Descartes Quotes - page 5
Descartes ... complained that Greek geometry was so much tied to figures "that is can exercise the understanding only on condition of greatly fatiguing the imagination." Descartes also deplored that the methods of Euclidean geometry were exceedingly diverse and specialized and did not allow for general applicability. Each theorem required a new kind of proof... What impressed Descartes especially was that algebra enables man to reason efficiently. It mechanizes thought, and hence produces almost automatically results that may otherwise be difficult to establish. ...historically it was Descartes who clearly perceived and called attention to this feature. Whereas geometry contained the truth about the universe, algebra offered the science of method. It is ... paradoxical that great thinkers should be enamored with ideas that mechanize thought. Of course, their goal is to get at more difficult problems, as indeed they do.
René Descartes
As long as algebra and geometry travelled separate paths their advance was slow and their applications limited. But when these two sciences joined company, they drew from each other fresh vitality and thenceforward marched on at a rapid pace towards perfection. It is to Descartes that we owe the application of algebra to geometry,-an application which has furnished the key to the greatest discoveries in all branches of mathematics.
René Descartes
The rationalism of René Descartes had a liberating effect on women because it assumed that the mind, not the body, was the instrument for sensation and knowledge and that men and women had the same potential for understanding. Cartesianism denied that formal education was the road to higher insight; anyone could think and reason logically. The effect of these ideas was not only to inspire a number of women, such as Mary Astell, Lady Damaris Masham, Marie de Gournay, to enter philosophical discourse with the outstanding male thinkers of their time, but it also helped them to create a new form for such a discourse through personal correspondence.
René Descartes
While Descartes' theory of vortices was spectacularly wrong (as Newton ruthlessly pointed out later), it was still interesting, being the first serious attempt to formulate a theory of the universe as a whole based upon the same laws that apply on the Earth's surface. In other words, to Descartes there was no difference between terrestrial and celestial phenomena-the Earth was part of a universe that obeyed uniform physical laws.
René Descartes
Descartes is rightly regarded as the father of modern philosophy primarily and generally because he helped the faculty of reason to stand on its own feet by teaching men to use their brains in place whereof the Bible, on the one hand, and Aristotle, on the other, had previously served.
René Descartes
In mechanics Descartes can hardly be said to have advanced beyond Galileo. ...His statement of the first and second laws of motion was an improvement in form, but his third law is false in substance. The motions of bodies in their direct impact was imperfectly understood by Galileo, erroneously given by Descartes, and first correctly stated by Wren, Wallis, and Huygens.
René Descartes
Descartes's so-called dualism is often taken to represent a fundamental revolution in ideas and the starting point of modern philosophy. ...but in substance his work is... better understood as an attempt to conserve the old truths in the face of new threats. His dualism was in essence an armistice... between the established religion and the emerging science of his time. ...isolating the mind from the physical world... ensured that many of the central doctrines of orthodoxy-immortality of the soul, the freedom of will, and, in general, the "special" status of humankind-were rendered immune to any possible contravention by the scientific investigation of the physical world. ...
For men such as Descartes, Malebranche, and Leibniz, solving the mind-body problem was vital to preserving the theological and political order inherited from the Middle Ages... For Spinoza, it was a means of destroying that same order and discovering a new foundation for human worth.
René Descartes
After Bruno's death, during the first half of the seventeenth century, Descartes seemed about to take the leadership of human thought... in promoting an evolution doctrine as regards the mechanical formation of the solar system... but his constant dread of persecution, both from Catholics and Protestants, led him steadily to veil his thoughts and even to suppress them. The execution of Bruno had occurred in his childhood, and in the midst of his career he had watched the Galileo struggle in all its stages. He had seen his own works condemned by university after university under the direction of theologians and placed upon the Roman Index. ...Since Roger Bacon, perhaps, no great thinker had been so completely abased and thwarted by theological oppression.
René Descartes
