feeble person, but sound in wind and limb, and in perfect condition for the great gymnastic trial of the mind. Justice herself can find no fault with natures such as these; and they will be the saviours of our State; disciples of another sort would only make philosophy more ridiculous than she is at present. Forgive my enthusiasm; I am becoming excited; but when I see her trampled underfoot, I am angry at the authors of her disgrace. ‘I did not notice that you were more excited than you ought to have been.’ But I felt that I was. Now do not let us forget another point in the selection of our disciples—that they must be young and not old. For Solon is mistaken in saying that an old man can be always learning; youth is the time of study, and here we must remember that the mind is free and dainty, and, unlike the body, must not be made to work against the grain. Learning should be at first a sort of play, in which the natural bent is detected. As in training them for war, the young dogs should at first only taste blood; but when the necessary gymnastics are over which during two or three years divide life between sleep and bodily exercise, then the education of the soul will become a more serious matter. At twenty years of age, a selection must be made of the more promising disciples, with whom a new epoch of education will begin. The sciences which they have hitherto learned in fragments will now be brought into relation with each other and with true being; for the power of combining them is the test of speculative and dialectical ability. And afterwards at thirty a further selection shall be made of those who are able to withdraw from the world of sense into the abstraction of ideas. But at this point, judging from present experience, there is a danger that dialectic may be the source of many evils. The danger may be illustrated by a parallel case:—Imagine a person who has been brought up in wealth and luxury amid a crowd of flatterers, and who is suddenly informed that he is a supposititious son. He has hitherto honoured his reputed parents and disregarded the flatterers, and now he does the reverse. This is just what happens with a man’s principles. There are certain doctrines which he learnt at home and which exercised a parental authority over him. Presently he finds that imputations are cast upon them; a troublesome querist comes and asks, ‘What is the just and good?’ or proves that virtue is vice and vice virtue, and his mind becomes unsettled, and he ceases to love, honour, and obey them as he has hitherto done. He is seduced into the life of pleasure, and becomes a lawless person and a rogue. The case of such speculators is very pitiable, and, in order that our thirty years’ old pupils may not require this pity, let us take every possible care that young persons do not study philosophy too early. For a young man is a sort of puppy who only plays with an argument; and is reasoned into and out of his opinions every day; he soon begins to believe nothing, and brings himself and philosophy into discredit. A man of thirty does not run on in this way; he will argue and not merely contradict, and adds new honour to philosophy by the sobriety of his conduct. What time shall we allow for this second gymnastic training of the soul?—say, twice the time required for the gymnastics of the body; six, or perhaps five years, to commence at thirty, and then for fifteen years let the student go down into the den, and command armies, and gain experience of life. At fifty let him return to the end of all things, and have his eyes uplifted to the idea of good, and order his life after that pattern; if necessary, taking his turn at the helm of State, and training up others to be his successors. When his time comes he shall depart in peace to the islands of the blest. He shall be honoured with sacrifices, and receive such worship as the Pythian oracle approves.

‘You are a statuary, Socrates, and have made a perfect image of our governors.’ Yes, and of our governesses, for the women will share in all things with the men. And you will admit that our State is not a mere aspiration, but may really come into being when there shall arise philosopher-kings, one or more, who will despise earthly vanities, and will be the servants of justice only. ‘And how will they begin their work?’ Their first act will be to send away into the country all those who are more than ten years of age, and to proceed with those who are left…

At the commencement of the sixth book, Plato anticipated his explanation of the relation of the philosopher to the world in an allegory, in this, as in other passages, following the order which he prescribes in education, and proceeding from the concrete to the abstract. At the commencement of Book VII, under the figure of a cave having an opening towards a fire and a way upwards to the true light, he returns to view the divisions of knowledge, exhibiting familiarly, as in a picture, the result which had been hardly won by a great effort of thought in the previous discussion; at the same time casting a glance onward at the dialectical process, which is represented by the way leading from darkness to light. The shadows, the images, the reflection of the sun and stars in the water, the stars and sun themselves, severally correspond,—the first, to the realm of fancy and poetry,—the second, to the world of sense,—the third, to the abstractions or universals of sense, of which the mathematical sciences furnish the type,—the fourth and last to the same abstractions, when seen in the unity of the idea, from which they derive a new meaning and power. The true dialectical process begins with the contemplation of the real stars, and not mere reflections of them, and ends with the recognition of the sun, or idea of good, as the parent not only of light but of warmth and growth. To the divisions of knowledge the stages of education partly answer:—first, there is the early education of childhood and youth in the fancies of the poets, and in the laws and customs of the State;—then there is the training of the body to be a warrior athlete, and a good servant of the mind;—and thirdly, after an interval follows the education of later life, which begins with mathematics and proceeds to philosophy in general.

There seem to be two great aims in the philosophy of Plato,—first, to realize abstractions; secondly, to connect them. According to him, the true education is that which draws men from becoming to being, and to a comprehensive survey of all being. He desires to develop in the human mind the faculty of seeing the universal in all things; until at last the particulars of sense drop away and the universal alone remains. He then seeks to combine the universals which he has disengaged from sense, not perceiving that the correlation of them has no other basis but the common use of language. He never understands that abstractions, as Hegel says, are ‘mere abstractions’—of use when employed in the arrangement of facts, but adding nothing to the sum of knowledge when pursued apart from them, or with reference to an imaginary idea of good. Still the exercise of the faculty of abstraction apart from facts has enlarged the mind, and played a great part in the education of the human race. Plato appreciated the value of this faculty, and saw that it might be quickened by the study of number and relation. All things in which there is opposition or proportion are suggestive of reflection. The mere impression of sense evokes no power of thought or of mind, but when sensible objects ask to be compared and distinguished, then philosophy begins. The science of arithmetic first suggests such distinctions. The follow in order the other sciences of plain and solid geometry, and of solids in motion, one branch of which is astronomy or the harmony of the spheres,—to this is appended the sister science of the harmony of sounds. Plato seems also to hint at the possibility of other applications of arithmetical or mathematical proportions, such as we employ in chemistry and natural philosophy, such as the Pythagoreans and even Aristotle make use of in Ethics and Politics, e.g. his distinction between arithmetical and geometrical proportion in the Ethics (Book V), or between numerical and proportional equality in the Politics.

The modern mathematician will readily sympathise with Plato’s delight in the properties of pure mathematics. He will not be disinclined to say with him:—Let alone the heavens, and study the beauties of number and figure in themselves. He too will be apt to depreciate their application to the arts. He will observe that Plato has a conception of geometry, in which figures are to be dispensed with; thus in a distant and shadowy way seeming to anticipate the possibility of working geometrical problems by a more general mode of analysis. He will remark with interest on the backward state of solid geometry, which, alas! was not encouraged by the aid of the State in the age of Plato; and he will recognize the grasp of Plato’s mind in