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FORE: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, Cyr��n��, 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.To the objection that his suspensive attitude would render action impossible, Arcesilaus replied that any mental representation was sufficient to set the will in motion; and that, in choosing between different courses, probability was the most rational means of determination. But the task of reducing probable evidence to a system was reserved for a still abler dialectician, who did not appear on the scene until a century after his time. Arcesilaus is commonly called the founder of the Middle, Carneades the founder of the New Academy. The distinction is, however, purely nominal. Carneades founded nothing. His principles were identical with those of his predecessor; and his claim to be considered the greatest of the Greek sceptics is due to his having given those principles a wider application and a more systematic development. The Stoics regarded it as a special dispensation of providence149 that Chrysippus, the organising genius of their school, should have come between its two most formidable opponents, being thus placed in a position to answer the objections of the one and to refute by anticipation those of the other.232 It might seem to less prejudiced observers that the thinker whose cause benefited most by this arrangement was Carneades. Parodying a well-known iambic, he used to say:

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FORE:"But, surely, my dear sir, the tragedy that took place here so recently----"

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FORE:

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