ONE:It was from mathematical science that the light of certainty first broke. Socrates had not encouraged the study of mathematics, either pure or applied; nor, if we may judge from some disparaging allusions to Hippias and his lectures in the Protagoras, did Plato at first regard it with any particular favour. He may have acquired some notions of arithmetic and geometry at school; but the intimate acquaintance with, and deep interest in them, manifested throughout his later works, probably dates from his visits to Italy, Sicily, Cyrn, and Egypt. In each of these places the exact sciences were cultivated with more assiduity than at Athens; in southern Italy they had been brought into close connexion with philosophy by a system of mystical interpretation. The glory of discovering their true speculative significance was reserved for Plato. Just as he had detected a profound analogy between the Socratic scepticism and the Heracleitean flux, so also, by another vivid intuition, he saw in the definitions and demonstrations of geometry a type of true reasoning, a particular application of the Socratic logic. Thus the two studies were brought into fruitful reaction, the one gaining a wider applicability, and the other an exacter method of proof. The mathematical spirit ultimately proved211 too strong for Plato, and petrified his philosophy into a lifeless formalism; but no extraneous influence helped so much to bring about the complete maturity of his constructive powers, in no direction has he more profoundly influenced the thought of later ages.We have already seen how this fundamental division is applied to the universe as a whole. But our philosopher is not content with classifying the phenomena as he finds360 them; he attempts to demonstrate the necessity of their dual existence; and in so doing is guilty of something very like a vicious circle. For, after proving from the terrestrial movements that there must be an eternal movement to keep them going, he now assumes the revolving aether, and argues that there must be a motionless solid centre for it to revolve round, although a geometrical axis would have served the purpose equally well. By a still more palpable fallacy, he proceeds to show that a body whose tendency is towards the centre, must, in the nature of things, be opposed by another body whose tendency is towards the circumference. In order to fill up the interval created by this opposition, two intermediate bodies are required, and thus we get the four elementsearth, water, air, and fire. These, again, are resolved into the antithetical couples, dry and wet, hot and cold, the possible combinations of which, by twos, give us the four elements once more. Earth is dry and cold, water cold and wet, air wet and hot, fire hot and dry; each adjacent pair having a quality in common, and each element being characterized by the excess of a particular quality; earth is especially dry, water cold, air wet, and fire hot. The common centre of each antithesis is what Aristotle calls the First Matter, the mere abstract unformed possibility of existence. This matter always combines two qualities, and has the power of oscillating from one quality to another, but it cannot, as a rule, simultaneously exchange both for their opposites. Earth may pass into water, exchanging dry for wet, but not so readily into air, which would necessitate a double exchange at the same moment.
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ONE:"The larger ones had suffered little; but the majority were jammed by fragments of concrete and steel, which struck between the armour and the front-armour. The small quick-fire cupolas had not been touched by any projectile. 'It is all right,' he said, 'we shall be able to repulse the enemy's attack.'
