ONE:It seems difficult to reconcile views about marriage involving a recognition of the fact that mental and moral qualities are hereditarily transmitted, with the belief in metempsychosis elsewhere professed by Plato. But perhaps his adhesion to the latter doctrine is not to be taken very seriously. In imitation of the objective world, whose essential truth is half hidden and half disclosed by its phenomenal manifestations, he loves to present his speculative teaching under a mythical disguise; and so he may have chosen the old doctrine of transmigration as an apt expression for the unity and continuity of life. And, at worst, he would not be guilty of any greater inconsistency than is chargeable to those modern philosophers who, while they admit that mental qualities are inherited, hold each individual soul to be a separate and independent creation.
TWO: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.
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