Monday, May 30, 2011

THE CARTESIAN REVOLUTION--THE LANGUAGE OF MATHEMATICS

While Galileo confined himself to the study of mathematical and astronomical phenomena, his contemporary, René Descartes (1596-1650), a French philosopher and mathematician, began to describe in clear-cut terms the full outline of the new universe discovered by the rationalists. When still a young man, Descartes became deeply dissatisfied with the scholasticism that still survived in the teachings of the Jesuits from whom he received his early training. A Catholic who never quarreled with the official custodians of religious tradition, he was determined to gain knowledge only from himself and from nature and the observation of man.

René Descartes is called the father of modern philosophy. He initiated the movement generally termed rationalism, and his book, "Discourse on Method and Meditations," defined the basic problems of philosophy for at least a century.

To appreciate the novelty of the thought of René Descartes, one must understand what modern philosophy, or rationalism, means in contrast to medieval, or scholastic, philosophy. The great European thinkers of the 9th to 14th century were not incapable of logical reasoning, but they differed in philosophic interests and aims from the rationalists. The moderns, from Descartes on, usually identified philosophy with the natural and pure sciences; the medievals, however, made little distinction between philosophical and theological concerns.

The medieval doctors, like St. Thomas Aquinas, wanted to demonstrate that the revelations of faith and the dictates of reason were not incompatible. Their universe was that outlined by Aristotle in his Physics - a universe in which everything was ordered and classified according to the end that it served. During the Renaissance, however, men began exploring scientific alternatives to Aristotle's hierarchical universe. Further, new instruments, especially Galileo's telescope, added precision to scientific generalizations.
By the beginning of the 17th century the medieval tradition had lost its creative impetus. But the schoolmen, so called because they dominated the European universities, continued to adhere dogmatically to the traditional philosophy because of its association with Catholic theology. The rationalists, however, persistently refused professorships in order to preserve their intellectual integrity or to avoid persecution. They rejected the medieval practice of composing commentaries on standard works in favor of writing original, usually anonymous, treatises on topics suggested by their own scientific or speculative interests. Thus the contrast is between a declining tradition of professorial disputes over trivialities and a new philosophy inspired by original, scientific research.

Descartes participated in this conflict between the scholastic and rationalist approaches. He established a new, clear way of thinking about philosophy and science by rejecting all ideas based on assumptions or emotional beliefs and accepting only those ideas which could be proved by or systematically deduced from direct observation. Descartes made major contributions to modern mathematics, especially in developing the Cartesian coordinate system and advancing the theory of equations.

In recognizing that mathematics constituted the fundamental basis of physical science, Descartes laid the groundwork for that exactness of observation and calculation that was to become the outstanding characteristic of modern science. His work is considered of such importance that it is generally recognized by the term, the Cartesian Revolution. The old Aristotelian idea that nature consists of a variety of unrelated objects, each seeking to fulfill its aim in its own way, was now superseded by the Cartesian principle that nothing in nature is accidental or arbitrary, but that everything is governed by universal mathematical laws. Cartesianism became the official beacon of the new science, even if its explanations were as yet a little too simple and not always proved by experimentation. Most important of all, it effectively prepared the way for the great synthesis of Newton, who has been called the greatest of the Cartesians.