THREE:The Alexandrian Sceptic��s general arguments against the possibility of knowledge resolve themselves into a criticism of what Sir W. Hamilton called Natural Realism, somewhat complicated and confused by a simultaneous attack on the theory of natural morality conceived as something eternal and immutable. They are summed up in the famous ten Tropes. Of these the first three are founded on the conflicting sensations produced by the same object when acting on different animals��as is inferred from the marked contrast presented by their several varieties of origin and structure,��on different men, and on the different senses of the same individual. The fourth, which has evidently an ethical bearing, enlarges on the changes in men��s views caused by mental and bodily changes, according to their health, age, disposition, and so forth. The next five Tropes relate to circumstances connected with the objects themselves: their distance and position as regards the spectator, the disturbance produced in their proper action by external influences such as air and light, together with the various membranes and humours composing the organs of sense through which they are apprehended; their quantitative variation, involving as it does opposite effects on the senses, or as with medicines, on the health; the law of relativity, according to which many things are only known when taken in company with others, such as double and half, right and left, whole and part; comparative frequency or rarity of occurrence, as with comets, which, while really of much less importance than the sun, excite much more interest from their being so seldom seen. Finally, the tenth Trope is purely ethical, and infers the non-existence of a fixed moral standard from the divergent and even opposite customs prevailing among different nations.297
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THREE:Meanwhile a new and powerful agency was about to interpose with decisive effect in the doubtful struggle. This was the study of mathematics. Revived by the Arabians and never wholly neglected during the Middle Ages, it had profited by the general movement of the Renaissance, and was finally applied to the cosmical problem by Galileo. In this connexion, two points of profound philosophical interest must be noted. The first is that, even in its fall, the Aristotelian influence survived, to some extent, both for good and for evil. To Aristotle belongs the merit of having been the first to base astronomy on physics. He maintains the earth��s immobility on experimental no less than on speculative grounds. A stone thrown straight up in the air returns to its starting-point instead of falling to the west of it; and the absence of stellar385 parallax seems to show that there is no change in our position relatively to the heavenly bodies. After satisfying himself, on empirical considerations, that the popular astronomy is true, he proceeds to show that it must be true, by considerations on the nature of matter and motion, which, although mistaken, are conceived in a genuinely scientific spirit. Now Galileo saw that, to establish the Copernican system, he must first grapple with the Peripatetic physics, and replace it by a new dynamical theory. This, which he could hardly have effected by the ordinary mathematical methods, he did by borrowing the analytical method of Atomism and applying it to the measurement of motion. The law of falling bodies was ascertained by resolving their descent into a series of moments, and determining its rate of velocity at successive intervals; and curvilinear motions were similarly resolved into the combination of an impulsive with an accelerating force, a method diametrically opposed to that of Bacon, who would not even accept the rough analysis of the apparent celestial motions proposed by Greek astronomers.
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THREE:
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