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disappeared, and the love of gain has succeeded to them ; in the third stage, or democracy, the various passions are allowed to have free play, and the virtues and vices are impartially cultivated. But this freedom, which leads to many curious extravagances of character, is in reality only a state of weakness and dissipation. At last, one monster passion takes possession of the whole nature of man — this is tyranny.

In all of them excess — the excess first of wealth and then of freedom, is the element of decay. The eighth book of the Republic abounds in pictures of life and fanciful allusions ; the use of metaphorical language is carried to a greater extent than anywhere else in Plato.

We may remark, (i), the description of the two nations in one, which become more and more divided in the Greek Republics, as in feudal times, and perhaps also in our own ; (2), the notion of democracy expressed in a sort of Pythagorean formula as equality among unequals; (3), the free and easy ways of men and animals, which are characteristic of liberty, as foreign mercenaries and universal mistrust are of the tyrant ; (4), the proposal that mere debts should not be recoverable by law is a speculation which has often been entertained by reformers of the law in modern times, and is in harmony with the tendencies of modern legislation.

Debt and land were the two great difficulties of the ancient lawgiver : in modern times we may be said to have almost, if not quite, solved the first of these difficulties, but hardly the second.

Still more remarkable are the corresponding portraits of individuals: there is the family picture of the father and mother and the old servant of the timocratical man, and the outward respectability and inherent meanness of the oligarchical ; the uncontrolled licence and freedom of the democrat, in which the young Alcibiades seems to be depicted, doing right or wrong as he pleases, and who at last, like the prodigal, goes into a far country (note here the play of language by which the democratic man is himself represented under the image of a State having a citadel and receiving embassies) ; and there is the wild-beast nature, which breaks loose in his successor. The hit about the tyrant being a parricide; the representation of the tyrant's life as VOL. III. — 9 an obscene dream ; the rhetorical surprise of a more miserable than the most miserable of men in Book ix ; the hint to the poets that if they are the friends of tyrants there is no place for them in a constitutional State, and that they are too clever not to see the propriety of their own expulsion ; the continuous image of the drones who are of two kinds, swelling at last into the monster drone having wings (see infra, Book ix), — are among Plato's happiest touches.

There remains to be considered the great difficulty of this book of the Republic, the so-called number of the State. This is a puzzle almost as great as the Number of the Beast in the Book of Revelation, and though apparently known to Aristotle, is referred to by Cicero as a proverb of obscurity (Ep. ad. Att. vii. 13, 5). And some have imagined that there is no answer to the puzzle, and that Plato has been practising upon his readers.

But such a deception as this is inconsistent with the manner in which Aristotle speaks of the number (Pol. v. 12, § 7), and would have been ridiculous to any reader of the Republic who was acquainted with Greek mathematics. As little reason is there for supposing that Plato intentionally used obscure expressions ; the obscurity arises from our want of familiarity with the subject.

' On the other hand, Plato himself indicates that he is not altogether serious, and in describing his number as a solemn jest of the Muses, he appears to imply some degree of satire on the symbolical use of number. (Cp. Cratylus, passitnj Protag. 342 ff.) Our hope of understanding the passage depends principally on an accurate study of the words themselves ; on which a faint light is thrown by the parallel passage in the ninth book.

Another help is the allusion in Aristotle, who makes the important remark that the latter part of the passage (from wv eTzirpiTog nv6fj.?)v, k. t. /..) describes a solid figure^. Some further clue may be gathered from the appearance of the Pythagorean triangle, which is denoted by the numbers 3, 4, 5, and in which, as in every right-angled

1 Pol. V. 12, $ 8 : — ' He only says that nothing is abiding, but that all things change in a certain cycle; and that the origin of the change is a base of numbers which are in the ratio of 4 : 3 ; and this when combined with a figure of five gives two harmonies ; he means when the number of this figure becomes solid.*

The Number of the State.

CXXXl

Introdic- TION.

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