Edwin Arthur Burtt (essay date 1925)
SOURCE: "Descartes," in The Metaphysical Foundations of Modern Physical Science: A Historical and Critical Essay, Kegan Paul, Trench, Trubner & Co., Ltd., 1925, pp. 96–116.
[In the following essay, Burtt examines Descartes' mathematical conception of nature and his motives for proposing a mind-body dualism.]
Descartes' importance in [the] mathematical movement [in science] was twofold; he worked out a comprehensive hypothesis in detail of the mathematical structure and operations of the material universe, with clearer consciousness of the important implications of the new method than had been shown by his predecessors; and he attempted both to justify and atone for the reading of man and his interests out of nature by his famous metaphysical dualism.
While still in his teens, Descartes became absorbed in mathematical study, gradually forsaking every other interest for it, and at the age of twenty-one was in command of all that was then known on the subject. During the next year or two we find him performing simple experiments in mechanics, hydrostatics, and optics, in the attempt to extend mathematical knowledge in these fields. He appears to have followed the more prominent achievements of Kepler and Galileo, though without being seriously affected by any of the details of their scientific philosophy. On the night of November 10th, 1619, he had a remarkable experience which confirmed the trend of his previous thinking and gave the inspiration and the guiding principle for his whole life-work.1 The experience can be compared only to the ecstatic illumination of the mystic; in it the Angel of Truth appeared to him and seemed to justify, through added supernatural insight, the conviction which had already been deepening in his mind, that mathematics was the sole key needed to unlock the secrets of nature. The vision was so vivid and compelling that Descartes in later years could refer to that precise date as the occasion of the great revelation that marked the decisive point in his career.
(A) Mathematics as the Key to Knowledge
The first intensive studies into which he plunged after this unique experience were in the field of geometry, where he was rewarded within a very few months by the signal invention of a new and most fruitful mathematical tool, analytical geometry. This great discovery not only confirmed his vision and spurred him on to further efforts in the same direction, but it was highly important for his physics generally. The existence and successful use of analytical geometry as a tool of mathematical exploitation presupposes an exact oneto-one correspondence between the realm of numbers, i.e., arithmetic and algebra, and the realm of geometry, i.e., space. That they had been related was, of course, a common possession of all mathematical science; that their relation was of this explicit and absolute correspondence was an intuition of Descartes. He perceived that the very nature of space or extension was such that its relations, however...
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