The Ε at Delphi (5-9)

For it is, as the Delphians assume, - and on this occasion Nicander, the priest, spoke for them and said, the figure and form of the consultation of the god, and it holds the

first place in every question of those who consult the oracle and inquire if they shall be victorious, if they shall marry, if it is to their advantage to sail the sea, if to take to farming, if to go abroad.[*] But the god in his wisdom bade a long farewell to the logicians who think that nothing real comes out of the particle if combined with what the consultant thinks proper to undertake, for the god conceives of all the inquiries subjoined to this as real things and welcomes them as such. And since to inquire from him as from a prophet is our individual prerogative, but to pray to him as to a god is common to all, they think that the particle contains an optative force no less than an interrogative. If only I could, is the regular expression of a wish, and Archilochus[*] says,

If to me it might be granted Neobulê’s hand to touch.

And in using if only they assert that the second word is added unnecessarily, like Sophron’s[*] surely:

Surely in want of children as well.

This is found also in Homer[*]

Since I surely shall break your might

but, as they assert, the optative force is adequately indicated by the if.

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.[*]

I said, therefore, that Eustrophus solved the difficulty most excellently with his number. For since, I continued, every number may be classified as even or odd, and unity, by virtue of its potentiality, is common to both, for the reason that its addition makes the odd number even and the even number odd,[*] and since twTo makes the first of the even numbers and three the first of the odd, and five is produced by the union of these numbers, very naturally five has come to be honoured as being the first number created out of the first numbers; and it has received the name of marriage[*] because of the resemblance of the even number to the female and of the odd number to the male.[*] For in the division of numbers into two equal factors, the even number separates completely and leaves a certain receptive opening and, as it were, a space within itself; but in the odd, when it undergoes this process, there is always left over from the division a generative middle part. Wherefore it is more generative than the other, and in combination it is always dominant and is never dominated.[*] For in no combination of these two numbers (even and odd) is there produced from the two an even number,

but in all combinations an odd. Moreover, each when applied to itself and made composite with itself shows the difference. For no even number united with even gives an odd number, nor does it ever show any departure from its own distinctive nature, being impotent through its weakness to produce the other number, and having no power of accomplishment; but odd numbers combined with odd produce a numerous progeny of even numbers because of their omnipresent generative function. It would not be timely at this moment to enumerate the other potent properties and divergences of numbers; let it suffice to say that the Pythagoreans called Five a Marriage on the ground that it was produced by the association of the first male number and the first female number.

There is also a sense in which it has been called Nature, since by being multiplied into itself it ends in itself again. For even as Nature receives wheat in the form of seed and puts it to its use, and creates in the interim many shapes and forms through which she carries out the process of growth to its end, but, to crown all, displays wheat again, and thus presents as her result the beginning at the end of the whole, so in like manner, while the other numbers when raised to a power end in different numbers as the result of the increase, only the numbers five and six, when multiplied by themselves, repeat themselves and preserve their identity. Thus six times six is thirty-six, and five times five is twenty-five; and furthermore, the number six does this but once, and the single instance is when it is squared; but with five this result is obtained in raising it to any power, and it has a unique characteristic, when added to

itself, of producing either itself or ten alternately[*] as the addition progresses, and of doing this to infinity, since this number takes its pattern from the primal principle which orders the whole. For as that principle by changes creates a complete universe out of itself, and then in turn out of the universe creates itself again, as Heracleitus[*] says, and exchanges fire for all and all for fire, as gold for goods and goods for gold, so, in like manner, the conjunction of five with itself is determined by Nature’s law to produce nothing incomplete or foreign, but it has strictly limited changes; it produces either itself or ten, that is to say, either its own characteristic or the perfect whole.

If, then, anyone ask, What has this to do with Apollo?, we shall say that it concerns not only him, but also Dionysus, whose share in Delphi is no less than that of Apollo.[*] Now we hear the theologians affirming and reciting, sometimes in verse and sometimes in prose, that the god is deathless and eternal in his nature,[*] but, owing forsooth to some predestined design and reason, he undergoes transformations of his person, and at one time enkindles his nature into fire and makes it altogether like all else, and at another time he undergoes all sorts of changes in his form, his emotions and his powers, even as the

universe does to-day; but he is called by the best known of his names.[*] The more enlightened, however, concealing from the masses the transformation into fire, call him Apollo because of his solitary state,[*] and Phoebus because of his purity and stainlessness.[*] And as for his turning into winds and water, earth and stars, and into the generations of plants and animals, and his adoption of such guises, they speak in a deceptive way of what he undergoes in his transformation as a tearing apart, as it were, and a dismemberment. They give him the names of Dionysus, Zagreus, Nyctelius, and Isodaetes; they construct destructions and disappearances, followed by returns to life and regenerations — riddles and fabulous tales quite in keeping with the aforesaid transformations. To this god they also sing the dithyrambic strains laden with emotion and with a transformation that includes a certain wandering and dispersion. Aeschylus,[*] in fact, says

Fitting it is that the dithyramb

With its fitful notes should attend

Dionysus in revel rout.

But to Apollo they sing the paean, music regulated and chaste.

Apollo the artists represent in paintings and sculpture as ever ageless and young, but Dionysus they depict in many guises and forms; and they attribute to Apollo in general a uniformity, orderliness, and unadulterated seriousness, but to Dionysus a certain

variability combined with playfulness, wantonness, seriousness, and frenzy. They call upon him[*]:

Euoe Bacchus who incites

Womankind, Dionysus who delights

’Mid his honours fraught with frenzy,

not inappositely apprehending the peculiar character of each transformation.

But since the time of the cycles in these transformations is not equal, but that of the one which they call Satiety,[*] is longer, and that of Dearth shorter, they observe the ratio, and use the paean at their sacrifices for a large part of the year; but at the beginning of winter they awake the dithyramb and, laying to rest the paean, they use the dithyramb instead of it in their invocations of the god; for they believe that, as three is to one, so is the relation of the creation to the conflagration.