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FORE:It seems strange that Galileo, having gone so far, did not go a step further, and perceive that the planetary orbits, being curvilinear, must result from the combination of a centripetal with a tangential force. But the truth is that he never seems to have grasped his own law of inertia in its full generality. He understood that the planets could not have been set in motion without a rectilinear impulse; but his idea was that this impulse continued only so long as was necessary in order to give them their present velocity, instead of acting on them for ever as a tangential force. The explanation of this strange inconsequence must be sought in a survival of Aristotelian conceptions, in the persistent belief that rectilinear motion was necessarily limited and temporary, while circular motion was natural, perfect, and eternal.548 Now such conceptions as386 Nature, perfection, and eternity always rebel against an analysis of the phenomena wherein they are supposed to reside. The same prejudice will explain why Galileo should have so persistently ignored Kepler��s Laws, for we can hardly imagine that they were not brought under his notice.

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FORE:Arcesilaus left no writings, and his criticisms on the Stoic theory, as reported by Cicero and Sextus Empiricus, have a somewhat unsatisfactory appearance. By what we can make out, he seems to have insisted on the infallibility of the wise man to a much greater extent than the Stoics themselves, not allowing that there was any class of judgments in which he was liable to be mistaken. But just as the Stoics were obliged to accept suicide as an indispensable safeguard for the inviolability of their personal dignity and happiness, so also Arcesilaus had recourse to a kind of intellectual suicide for the purpose of securing immunity from error. The only way, according to him, in which the sage can make sure of never being mistaken is never to be certain about anything. For, granting that every mental representation is produced by a corresponding object in the external world, still different objects are connected by such a number of insensible gradations that the impressions produced by them are virtually indistinguishable from one another; while a fertile source of illusions also exists in the diversity of impressions produced by the same object acting on different senses and at different times. Moreover, the Stoics themselves admitted that the148 sage might form a mistaken opinion; it was only for his convictions that they claimed unerring accuracy, each of the two��opinion and conviction��being the product of a distinct intellectual energy. Here again, Arcesilaus employed his method of infinitesimal transitions, refusing to admit that the various cognitive faculties could be separated by any hard and fast line; especially as, according to the theory then held by all parties, and by none more strongly than the Stoics, intellectual conceptions are derived exclusively from the data of sense and imagination. We can see that the logic of Scepticism is, equally with that of the other Greek systems, determined by the three fundamental moments of Greek thought. There is first the careful circumscription of certainty; then there is the mediating process by which it is insensibly connected with error; and, lastly, as a result of this process, there is the antithetical opposition of a negative to an affirmative proposition on every possible subject of mental representation.231

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