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 thePassions of the Soul, anearly 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").
Descartes has often been called the father of modern philosophy, and he is largely seen as responsible for the increased attention given toepistemology in the 17th century.[4] He was one of the key figures in theScientific Revolution, and hisMeditations on First Philosophy and other philosophical works continue to be studied. His influence in mathematics is equally apparent, being the namesake of theCartesian coordinate system. Descartes is also credited as the father of analytic geometry, which facilitated the discovery of infinitesimalcalculus andanalysis.
In accordance with his ambition to become a professional military officer in 1618, Descartes joined, as amercenary, theProtestantDutch States Army inBreda under the command ofMaurice of Nassau,[11] and undertook a formal study ofmilitary engineering, as established bySimon Stevin.[14] Descartes, therefore, received much encouragement in Breda to advance his knowledge of mathematics. In this way, he became acquainted withIsaac Beeckman,[11] the principal of aDordrecht school, for whom he wrote theCompendium of Music (written 1618, published 1650).[15]
According toAdrien Baillet, on the night of 10–11 November 1619 (St. Martin's Day), while stationed inNeuburg an der Donau, Descartes shut himself in a room with an "oven" (probably acocklestove)[19] to escape the cold. While within, he had three dreams,[20] and believed that a divine spirit revealed to him a new philosophy. However, it is speculated that what Descartes considered to be his second dream was actually an episode ofexploding head syndrome.[21] Upon exiting, he had formulatedanalytic 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.[22][23]
In 1620, Descartes left the army. He visitedBasilica 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).[24] He arrived inLa Haye in 1623, selling all of his property to invest inbonds, which provided a comfortable income for the rest of his life.[25][26]: 94 Descartes was present at thesiege of La Rochelle byCardinal Richelieu in 1627 as an observer.[26]: 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 mathematicianGirard Desargues.[27] In the autumn of that year, in the residence of the papalnuncioGuidi di Bagno, where he came withMersenne 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,[28] CardinalBérulle urged him to write an exposition of his new philosophy in some location beyond the reach of the Inquisition.[29]
Descartes returned to theDutch Republic in 1628.[20] In April 1629, he joined theUniversity of Franeker, studying underAdriaan Metius, either living with a Catholic family or renting theSjaerdemaslot. The next year, under the name "Poitevin", he enrolled atLeiden University, which at the time was a Protestant University.[30] He studied both mathematics withJacobus Golius, who confronted him withPappus's hexagon theorem, andastronomy withMartin Hortensius.[31] 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 inDeventer. She was baptized a Protestant[32][33] 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;[34] he wept upon Francine's death in 1640.[35] 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."[36]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.[37]
Despite frequent moves,[note 2] he wrote all of his major work during his 20-plus years in the Netherlands, initiating a revolution in mathematics and philosophy.[note 3] In 1633, Galileo was condemned by theItalian Inquisition, and Descartes abandoned plans to publishTreatise on the World, his work of the previous four years. Nevertheless, in 1637, he published parts of this work in three essays:[38] "Les Météores" (The Meteors), "La Dioptrique" (Dioptrics) andLa Géométrie (Geometry), preceded by an introduction, his famousDiscours de la méthode (Discourse on the Method).[38] In it, Descartes lays out four rules of thought, meant to ensure that our knowledge rests upon a firm foundation:[39]
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.
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.[41] It was followed in 1644 byPrincipia Philosophiae (Principles of Philosophy),[42] a kind of synthesis of theDiscourse on the Method andMeditations on First Philosophy.
In 1643, Cartesian philosophy was condemned at theUniversity of Utrecht, and Descartes was obliged to flee to the Hague, then eventually to the north of Amsterdam, ultimately settling inEgmond-Binnen.[citation needed]
Between 1643 and 1649 Descartes lived with his girlfriend at Egmond-Binnen in an inn.[43] Descartes became friendly with Anthony Studler van Zurck, lord ofBergen, and participated in the design of his mansion and estate.[44][45][46] He also metDirck Rembrantsz van Nierop, a mathematician andsurveyor.[47] He was so impressed by Van Nierop's knowledge that he even brought him to the attention ofConstantijn Huygens and Frans van Schooten.[48]
Descartes began (through Alfonso Polloti, an Italian general in Dutch service) a six-year correspondence withPrincess Elisabeth of Bohemia, devoted mainly to moral and psychological subjects.[49] Connected with this correspondence, in 1649 he publishedLes Passions de l'âme (The Passions of the Soul), which he dedicated to the Princess. A French translation ofPrincipia Philosophiae, prepared by Abbot Claude Picot, was published in 1647. This edition was also dedicated to Princess Elisabeth. Inthe 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.[50]
By 1649, Descartes had become one of Europe's most famous philosophers and scientists.[38] 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.[51] Descartes accepted, and moved to theSwedish Empire in the middle of winter.[52] Christina was interested in and stimulated Descartes to publishThe Passions of the Soul.[53]
He was a guest at the house ofPierre Chanut, living onVästerlånggatan, less than 500 meters from CastleTre Kronor in Stockholm. There, Chanut and Descartes made observations with aTorricellian mercury barometer.[51] ChallengingBlaise Pascal, Descartes took the first set of barometric readings in Stockholm to see ifatmospheric pressure could be used in forecasting the weather.[54]
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.[51] It soon became clear they did not like each other, as she did not care for hismechanical philosophy, nor did he share her interest inAncient Greek language andliterature.[51] On 1 February 1650, he contractedpneumonia and died on 11 February at Chanut.[55][56]
According to Chanut, the cause of death was pneumonia, butperipneumonia according to Christina's physician Johann van Wullen, who was not allowed to bleed him.[57] (The winter seems to have been mild,[58] 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.")[53]
(left) The tomb of Descartes (middle, with detail of the inscription), in theAbbey of Saint-Germain-des-Prés, Paris; (right) memorial to Descartes, erected in the 1720s, in the Adolf Fredriks kyrka
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.[59]
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![60]
As a Catholic[61][62][63] in a Protestant nation, he was interred in the churchyard of what was to becomeAdolf Fredrik Church in Stockholm, where mainly orphans had been buried. His manuscripts came into the possession ofClaude 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."[64][65]: 137–154 In 1663, thePope placed Descartes's works on theIndex of Prohibited Books. In 1666, sixteen years after his death, his remains were taken to France and buried inSaint-Étienne-du-Mont. In 1671,Louis XIV prohibited all lectures inCartesianism. Although theNational Convention in 1792 had planned to transfer his remains to thePanthéon, he was reburied in theAbbey of Saint-Germain-des-Prés in 1819, missing a finger and the skull.[note 4] His alleged skull is in theMusée de l'Homme in Paris,[66] 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 theUniversity of Lund in 1691, where it is still preserved.[67]
In hisDiscourse 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 orCartesian doubt: he rejected any ideas that can be doubted and then re-established them in order to acquire a firm foundation for genuine knowledge.[68] 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'sfoundationalism was incomplete and his method of doubt enhances foundationalism.[69]
Initially, Descartes arrives at only a single first principle: he thinks. This is expressed in the Latin phrase inthe Discourse on Method "Cogito, ergo sum" (English: "I think, therefore I am"), originally written in French, "Je pense, donc je suis."[70] 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."[71] These two first principles—I think and I exist—were later confirmed by Descartes's clear and distinct perception (delineated in his Third Meditation fromThe 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 athinking 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 immediatelyconscious.[72] He gave reasons for thinking that waking thoughts are distinguishable fromdreams, and that one's mind cannot have been "hijacked" by anevil demon placing an illusory external world before one's senses.[69]
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.[73]: 109
In this manner, Descartes proceeds to construct a system of knowledge, discardingperception as unreliable and, instead, admitting onlydeduction as a method.[74]
Descartes, influenced by theautomatons on display at theChâteau de Saint-Germain-en-Laye near Paris, investigated the connection between mind and body, and how they interact.[75] His main influences fordualism weretheology andphysics.[76] The theory on the dualism of mind and body is Descartes's signature doctrine and permeates other theories he advanced. Known asCartesian dualism (or mind–body dualism), his theory on the separation between the mind and the body went on to influence subsequent Western philosophies.[77] InMeditations on First Philosophy, Descartes attempted to demonstrate the existence ofGod and the distinction between the human soul and the body. Humans are a union of mind and body;[78] 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 ofmodes, which are the ways in which substances exist. InPrinciples 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,[79] 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.[79]
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.[80] He argued that the great differences between body (an extended thing) and mind (an un-extended, immaterial thing) make the twoontologically 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."[81]
Moreover, in TheMeditations, Descartes discusses a piece ofwax 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 asthinking, and the body defined as matter and unthinking.[82] TheAristotelian philosophy of Descartes's day held that the universe was inherently purposeful or teleological. Everything that happened, be it the motion of thestars or the growth of atree, 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 ofKepler 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 (orres extensa) in favor of the mind (orres cogitans). Therefore, while Cartesian dualism paved the way for modernphysics, it also held the door open for religious beliefs about the immortality of thesoul.[83]
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 TheMeditations, Descartes even argues that while the mind is a substance, the body is composed only of "accidents".[84] But he did argue that mind and body are closely joined:[85]
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.[85]
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?[85] Therefore, Cartesian dualism set the agenda for philosophical discussion of themind–body problem for many years after Descartes's death.[86] Descartes argued the theory ofinnate 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 philosopherJohn Locke (1632–1704), anempiricist.[87]
InThe Passions of the Soul, published in 1649,[88] Descartes discussed the common contemporary belief that the human body contained animal spirits. These animal spirits were believed to be light and roaming fluids circulating rapidly around the nervous system between the brain and the muscles. These animal spirits were believed to affect the human soul, or passions of the soul. Descartes distinguished six basic passions: wonder, love, hatred, desire, joy and sadness. All of these passions, he argued, represented different combinations of the original spirit, and influenced the soul to will or want certain actions. He argued, for example, that fear is a passion that moves the soul to generate a response in the body. In line with his dualist teachings on the separation between the soul and the body, he hypothesized that some part of the brain served as a connector between the soul and the body and singled out thepineal gland as connector.[89] 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.[90]
Descartes advanced a theory on automatic bodily reactions to external events, which influenced 19th-centuryreflex 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.[90] Through this chain of reactions, the automatic reactions of the body do not require a thought process.[91]
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 wasdivine, thus religious authorities regarded his books as dangerous.[92] Descartes's writings went on to form the basis for theories onemotions and howcognitive 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.[93]
It is generally accepted that Descartes had denied that animals had reason or intelligence, as historians have generally reduced Descartes's interpretation of animals to a comparison to machines.[94] 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.[95] 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.[96] Whereas humans had a soul, or mind, and were able to feelpain andanxiety, 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 tosuffer was absent.[97] 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 merelymachines allowed for themaltreatment of animals, and was sanctioned in law and societal norms until the middle of the 19th century.[98]: 180–214 The publications ofCharles Darwin would eventually erode the Cartesian view of animals.[99]: 37 Darwin argued that the continuity between humans and other species suggested the possibility of animal suffering.[100]: 177
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.[74] 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 defendsfree 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, andvirtue 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.[101]: 189 He discussed this subject in the correspondence withPrincess Elisabeth of Bohemia, and as a result wrote his workThe Passions of the Soul, that contains a study of thepsychosomatic processes and reactions in man, with an emphasis on emotions or passions.[102] 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.[103]
The moral writings of Descartes came at the last part of his life, but earlier, in hisDiscourse 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".[citation needed]
In the third and fifthMeditation, Descartes offersproofs of a benevolent God (thetrademark argument and theontological 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 andsensory 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. Regardingepistemology, therefore, Descartes can be said to have contributed such ideas as a conception of foundationalism and the possibility thatreason is the only reliable method of attaining knowledge. Descartes, however, was very much aware that experimentation was necessary to verify and validate theories.[74]
Descartes invokes hiscausal adequacy principle[104] to support his trademark argument for the existence of God, quoting Lucretius in defence:"Ex nihilo nihil fit", meaning "Nothing comes from nothing" (Lucretius).[105] 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."[106] 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."[107]
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 ofdeism: "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 ofatheist beliefs, though Descartes had provided an explicit critique of atheism in hisMeditations. The Catholic Church prohibited his books in 1663.[108][109][110]: 274
Descartes also wrote a response toexternal 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 sensoryperceptions come to him involuntarily, and are not willed by him. They are external to his senses, and according to Descartes, this is evidence of the existence of something outside of his mind, and thus, an external world. Descartes goes on to argue that the things in the external world are material by arguing that God would not deceive him as to the ideas that are being transmitted, and that God has given him the "propensity" to believe that such ideas are caused by material things. Descartes also believes a substance is something that does not need any assistance to function or exist. Descartes further explains how only God can be a true "substance". But minds are substances, meaning they need only God for it to function. The mind is a thinking substance. The means for a thinking substance stem from ideas.[111]
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."[112]
Descartes "invented the convention of representing unknowns in equations byx,y, andz, and knowns bya,b, andc". He also "pioneered the standard notation" that usessuperscripts to show the powers or exponents; for example, the 2 used in x2 to indicate x squared.[113][114]: 19
A Cartesian coordinates graph, using his inventedx andy axes
One of Descartes's most enduring legacies was his development – together withPierre de Fermat – of Cartesian oranalytic geometry, which uses algebra to describe geometry; theCartesian coordinate system is named after him.[115] Descartes' work on geometry was written to demonstrate its application to correct reasoning he discussed in theDiscourse on the Method, which consists of reasoning based on self-evident principles.[116] He was first to assign a fundamental place for algebra in the system of knowledge, using it as a method to automate or mechanize reasoning, particularly about abstract, unknown quantities.[117]: 91–114
Both Descartes and Fermat were inspired by the works of the Ancient Greek mathematiciansPappus of Alexandria andApollonius of Perga, especially by their techniques of analysis.[118] Crucial for their work was also the symbolic algebra ofFrançois Viète . The step that their predecessors failed to take was using coordinates to study the relationship between geometry and algebra.[119]
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 asPacioli,Cardano,Tartaglia andFerrari. Equations ofdegree 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 quantitya2 could represent length as well as an area. This was in opposition to the teachings of mathematicians such asFrançois Viète, who insisted that a second power must represent an area.[citation needed]
Although Descartes did not pursue the subject, he precededGottfried Wilhelm Leibniz in envisioning a more general science of algebra or "universal mathematics", as a precursor tosymbolic logic, that could encompass logical principles and methods symbolically, and mechanize general reasoning.[120]: 280–281
It is often said that Descartes had the most influence of anyone on the youngIsaac Newton.[121] Descartes's influence extended not directly from his original French edition ofLa Géométrie, however, but rather fromFrans van Schooten's expanded second Latin edition of the work.[122]: 100 Newton continued Descartes's work oncubic equations, which freed the subject from the fetters of the Greek perspectives. The most important concept was his very modern treatment of single variables.[123]: 109–129
Descartes's work provided the basis for thecalculus developed byLeibniz andNewton, who applied the infinitesimal calculus to thetangent line problem, thus permitting the evolution of that branch of modern mathematics.[124] Hisrule of signs is also a commonly used method to determine the number of positive and negative roots of a polynomial.
The beginning of Descartes's interest in physics is accredited to the amateur scientist and mathematicianIsaac Beeckman, whom he met in 1618, and who was at the forefront of a new school of thought known asmechanical philosophy. With this foundation of reasoning, Descartes formulated many of his theories onmechanical and geometric physics.[125] 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.[126] 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.[127][126] In 1628, Beeckman also introduced him to many ofGalileo's ideas.[127] Together, they worked onfree fall,catenaries,conic sections, andfluid statics. Both believed that it was necessary to create a method that thoroughly linked mathematics and physics.[24]
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.[128] This experimental work with metals and inert bodies reveals a different Descartes, investigating nature by means of observations and the uses of microscopes.[129] But there is more, as Descartes tried to explain in the mecahnical terms of his philosophy living nature too - namely, plants and animals.[130] 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.[131][132] Recently, historians have recognized the importance of Descartes's scientific enterprise in his philosophical work.
InPrinciples of Philosophy (Principia Philosophiae) from 1644 Descartes outlined his views on the universe. In it he describes his threelaws of motion.[135] (Newton's own laws of motion would later be modeled on Descartes's exposition.[125]) 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.[136]
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 ofconservation of momentum.[137] He envisioned quantity of motion as pertaining to motion in a straight line, as opposed to perfect circular motion, as Galileo had envisioned it.[125][137] 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.[138][139][140]
Descartes's 1664 diagram of effluvia emitted by magnets. It is a predecessor of the concept ofmagnetic field.
Descartes proposed a theory to explain magnetism and explain the observation inDe Magnete byWilliam Gilbert. Descartes considered that 'effluvia' were emitted by a magnet, the effluvia rarefied the air creating pressure differences, and thus forces.[141][142]
In 1644, Descartes provides one of the earliest microscopic theories ofglass. 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 byannealing.[143]
Descartes also made contributions to the field ofoptics. He showed by using geometric construction and thelaw of refraction (also known as Descartes's law in France, or more commonlySnell's law elsewhere) that the angular radius of arainbow 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°).[144] He also independently discovered thelaw of reflection, and his essay on optics was the first published mention of this law.[145]
"Les Météores" redirects here. For Michel Tournier's novel, seeGemini (novel).
WithinDiscourse on the Method, there is an appendix in which Descartes discusses his theories onmeteorology known asLes 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."[146] 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.[147] This first idea is the basis for the rest of Descartes's theory on meteorology.
While rejecting most ofAristotle'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.[146] 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."[147]
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.[147] 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.[146][147]
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.[146]
Descartes has often been dubbed the father of modernWestern philosophy, the thinker whose approaches have profoundly changed the course of Western philosophy and set the basis formodernity.[4][148] The first two of hisMeditations on First Philosophy, those that formulate the famous methodic doubt, represent the portion of Descartes's writings that most influenced modern thinking.[149] It has been argued that Descartes himself did not realize the extent of this revolutionary move.[150] 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 ananthropocentric revolution, the human being is now raised to the level of a subject, an agent, anemancipated being equipped with autonomous reason. This was a revolutionary step that contributed to the basis of theModern Era, the repercussions of which are still being felt: the emancipation of humanity from Christianrevelational truth andChurch doctrine; humanity making its own law and taking its own stand.[151][152][153] 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.[154][155] In that way, each person is turned into a reasoning adult, a subject and agent,[154] 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.[154][156]
This anthropocentric perspective of Descartes's work, establishing human reason as autonomous, provided the basis for theEnlightenment's emancipation from God and the Church. According toMartin Heidegger, the perspective of Descartes's work also provided the basis for all subsequentanthropology.[157] Descartes's philosophical revolution is sometimes said to have sparked modernanthropocentrism andsubjectivism.[4][158][159][160]
TheDiscourse 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 TheMeditations, 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.[161]: 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.[162]
According to philosophy professorJohn Cottingham, Descartes'sMeditations on First Philosophy is considered to be "one of the key texts of Western philosophy". Cottingham said that theMeditations is the "most widely studied of all Descartes' writings".[163]: 50 According to authorAnthony Gottlieb, one of the reasons Descartes andThomas 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?"[164]
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).[165]: 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 ofPlatonic solids and three-dimensionalfigurate numbers. Said by some scholars to prefigureEuler's polyhedral formula. Unpublished; discovered in Descartes's estate in Stockholm 1650, soaked for three days in the Seine in a shipwreck while being shipped back to Paris, copied in 1676 by Leibniz, and lost. Leibniz's copy, also lost, was rediscovered circa 1860 in Hannover.[166]
1630–1633.Le Monde (The World) andL'Homme (Man). Descartes's first systematic presentation of his natural philosophy.Man was published posthumously in Latin translation in 1662; andThe World posthumously in 1664.
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 asMetaphysical Meditations. In Latin; a second edition, published the following year, included an additional objection and reply, and aLetter to Dinet. A French translation by theDuke of Luynes, probably done without Descartes's supervision, was published in 1647. Includes sixObjections 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.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).
1657.Correspondance (three volumes: 1657, 1659, 1667). Published by Descartes's literary executorClaude 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 throughGoogle. Bos found the letter mentioned in a summary of autographs kept byHaverford College inHaverford, 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.[168][169]
Oeuvres de Descartes edited by Charles Adam andPaul 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 initialsAT (for Adam and Tannery) followed by a volume number in Roman numerals; thusAT VII refers toOeuvres 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. SaviniISBN978-88-452-6332-3.
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. SaviniISBN978-88-452-6333-0.
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. ArmogatheISBN978-88-452-3422-4.
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-ArmogatheISBN978-88-452-8071-9.
1955.The Philosophical Works,E.S. Haldane and G.R.T. Ross, trans. Dover Publications. This work is traditionally cited with the initialsHR (for Haldane and Ross) followed by a volume number in Roman numerals; thusHR 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 initialsCSM (for Cottingham, Stoothoff, and Murdoch) orCSMK (for Cottingham, Stoothoff, Murdoch, and Kenny) followed by a volume number in Roman numeral; thusCSM II refers to volume 2 of this edition.
1998.René Descartes: The World and Other Writings. Translated and edited byStephen 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'sphilosophical works.)
1641.Meditations on First Philosophy, tr. by J. Cottingham, Cambridge: Cambridge University Press, 1996. Latin original. Alternative English title:Metaphysical Meditations. Includes sixObjections and Replies. A second edition published the following year, includes an additionalObjection and Reply and aLetter to Dinet.HTML Online Latin-French-English EditionArchived 27 August 2006 at theWayback Machine.
1619–1648.René Descartes, Isaac Beeckman, Marin Mersenne. Lettere 1619–1648, ed. by Giulia Beglioioso and Jean Robert-Armogathe, Milano, Bompiani, 2015 pp. 1696.ISBN978-88-452-8071-9
^Although the uncertain authorship of this most iconic portrait of Descartes was traditionally attributed to Frans Hals, there is no record of their meeting. During the 20th century the assumption was widely challenged.[1]
^While in the Netherlands he changed his address frequently, living among other places in Dordrecht (1628),Franeker (1629), Amsterdam (1629–1630),Leiden (1630), Amsterdam (1630–1632), Deventer (1632–1634), Amsterdam (1634–1635),Utrecht (1635–1636), Leiden (1636),Egmond (1636–1638),Santpoort (1638–1640), Leiden (1640–1641), Endegeest (a castle nearOegstgeest) (1641–1643), and finally for an extended time inEgmond-Binnen (1643–1649).
^Porter, Roy (1999) [1997]. "The New Science".The Greatest Benefit to Mankind: A Medical History of Humanity from Antiquity to the Present. Great Britain: Harper Collins. p. 217.ISBN978-0-00-637454-1.
^Baird, Forrest E.; Kaufmann, Walter (2008).From Plato to Derrida. Upper Saddle River, New Jersey: Pearson Prentice Hall. pp. 373–77.ISBN978-0-13-158591-1.
^abShea, William R. 1991.The Magic of Numbers and Motion. Science History Publications.
^Aczel, Amir D. (10 October 2006).Descartes's Secret Notebook: A True Tale of Mathematics, Mysticism, and the Quest to Understand the Universe. Crown. p. 127.ISBN978-0-7679-2034-6.
^Matton, Sylvain, ed. 2013.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, by Nicolas de Villiers. Paris: Préface de Vincent Carraud.
^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
^abNewman, Lex (2016). Zalta, Edward N. (ed.).Stanford Encyclopedia of Philosophy (Winter 2016 ed.). Metaphysics Research Lab, Stanford University.Archived from the original on 8 March 2021. Retrieved22 February 2017.
^Olson, Richard (1982).Science Deified & Science Defied: The Historical Significance of Science in Western Culture. Vol. 2. University of California Press. p. 33.
^Gaukroger, S.,Descartes' System of Natural Philosophy (Cambridge: Cambridge University Press, 2002),pp. 180–214Archived 16 August 2021 at theWayback Machine.
^Spencer, J.,"'Love and Hatred are Common to the Whole Sensitive Creation': Animal Feeling in the Century before Darwin," in A. Richardson, ed.,After Darwin: Animals, Emotions, and the Mind (Amsterdam and New York:Rodopi, 2013),p. 37Archived 16 August 2021 at theWayback Machine.
^Pickavé, M., &Shapiro, L., eds.,Emotion and Cognitive Life in Medieval and Early Modern Philosophy (Oxford: Oxford University Press, 2012),p. 189Archived 16 August 2021 at theWayback Machine.
^Blom, John J., Descartes. His moral philosophy and psychology. New York University Press. 1978.ISBN0-8147-0999-0
^Jacob, Margaret C. (2009).The Scientific Revolution A Brief History with Documents. Boston: Bedford/St. Martin's. pp. 16–17.ISBN978-0-312-65349-1.
^Descartes, Rene "Meditations on First Philosophy, 3rd Ed., Translated from Latin by: Donald A. Cress
^Descartes, René. (2009).Encyclopædia Britannica 2009 Deluxe Edition. Chicago: Encyclopædia Britannica.
^Edward C. Mendler,False Truths: The Error of Relying on Authority, p. 16
^Peterson, L. L.,American Trinity: Jefferson, Custer, and the Spirit of the West (Helena, MT: Sweetgrass Books, 2017),p. 274Archived 16 August 2021 at theWayback Machine.
^René Descartes,Discourse de la Méthode (Leiden, Netherlands): Jan Maire, 1637, appended book:La Géométrie, book one,p. 299.Archived 8 October 2017 at theWayback Machine From p. 299:" ... Etaa, oua2, pour multipliera par soy mesme; Eta3, pour le multiplier encore une fois para, & ainsi a l'infini; ... " ( ... andaa, ora2, in order to multiplya by itself; anda3, in order to multiply it once more bya, and thus to infinity; ... )
^Katz, V. J. (2008).A History of Mathematics (2nd ed.). Pearson. p. 473.
^Katz, V. J. (2008).A History of Mathematics (2nd ed.). Pearson. p. 478.
^Gaukroger, S., "The nature of abstract reasoning: philosophical aspects of Descartes' work in algebra", inJ. Cottingham, ed.,The Cambridge Companion to Descartes (Cambridge: Cambridge University Press, 1992),pp. 91–114Archived 16 August 2021 at theWayback Machine.
^Katz, V. J. (2008).A History of Mathematics (2nd ed.). Pearson. p. 473.
^Katz, V. J. (2008).A History of Mathematics (2nd ed.). Pearson. p. 478.
^Whiteside, D. T., "Newton the Mathematician", in Z. Bechler, ed.,Contemporary Newtonian Research (Berlin/Heidelberg: Springer, 1982),pp. 109–29Archived 16 August 2021 at theWayback Machine.
^abcSlowik, Edward (22 August 2017)."Descartes' Physics". In Edward N. Zalta (ed.).Stanford Encyclopedia of Philosophy Archive.Archived from the original on 18 March 2019. Retrieved1 October 2018.
^Garber, Daniel (1992). "Descartes' Physics". In John Cottingham (ed.).The Cambridge Companion to Descartes. Cambridge: Cambridge University Press. pp. 310–319.ISBN978-0-521-36696-0.
The Descartes most familiar to twentieth-century philosophers is the Descartes of the first twoMeditations, someone preoccupied 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 "Husserl has taken Descartes very seriously in a historical as well as in a systematic sense [...] [inThe 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."
For up to Descartes...a particularsub-iectum...lies at the foundation of its own fixed qualities and changing circumstances. The superiority of asub-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.
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, theMeditations were epoch-making in a quite unique sense, and precisely because of their going back to the pureego 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.
^Maclean, I., introduction to Descartes, R.,A Discourse on the Method of Correctly Conducting One's Reason and Seeking Truth in the Sciences (Oxford: Oxford University Press, 2006),pp. xliii–xlivArchived 16 August 2021 at theWayback Machine.
^Cottingham, J., Murdoch, D., & Stoothof, R., trans. and eds.,The Philosophical Writings of Descartes, Vol. 2 (Cambridge: Cambridge University, 1984),pp. 264ffArchived 16 August 2021 at theWayback Machine.
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.ISBN978-0521558181.
Farrell, John. "Demons of Descartes and Hobbes."Paranoia and Modernity: Cervantes to Rousseau (Cornell UP, 2006), chapter 7.
Sasaki Chikara (2003).Descartes's Mathematical ThoughtArchived 5 March 2021 at theWayback Machine. (Boston Studies in the Philosophy of Science, 237.) xiv + 496 pp., bibl., indexes. Dordrecht/Boston/London: Kluwer Academic Publishers.
Serfati, Michel, 2005, "Géometrie" inIvor 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.ISBN978-1-56792-335-3. 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.ISBN978-0882020365
Martin, Craig. “Chapter 6.” Renaissance Meteorology: Pomponazzi to Descartes, Johns Hopkins University Press, Baltimore, MD, 2011.ISBN978-1421401874
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