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Elements of Cartesian Philosophy
It was with the intention of extending mathematical method to all fields of human knowledge that Descartes developed his methodology, the cardinal aspect of his philosophy. He discards the authoritarian system of the scholastics and begins with universal doubt. But there is one thing that cannot be doubted: doubt itself. This is the kernel expressed in his famous phrase, Cogito, ergo sum [I think, therefore I am].
From the certainty of the existence of a thinking being, Descartes passed to the existence of God, for which he offered one proof based on St. Anselm's ontological proof and another based on the first cause that must have produced the idea of God in the thinker. Having thus arrived at the existence of God, he reaches the reality of the physical world through God, who would not deceive the thinking mind by perceptions that are illusions. Therefore, the external world, which we perceive, must exist. He thus falls back on the acceptance of what we perceive clearly and distinctly as being true, and he studies the material world to perceive connections. He views the physical world as mechanistic and entirely divorced from the mind, the only connection between the two being by intervention of God. This is almost complete dualism.
The development of Descartes' philosophy is in Meditationes de prima philosophia (1641); his Principia philosophiae (1644) is also very important. His influence on philosophy was immense, and was widely felt in law and theology also. Frequently he has been called the father of modern philosophy, but his importance has been challenged in recent years with the demonstration of his great debt to the scholastics. He influenced the rationalists, and Baruch Spinoza also reflects Descartes's doctrines in some degree. The more direct followers of Descartes, the Cartesian philosophers, devoted themselves chiefly to the problem of the relation of body and soul, of matter and mind. From this came the doctrine of occasionalism, developed by Nicolas Malebranche and Arnold Geulincx.
Major Contributions to Science
See biographies by J. R. Vrooman (1970), S. Gaukroger (1995), R. Watson (2002), A. C. Grayling (2005), and D. Clarke (2006); see studies by J. Maritain (tr. 1944, repr. 1969), A. G. Balz (1952, repr. 1967), H. Caton (1973), S. Gaukroger (1989 and 2002; as ed. 1980, 1998, 2000, and 2006), and S. Nadler (2013).
(Latinized name, Renatus Cartesius). Born at La Haye in Touraine on May 31, 1596; died in Stockholm on Feb. 11, 1650. French philosopher and mathematician.
Descartes was a member of an old noble family and was educated at the Jesuit school of La Fleche in Anjou. At the beginning of the Thirty Years’ War he served in the army, which he left in 1621. After traveling for a few years, he settled in 1629 in the Netherlands, where he spent 20 years in seclusion engaged in scientific studies. There he published his main works, Discourse on Method (1637; Russian translation, 1953), Meditations on First Philosophy (1641; Russian translation, 1950), and Principles of Philosophy (1644; Russian translation, 1950). In 1649, at the invitation of Queen Christina of Sweden, he went to Stockholm, where he died soon afterward.
The main feature of Descartes’s philosophy is the dualism of soul and body—of thinking substance and extended substance. In identifying matter with extension, Descartes considers it not so much as physical substance but rather as stereometric space. In contrast to the medieval concept of a finite world and of qualitative diversity of natural phenomena, he affirms that the world’s matter (space) is limitless and homogeneous; it has no voids and can be endlessly divided. This theory contradicts classical atomism, revived in Descartes’s time, which considered the world as consisting of indivisible particles separated by voids. Descartes considered each particle of matter an inert and passive mass. Motion, which Descartes reduced to the displacement of bodies, was always the result of an impulse given by one body to another. The universal cause of motion in Descartes’s dualist conception is god, who created matter together with motion and rest and preserves them.
Descartes’s teachings on man are also dualist. Man is the real union of the soulless and lifeless bodily mechanism and the soul, which possesses thought and will. The interaction between body and soul takes place as a result of a special organ, the pineal gland. Descartes placed the will first among the faculties of the human soul.
The main action of the affects, or passions, is to incline the soul to want those things for which the body is prepared. God himself has united body and soul, thereby distinguishing man from animals. Descartes denied the existence of consciousness in animals. Since they were automatons without souls, they could not think. The human body, like the body of animals, is merely a complex mechanism formed out of material elements and capable, as a result of the mechanical effect of the objects around it, of performing complex movements.
Descartes studied the structure of various organs of animals and of their embryos at different stages of their development. His physiological works are based on the teachings of W. Harvey on the circulation of the blood. He was the first to try to explain the nature of voluntary and involuntary movements and described the system of reflex movements in which the centripetal and centrifugal parts of the reflex arc are distinguished. Descartes regarded not only the contraction of the skeletal muscular system but also many vegetative acts as being reflex movements.
Among the philosophical questions that Descartes studied, the most significant was that of the method of knowledge. Like F. Bacon he considered the ultimate purpose of knowledge to be man’s mastery over the forces of nature, the discovery and invention of technical methods, the knowledge of causes and effects, and the betterment of the nature of man himself. Descartes seeks the absolutely certain fundamental point of departure for all knowledge and a method that makes it possible, by basing oneself on this point of departure, to build an equally certain edifice of all knowledge. He does not find such a point of departure or such a method in scholastic philosophy. For that reason the point of departure in Descartes’s philosophical thought is doubt of the truth of generally accepted knowledge, including all existing forms of knowledge. However, as in the case of Bacon, Descartes’s initial doubting is not the conviction of an agnostic but merely a preliminary methodological technique. I may doubt the existence of a world outside myself and even the existence of my own body. However, my own doubting does in any case exist, and doubting is an act of thinking. I doubt inasmuch as I think. If doubting is an established fact, then it must exist insofar as thought exists and insofar as I exist myself as a thinking being: “I think, therefore I am” (Sobr. soch., Moscow, 1950, p. 282).
Descartes’s idealism is linked to the religious premises of his system. To prove the reality of the existence of the world, Descartes considers it essential to prove first the existence of god. He constructs his proof on the model of the ontological proof of the existence of god given by Anselm of Canterbury. And if god exists, then his perfection excludes the possibility that he could deceive us. Consequently, the existence of the objective world is also beyond doubt.
In his teaching on knowledge, Descartes was the founder of rationalism, which developed from the observation of the logical character of mathematical knowledge. Mathematical truths, according to Descartes, are beyond all doubt, and possess a universality and necessity inherent in the nature of the intellect itself. Consequently, Descartes attributed an exceptionally important role to the processes of deduction, by which he understood reasoning based on completely certain points of departure (axioms) and consisting of a chain of equally certain logical deductions. The certainty of the axioms is perceived by the mind intuitively, with full clarity and distinctness. For a clear and distinct understanding of the whole chain of deductions, a strong memory is required. Consequently , immediately evident points of departure, or intuitions, are preferable to deductive judgments.
Equipped with the right means for thinking—intuition and deduction—the mind may attain completely certain knowledge in all fields, provided that it is guided by the right methods. The rules for Descartes’s rationalist method consist of the four following precepts: (1) never accept anything as true unless it is recognized to be certainly and evidently such and unless it presents itself so clearly and distinctly that there can be no reason for doubting its truth; (2) divide each complex problem into its component parts; (3) proceed in an orderly fashion from what is known and proved to what is not known and not proved; (4) allow for no omissions in the logical chain of reasoning. The perfection of our knowledge and its extent are determined according to Descartes by the existence in us of innate ideas, which he divides into innate conceptions and innate axioms. Very little is known for certain about physical things; we know considerably more about the human spirit and even more about god.
The teachings of Descartes and the trends in philosophy and the natural sciences that carried on his ideas were given the name Cartesianism, from the Latinized form of his name. He exerted considerable influence on the subsequent development of science and philosophy, both materialist and idealist. Descartes’s teachings on the immediate certainty of self-consciousness, on innate ideas, on the intuitive nature of axioms, and on the opposition of the material and the ideal laid the foundation for the development of idealism. On the other hand his teachings on nature and his general mechanistic method make his philosophy one of the milestones of the modern materialist conception of the world.
V. F. ASMUS
In his Geometry (1637), Descartes introduced the concepts of variable and function. He considered a variable in two ways: as a line segment of variable length and constant direction—the hanging coordinate of a point whose motion describes a curve—and as a continuous numerical variable that runs through the set of values representing that line segment. This twofold treatment of a variable resulted in an interweaving of geometry and algebra. Descartes treated a real number as the ratio of any line segment to the unit segment, although such a definition for real numbers was explicitly stated much later by I. Newton; negative numbers were given a real interpretation in Descartes’s work as directed ordinates. He greatly improved the existing system of notation, introducing the now familiar symbols for variables (x, y, z , …) and coefficients (a, b, c, …), as well as the notation for powers (x4, a5, …). His style for writing formulas was almost identical with the style in use today.
Descartes laid the foundations for a number of investigations into the properties of equations: he formulated the rule of signs for determining the number of positive and negative roots, raised the question of the boundaries of real roots, propounded the problem of reducibility (the representation of an entire rational function with rational coefficients as the product of two functions of the same kind), and indicated that a third-degree equation can be solved in terms of quadratic radicals and is solvable with ruler and compass when it is reducible.
In analytic geometry, which P. Fermat developed at the same time as Descartes, Descartes’s main achievement was his system of coordinates. He included within the field of geometric studies the study of “geometric” curves (later called algebraic curves by Leibniz), which can be described by the movements of hinged mechanisms. Transcendental (“mechanical”) curves are excluded from Descartes’s geometry. In his Geometry he described a method for constructing normals and tangents to plane curves (in connection with investigations on lenses) and applied the method, in particular, to certain fourth-order curves, the so-called Cartesian ovals.
Although he laid the foundations of analytic geometry, he himself did not advance very far into the field: he did not consider negative abscissas and did not touch upon the problems involved in the analytic geometry of three-dimensional space. Nevertheless, the Geometry had a tremendous influence on the development of mathematics. Descartes’s correspondence also includes other discoveries: he calculated the area of the cycloid, showed how to draw tangents to the cycloid, and determined the properties of the logarithmic spiral. From his manuscripts it is clear that he knew the relation (subsequently discovered by L. Euler) between the numbers of faces, vertices, and edges of convex polyhedra.
WORKSOeuvres. Edited by C. Adam and P. Tannery. Vols. 1–12 (with supplement). Paris, 1897–1913.
Correspondance. Edited by C. Adam and G. Milhaud. Vols. 1–6. Paris, 1936–56.
In Russian translation.
Soch., vol. 1. Kazan, 1914.
Izbrannye proizvedeniia. [Moscow] 1950.
Geometriia. Moscow-Leningrad, 1938. (Includes selected works of P. Fermat and selected letters of Descartes.)
REFERENCESWieleitner, H. Istoriia matematiki ot Dekarta do serediny 19 stoletiia, 2nd ed. Moscow, 1966. (Translated from German.)
Liubimov, N. A. Filosofiia Dekarta, St. Petersburg, 1886.
Fouillée, A. Dekart. Moscow, 1895. (Translated from French.)
Fischer, K. Istoriia novoi filosofii, vol. 1: Dekart, ego zhizn’, sochineniia i uchenie. St. Petersburg, 1906. (Translated [from German.])
Spinoza, B. Printsipy filosofii Dekarta. Moscow, 1926.
Bykhovskii, B. E. Filosofiia Dekarta. Moscow-Leningrad, 1940.
Asmus, V. F. Dekart. Moscow, 1956.
Laporte, J. Le Rationalisme de Descartes. Paris, 1945.
Lefèvre, R. La Vocation de Descartes, part 1. Paris, 1956.
Alquié, F. Descartes. Paris, 1963.
Sebba, G. Bibliografia cartesiana. The Hague, 1964.