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Descartes implicitly assumed a complete correspondence existed between — René Descartes

"Descartes implicitly assumed a complete correspondence existed between the real numbers and the points of a fixed axis. ...tacitly, because it seemed so natural as to go without saying, he accepted it as axiomatic that between the points of a plane and the aggregate of all pairs of real numbers there can be established a perfect correspondence. Thus the Dedekind-Cantor axiom, extended to two dimensions, was tacitly incorporated in a discipline which was created two hundred years before Dedekind and Cantor saw the day. This discipline became the [tool and] proving-grounds for all achievements of the following two centuries: the calculus, the theory of functions, mechanics, and physics. Nowhere did this discipline, analytic geometry, strike any contradictions; and such was its power to suggest new problems and forecast the results that wherever applied it would soon become the indispensable tool of investigation."
Descartes implicitly assumed a complete correspondence existed between the real numbers and the points of a fixed axis.
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René Descartes
René Descartes
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René Descartes was a French philosopher, scientist, logician, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science during the Renaissance era. Mathematics was paramount to his method of inquiry, and he connected the previously separate fields of geometry and algebra into analytic geometry.

About René Descartes

René Descartes was a French philosopher, scientist, logician, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science during the Renaissance era. Mathematics was paramount to his method of inquiry, and he connected the previously separate fields of geometry and algebra into analytic geometry.

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"René Descartes played his part in the world as a man in a mask. The phrase is his own. It implied no conscious duplicity but a certain apartness rendering him incapable of taking his share unreservedly in the game of life. His attitude was that of an unimpassioned spectator. He looked on and learned while others struggled for the stakes. A born recluse, he remained solitary even in the throng of social intercourse. ...The transport felt by Bacon at the glorious vision of a future in which the harvest he had sown would be reaped was not shared by Descartes. He indeed held himself to be the sower and the reaper in one. Calmly, and with settled conviction, he claimed to have virtually expounded all the phenomena of nature. He had crossed the frontier of the new world of knowledge; those who desired to follow him needed only to purge their eyes with the euphrasy of methodic doubt in order to obtain those crystal-clear intuitions from which, by sure reasoning, universal science could be deduced. ...He was a mathematician of first rate originality and power. ...Unfortunately, however, he was misled by false analogies of thought; he sought to universalise what was by its nature special and restricted; and thus pursued the flitting vision of a deceptive unity in knowledge. As the upshot, he gave to his philosophy a pseudo-mathematical character, and sacrificed the solid achievement of much by aiming at the illusory certainty of everything."
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René Descartes

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"In a Thumbnail Sketch here is [the Multiple Drafts theory of consciousness] so far:There is no single, definitive "stream of consciousness," because there is no central Headquarters, no Cartesian Theatre where "it all comes together" for the perusal of a Central Meaner. Instead of such a single stream (however wide), there are multiple channels in which specialist circuits try, in parallel pandemoniums, to do their various things, creating Multiple Drafts as they go. Most of these fragmentary drafts of "narrative" play short-lived roles in the modulation of current activity but some get promoted to further functional roles, in swift succession, by the activity of a virtual machine in the brain. The seriality of this machine (its "von Neumannesque" character) is not a "hard-wired" design feature, but rather the upshot of a succession of coalitions of these specialists.The basic specialists are part of our animal heritage. They were not developed to perform peculiarly human actions, such as reading and writing, but ducking, predator-avoiding, face-recognizing, grasping, throwing, berry-picking, and other essential tasks. They are often opportunistically enlisted in new roles, for which their talents may more or less suit them. The result is not bedlam only because the trends that are imposed on all this activity are themselves part of the design. Some of this design is innate, and is shared with other animals. But it is augmented, and sometimes even overwhelmed in importance, by microhabits of thought that are developed in the individual, partly idiosyncratic results of self-exploration and partly the predesigned gifts of culture. Thousands of memes, mostly borne by language, but also by wordless "images" and other data structures, take up residence in an individual brain, shaping its tendencies and thereby turning it into a mind."
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"We foreign journalists in Moscow used to amuse ourselves, as a matter of fact, by competing with one another as to who could wish upon one of these intelligentsia visitors to the USSR the most outrageous fantasy…One story I floated myself, for which I received considerable acclaim, was that the huge queues outside food shops came about because the Soviet workers were so ardent in building Socialism that they just wouldnt rest, and the only way the government could get them to rest for even two or three hours was organizing a queue for them to stand in. I laugh at it all now, but at the time you can imagine what a shock it was to someone like myself, who had been brought up to regard liberal intellectuals as the samurai, the absolute elite, of the human race, to find that they could be taken in by deceptions which a half-witted boy would see through in an instant…I could never henceforth regard the intelligentsia as other than credulous fools who nonetheless became the medias prophetic voices, their heirs and successors remaining so still."
Malcolm MuggeridgeMalcolm Muggeridge