The Ε at Delphi (6-7)

When Nicander had expounded all this, my friend Theon, whom I presume you know, asked

Ammonius if Logical Reason had any rights in free speech, after being spoken of in such a very insulting manner. And when Ammonius urged him to speak and come to her assistance, he said, That the god is a most logical reasoner the great majority of his oracles show clearly; for surely it is the function of the same person both to solve and to invent ambiguities. Moreover, as Plato said, when an oracle was given that they should double the size of the altar at Delos[*] (a task requiring the highest skill in geometry), it was not this that the god was enjoining, but he was urging the Greeks to study geometry. And so, in the same way, when the god gives out ambiguous oracles, he is promoting and organizing logical reasoning as indispensable for those who are to apprehend his meaning aright. Certainly in logic this copulative conjunction has the greatest force, inasmuch as it clearly gives us our most logical form, the syllogism. Must not the character of the hypothetical syllogism be of this sort: granted that even wild animals have apperception of the existence of things, yet to man alone has Nature given the power to observe and judge the consequences? That it is day and that it is light assuredly wolves and dogs and birds perceive by their senses; but if it is day, then it is light, no creature other than man apprehends,[*] for he alone has a concept of antecedent and consequent, of apparent implication and connexion of these things one with another, and their relations and differences, from which our demonstrations derive their most authoritative inception. Since, then, philosophy is concerned with truth, and the illumination of truth is demonstration, and the inception of demonstration is the hypothetical syllogism, then with good reason the potent element that effects the connexion and produces this was consecrated by wise men to the god who is, above all, a lover of the truth.

The god, moreover, is a prophet, and the prophetic art concerns the future that is to result from things present and past. For there is nothing of which either the origin is without cause or the foreknowledge thereof without reason; but since all present events follow in close conjunction with past events, and all future events follow in close conjunction with present events, in accordance with a regular procedure which brings them to fulfilment from beginning to end, he who understands, in consonance with Nature, how to fathom the connexions and interrelations of the causes one with another knows and can declare

What now is, and in future shall be, and has been of aforetime.[*]

Very excellently did Homer place first in order the present, then the future and the past, for the syllogism based on hypothesis has its source in what is; for example, if this is, then that has preceded, and again, if this is, then that shall be. The technical and rational element here, as has been stated, is the knowledge of consequences; but the senses provide the argument with its premise. Therefore, even if it be a poor thing to say, I shall not be turned aside from saying it, that this is the tripod of truth, namely, argument, which lays down the consequent relation of the conclusion to the antecedent, and then, premising the existent condition, induces the completion of the demonstration. Therefore, if the Pythian god plainly finds pleasure in music and the songs of swans and the sound of lyres, what wonder is it that, because of his fondness for logical reasoning, he should welcome and love that portion of discourse of which he observes philosophers making the most particular and the most constant use?

Heracles, before he had released Prometheus or had conversed with the sophists that were associated with Cheiron and Atlas, when he was young and a thorough Boeotian,[*] would do away with logical reasoning;. he ridiculed the if the first, then the second, and resolved to carry off the tripod by force[*] and fight it out with the god over his art; since, at any rate, as he advanced in years, he also appears to have become most skilled in prophecy and in logic.

When Theon ceased, Eustrophus the Athenian, I think it was, said to us in answer, Do you see how zealously Theon defends logic, all but arraying himself in the lion’s skin? Under such conditions, we who repose in the Theory of Numbers all affairs together, natures and principles of things divine and human alike, and make this theory far above all else our guide and authority in all that is beautiful and valuable, should not be likely to hold our peace, but to offer to the god the first-fruits of our beloved mathematics, believing, as we do, that, taken by itself, E is not unlike the other letters either in power or in form or as a spoken word, but that it has come to be held in honour as the symbol of a great and sovereign number, the pempad, from which the wise

gave the name pempazein to counting which is done by fives. [*]

These words Eustrophus addressed to us not in jest, but for the reason that at this time I was devoting myself to mathematics with the greatest enthusiasm, although I was destined soon to pay all honour to the maxim Avoid extremes, when I had once become a member of the Academy.[*]