If it might be mine, prevailing, Neobule’s hand to touch!
When If-so-be is used, the latter part is dragged in (compare Sophron’s “Bereaved of children, I trow”, or Homer’s “As I will break thy might, I trow”[[54]]). But If gives the sense of prayer sufficiently.’
VI. When Nicander had finished, our friend Theon, whom I am sure you know, asked Ammonius whether Dialectic might |E| speak freely, after the insulting remarks to which she had been treated. Ammonius told him to speak out on her behalf. ‘That the God is a master of Dialectic,’ Theon said, ‘is shown clearly by most of his oracles; for you will grant that the solution of puzzles belongs to the same person as their invention. Again, as Plato used to say, when a response was given that the altar at Delos should be doubled,[[55]] a matter requiring the most advanced geometry, the God was not merely enjoining this, but was also putting his strong command upon the Greeks to practise geometry. Just so, when the God puts out ambiguous |F| oracles, he is exalting and establishing Dialectic, as essential to the right understanding of himself. You will grant again, that in Dialectic this conjunctive particle has great force, because it formulates the most logical of all sentences. This is certainly the “conjunctive”, seeing that the other animals know the existence of things, but man alone has been gifted by nature with the power of observing and discerning their sequence. That “it is day” and “it is light” we may take it that wolves and dogs and birds perceive. But “if it is day it is light”, is |387| intelligible only to man; he alone can apprehend antecedent and consequent, the enunciation of each and their connexion, their mutual relation and difference, and it is in these that all demonstration has its first and governing principle. Since then Philosophy is concerned with truth, and the light of truth is demonstration, and the principle of demonstration is the conjunctive proposition, the faculty which includes and produces this was rightly consecrated by the wise men to that |B| God who is above all things a lover of truth. Also, the God is a prophet, and prophetic art deals with that future which is to come out of things present or things past. Nothing comes into being without a cause, nothing is known beforehand without a reason. Things which come into being follow things which have been, things which are to be follow things which now are coming into being, all bound in one continuous chain of evolution. Therefore he who knows how to link causes together into one, and combine them into a natural process, can also declare beforehand things
Which are, which shall be, and which were of old.[[56]]
Homer did well in putting the present first, the future next, and the past last. Inference starts with the present, and works |C| by the force of the conjunction: “If this is, that was its antecedent”, “If this is, that will be.” As we have said, the technical and logical requirement is knowledge of consequence; sense supplies the minor premiss. Hence, though it may perhaps seem a petty thing to say, I will not shrink from it; the real tripod of truth is the logical process which assumes the relation of consequent to antecedent, then introduces the fact, and so establishes the conclusion. If the Pythian God really finds pleasure in music, and in the voices of swans, and the |D| tones of the lyre, what wonder is it that as a friend to Dialectic, he should welcome and love that part of speech which he sees philosophers use more, and more often, than any other. So Hercules, when he had not yet loosed Prometheus, nor yet conversed with the sophists Chiron and Atlas, but was young and just a Boeotian, first abolished Dialectic, made a mock at the “If the first then the second”[[57]], and bethought him to remove the tripod by force, and to try conclusions with the God for his art. At any rate, as time went on, he also appears to |E| have become a great prophet and a great dialectician.’
VII. When Theon had done, I think it was Eustrophus of Athens who addressed us: ‘Do you see with what a will Theon backs Dialectic? He has only to put on the lion’s skin! Now then for you who put down under number all things in one mass, all natures and principles divine as well as human, and take it to be leader and lord in all that is beautiful and honourable! It is no time for you to keep quiet; offer to the God a first-fruits of your dear Mathematics, if you think that “E” rises above |F| the other letters, not in its own right by power or shape, or by its meaning as a word, but as the honoured symbol of an absolutely great and sovereign number, the “Pempad”, from which the Wise Men took their verb “to count”.’ Eustrophus was not jesting when he said this to us; he said it because I was at the time passionately devoted to Mathematics, though soon to find the value of the maxim, ‘NOTHING TOO MUCH‘, having joined the Academy.
VIII. So I said that Eustrophus’ solution of the problem by number was excellent. ‘For since,’ I continued, ‘when all number is divided into even and odd, unity alone is in its effect |388| common to both, and therefore, if added to an odd number makes it even, and vice versa; and since even numbers start with two, odd numbers with three, and five is produced by combination of these, it has rightly received honour as the product of first principles, and it has further been called “Marriage”, because even resembles the female, odd the male. For when we divide the several numbers into equal segments, the even parts asunder perfectly, and leaves inside a sort of recipient principle or space; if the odd is treated in the same way, a middle part is always left |B| over, which is generative. Hence the odd is the more generative, and when brought into combination invariably prevails; in no combination does it give an even result, but in all cases an odd. Moreover, when each is applied to itself and added, the difference is shown. Even with even never gives odd, or passes out of its proper nature; it wants the strength to produce anything different. Odd numbers with odd yield even numbers in |C| plenty because of their unfailing fertility. The other powers of numbers and their distinctions cannot be now pursued in detail. However, the Pythagoreans called five “Marriage”, as produced by the union of the first male number and the first female. From another point of view it has been called “Nature”, because when multiplied into itself it ends at last in itself. For as Nature takes a grain of wheat, and in the intermediate stages of growth gives forms and shapes in abundance, through which she brings her work to perfection, and, after them all, shows us again a grain of wheat, thus restoring the beginning in the end of the whole process, so it is with numbers. When other numbers are multiplied into themselves, they end in different numbers after being squared; only those formed |D| of five or of six recover and preserve themselves every time. Thus six times six gives thirty-six, five times five twenty-five. And again, a number formed of six does this only once, in the single case of being squared. Five has the same property in multiplication, and also a special property of its own when added to itself; it produces alternately itself or ten, and that to infinity. For this number mimics the principle which orders all things. As Heraclitus[[58]] tells us that Nature successively produces the universe out of herself and herself out of the universe, bartering “fire for things and things for fire, as goods for gold |E| and gold for goods”, even so it is with the Pempad. In union with itself, it does not by its nature produce anything imperfect or foreign. All its changes are defined; it either produces itself or the Decad, either the homogeneous or the perfect.
IX. ‘Then if any one ask “What is all this to Apollo?”[[59]] Much, we will answer, not to Apollo only but also to Dionysus, who has no less to do with Delphi than has Apollo. Now we |F| hear theologians saying or singing, in poems or in plain prose, that the God subsists indestructible and eternal, and that, by force of some appointed plan and method, he passes through changes of his person; at one time he sets fire to Nature and so makes all like unto all, at another passes through all phases of difference—shapes, sufferings, powers—at the present time, for instance, he becomes “Cosmos”, and that is his most familiar name. The wiser people disguise from the vulgar the change |389| into fire, and call him “Apollo[[60]]” from his isolation, “Phoebus[[61]]” from his undefiled purity. As for his passage and distribution into waves and water, and earth, and stars, and nascent plants and animals, they hint at the actual change undergone as a rending and dismemberment, but name the God himself Dionysus or Zagreus or Nyctelius or Isodaites. Deaths too and vanishings do they construct, passages out of life and new births, all riddles and tales to match the changes mentioned. So they sing to Dionysus dithyrambic strains, charged with sufferings and a change wherein are wanderings and dismemberment. |B|
In mingled cries (says Aeschylus)[[62]] the dithyramb should ring,
With Dionysus revelling, its King.