ONE: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 earths 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.Temperance and justice are very clearly distinguished in our minds. The one is mainly a self-regarding, the other mainly a social virtue. But it would be a mistake to suppose that the distinction was equally clear to Plato. He had learned from Socrates that all virtue is one. He found himself confronted by men who pointedly opposed interest to honour and expediency to fair-dealing, without making any secret of their preference for the former. Here, as elsewhere, he laboured to dissolve away the vulgar antithesis and to231 substitute for it a deeper onethe antithesis between real and apparent goods. He was quite ready to imagine the case of a man who might have to incur all sorts of suffering in the practice of justice even to the extent of infamy, torture, and death; but without denying that these were evils, he held that to practise injustice with the accompaniment of worldly prosperity was a greater evil still. And this conviction is quite unconnected with his belief in a future life. He would not have agreed with St. Paul that virtue is a bad calculation without the hope of a reward for it hereafter. His morality is absolutely independent of any extrinsic considerations. Nevertheless, he holds that in our own interest we should do what is right; and it never seems to have entered his thoughts that there could be any other motive for doing it. We have to explain how such a paradox was possible.
Nunc at viverra risus. In euismod quam ac dictum varius. Nunc at viverra risus. In euismod quam ac dictum varius. Nunc at viverra risus. In euismod quam ac dictum varius. Nunc at viverra risus.
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