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.
Such a view was essentially unfavourable to the progress of science, assigning, as it did, a higher dignity to meagre and very questionable abstractions than to the far-reaching combinations by which alone we are enabled to unravel the inmost texture of visible phenomena. Instead of using reason to supplement sense, Aristotle turned it into a more subtle and universal kind of sense; and if this disastrous assimilation was to a certain extent imposed upon him by the traditions of Athenian thought, it harmonised admirably with the descriptive and superficial character of his own intelligence. Much was also due to the method of geometry, which in his time had already assumed the form made familiar to us by Euclids Elements. The employment of axioms side by side with definitions, might, indeed, have drawn his attention to the existence and importance of judgments which, in Kantian terminology, are not analytic but syntheticthat is, which add to the content of a notion instead of simply analysing it. But although he mentions axioms, and states that mathematical theorems are deduced from them, no suspicion of their essential difference from definitions, or of the typical significance which they were destined to assume in the theory of reasoning, seems ever to have crossed his mind; otherwise he could hardly have failed to ask how we come by our knowledge of them, and to what they correspond in Nature. On the whole,385 it seems likely that he looked on them as an analysis of our ideas, differing only from definition proper by the generality of its application; for he names the law of contradiction as the most important of all axioms, and that from which the others proceed;277 next to it he places the law of excluded middle, which is also analytical; and his only other example is, that if equals be taken from equals the remainders are equal, a judgment the synthetic character of which is by no means clear, and has occasionally been disputed.278It was a little before eleven that Balmayne came in. He was very quiet and subdued; he sat and unfolded an evening paper. He shot a sign across to the Countess from a pair of eyes that gleamed like flames.
ONE:"Never mind that. Years ago I got a whiff of it in Vienna, and it appealed to my imagination. I saw a way of bringing it into fiction, much as it was done in the case of the play called 'Dora.' I am going to do so."His face slowly changed, gradually became red.
THREE:Lucretius has been called Romes only great speculative genius. This is, of course, absurd. A talent for lucid ex101position does not constitute speculative genius, especially when it is unaccompanied by any ability to criticise the opinions expounded. The author of the De Rerum Natura probably had a lawyers education. He certainly exhibits great forensic skill in speaking from his brief. But Cicero and Seneca showed the same skill on a much more extensive scale; and the former in particular was immensely superior to Lucretius in knowledge and argumentative power. Besides, the poet, who was certainly not disposed to hide his light under a bushel, and who exalts his own artistic excellences in no measured terms, never professes to be anything but a humble interpreter of truths first revealed to his Greek instructors vivid intellect. It has, indeed, been claimed for Lucretius that he teaches a higher wisdom than his acknowledged guide.195 This assertion is, however, not borne out by a careful comparison between the two.196 In both there is the same theory of the universe, of man, and of the relations connecting them with one another. The idea of Nature in Lucretius shows no advance over the same idea in Epicurus. To each it expresses, not, as with the Stoics, a unifying power, a design by which all things work together for the best, but simply the conditions of a permanent mechanical aggregation. When Lucretius speaks of foedera Naturai, he means, not what we understand by laws of nature, that is, uniformities of causation underlying all phenomenal differences, to understand which is an exaltation of human dignity through the added power of prevision and control which it bestows, but rather the limiting possibilities of existence, the barriers against which human hopes and aspirations dash themselves in vainan objective logic which guards us against fallacies instead of enabling us to arrive at positive conclusions. We have here the pervadingly negative character of Epicureanism,102 though probably presented with something of Roman solemnity and sternness. The idea of individuality, with which Lucretius has also been credited, occupies but a small place in his exposition, and seems to have interested him only as a particular aspect of the atomic theory. The ultimate particles of matter must be divided into unlike groups of units, for otherwise we could not explain the unlikenesses exhibited by sensible objects. This is neither the original Greek idea, that every man has his own life to lead, irrespective of public opinion or arbitrary convention; nor is it the modern delight in Natures inexhaustible variety as opposed to the poverty of human invention, or to the restrictions of fashionable taste. Nor can we admit that Lucretius developed Epicurean philosophy in the direction of increased attention to the external world. The poet was, no doubt, a consummate observer, and he used his observations with wonderful felicity for the elucidation and enforcement of his philosophical reasoning; but in this respect he has been equalled or surpassed by other poets who either knew nothing of systematic philosophy, or, like Dante, were educated in a system as unlike as possible to that of Epicurus. There is, therefore, every reason for assuming that he saw and described phenomena not by virtue of his scientific training, but by virtue of his artistic endowment. And the same may be said of the other points in which he is credited with improvements on his masters doctrine. There is, no doubt, a strong consciousness of unity, of individuality, and of law running through his poem. But it is under the form of intuitions or contemplations, not under the form of speculative ideas that they are to be found. And, as will be presently shown, it is not as attributes of Nature but as attributes of life that they present themselves to his imagination.Philosophy was no sooner domiciled at Athens than its professors came in for their full share of the scurrilous personalities which seem to have formed the staple of conversation in that enlightened capital. Aristotle, himself a trenchant and sometimes a bitterly scornful controversialist, did not escape; and some of the censures passed on him were, rightly or wrongly, attributed to Plato. The Stagirite, who had been brought up at or near the Macedonian Court, and had inherited considerable means, was, if report speaks truly, somewhat foppish in his dress, and luxurious, if not dissipated in his habits. It would not be surprising if one who was left his own master at so early an age had at first exceeded the limits of that moderation which he afterwards inculcated as the golden rule of morals; but the charge of extravagance was such a stock accusation at Athens, where the continued influence of country life seems to have bred a prejudice in favour283 of parsimony, that it may be taken almost as an exoneration from graver imputations; and, perhaps, an admonition from Plato, if any was needed, sufficed to check his disciples ambition for figuring as a man of fashion.
THREE:We have next the disposition of individuals, no longer to interfere in making the law, but to override it, or to bend it into an instrument for their own purposes. Doubtless there existed such a tendency in Platos time, and his polity was very largely designed to hold it in check. But such unprincipled ambition was nothing new in Greece, however the mode of its manifestations might vary. What had formerly been seized by armed violence was now sought after with the more subtle weapons of rhetorical skill; just as at the present moment, among these same Greeks, it is the prize of parliamentary intrigue. The Cretan and Spartan institutions may very possibly have been designed with a view to checking this spirit of selfish lawlessness, by reducing private interests to a minimum; and Plato most certainly had them in his mind when he pushed the same method still further; but those institutions were not types of Hellenism as a whole, they only represented one, and that a very abnormal, side of it. Plato borrowed some elements from this quarter, but, as we shall presently show, he incorporated them with others of a widely different character. Sparta was, indeed, on any high theory of government, not a State at all, but a robber-clan established among a plundered population whom they never tried or cared to conciliate. How little weight her rulers attributed to the interests of the State as such, was well exhibited during the Peloponnesian War, when political advantages of the utmost importance were surrendered in deference to the noble families whose kinsmen had been captured at Sphactria, and whose sole object was to rescue them from the fate with which they were threatened by the Athenians as a means of extorting concessions;conduct with which the refusal of Rome to ransom the soldiers who had surrendered at Cannae may be instructively contrasted.
