Aristotle we note the illusion under which the ancients fell of regarding the transience of pleasure as a proof of its unreality, and of confounding the permanence of the intellectual pleasures with the unchangeableness of the knowledge from which they are derived. Neither do we like to admit that the pleasures of knowledge, though more elevating, are not more lasting than other pleasures, and are almost equally dependent on the accidents of our bodily state (Introduction to Philebus).

The number of the interval which separates the king from the tyrant, and royal from tyrannical pleasures, is 729, the cube of 9. Which Plato characteristically designates as a number concerned with human life, because NEARLY equivalent to the number of days and nights in the year. He is desirous of proclaiming that the interval between them is immeasurable, and invents a formula to give expression to his idea. Those who spoke of justice as a cube, of virtue as an art of measuring (Prot.), saw no inappropriateness in conceiving the soul under the figure of a line, or the pleasure of the tyrant as separated from the pleasure of the king by the numerical interval of 729. And in modern times we sometimes use metaphorically what Plato employed as a philosophical formula. ‘It is not easy to estimate the loss of the tyrant, except perhaps in this way,’ says Plato. So we might say, that although the life of a good man is not to be compared to that of a bad man, yet you may measure the difference between them by valuing one minute of the one at an hour of the other (‘One day in thy courts is better than a thousand’), or you might say that ‘there is an infinite difference.’ But this is not so much as saying, in homely phrase, ‘They are a thousand miles asunder.’ And accordingly Plato finds the natural vehicle of his thoughts in a progression of numbers; this arithmetical formula he draws out with the utmost seriousness, and both here and in the number of generation seems to find an additional proof of the truth of his speculation in forming the number into a geometrical figure; just as persons in our own day are apt to fancy that a statement is verified when it has been only thrown into an abstract form. In speaking of the number 729 as proper to human life, he probably intended to intimate that one year of the tyrannical = 12 hours of the royal life.

The simple observation that the comparison of two similar solids is effected by the comparison of the cubes of their sides, is the mathematical groundwork of this fanciful expression. There is some difficulty in explaining the steps by which the number 729 is obtained; the oligarch is removed in the third degree from the royal and aristocratical, and the tyrant in the third degree from the oligarchical; but we have to arrange the terms as the sides of a square and to count the oligarch twice over, thus reckoning them not as = 5 but as = 9. The square of 9 is passed lightly over as only a step towards the cube.

3. Towards the close of the Republic, Plato seems to be more and more convinced of the ideal character of his own speculations. At the end of the 9th Book the pattern which is in heaven takes the place of the city of philosophers on earth. The vision which has received form and substance at his hands, is now discovered to be at a distance. And yet this distant kingdom is also the rule of man’s life. (‘Say not lo! here, or lo! there, for the kingdom of God is within you.’) Thus a note is struck which prepares for the revelation of a future life in the following Book. But the future life is present still; the ideal of politics is to be realized in the individual.

Book X.

Many things pleased me in the order of our State, but there was nothing which I liked better than the regulation about poetry. The division of the soul throws a new light on our exclusion of imitation. I do not mind telling you in confidence that all poetry is an outrage on the understanding, unless the hearers have that balm of knowledge which heals error. I have loved Homer ever since I was a boy, and even now he appears to me to be the great master of tragic poetry. But much as I love the man, I love truth more, and therefore I must speak out: and first of all, will you explain what is imitation, for really I do not understand? ‘How likely then that I should understand!’ That might very well be, for the duller often sees better than the keener eye. ‘True, but in your presence I can hardly venture to say what I think.’ Then suppose that we begin in our old fashion, with the doctrine of universals. Let us assume the existence of beds and tables. There is one idea of a bed, or of a table, which the maker of each had in his mind when making them; he did not make the ideas of beds and tables, but he made beds and tables according to the ideas. And is there not a maker of the works of all workmen, who makes not only vessels but plants and animals, himself, the earth and heaven, and things in heaven and under the earth? He makes the Gods also. ‘He must be a wizard indeed!’ But do you not see that there is a sense in which you could do the same? You have only to take a mirror, and catch the reflection of the sun, and the earth, or anything else—there now you have made them. ‘Yes, but only in appearance.’ Exactly so; and the painter is such a creator as you are with the mirror, and he is even more unreal than the carpenter; although neither the carpenter nor any other artist can be supposed to make the absolute bed. ‘Not if philosophers may be believed.’ Nor need we wonder that his bed has but an imperfect relation to the truth. Reflect:—Here are three beds; one in nature, which is made by God; another, which is made by the carpenter; and the third, by the painter. God only made one, nor could he have made more than one; for if there had been two, there would always have been a third—more absolute and abstract than either, under which they would have been included. We may therefore conceive God to be the natural maker of the bed, and in a lower sense the carpenter is also the maker; but the painter is rather the imitator of what the other two make; he has to do with a creation which is thrice removed from reality. And the tragic poet is an imitator, and, like every other imitator, is thrice removed from the king and from the truth. The painter imitates not the original bed, but the bed made by the carpenter. And this, without being really different, appears to be different, and has many points of view, of which only one is caught by the painter, who represents everything because he represents a piece of everything, and that piece an image. And he can paint any other artist, although he knows nothing of their arts; and this with sufficient skill to deceive children or simple people. Suppose now that somebody came to us and told us, how he had met a man who knew all that everybody knows, and better than anybody:—should we not infer him to be a simpleton who, having no discernment of truth and falsehood, had met with a wizard or enchanter, whom he fancied to be all-wise? And when we hear persons saying that Homer and the tragedians know all the arts and all the virtues, must we not infer that they are under a similar delusion? they do not see that the poets are imitators, and that their creations are only imitations. ‘Very true.’ But if a person could create as well as imitate, he would rather leave some permanent work and not an imitation only; he would rather be the receiver than the giver of praise? ‘Yes, for then he would have more honour and advantage.’

Let us now interrogate Homer and the poets. Friend Homer, say I to him, I am not going to ask you about medicine, or any art to which your poems incidentally refer, but about their main subjects—war, military tactics, politics. If you are only twice and not thrice removed from the truth—not an imitator or an image-maker, please to inform us what good you have ever done to mankind? Is there any city which professes to have received laws from you, as Sicily and Italy have from Charondas, Sparta from Lycurgus, Athens from Solon? Or was any war ever carried on by your counsels? or is any invention attributed to you, as there is to Thales and Anacharsis? Or is there any Homeric way of life, such as the Pythagorean was, in which you instructed men, and which is called after you? ‘No, indeed; and Creophylus (Flesh-child) was even more unfortunate in his breeding than he was in his name, if, as tradition says, Homer in his lifetime was allowed by him and his other friends to starve.’ Yes, but could this ever have happened if Homer had really been the educator of Hellas? Would he not have had many devoted followers? If Protagoras and Prodicus