h in war and peace, are to be common, and kings are to be philosophers and warriors, and the soldiers of the State are to live together, having all things in co

on, and do you repeat your question. 'I should like to know of what constitutions you were speaking?' Besides the perfect State there are only four of any note in Hellas:- first, the famous Lacedaemonian or Cretan commonwealth; secondly, oligarchy, a State full of evils; thirdly, democracy, which follows next in order; fourthly, tyranny, which is the disease or death of all government. Now, States are not made of 'oak and rock,' but of flesh and blood; and therefore as there are five States there must be five human natures in individuals, which correspond to them. And first, there is the ambitiou

four terms and three intervals of numbers, increasing, waning, assimilating, dissimilating, and yet perfectly commensurate with each other. The base of the number with a fourth added (or which is 3:4), multiplied by five and cubed, gives two harmonies:- the first a square number, which is a hundred times the base (or a hundred times a hundred); the second, an oblong, being a hundred squares of the rational diameter of a figure the side of which is five, subtracting one from each square or two perfect squares from all, and adding a hundred cubes of three. This entire number is geometrical and contains the rule or law of generation. When this law is neglected marriages will be unpropitious; the inferior offspring who are then born will in time become the rulers; the State will decline, and education fall into decay; g

litary class. Arts of war begin to prevail over arts of peace; the ruler is no longer a philosopher; as in oligarchies, there springs up among them an extravagant love of gain - get another man's and save your own, is their principle; and they have dark places in which they hoard their gold and sil

rows avaricious, for he has lost philosophy, which is the only saviour and guardian of men. His origin is as follows:- His father is a good man dwelling in an ill-ordered State, who has retired from politics in order that he may lead a quiet life. His mother is angry at her loss of precedence among other women; she is disgusted at her husband's selfishness, and she expatiates to her son on the unmanliness and indolence of his father. The old family ser

e decline begins with the possession of gold and silver; illegal modes of expenditure are invented; one draws another on, and the multitude are infected; riches outweigh virtue; lovers of money

nd have we not already condemned that State in which the same persons are warriors as well as shopkeepers? The greatest evil of all is that a man may sell his property and have no place in the State; while there is one class which has enormous wealth, the other is entirely destitute. But observe that these destitutes had not really any more of the governing nature in them when they were rich than now that they are poor; they were miserable spendthrifts always. They are the

l and spirited elements sit humbly on the ground at either side, the one immersed in calculation, the other absorbed in the admiration of wealth. The love of honour turns to love of money; the conversion is instantaneous. The man is mean, saving, toiling, the slave of one passion which is the master of the rest: Is he not the very image of the State? He has had no education, or he would never have allowed the blind god of riches to lead the dance within him. And being uneducated he will have many slavish desires, some beggarly, some k

n has to pay the parent or principal sum multiplied into a family of children, and is reduced into a state of dronage by him. The only way of diminishing the evil is either to limit a man in his use of his property, or to insist that he shall lend at his own risk. But the ruling class do not want remedies; they care only for money, and are as careless of virtue as the poorest of the citizens. Now there are occasions on which the governors and the governed meet together - at festivals, on a journey, voyaging or fighting. The sturdy pauper finds that in the hour of dan

auty and excellence. The State is not one but many, like a bazaar at which you can buy anything. The great charm is, that you may do as you like; you may govern if you like, let it alone if you like; go to war and make peace if you feel disposed, and all quite irrespective of anybody else. When you condemn men to death they remain alive all the same; a gentleman is desired to go into exile, and he stalks ab

which are good, and which we cannot do without; unnecessary pleasures are those which do no good, and of which the desire might be eradicated by early training. For example, the pleasures of eating and drinking are necessary and healthy, up to a certain point; beyond that point they are alike hurtfu

rks. Falsehoods and illusions ascend to take their place; the prodigal goes back into the country of the Lotophagi or drones, and openly dwells there. And if any offer of alliance or parley of individual elders comes from home, the false spirits shut the gates of the castle and permit no one to enter - there is a battle, and they gain the victory; and straightway making alliance with the desires, they banish modesty, which they call folly, and send temperance over the border. When the house has been swept and garnished, they dress up the exiled vices, and, crowning them with garlands, bring them back under new names. Insolence they call good breeding, anarchy freedom, waste magnificence, impudence courage. Such is the process by which the yo

by starts and

citizens become so sensitive that they cannot endure the yoke of laws, written or unwritten; they would have no man call himself their master. Such is the glorious beginning of things out of which tyranny springs. 'Glorious, indeed; but what is to follow?' The ruin of oligarchy is the ruin of democracy; for there is a law of contraries; the excess of freedom passes into the excess of slavery, and the greater the freedom the greater the slavery. You will remember that in the oligarchy were found two classes - rogues and paupers, whom we compared to drones with and without stings. These two classes are to the State what phlegm and bile are to the human body; and the State-physician, or legislator, must get rid of them, just as the bee-master keeps the drones out of the hive. Now in a democracy, too, there are drones, but they are more numerous and more dangerous than in the oligarchy; there they are inert and unpractised, here they are full of life and animation; and the keener sort speak and act, while the others buzz about the bema and prevent their opponents from being heard. And there is another class in democratic States, of respectable, thriving individuals, who can be squeezed when the drones have need of their possessions; there is moreover a third class, who are the labourers and the artisans, and they make up the mass of the people. When the people meet, they are omnipotent, but they cannot be brought together unless they are

ain them? 'They will come flocking like birds - for pay.' Will he not rather obtain them on the spot? He will take the slaves from their owners and make them his body-guard; these are his trusted friends, who admire and look up to him. Are not the tragic poets wise who magnify and exalt the tyrant, and say that he is wise by association with the wise? And are not their praises of tyranny alone a sufficient reason why we should exclude them from our State? They may go to other cities, and gather the mob about them with fine words, and change commonwealths into tyrannies and democracies, receiving honours and rewards for their services; but the higher they and their friends ascend constitution hill, the more their honour will fail and become 'too asthmatic to mount.' To return to the tyrant - How will he support that rare army of h

scribes in a succession of parallels between the individuals and the States, tracing the origin of either in the State or individual which has preceded them. He begins by asking

is the expression. Like the ancients in general, he had no idea of the gradual perfectibility of man or of the education of the human race. His ideal was not to be attained in the course of ages, but was to spring in full armour from the head of the legislator. When good laws had been given, he thought only of the manner in which they were likely to be corrupted, or of how they might be filled up in detail or restored in accordance with t

e, rules in his stead. The individual who answers to timocracy has some noticeable qualities. He is described as ill educated, but, like the Spartan, a lover of literature; and although he is a harsh master to his servants he has no natural superiority over them. His character is based upon a reaction against the circumstances of his father, who in a troubled city has retired from politics; and his mother, who is di

operty, which, according to Aristotle's mode of using words, would have been called a timocracy; and this in some cities, as at Athens, became the conducting medium to democracy. But such was not the necessary order of succession in States; nor, indeed, can any order be discerned in the endless fluctuation of Greek history (like the tides in the Euripus), except, perhaps, in the almost uniform tendency from monarchy to aristocracy in the earliest times. At first sight there appears to be a similar inversion in the last step of the Platonic succession; for tyranny, instead of being the natural end of democracy, in early Greek history appears rather as a stage

e tyrant was the negation of government and law; his assassination was glorious; there was no crime, however unnatural, which might not with probability be attributed to him. In this, Plato was only following the common thought of his countrymen, which he embellished and exaggerated with all the power of his genius. There is no need to sup

cy in Herodotus and Thucydides, he never seems to think. But if he is not a believer in liberty, still less is he a lover of tyranny. His deeper and more serious condemnation is reserved for the tyrant, who is the ideal of wickedness and also of weakness, and who in his utter helplessness and suspiciousness is leading an almost impossible existence, without that remnant of good

y, upon the love of honour; this latter virtue, which is hardly to be esteemed a virtue, has superseded all the rest. In the second stage of decline the virtues have altogether 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

fanciful allusions; the use of metaphorical language is carrie

ch become more and more divided in the Greek Republ

essed in a sort of Pythagorean fo

hich are characteristic of liberty, as foreign me

law in modern times, and is in harmony with the tendencies of modern legislation. Debt and land were the two great difficulties of the an

e 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 an obscene dream; the rhetorical surprise of a more

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.), 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 i

ek) describes a solid figure. (Pol. -'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 n

to figures, and finds in them when they have been raised to the third power certain elements of number, which give two 'harmonies,' the one square, the other oblong; but he does not say that the square number answers to the divine, or the oblong number to the human cycle; nor is any intimation given that the first or divine number represents the period of the world, the second the period of th

'; the mysterious disappearance of the Spartan population may possibly have suggested to him the first cause of his decline of States. The lesser or square 'harmony,' of 400, might be a symbol of the guardians - the larger or oblong 'harmony,' of the people, and the numbers 3, 4, 5 might refer respectively to the three or

present are or are not in the same ratio: e.g. 8 and 27 = 2 cubed and 3 cubed; and conversely. 'Waxing' (Greek) numbers, called also 'increasing' (Greek), are those which are exceeded by the sum of their divisors: e.g. 12 and 18 are less than 16 and 21. 'Waning' (Greek) numbers, called also 'decreasing' (Greek) are those which succeed the sum of their divisors: e.g. 8 and 27 exceed 7 and 13. The words translated 'commensurable and agreeable to one another' (Greek) seem to be different ways of describing the same relation, with more or less precision. They are equivalent to 'expressible in terms having the same relation to one another,' like the series 8, 12, 18, 27, each of which numbers is in the relation of (1 and 1/2) to the preceding. The 'base,' or 'fundamental number, which has 1/3 added to it' (1 and 1/

ted to one another in the sesqui-altera ratio, i.e. each term is to the preceding as 3/2. Now if we remember that the number 216 = 8 x 27 = 3 cubed + 4 cubed + 5 cubed, and 3 squared + 4 squared = 5 squared, we must admit that this number implies the numbers 3, 4, 5, to which musicians attach so much importance. And if we combine the ratio 4/3 with the number 5, or multiply the ratios of the sides by the hypotenuse, we shall by first squaring and then cubing obtain two expressions, which denote the ratio of the two last pairs of terms in the Platonic Tetractys, the former multiplied by the square, the latter by the cube of the number 10, the sum of the first four digits which constitute the Platonic Tetractys.' The two (Gre

f 6, and also the sum of 3 cubed, 4 cubed, 5 cubed, the numbers 3, 4, 5 representing the Pythagorean triangle, of which the sides when squared equal the square of the hypotenuse (9 + 16 = 25): (4) that it is also the period of the Pythagorean Metempsychosis: (5) the three ultimate terms or bases (3, 4, 5) of which 216 is composed answer to the third, fourth, fifth in the musical scale: (6) that the number 216

r the state; nor has he given any proof that the second harmony is a cube. Nor do I think that (Greek) can mean 'two incommensurables,' which he arbitrarily assumes to

mewhat forced manner Plato introduces once more the numbers of the Pythagorean triangle. But the coincidences in the numbers which follow are in favour of

namely, the convenience of the number for division; it is also made up of the first seven digits multiplied by one another. The contrast of the perfect and imperfect number may have been easily suggested by the corrections of the cycle, which were made first by Meton and secondly by Callippus; (the latter is said to have been a pupil of Plato). Of the degree of importance or of exactness to be attributed to the problem, the number of the tyrant in Book IX (729 = 365 x 2), and the slight correction of the error in the number 5040/12 (Laws), may furnish a criterion. There is nothing surprising in the circumstance that th