ONE:63
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THREE:Turning from sense to reason, Carneades attacks the syllogistic process on grounds already specified in connexion150 with the earlier Sceptics; and also on the plea that to prove the possibility of syllogism is itself to syllogise, and thus involves either a petitio principii or a regress ad infinitum.235 Such a method is, of course, suicidal, for it disproves the possibility of the alleged disproof, a consideration which the Stoics did not fail to urge, and which the later Sceptics could only meet by extending the rule of suspense to their own arguments against argument.236 Nevertheless the sceptical analysis detected some difficulties in the ordinary theory of logic, which have been revived in modern times, and have not yet received any satisfactory solution. Sextus Empiricus, probably copying an earlier authority, it may be Carneades himself, observes that, as the major premise of every syllogism virtually contains the minor, it is either superfluous, or assumes the proposition to be proved. Thus we argue that Socrates is an animal because he is a man, and all men are animals. But if we do not know this latter proposition to be true in the case of Socrates, we cannot be sure that it is true in any case; while if we know it to be true in his case, we do not need to begin by stating it in general terms. And he also attempts to show the impossibility of a valid induction by the consideration, since so often urged, that to generalise from a limited number of instances to a whole class is unsafe, for some of the unknown instances may be contradictory, while the infinite, or at least indefinite multiplicity of individuals precludes the possibility of their exhaustive enumeration.237
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THREE: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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THREE:
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Lorem ipsum dolor sit amet, consectetuer adipiscing elit, sed diam nonummy nibh euismod tincidunt ut laoreet dolore magna aliquam erat volutpat. Ut wisi enim ad minim veniam, quis nostrud exerci tation ullamcorper suscipit lobortis nisl ut aliquip ex ea commodo consequat. Duis autem vel eum iriure dolor in hendrerit in vulputate velit esse molestie consequat, vel illum dolore eu feugiat nulla