René Descartes

I

Introduction

René Descartes (1596-1650), French philosopher, scientist, and mathematician, often called the founder of modern philosophy. Born in La Haye, Touraine (a region and former province of France), Descartes was the son of a minor nobleman and belonged to a family that had produced a number of learned men. At the age of eight he was enrolled in the Jesuit school of La Flèche in Anjou, where he spent the rest of his schooldays. Besides the usual classical studies, Descartes received instruction in mathematics and scholasticism, which attempted to use human reason to understand Christian doctrine. Roman Catholicism exerted a strong influence on Descartes throughout his life.

Upon finishing school, he studied law at the University of Poitiers, graduating in 1616. He never practised law, however; in 1618 he entered the service of Prince Maurice of Nassau, leader of the United Provinces of the Netherlands, with the intention of following a military career. In succeeding years Descartes served in other armies, but his attention had already been attracted to the problems of mathematics and philosophy, to which he was to devote the rest of his life. One of the important influences on Descartes during this period was Dutch mathematician Isaac Beeckman, who encouraged him to pursue his studies.

Descartes made a pilgrimage to Italy between 1623 and 1624, then spent the years from 1624 to 1628 in France, where he devoted himself to the study of philosophy and also experimented in the science of optics. In 1628, having sold his properties in France, he moved to the Netherlands, where he spent most of the rest of his life, living in a number of different cities, including Amsterdam, Deventer, Utrecht, and Leiden.

It was probably during the first years of his residence in the Netherlands that Descartes wrote his first major work, Essais Philosophiques (Philosophical Essays), published in 1637. The work contained four parts: an essay on geometry, another on optics, a third on meteors, and, lastly, Discours de la Méthode (Discourse on Method), which described his philosophical speculations. This was followed by other philosophical works, among them Meditationes de Prima Philosophia (Meditations on First Philosophy, 1641; revised 1642) and Principia Philosophiae (The Principles of Philosophy, 1644). The latter volume was dedicated to Princess Elizabeth of Bohemia, who lived in the Netherlands and with whom Descartes had formed a deep friendship. In 1649 Descartes was invited to the court of Queen Christina of Sweden in Stockholm to give the Queen instruction in philosophy. However, the rigours of the northern winter brought on the pneumonia that caused his death in 1650.

II

Philosophy

Descartes attempted to apply the rational deductive methods of science, and particularly of mathematics, to philosophy. Before his time, philosophy had been dominated by the method of scholasticism, which was entirely based on comparing and contrasting the views of recognized authorities. Rejecting this method, Descartes stated: “In our search for the direct road to truth, we should busy ourselves with no object about which we cannot attain a certitude equal to that of the demonstration of arithmetic and geometry.” He therefore determined to hold nothing true until he could be absolutely certain of it. His method for discovering a truth of which he could be absolutely certain was to use scepticism: he attempted to doubt everything that he believed to be true and investigate if it was indeed possible to doubt it. Using this “method of doubt” he found that he could doubt whether he was in fact awake, since it was always possible that he was dreaming. He could also doubt whether the physical world and his own body existed, since it was always possible that a powerful and malicious demon was creating the illusion of these things in his mind. However, try as he might, he could not doubt that he himself existed, since the very act of doubting required a doubter, namely himself. In order to doubt, he had to exist. Descartes expressed this conclusion in the famous words “Cogito, ergo sum” (“I think, therefore I am”). He used it as the foundation stone on which to build a complete system of indubitable knowledge. From the principle that thinking proved his own existence, he argued that his essential characteristic was thinking.

Descartes then went on to argue for the existence of God, and to claim that God must have created two kinds of substance that make up the whole of reality. One kind was thinking substance, or minds, entities such as himself whose essential characteristic was thinking, and the other was extended substance, or bodies, for example, rocks or trees or his own body, whose essential characteristic was being extended over a certain amount of physical space. While thinking substances acted in accordance with the laws of thinking, extended substances acted in accordance with the mechanical laws of physics. This division of reality into two kinds of substance, one physical and one mental, has become known as Cartesian dualism. In one form or another it has been extraordinarily influential on Western philosophy ever since Descartes's time.

III

Science

Descartes's philosophy carried him into elaborate and erroneous explanations of a number of physical phenomena. These explanations, however, were valuable, in that he substituted a system of mechanical interpretation of physical phenomena for the vague spiritual concepts of most earlier writers.

Although Descartes had at first been inclined to accept the new Copernican theory of the universe, with its concept of a system of spinning planets revolving around the Sun, he abandoned this theory when it was pronounced heretical by the Roman Catholic Church. In its place he devised a theory of vortices in which space was entirely filled with matter, in various states, whirling about the Sun.

In the field of physiology, Descartes held that part of the blood was a subtle fluid, which he called “animal spirits”. The animal spirits, he believed, came into contact with the thinking substance at a point in the brain and flowed out along the channels of the nerves to animate the muscles and other parts of the body.

Descartes's study of optics led him to the independent discovery of the fundamental law of reflection: that the angle of incidence is equal to the angle of reflection. His essay on optics was the first published statement of this law. Descartes's treatment of light as a type of pressure in a solid medium paved the way for the undulatory, or wave, theory of light.

IV

Mathematics

The most notable contribution that Descartes made to mathematics was his systematization of analytic geometry. This is a method for translating any point, line, or curve on a plane into numerical form. If the plane is marked off into a grid based on a horizontal and a vertical axis, then every point on the plane can be identified by two numbers that give its distances from the two axes. These numbers are known as the point's Cartesian coordinates. It is then possible, for a given line or curve, to find an equation relating the two Cartesian coordinates that holds true for all points on the curve. This equation provides an exact translation of the curve into numerical form. Descartes was the first mathematician to attempt to classify curves according to the types of equations that produce them, as well as contributing to the theory of equations. He was the originator of the use of the last letters of the alphabet to designate unknown quantities and first letters to designate known ones. He also invented the method of indices (as in x²) to express the powers of numbers. In addition, he formulated the rule, which is known as Descartes's rule of signs, for finding the number of positive and negative roots for any algebraic equation.