edition 1650).
- 1626–1628. Regulae ad directionem ingenii (Rules for the Direction of the Mind). Incomplete. First published posthumously in Dutch translation in 1684 and in the original Latin at Amsterdam in 1701 (R. Des-Cartes Opuscula Posthuma Physica et Mathematica). The best critical edition, which includes the Dutch translation of 1684, is edited by Giovanni Crapulli (The Hague: Martinus Nijhoff, 1966).
- 1630–1631. La recherche de la vérité par la lumière naturelle (The Search for Truth) unfinished dialogue published in 1701.
- 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 second edition, published the following year, included an additional objection and reply, and a Letter to Dinet. A French translation by the Duke of Luynes, probably done without Descartes' supervision, was published in 1647. Includes six Objections and Replies.
- 1644. Principia philosophiae (Principles of Philosophy), a Latin textbook at first intended by Descartes to replace the Aristotelian textbooks then used in universities. A French translation, Principes de philosophie by Claude Picot, under the supervision of Descartes, appeared in 1647 with a letter-preface to Princess Elisabeth of Bohemia.
- 1647. Notae in programma (Comments on a Certain Broadsheet). A reply to Descartes' one-time disciple Henricus Regius.
- 1648. La description du corps humain (The Description of the Human Body). Published posthumously by Clerselier in 1667.
- 1648. Responsiones Renati Des Cartes... (Conversation with Burman). Notes on a Q&A session between Descartes and Frans Burman on 16 April 1648. Rediscovered in 1895 and published for the first time in 1896. An annotated bilingual edition (Latin with French translation), edited by Jean-Marie Beyssade, was published in 1981 (Paris: PUF).
- 1649. Les passions de l'âme (Passions of the Soul). Dedicated to Princess Elisabeth of the Palatinate.
- 1657. Correspondance (three volumes: 1657, 1659, 1667). Published by Descartes' 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.
- Shorto, Russell (2008). "Descartes' Bones". Doubleday. p. 218. see also The Louvre, Atlas Database
- Tad M. Schmaltz, Radical Cartesianism: The French Reception of Descartes, Cambridge University Press, 2002, p. 257.
- Fumerton, Richard (21 February 2000). "Foundationalist Theories of Epistemic Justification". Stanford Encyclopedia of Philosophy. Retrieved 19 August 2018.
- David Bostock, Philosophy of Mathematics: An Introduction, Wiley-Blackwell, 2009, p. 43: "All of Descartes, Locke, Berkeley, and Hume supposed that mathematics is a theory of our ideas, but none of them offered any argument for this conceptualist claim, and apparently took it to be uncontroversial."
- John W. Yolton, Realism and Appearances: An Essay in Ontology, Cambridge University Press, 2000, p. 136.
- The Correspondence Theory of Truth (Stanford Encyclopedia of Philosophy)
- Stephen Gaukroger, Descartes: An Intellectual Biography, Clarendon Press, 1995, p. 228.
- Étienne Gilson argued in La Liberté chez Descartes et la Théologie (Alcan, 1913, pp. 132–47) that Duns Scotus was not the source of Descartes' Voluntarism. Although there exist doctrinal differences between Descartes and Scotus "it is still possible to view Descartes as borrowing from a Scotist Voluntarist tradition" (see: John Schuster, Descartes-Agonistes: Physico-mathematics, Method & Corpuscular-Mechanism 1618–33, Springer, 2012, p. 363 n. 26).
- Alexander Afriat, "Cartesian and Lagrangian Momentum" (2004).
- Marenbon, John (2007). Medieval Philosophy: an historical and philosophical introduction. Routledge. p. 174. ISBN 978-0415281133.
- H. Ben-Yami, Descartes' Philosophical Revolution: A Reassessment, Palgrave Macmillan, 2015, p. 76.
- H. Ben-Yami, Descartes' Philosophical Revolution: A Reassessment, Palgrave Macmillan, 2015, p. 179: "[Descartes'] work in mathematics was apparently influenced by Vieta's, despite his denial of any acquaintance with the latter’s work."
- "She thinks, therefore I am". Columbia Magazine. Fall 2017. Retrieved 2017-09-17.
- "Jacques Bénigne Bossuet, French prelate and historian (1627–1704)" from the Encyclopædia Britannica, 10th Edition (1902)
- "Descartes" entry in Collins English Dictionary.
- Colie, Rosalie L. (1957). Light and Enlightenment. Cambridge University Press. p. 58.
- Nadler, Steven: The Philosopher, the Priest, and the Painter: A Portrait of Descartes. (Princeton University Press, 2015, ISBN 978-0691165752)
- This idea had already been proposed by the Spanish philosopher Gómez Pereira a hundred years ago in the form: "I know that I know something, anyone who knows exists, then I exist" (nosco me aliquid noscere, & quidquid noscit, est, ergo ego sum). See: Gómez Pereira, Antoniana Margarita: "De Immortalitate Animae", 1749 , p. 277; Santos López, Modesto (1986). "Gómez Pereira, médico y filósofo medinense". In: Historia de Medina del Campo y su Tierra, volumen I: Nacimiento y expansión, ed. by Eufemio Lorenzo Sanz, 1986.
- Carlson, Neil R. (2001). Physiology of Behavior. Needham Heights, Massachusetts: Pearson: Allyn & Bacon. p. 8. ISBN 0205308406.
- R.H. Moorman, "The Influence of Mathematics on the Philosophy of Spinoza", National Mathematics Magazine, Vol. 18, No. 3. (Dec., 1943), pp. 108–115.
- Bruno, Leonard C. (2003) . Math and Mathematicians: The History of Math Discoveries Around the World. Baker, Lawrence W. Detroit, Mich.: U X L. p. 99. ISBN 0787638137. OCLC 41497065.
- Rodis-Lewis, Geneviève (1992). "Descartes' Life and the Development of His Philosophy". In Cottingham, John. The Cambridge Companion to Descartes. Cambridge University Press. p. 22. ISBN 978-0521366960.
- Bruno, Leonard C. (2003) . Math and Mathematicians: The History of Math Discoveries Around the World. Baker, Lawrence W. Detroit, Mich.: U X L. p. 100. ISBN 0787638137. OCLC 41497065.
- Clarke (2006), p. 24
- Porter, Roy (1999) . "The New Science". The Greatest Benefit to Mankind: A Medical History of Humanity from Antiquity to the Present (paperback edition, 135798642 ed.). Great Britain: Harper Collins. p. 217. ISBN 0006374549.
- Baird, Forrest E.; Kaufmann, Walter (2008). From Plato to Derrida. Upper Saddle River, New Jersey: Pearson Prentice Hall. pp. 373–377. ISBN 0131585916.
- Guy Durandin (1970. Les Principes de la Philosophie. Introduction et notes. Librairie Philosophique. Paris: J. Vrin.
- Battle of White Mountain, Britannica Online Encyclopedia
- Bruno, Leonard C. (2003) . Math and mathematicians : the history of math discoveries around the world. Baker, Lawrence W. Detroit, Mich.: U X L. p. 101. ISBN 0787638137. OCLC 41497065.
- Otaiku AI (2018). "Did René Descartes have Exploding Head Syndrome?". J Clin Sleep Med. 14 (4): 675–8. doi:10.5664/jcsm.7068. PMC 5886445. PMID 29609724.
- Durant, Will; Durant, Ariel (1961). The Story of Civilization: Part VII, the Age of Reason Begins. New York: Simon and Schuster. p. 637. ISBN 0671013203.
- Clarke (2006), pp. 58–59.
- Shea, William R., The Magic of Numbers and Motion, Science History Publications, 1991, p. 94; Gaukroger, S. Descartes an intellectual biography, p. 132.
- WR Shea, The Magic of Numbers and Motion, p. 128 citing Baillet
- Nicolas de Villiers, Sieur de Chandoux, Lettres sur l'or potable suivies du traité De la connaissance des vrais principes de la nature et des mélanges et de fragments d'un Commentaire sur l'Amphithéâtre de la Sapience éternelle de Khunrath, Textes édités et présentés par Sylvain Matton avec des études de Xavier Kieft et de Simone Mazauric. Préface de Vincent Carraud, Paris, 2013.
- A.C.Grayling, Descartes in his times, 2005, pgs 130 to 140
- A.C. Grayling, Descartes: The Life of René Descartes and Its Place in His Times, Simon and Schuster, 2006, pp. 151–152
- Durant, Will and Ariel (1961). The Story of Civilization: Par VII, the Age of reason Begins. New York: Simon and Schuster. p. 638. ISBN 0671013203.
- Russell Shorto, Descartes' Bones: A Skeletal History of the Conflict Between Faith and Reason ISBN 978-0385517539 (New York, Random House, 2008)
- While in the Netherlands he changed his address frequently, living among other places in Dordrecht (1628), Franeker (1629), Amsterdam (1629–30), Leiden (1630), Amsterdam (1630–32), Deventer (1632–34), Amsterdam (1634–35), Utrecht (1635–36), Leiden (1636), Egmond (1636–38), Santpoort (1638–1640), Leiden (1640–41), Endegeest (a castle near Oegstgeest) (1641–43), and finally for an extended time in Egmond-Binnen (1643–49).
- He had lived with Henricus Reneri in Deventer and Amsterdam, and had met with Constantijn Huygens and Vopiscus Fortunatus Plempius; Descartes was interviewed by Frans Burman at Egmond-Binnen in 1648. Henricus Regius, Jan Stampioen, Frans van Schooten, Comenius and Gisbertus Voetius were his main opponents.
- Bruno, Leonard C. (2003) . Math and mathematicians : the history of math discoveries around the world. Baker, Lawrence W. Detroit, Mich.: U X L. p. 103. ISBN 0787638137. OCLC 41497065.
- "Pierre de Fermat | Biography & Facts". Encyclopedia Britannica. Retrieved 2017-11-14.
- Descartes, René. (2009). Encyclopædia Britannica. Encyclopædia Britannica 2009 Deluxe Edition. Chicago: Encyclopædia Britannica.
- Blom, John J., Descartes. His Moral Philosophy and Psychology. New York University Press, 1978. ISBN 0814709990
- Smith, Kurt (Fall 2010). "Descartes' Life and Works". The Stanford Encyclopedia of Philosophy.
- Bruno, Leonard C. (2003) . Math and mathematicians : the history of math discoveries around the world. Baker, Lawrence W. Detroit, Mich.: U X L. pp. 103–4. ISBN 0787638137. OCLC 41497065.
- Bruno, Leonard C. (2003) . Math and mathematicians: the history of math discoveries around the world. Baker, Lawrence W. Detroit, Mich.: U X L. p. 104. ISBN 0787638137. OCLC 41497065.
- Severity of winter seasons in the northern Baltic Sea between 1529 and 1990: reconstruction and analysis by S. Jevrejeva, p. 6, Table 3
- Pies Е., Der Mordfall Descartes, Solingen, 1996, and Ebert Т., Der rätselhafte Tod des René Descartes, Aschaffenburg, Alibri, 2009. French translation: L'Énigme de la mort de Descartes, Paris, Hermann, 2011
- "Descartes was "poisoned by Catholic priest" – The Guardian, Feb 14 2010". The Guardian. Retrieved 8 October 2014.
- "Was Descartes murdered in Stockholm?". Stockholm News. 22 February 2010. Archived from the original on 15 December 2014.[self-published source]
- Rome and the Counter-Reformation in Scandinavia: The Age of Gustavus Adolphus and Queen Christina of Sweden, 1992, p. 510
- Descartes: His Life and Thought, 1999, p. 207
- Early Modern Philosophy of Religion: The History of Western Philosophy of Religion, 2014, p. 107
- The remains 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.
- "5 historical figures whose heads have been stolen". Strange Remains. 2015-07-23. Retrieved 2016-11-29.
- "Ten books: Chosen by Raj Persuade". The British Journal of Psychiatry.
- Descartes, René (1644). The Principles of Philosophy (IX).
- Newman, Lex (2016). Zalta, Edward N., ed. The Stanford Encyclopedia of Philosophy (Winter 2016 ed.). Metaphysics Research Lab, Stanford University.
- Descartes, René. "Letter of the Author to the French Translator of the Principles of Philosophy serving for a preface". Translated by Veitch, John. Retrieved 6 December 2011.
- Cottingham, John. "'A Brute to the Brutes?': Descartes' Treatment of Animals" (PDF). Whitman People. Retrieved 24 February 2018.
- Watson, Richard A. (January 1982). "What Moves the Mind: An Excursion in Cartesian Dualism". American Philosophical Quarterly. University of Illinois Press. 19 (1): 73–81. JSTOR 20013943.
- David Cunning (2014). The Cambridge Companion to Descartes’ Meditations. Cambridge University Press. p. 277. ISBN 978-1107729148.
- David Cunning (2014). The Cambridge Companion to Descartes’ Meditations. Cambridge University Press. p. 278. ISBN 978-1107729148.
- David Cunning (2014). The Cambridge Companion to Descartes’ Meditations. Cambridge University Press. p. 279. ISBN 978-1107729148.
- David Cunning (2014). The Cambridge Companion to Descartes’ Meditations. Cambridge University Press. p. 280. ISBN 978-1107729148.
- Georges Dicker (2013). Descartes: An Analytic and Historical Introduction. OUP. p. 86. ISBN 978-0195380323.
- Georges Dicker (2013). Descartes: An Analytic and Historical Introduction. OUP. p. 87. ISBN 978-0195380323.
- Georges Dicker (2013). Descartes: An Analytic and Historical Introduction. OUP. p. 301. ISBN 978-0195380323.
- Georges Dicker (2013). Descartes: An Analytic and Historical Introduction. OUP. p. 303. ISBN 978-0195380323.
- Stanford Encyclopaedia of Philosophy (online): Descartes and the Pineal Gland.
- Eric Shiraev (2010). A History of Psychology: A Global Perspective: A Global Perspective. Sage. p. 88. ISBN 978-1412973830.
- Baldwin, Bird T. (April 1913). "John Locke's Contributions to Education". The Sewanee Review. The Johns Hopkins University Press. 21 (2): 177–187. JSTOR 27532614.
- Eric Shiraev (2010). A History of Psychology: A Global Perspective: A Global Perspective. Sage. p. 86. ISBN 978-1412973830.
- Eric Shiraev (2010). A History of Psychology: A Global Perspective: A Global Perspective. Sage. p. 87. ISBN 978-1412973830.
- Eric Shiraev (2010). A History of Psychology: A Global Perspective. Sage. p. 88. ISBN 978-1412973830.
- Blom, John J., Descartes. His moral philosophy and psychology. New York University Press. 1978. ISBN 0814709990
- Jacob, Margaret C. (2009). The Scientific Revolution A Brief History with Documents. Boston: Bedford/St. Martin's. pp. 16, 17. ISBN 0312653492.
- Descartes, Rene "Meditations on First Philosophy, 3rd Ed., Translated from Latin by: Donald A. Cress
- Edward C. Mendler, False Truths: The Error of Relying on Authority, p. 16
- "Descartes, Rene | Internet Encyclopaedia of Philosophy". www.iep.utm.edu. Retrieved 2017-02-22.
Grosholz, Emily (1991). Cartesian method and the problem of reduction. Oxford University Press. ISBN 0198242506.
But contemporary debate has tended to...understand [Cartesian method] merely as the 'method of doubt'...I want to define Descartes' method in broader terms...to trace its impact on the domains of mathematics and physics as well as metaphysics.
- Copenhaver, Rebecca. "Forms of skepticism". Archived from the original on 8 January 2005. Retrieved 15 August 2007.
- "Animal Consciousness, No. 2. Historical background". Stanford Encyclopaedia of Philosophy. 23 December 1995. Retrieved 16 December 2014.
- Lance Workman (2013). Charles Darwin: The Shaping of Evolutionary Thinking. Palgrave Macmillan. p. 177. ISBN 978-1137313232.
- Bertrand Russell (2004) History of western philosophy pp. 511, 516–17
- Heidegger  (2002), p. 76 quotation:
Descartes... that which he himself founded... modern (and that means, at the same time, Western) metaphysics.
- Schmaltz, Tad M. Radical Cartesianism: The French Reception of Descartes p. 27 quotation:
The Descartes most familiar to twentieth-century philosophers is the Descartes of the first two Meditations, someone proccupied with hyperbolic doubt of the material world and the certainty of knowledge of the self that emerges from the famous cogito argument.
- Roy Wood Sellars (1949) Philosophy for the future: the quest of modern materialism quotation:
Husserl has taken Descartes very seriously in a historical as well as in a systematic sense [...] [in The Crisis of the European Sciences and Transcendental Phenomenology, Husserl] finds in the first two Meditations of Descartes a depth which it is difficult to fathom, and which Descartes himself was so little able to appreciate that he let go "the great discovery" he had in his hands.
- Martin Heidegger  (2002) The Age of the World Picture quotation:
For up to Descartes...a particular sub-iectum...lies at the foundation of its own fixed qualities and changing circumstances. The superiority of a sub-iectum...arises out of the claim of man to a...self-supported, unshakeable foundation of truth, in the sense of certainty. Why and how does this claim acquire its decisive authority? The claim originates in that emancipation of man in which he frees himself from obligation to Christian revelational truth and Church doctrine to a legislating for himself that takes its stand upon itself.
- Ingraffia, Brian D. (1995) Postmodern theory and biblical theology: vanquishing God's shadow p. 126
- Norman K. Swazo (2002) Crisis theory and world order: Heideggerian reflections pp. 97–99
- Lovitt, Tom (1977) introduction to Martin Heidegger's The question concerning technology, and other essays, pp. xxv–xxvi
- Briton, Derek The modern practice of adult education: a postmodern critique p. 76
- Martin Heidegger The Word of Nietzsche: God is Dead pp. 88–90
- Heidegger  (2002), p. 75 quotation:
With the interpretation of man as subiectum, Descartes creates the metaphysical presupposition for future anthropology of every kind and tendency.
- Benjamin Isadore Schwart China and Other Matters p. 95 quotation:
... the kind of anthropocentric subjectivism which has emerged from the Cartesian revolution.
- Charles B. Guignon Heidegger and the problem of knowledge p. 23
- Husserl, Edmund (1931) Cartesian Meditations: An Introduction to Phenomenology quotation:
When, with the beginning of modern times, religious belief was becoming more and more externalized as a lifeless convention, men of intellect were lifted by a new belief: their great belief in an autonomous philosophy and science. [...] in philosophy, the Meditations were epoch-making in a quite unique sense, and precisely because of their going back to the pure ego cogito. Descartes work has been used, in fact to inaugurates an entirely new kind of philosophy. Changing its total style, philosophy takes a radical turn: from naïve objectivism to transcendental subjectivism.
- René Descartes, Discourse de la Méthode (Leiden, Netherlands): Jan Maire, 1637, appended book: La Géométrie, book one, p. 299. From p. 299: " ... Et aa, ou a2, pour multiplier a par soy mesme; Et a3, pour le multiplier encore une fois par a, & ainsi a l'infini ; ... " ( ... and aa, or a2, in order to multiply a by itself; and a3, in order to multiply it once more by a, and thus to infinity ; ... )
- Tom Sorell, Descartes: A Very Short Introduction (2000). New York: Oxford University Press. p. 19.
- Morris Kline, Mathematical Thought from Ancient to Modern Times (1972). New York: Oxford University Press. pp. 280–281
- Gullberg, Jan (1997). Mathematics From The Birth of Numbers. W.W. Norton. ISBN 039304002X.
- Slowik, Edward (22 August 2017). Edward N. Zalta, ed. "Descartes' Physics". The Stanford Encyclopedia of Philosophy Archive. Retrieved 1 October 2018.
- Tipler, P.A. and G. Mosca (2004). Physics For Scientists And Engineers. W.H. Freeman. ISBN 0716743892.
- "René Descartes". Encarta. Microsoft. 2008. Archived from the original on 7 September 2007. Retrieved 15 August 2007.
- Contemporary Newtonian Research, edited by Z. Bechler, pp. 109–129, Newton the Mathematician, by Daniel T. Whiteside, Springer, 1982.
- Cottingham, John; Murdoch, Dugald; Stoothof, Robert (1984). "Comments on a Certain Broadsheet". The Philosophical Writings of Descartes. Cambridge University Press. p. 293. ISBN 978-0521288071.
- Vlasblom, Dirk (25 February 2010). "Unknown letter from Descartes found". NRC.nl (in Dutch). Archived from the original on 8 November 2016. Retrieved 30 May 2012.
- Vlasblom, Drik. "Hoe Descartes in 1641 op andere gedachten kwam". NRC.nl (in Dutch). Archived from the original on 27 October 2016.
- 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 5 volumes contains 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 978-8845263323.
- 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 978-8845263330.
- 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 978-8845234224.
- 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 978-8845280719.
- Discours de la methode, 1637
- Renati Des-Cartes Principia philosophiæ, 1644
- Le monde de Mr. Descartes ou le traité de la lumiere, 1664
- Geometria, 1659
- Meditationes de prima philosophia, 1670
- Opera philosophica, 1672
Collected English translations
- 1955. The Philosophical Works, E.S. Haldane and G.R.T. Ross, trans. Dover Publications. This work is traditionally cited with the initials HR (for Haldane and Ross) followed by a volume number in Roman numerals; thus HR II refers to volume 2 of this edition.
- 1988. The Philosophical Writings of Descartes in 3 vols. Cottingham, J., Stoothoff, R., Kenny, A., and Murdoch, D., trans. Cambridge University Press. This work is traditionally cited with the initials CSM (for Cottingham, Stoothoff, and Murdoch) or CSMK (for Cottingham, Stoothoff, Murdoch, and Kenny) followed by a volume number in Roman numeral; thus CSM II refers to volume 2 of this edition.
- 1998. René Descartes: The World and Other Writings. Translated and edited by Stephen Gaukroger. Cambridge University Press. (This consists mainly of scientific writings, on physics, biology, astronomy, optics, etc., which were very influential in the 17th and 18th centuries, but which are routinely omitted or much abridged in modern collections of Descartes' philosophical works.)
Translation of single works
- 1628. Regulae ad directionem ingenii. Rules for the Direction of the Natural Intelligence. A Bilingual Edition of the Cartesian Treatise on Method, ed. and tr. by G. Heffernan, Amsterdam-Atlanta: Rodopi, 1998.
- 1633. The World, or Treatise on Light, 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, tr. Paul J. Olscamp, Revised edition, Indianapolis: Hackett, 2001.
- 1637. The Geometry of René Descartes, tr. by David E. Smith and M.L. Lantham, New York: Dover, 1954.
- 1641. Meditations on First Philosophy, tr. by J. Cottingham, Cambridge: Cambridge University Press, 1996. Latin original. Alternative English title: Metaphysical Meditations. Includes six Objections and Replies. A second edition published the following year, includes an additional Objection and Reply and a Letter to Dinet. HTML Online Latin-French-English Edition.
- 1644. Principles of Philosophy, tr. by V.R. Miller and R.P. Dordrecht: Reidel, 1983.
- 1648. Descartes' Conversation with Burman, tr. by J. Cottingham, Oxford: Clarendon Press, 1989.
- 1649. Passions of the Soul. tr. by S.H. Voss, Indianapolis: Hackett, 1989. Dedicated to Princess Elizabeth of Bohemia.
- 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 978-8845280719
- Agostini, Siegrid; Leblanc, Hélène, eds. (2015). Examina Philosophica. I Quaderni di Alvearium (PDF). Le fondement de la science. Les dix premières années de la philosophie cartésienne (1619–1628).
- Boyer, Carl (1985). A History of Mathematics. Princeton, NJ: Princeton University Press. ISBN 0691023913.
- Carriero, John (2008). Between Two Worlds. Princeton University Press. ISBN 978-0691135618.
- Chomsky, Noam (1966). Cartesian Linguistics: A Chapter in the History of Rationalist Thought. New York: Harper & Row. ISBN 1877275344.; (2009) Third Edition, edited with a new introduction by James McGilvray, Cambridge University Press, ISBN 978-0521708173
- Clarke, Desmond (2006). Descartes: A Biography. Cambridge: Cambridge University Press. ISBN 0521823013.
- Costabel, Pierre (1987). René Descartes – Exercices pour les éléments des solides. Paris: Presses Universitaires de France. ISBN 213040099X.
- Cottingham, John (1992). The Cambridge Companion to Descartes. Cambridge: Cambridge University Press. ISBN 0521366968.
- Duncan, Steven M. (2008). The Proof of the External World: Cartesian Theism and the Possibility of Knowledge. Cambridge: James Clarke & Co. ISBN 978-0227172674. Archived from the original on 23 December 2008.
- Farrell, John. "Demons of Descartes and Hobbes." Paranoia and Modernity: Cervantes to Rousseau (Cornell UP, 2006), chapter 7.
- Garber, Daniel (1992). Descartes' Metaphysical Physics. Chicago: University of Chicago Press. ISBN 0226282198.
- Garber, Daniel; Ayers, Michael (1998). The Cambridge History of Seventeenth-Century Philosophy. Cambridge: Cambridge University Press. ISBN 0521537215.
- Gaukroger, Stephen (1995). Descartes: An Intellectual Biography. Oxford: Oxford University Press. ISBN 0198239947.
- Gillespie, A. (2006). Descartes' demon: A dialogical analysis of 'Meditations on First Philosophy.' Theory & Psychology, 16, 761–781.
- Grayling, A.C. (2005). Descartes: The Life and times of a Genius. New York: Walker Publishing Co., Inc. ISBN 080271501X.
- Heidegger, Martin  (2002) The Age of the World Picture in Off the beaten track pp. 57–85
- Keeling, S. V. (1968). Descartes. Oxford: Oxford University Press.
- Melchert, Norman (2002). The Great Conversation: A Historical Introduction to Philosophy. New York: McGraw Hill. ISBN 0195175107.
- Monnoyeur, Françoise (November 2017), Matière et espace dans le système cartésien, Paris, Harmattan, 266 pages. ISBN 978-2343133942.
- 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'
- Naaman-Zauderer, Noa (2010). Descartes' Deontological Turn: Reason, Will and Virtue in the Later Writings. Cambridge University Press. ISBN 978-0521763301.
- Negri, Antonio (2007) The Political Descartes, Verso.
- Ozaki, Makoto (1991). Kartenspiel, oder Kommentar zu den Meditationen des Herrn Descartes. Berlin: Klein Verlag. ISBN 392719901X.
- Schäfer, Rainer (2006). Zweifel und Sein – Der Ursprung des modernen Selbstbewusstseins in Descartes' cogito. Wuerzburg: Koenigshausen&Neumann. ISBN 3826032020.
- Serfati, Michel, 2005, "Géometrie" in Ivor Grattan-Guinness, ed., Landmark Writings in Western Mathematics. Elsevier: 1–22.
- Sorrell, Tom (1987). Descartes. Oxford: Oxford University Press. ISBN 0192876368.
- Vrooman, Jack Rochford (1970). René Descartes: A Biography. Putnam Press.
- Watson, Richard A. (2012). "René Descartes". Encyclopædia Britannica. Encyclopædia Britannica Online. Encyclopædia Britannica Inc. Retrieved 31 March 2012.
- Watson, Richard A. (2007). Cogito, Ergo Sum: a life of René Descartes. David R Godine. 2002, reprint 2007. ISBN 978-1567923353. Was chosen by the New York Public library as one of "25 Books to Remember from 2002"
- Woo, B. Hoon (2013). "The Understanding of Gisbertus Voetius and René Descartes on the Relationship of Faith and Reason, and Theology and Philosophy". Westminster Theological Journal. 75 (1): 45–63.
- The Correspondence of René Descartes in EMLO
- Works by René Descartes at Project Gutenberg
- Works by or about René Descartes at Internet Archive
- Works by René Descartes at LibriVox (public domain audiobooks)
- Detailed biography of Descartes at MacTutor
- Herbermann, Charles, ed. (1913). "René Descartes". Catholic Encyclopedia. New York: Robert Appleton Company.
- John Cottingham translation of Meditations and Objections and Replies.
- René Descartes (1596–1650) Published in Encyclopedia of Rhetoric and Composition (1996)
- A site containing Descartes' main works, including correspondence, slightly modified for easier reading
- Descartes Philosophical Writings tr. by Norman Kemp Smith at archive.org
- Studies in the Cartesian philosophy (1902) by Norman Kemp Smith at archive.org
- The Philosophical Works Of Descartes Volume II (1934) at archive.org
- Descartes featured on the 100 French Franc banknote from 1942.
- Free scores by René Descartes at the International Music Score Library Project (IMSLP)
- René Descartes at the Mathematics Genealogy Project
- Centro Interdipartimentale di Studi su Descartes e il Seicento
- Livre Premier, La Géométrie, online and analyzed by A. Warusfel, BibNum[click 'à télécharger' for English analysis]
Stanford Encyclopedia of Philosophy
- Life and works
- Modal Metaphysics
- Ontological Argument
- Theory of Ideas
- Pineal Gland
- Law Thesis
Internet Encyclopedia of Philosophy