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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 his ability to conceive of one
science of solids in motion including the earth as well as the
heavens,—not forgetting to notice the intimation to which allusion has
been already made, that besides astronomy and harmonics the science of
solids in motion may have other applications. Still more will he be
struck with the comprehensiveness of view which led Plato, at a time
when these sciences hardly existed, to say that they must be studied in
relation to one another, and to the idea of good, or common principle
of truth and being. But he will also see (and perhaps without surprise)
that in that stage of physical and mathematical knowledge, Plato has
fallen into the error of supposing that he can construct the heavens a
priori by mathematical problems, and determine the principles of
harmony irrespective of the adaptation of sounds to the human ear. The
illusion was a natural one in that age and country. The simplicity and
certainty of astronomy and harmonics seemed to contrast with the
variation and complexity of the world of sense; hence the circumstance
that there was some elementary basis of fact, some measurement of
distance or time or vibrations on which they must ultimately rest, was
overlooked by him. The modern predecessors of Newton fell into errors
equally great; and Plato can hardly be said to have been very far
wrong, or may even claim a sort of prophetic insight into the subject,
when we consider that the greater part of astronomy at the present day
consists of abstract dynamics, by the help of which most astronomical
discoveries have been made.

The metaphysical philosopher from his point of view recognizes
mathematics as an instrument of education,—which strengthens the power
of attention, developes the sense of order and the faculty of
construction, and enables the mind to grasp under simple formulae the
quantitative differences of physical phenomena. But while acknowledging
their value in education, he sees also that they have no connexion with
our higher moral and intellectual ideas. In the attempt which Plato
makes to connect them, we easily trace the influences of ancient
Pythagorean notions. There is no reason to suppose that he is speaking
of the ideal numbers; but he is describing numbers which are pure
abstractions, to which he assigns a real and separate existence, which,
as ‘the teachers of the art’ (meaning probably the Pythagoreans) would
have affirmed, repel all attempts at subdivision, and in which unity
and every other number are conceived of as absolute. The truth and
certainty of numbers, when thus disengaged from phenomena, gave them a
kind of sacredness in the eyes of an ancient philosopher. Nor is it
easy to say how far ideas of order and fixedness may have had a moral
and elevating influence on the minds of men, ‘who,’ in the words of the
Timaeus, ‘might learn to regulate their erring lives according to
them.’ It is worthy of remark that the old Pythagorean ethical symbols
still exist as figures of speech among ourselves. And those who in
modern times see the world pervaded by universal law, may also see an
anticipation of this last word of modern philosophy in the Platonic
idea of good, which is the source and measure of all things, and yet
only an abstraction (Philebus).

Two passages seem to require more particular explanations. First, that
which relates to the analysis of vision. The difficulty in this passage
may be explained, like many others, from differences in the modes of
conception prevailing among ancient and modern thinkers. To us, the
perceptions of sense are inseparable from the act of the mind which
accompanies them. The consciousness of form, colour, distance, is
indistinguishable from the simple sensation, which is the medium of
them. Whereas to Plato sense is the Heraclitean flux of sense, not the
vision of objects in the order in which they actually present
themselves to the experienced sight, but as they may be imagined to
appear confused and blurred to the half-awakened eye of the infant. The
first action of the mind is aroused by the attempt to set in order this
chaos, and the reason is required to frame distinct conceptions under
which the confused impressions of sense may be arranged. Hence arises
the question, ‘What is great, what is small?’ and thus begins the
distinction of the visible and the intelligible.

The second difficulty relates to Plato’s conception of harmonics. Three
classes of harmonists are distinguished by him:—first, the
Pythagoreans, whom he proposes to consult as in the previous discussion
on music he was to consult Damon—they are acknowledged to be masters in
the art, but are altogether deficient in the knowledge of its higher
import and relation to the good; secondly, the mere empirics, whom
Glaucon appears to confuse with them, and whom both he and Socrates
ludicrously describe as experimenting by mere auscultation on the
intervals of sounds. Both of these fall short in different degrees of
the Platonic idea of harmony, which must be studied in a purely
abstract way, first by the method of problems, and secondly as a part
of universal knowledge in relation to the idea of good.

The allegory has a political as well as a philosophical meaning. The
den or cave represents the narrow sphere of politics or law (compare
the description of the philosopher and lawyer in the Theaetetus), and
the light of the eternal ideas is supposed to exercise a disturbing
influence on the minds of those who return to this lower world. In
other words, their principles are too wide for practical application;
they are looking far away into the past and future, when their business
is with the present. The ideal is not easily reduced to the conditions
of actual life, and may often be at variance with them. And at first,
those who return are unable to compete with the inhabitants of the den
in the measurement of the shadows, and are derided and persecuted by
them; but after a while they see the things below in far truer
proportions than those who have never ascended into the upper world.
The difference between the politician turned into a philosopher and the
philosopher turned into a politician, is symbolized by the two kinds of
disordered eyesight, the one which is experienced by the captive who is
transferred from darkness to day, the other, of the heavenly messenger
who voluntarily for the good of his fellow-men descends into the den.
In what way the brighter light is to dawn on the inhabitants of the
lower world, or how the idea of good is to become the guiding principle
of politics, is left unexplained by Plato. Like the nature and
divisions of dialectic, of which Glaucon impatiently demands to be
informed, perhaps he would have said that the explanation could not be
given except to a disciple of the previous sciences. (Symposium.)

Many illustrations of this part of the Republic may be found in modern
Politics and in daily life. For among ourselves, too, there have been
two sorts of Politicians or Statesmen, whose eyesight has become
disordered in two different ways. First, there have been great men who,
in the language of Burke, ‘have been too much given to general maxims,’
who, like J.S. Mill or Burke himself, have been theorists or
philosophers before they were politicians, or who, having been students
of history, have allowed some great historical parallel, such as the
English Revolution of 1688, or possibly Athenian democracy or Roman
Imperialism, to be the medium through which they viewed contemporary
events. Or perhaps the long projecting shadow of some existing
institution may have darkened their vision. The Church of the future,
the Commonwealth of the future, the Society of the future, have so
absorbed their minds, that they are unable to see in their true
proportions the Politics of to-day. They have been intoxicated with
great ideas, such as liberty, or equality, or the greatest happiness of
the greatest number, or the brotherhood of humanity, and they no longer
care to consider how these ideas must be limited in practice or
harmonized with the conditions of human life. They are full of light,
but the light to them has become only a sort of luminous mist or
blindness. Almost every one has known some enthusiastic half-educated
person, who sees everything at false distances, and in erroneous
proportions.

With this disorder of eyesight may be contrasted another—of those who
see not far into the distance, but what is near only; who have been
engaged all their lives in a trade or a profession; who are limited to
a set or sect of their own. Men of this kind have no universal except
their own interests or the interests of their class, no principle but
the opinion of persons like themselves, no knowledge of affairs beyond
what they pick up in the streets or at their club. Suppose them to be
sent into a larger world, to undertake some higher calling, from being
tradesmen to turn generals or politicians, from being schoolmasters to
become philosophers:—or imagine them on a sudden to receive an inward
light which reveals to them for the first time in their lives a higher
idea of God and the existence of a spiritual world, by this sudden
conversion or change is not their daily life likely to be upset; and on
the other hand will not many of their old prejudices and narrownesses
still adhere to them long after they have begun to take a more
comprehensive view of human things? From familiar examples like these
we may learn what Plato meant by the eyesight which is liable to two
kinds of disorders.

Nor have we any difficulty in drawing a parallel between the young
Athenian in the fifth century before Christ who became unsettled by new
ideas, and the student of a modern University who has been the subject
of a similar ‘aufklärung.’ We too observe that when young men begin to
criticise customary beliefs, or to analyse the constitution of human
nature, they are apt to lose hold of solid principle (ἅπαν τὸ βέβαιον
αὐτῶν ἐξοίχεται). They are like trees which have been frequently
transplanted. The earth about them is loose, and they have no roots
reaching far into the soil. They ‘light upon every flower,’ following
their own wayward wills, or because the wind blows them. They catch
opinions, as diseases are caught—when they are in the air. Borne hither
and thither, ‘they speedily fall into beliefs’ the opposite of those in
which they were brought up. They hardly retain the distinction of right
and wrong; they seem to think one thing as good as another. They
suppose themselves to be searching after truth when they are playing
the game of ‘follow my leader.’ They fall in love ‘at first sight’ with
paradoxes respecting morality, some fancy about art, some novelty or
eccentricity in religion, and like lovers they are so absorbed for a
time in their new notion that they can think of nothing else. The
resolution of some philosophical or theological question seems to them
more interesting and important than any substantial knowledge of
literature or science or even than a good life. Like the youth in the
Philebus, they are ready to discourse to any one about a new
philosophy. They are generally the disciples of some eminent professor
or sophist, whom they rather imitate than understand. They may be
counted happy if in later years they retain some of the simple truths
which they acquired in early education, and which they may, perhaps,
find to be worth all the rest. Such is the picture which Plato draws
and which we only reproduce, partly in his own words, of the dangers
which beset youth in times of transition, when old opinions are fading
away and the new are not yet firmly established. Their condition is
ingeniously compared by him to that of a supposititious son, who has
made the discovery that his reputed parents are not his real ones, and,
in consequence, they have lost their authority over him.

The distinction between the mathematician and the dialectician is also
noticeable. Plato is very well aware that the faculty of the
mathematician is quite distinct from the higher philosophical sense
which recognizes and combines first principles. The contempt which he
expresses for distinctions of words, the danger of involuntary
falsehood, the apology which Socrates makes for his earnestness of
speech, are highly characteristic of the Platonic style and mode of
thought. The quaint notion that if Palamedes was the inventor of number
Agamemnon could not have counted his feet; the art by which we are made
to believe that this State of ours is not a dream only; the gravity
with which the first step is taken in the actual creation of the State,
namely, the sending out of the city all who had arrived at ten years of
age, in order to expedite the business of education by a generation,
are also truly Platonic. (For the last, compare the passage at the end
of the third book, in which he expects the lie about the earthborn men
to be believed in the second generation.)

BOOK VIII. And so we have arrived at the conclusion, that in the
perfect State wives and children are to be in common; and the education
and pursuits of men and women, both 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 common; and they are
to be warrior athletes, receiving no pay but only their food, from the
other citizens. Now let us return to the point at which we digressed.
‘That is easily done,’ he replied: ‘You were speaking of the State
which you had constructed, and of the individual who answered to this,
both of whom you affirmed to be good; and you said that of inferior
States there were four forms and four individuals corresponding to
them, which although deficient in various degrees, were all of them
worth inspecting with a view to determining the relative happiness or
misery of the best or worst man. Then Polemarchus and Adeimantus
interrupted you, and this led to another argument,—and so here we are.’
Suppose that we put ourselves again in the same position, 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 ambitious nature, which answers to the Lacedaemonian
State; secondly, the oligarchical nature; thirdly, the democratical;
and fourthly, the tyrannical. This last will have to be compared with
the perfectly just, which is the fifth, that we may know which is the
happier, and then we shall be able to determine whether the argument of
Thrasymachus or our own is the more convincing. And as before we began
with the State and went on to the individual, so now, beginning with
timocracy, let us go on to the timocratical man, and then proceed to
the other forms of government, and the individuals who answer to them.

But how did timocracy arise out of the perfect State? Plainly, like all
changes of government, from division in the rulers. But whence came
division? ‘Sing, heavenly Muses,’ as Homer says;—let them condescend to
answer us, as if we were children, to whom they put on a solemn face in
jest. ‘And what will they say?’ They will say that human things are
fated to decay, and even the perfect State will not escape from this
law of destiny, when ‘the wheel comes full circle’ in a period short or
long. Plants or animals have times of fertility and sterility, which
the intelligence of rulers because alloyed by sense will not enable
them to ascertain, and children will be born out of season. For whereas
divine creations are in a perfect cycle or number, the human creation
is in a number which declines from perfection, and has 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;
gymnastic will be preferred to music, and the gold and silver and brass
and iron will form a chaotic mass—thus division will arise. Such is the
Muses’ answer to our question. ‘And a true answer, of course:—but what
more have they to say?’ They say that the two races, the iron and
brass, and the silver and gold, will draw the State different ways;—the
one will take to trade and moneymaking, and the others, having the true
riches and not caring for money, will resist them: the contest will end
in a compromise; they will agree to have private property, and will
enslave their fellow-citizens who were once their friends and
nurturers. But they will retain their warlike character, and will be
chiefly occupied in fighting and exercising rule. Thus arises
timocracy, which is intermediate between aristocracy and oligarchy.

The new form of government resembles the ideal in obedience to rulers
and contempt for trade, and having common meals, and in devotion to
warlike and gymnastic exercises. But corruption has crept into
philosophy, and simplicity of character, which was once her note, is
now looked for only in the military 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 silver, for the use
of their women and others; they take their pleasures by stealth, like
boys who are running away from their father—the law; and their
education is not inspired by the Muse, but imposed by the strong arm of
power. The leading characteristic of this State is party spirit and
ambition.

And what manner of man answers to such a State? ‘In love of
contention,’ replied Adeimantus, ‘he will be like our friend Glaucon.’
In that respect, perhaps, but not in others. He is self-asserting and
ill-educated, yet fond of literature, although not himself a
speaker,—fierce with slaves, but obedient to rulers, a lover of power
and honour, which he hopes to gain by deeds of arms,—fond, too, of
gymnastics and of hunting. As he advances in years he grows 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 servant takes up the tale, and says to the youth:—‘When
you grow up you must be more of a man than your father.’ All the world
are agreed that he who minds his own business is an idiot, while a
busybody is highly honoured and esteemed. The young man compares this
spirit with his father’s words and ways, and as he is naturally well
disposed, although he has suffered from evil influences, he rests at a
middle point and becomes ambitious and a lover of honour.

And now let us set another city over against another man. The next form
of government is oligarchy, in which the rule is of the rich only; nor
is it difficult to see how such a State arises. The 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 take the place of lovers of honour;
misers of politicians; and, in time, political privileges are confined
by law to the rich, who do not shrink from violence in order to effect
their purposes.

Thus much of the origin,—let us next consider the evils of oligarchy.
Would a man who wanted to be safe on a voyage take a bad pilot because
he was rich, or refuse a good one because he was poor? And does not the
analogy apply still more to the State? And there are yet greater evils:
two nations are struggling together in one—the rich and the poor; and
the rich dare not put arms into the hands of the poor, and are
unwilling to pay for defenders out of their own money. And 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 drones of the hive; only
whereas the actual drone is unprovided by nature with a sting, the
two-legged things whom we call drones are some of them without stings
and some of them have dreadful stings; in other words, there are
paupers and there are rogues. These are never far apart; and in
oligarchical cities, where nearly everybody is a pauper who is not a
ruler, you will find abundance of both. And this evil state of society
originates in bad education and bad government.

Like State, like man,—the change in the latter begins with the
representative of timocracy; he walks at first in the ways of his
father, who may have been a statesman, or general, perhaps; and
presently he sees him ‘fallen from his high estate,’ the victim of
informers, dying in prison or exile, or by the hand of the executioner.
The lesson which he thus receives, makes him cautious; he leaves
politics, represses his pride, and saves pence. Avarice is enthroned as
his bosom’s lord, and assumes the style of the Great King; the rational
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 knavish,
breeding in his soul. If he is the trustee of an orphan, and has the
power to defraud, he will soon prove that he is not without the will,
and that his passions are only restrained by fear and not by reason.
Hence he leads a divided existence; in which the better desires mostly
prevail. But when he is contending for prizes and other distinctions,
he is afraid to incur a loss which is to be repaid only by barren
honour; in time of war he fights with a small part of his resources,
and usually keeps his money and loses the victory.

Next comes democracy and the democratic man, out of oligarchy and the
oligarchical man. Insatiable avarice is the ruling passion of an
oligarchy; and they encourage expensive habits in order that they may
gain by the ruin of extravagant youth. Thus men of family often lose
their property or rights of citizenship; but they remain in the city,
full of hatred against the new owners of their estates and ripe for
revolution. The usurer with stooping walk pretends not to see them; he
passes by, and leaves his sting—that is, his money—in some other
victim; and many a man 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 danger he is not
despised; he sees the rich man puffing and panting, and draws the
conclusion which he privately imparts to his companions,—‘that our
people are not good for much;’ and as a sickly frame is made ill by a
mere touch from without, or sometimes without external impulse is ready
to fall to pieces of itself, so from the least cause, or with none at
all, the city falls ill and fights a battle for life or death. And
democracy comes into power when the poor are the victors, killing some
and exiling some, and giving equal shares in the government to all the
rest.

The manner of life in such a State is that of democrats; there is
freedom and plainness of speech, and every man does what is right in
his own eyes, and has his own way of life. Hence arise the most various
developments of character; the State is like a piece of embroidery of
which the colours and figures are the manners of men, and there are
many who, like women and children, prefer this variety to real beauty
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 about the streets
like a hero; and nobody sees him or cares for him. Observe, too, how
grandly Democracy sets her foot upon all our fine theories of
education,—how little she cares for the training of her statesmen! The
only qualification which she demands is the profession of patriotism.
Such is democracy;—a pleasing, lawless, various sort of government,
distributing equality to equals and unequals alike.

Let us now inspect the individual democrat; and first, as in the case
of the State, we will trace his antecedents. He is the son of a miserly
oligarch, and has been taught by him to restrain the love of
unnecessary pleasures. Perhaps I ought to explain this latter
term:—Necessary pleasures are those 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 hurtful to body and
mind, and the excess may be avoided. When in excess, they may be
rightly called expensive pleasures, in opposition to the useful ones.
And the drone, as we called him, is the slave of these unnecessary
pleasures and desires, whereas the miserly oligarch is subject only to
the necessary.

The oligarch changes into the democrat in the following manner:—The
youth who has had a miserly bringing up, gets a taste of the drone’s
honey; he meets with wild companions, who introduce him to every new
pleasure. As in the State, so in the individual, there are allies on
both sides, temptations from without and passions from within; there is
reason also and external influences of parents and friends in alliance
with the oligarchical principle; and the two factions are in violent
conflict with one another. Sometimes the party of order prevails, but
then again new desires and new disorders arise, and the whole mob of
passions gets possession of the Acropolis, that is to say, the soul,
which they find void and unguarded by true words and works. 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 youth passes from the necessary
pleasures to the unnecessary. After a while he divides his time
impartially between them; and perhaps, when he gets older and the
violence of passion has abated, he restores some of the exiles and
lives in a sort of equilibrium, indulging first one pleasure and then
another; and if reason comes and tells him that some pleasures are good
and honourable, and others bad and vile, he shakes his head and says
that he can make no distinction between them. Thus he lives in the
fancy of the hour; sometimes he takes to drink, and then he turns
abstainer; he practises in the gymnasium or he does nothing at all;
then again he would be a philosopher or a politician; or again, he
would be a warrior or a man of business; he is

‘Every thing by starts and nothing long.’


There remains still the finest and fairest of all men and all
States—tyranny and the tyrant. Tyranny springs from democracy much as
democracy springs from oligarchy. Both arise from excess; the one from
excess of wealth, the other from excess of freedom. ‘The great natural
good of life,’ says the democrat, ‘is freedom.’ And this exclusive love
of freedom and regardlessness of everything else, is the cause of the
change from democracy to tyranny. The State demands the strong wine of
freedom, and unless her rulers give her a plentiful draught, punishes
and insults them; equality and fraternity of governors and governed is
the approved principle. Anarchy is the law, not of the State only, but
of private houses, and extends even to the animals. Father and son,
citizen and foreigner, teacher and pupil, old and young, are all on a
level; fathers and teachers fear their sons and pupils, and the wisdom
of the young man is a match for the elder, and the old imitate the
jaunty manners of the young because they are afraid of being thought
morose. Slaves are on a level with their masters and mistresses, and
there is no difference between men and women. Nay, the very animals in
a democratic State have a freedom which is unknown in other places. The
she-dogs are as good as their she-mistresses, and horses and asses
march along with dignity and run their noses against anybody who comes
in their way. ‘That has often been my experience.’ At last the 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
attracted by a little honey; and the rich are made to supply the honey,
of which the demagogues keep the greater part themselves, giving a
taste only to the mob. Their victims attempt to resist; they are driven
mad by the stings of the drones, and so become downright oligarchs in
self-defence. Then follow informations and convictions for treason. The
people have some protector whom they nurse into greatness, and from
this root the tree of tyranny springs. The nature of the change is
indicated in the old fable of the temple of Zeus Lycaeus, which tells
how he who tastes human flesh mixed up with the flesh of other victims
will turn into a wolf. Even so the protector, who tastes human blood,
and slays some and exiles others with or without law, who hints at
abolition of debts and division of lands, must either perish or become
a wolf—that is, a tyrant. Perhaps he is driven out, but he soon comes
back from exile; and then if his enemies cannot get rid of him by
lawful means, they plot his assassination. Thereupon the friend of the
people makes his well-known request to them for a body-guard, which
they readily grant, thinking only of his danger and not of their own.
Now let the rich man make to himself wings, for he will never run away
again if he does not do so then. And the Great Protector, having
crushed all his rivals, stands proudly erect in the chariot of State, a
full-blown tyrant: Let us enquire into the nature of his happiness.

In the early days of his tyranny he smiles and beams upon everybody; he
is not a ‘dominus,’ no, not he: he has only come to put an end to debt
and the monopoly of land. Having got rid of foreign enemies, he makes
himself necessary to the State by always going to war. He is thus
enabled to depress the poor by heavy taxes, and so keep them at work;
and he can get rid of bolder spirits by handing them over to the enemy.
Then comes unpopularity; some of his old associates have the courage to
oppose him. The consequence is, that he has to make a purgation of the
State; but, unlike the physician who purges away the bad, he must get
rid of the high-spirited, the wise and the wealthy; for he has no
choice between death and a life of shame and dishonour. And the more
hated he is, the more he will require trusty guards; but how will he
obtain 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
his? First, by robbing the temples of their treasures, which will
enable him to lighten the taxes; then he will take all his father’s
property, and spend it on his companions, male or female. Now his
father is the demus, and if the demus gets angry, and says that a great
hulking son ought not to be a burden on his parents, and bids him and
his riotous crew begone, then will the parent know what a monster he
has been nurturing, and that the son whom he would fain expel is too
strong for him. ‘You do not mean to say that he will beat his father?’
Yes, he will, after having taken away his arms. ‘Then he is a parricide
and a cruel, unnatural son.’ And the people have jumped from the fear
of slavery into slavery, out of the smoke into the fire. Thus liberty,
when out of all order and reason, passes into the worst form of
servitude...

In the previous books Plato has described the ideal State; now he
returns to the perverted or declining forms, on which he had lightly
touched at the end of Book IV. These he describes 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 the point at which he digressed; and is thus led shortly to
recapitulate the substance of the three former books, which also
contain a parallel of the philosopher and the State.

Of the first decline he gives no intelligible account; he would not
have liked to admit the most probable causes of the fall of his ideal
State, which to us would appear to be the impracticability of communism
or the natural antagonism of the ruling and subject classes. He throws
a veil of mystery over the origin of the decline, which he attributes
to ignorance of the law of population. Of this law the famous
geometrical figure or number 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 their original
spirit. He appears not to have reflected upon the full meaning of his
own words, ‘In the brief space of human life, nothing great can be
accomplished’; or again, as he afterwards says in the Laws, ‘Infinite
time is the maker of cities.’ The order of constitutions which is
adopted by him represents an order of thought rather than a succession
of time, and may be considered as the first attempt to frame a
philosophy of history.

The first of these declining States is timocracy, or the government of
soldiers and lovers of honour, which answers to the Spartan State; this
is a government of force, in which education is not inspired by the
Muses, but imposed by the law, and in which all the finer elements of
organization have disappeared. The philosopher himself has lost the
love of truth, and the soldier, who is of a simpler and honester
nature, 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
dissatisfied at her own position, is always urging him towards the life
of political ambition. Such a character may have had this origin, and
indeed Livy attributes the Licinian laws to a feminine jealousy of a
similar kind. But there is obviously no connection between the manner
in which the timocratic State springs out of the ideal, and the mere
accident by which the timocratic man is the son of a retired statesman.

The two next stages in the decline of constitutions have even less
historical foundation. For there is no trace in Greek history of a
polity like the Spartan or Cretan passing into an oligarchy of wealth,
or of the oligarchy of wealth passing into a democracy. The order of
history appears to be different; first, in the Homeric times there is
the royal or patriarchal form of government, which a century or two
later was succeeded by an oligarchy of birth rather than of wealth, and
in which wealth was only the accident of the hereditary possession of
land and power. Sometimes this oligarchical government gave way to a
government based upon a qualification of property, 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 leading to democracy; the reign of
Peisistratus and his sons is an episode which comes between the
legislation of Solon and the constitution of Cleisthenes; and some
secret cause common to them all seems to have led the greater part of
Hellas at her first appearance in the dawn of history, e.g. Athens,
Argos, Corinth, Sicyon, and nearly every State with the exception of
Sparta, through a similar stage of tyranny which ended either in
oligarchy or democracy. But then we must remember that Plato is
describing rather the contemporary governments of the Sicilian States,
which alternated between democracy and tyranny, than the ancient
history of Athens or Corinth.

The portrait of the tyrant himself is just such as the later Greek
delighted to draw of Phalaris and Dionysius, in which, as in the lives
of mediaeval saints or mythic heroes, the conduct and actions of one
were attributed to another in order to fill up the outline. There was
no enormity which the Greek was not today to believe of them; the
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 suppose that he
drew from life; or that his knowledge of tyrants is derived from a
personal acquaintance with Dionysius. The manner in which he speaks of
them would rather tend to render doubtful his ever having ‘consorted’
with them, or entertained the schemes, which are attributed to him in
the Epistles, of regenerating Sicily by their help.

Plato in a hyperbolical and serio-comic vein exaggerates the follies of
democracy which he also sees reflected in social life. To him democracy
is a state of individualism or dissolution; in which every one is doing
what is right in his own eyes. Of a people animated by a common spirit
of liberty, rising as one man to repel the Persian host, which is the
leading idea of democracy 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 which, in
Plato’s opinion, was required to give power to evil (Book I). This
ideal of wickedness living in helpless misery, is the reverse of that
other portrait of perfect injustice ruling in happiness and splendour,
which first of all Thrasymachus, and afterwards the sons of Ariston had
drawn, and is also the reverse of the king whose rule of life is the
good of his subjects.

Each of these governments and individuals has a corresponding ethical
gradation: the ideal State is under the rule of reason, not
extinguishing but harmonizing the passions, and training them in
virtue; in the timocracy and the timocratic man the constitution,
whether of the State or of the individual, is based, first, upon
courage, and secondly, 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 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,

(1), 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 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 (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.). 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.), 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. (Compare Cratylus; Protag.)

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 (Greek) 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 number of this figure becomes solid.’)
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 triangle, the squares of the two lesser
sides equal the square of the hypotenuse (9 + 16 = 25).

Plato begins by speaking of a perfect or cyclical number (Tim.), i.e. a
number in which the sum of the divisors equals the whole; this is the
divine or perfect number in which all lesser cycles or revolutions are
complete. He also speaks of a human or imperfect number, having four
terms and three intervals of numbers which are related to one another
in certain proportions; these he converts into 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 the state, or of the human race as Zeller
supposes; nor is the divine number afterwards mentioned (Arist.). The
second is the number of generations or births, and presides over them
in the same mysterious manner in which the stars preside over them, or
in which, according to the Pythagoreans, opportunity, justice,
marriage, are represented by some number or figure. This is probably
the number 216.

The explanation given in the text supposes the two harmonies to make up
the number 8000. This explanation derives a certain plausibility from
the circumstance that 8000 is the ancient number of the Spartan
citizens (Herod.), and would be what Plato might have called ‘a number
which nearly concerns the population of a city’; 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 orders in the State or parts of the soul, the
four virtues, the five forms of government. The harmony of the musical
scale, which is elsewhere used as a symbol of the harmony of the state,
is also indicated. For the numbers 3, 4, 5, which represent the sides
of the Pythagorean triangle, also denote the intervals of the scale.

The terms used in the statement of the problem may be explained as
follows. A perfect number (Greek), as already stated, is one which is
equal to the sum of its divisors. Thus 6, which is the first perfect or
cyclical number, = 1 + 2 + 3. The words (Greek), ‘terms’ or ‘notes,’
and (Greek), ‘intervals,’ are applicable to music as well as to number
and figure. (Greek) is the ‘base’ on which the whole calculation
depends, or the ‘lowest term’ from which it can be worked out. The
words (Greek) have been variously translated—‘squared and cubed’
(Donaldson), ‘equalling and equalled in power’ (Weber), ‘by involution
and evolution,’ i.e. by raising the power and extracting the root (as
in the translation). Numbers are called ‘like and unlike’ (Greek) when
the factors or the sides of the planes and cubes which they represent
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 1/3) = 4/3 or
a musical fourth. (Greek) is a ‘proportion’ of numbers as of musical
notes, applied either to the parts or factors of a single number or to
the relation of one number to another. The first harmony is a ‘square’
number (Greek); the second harmony is an ‘oblong’ number (Greek), i.e.
a number representing a figure of which the opposite sides only are
equal. (Greek) = ‘numbers squared from’ or ‘upon diameters’; (Greek) =
‘rational,’ i.e. omitting fractions, (Greek), ‘irrational,’ i.e.
including fractions; e.g. 49 is a square of the rational diameter of a
figure the side of which = 5: 50, of an irrational diameter of the
same. For several of the explanations here given and for a good deal
besides I am indebted to an excellent article on the Platonic Number by
Dr. Donaldson (Proc. of the Philol. Society).

The conclusions which he draws from these data are summed up by him as
follows. Having assumed that the number of the perfect or divine cycle
is the number of the world, and the number of the imperfect cycle the
number of the state, he proceeds: ‘The period of the world is defined
by the perfect number 6, that of the state by the cube of that number
or 216, which is the product of the last pair of terms in the Platonic
Tetractys (a series of seven terms, 1, 2, 3, 4, 9, 8, 27); and if we
take this as the basis of our computation, we shall have two cube
numbers (Greek), viz. 8 and 27; and the mean proportionals between
these, viz. 12 and 18, will furnish three intervals and four terms, and
these terms and intervals stand related 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 (Greek) he elsewhere explains as follows: ‘The first (Greek) is
(Greek), in other words (4/3 x 5) all squared = 100 x 2 squared over 3
squared. The second (Greek), a cube of the same root, is described as
100 multiplied (alpha) by the rational diameter of 5 diminished by
unity, i.e., as shown above, 48: (beta) by two incommensurable
diameters, i.e. the two first irrationals, or 2 and 3: and (gamma) by
the cube of 3, or 27. Thus we have (48 + 5 + 27) 100 = 1000 x 2 cubed.
This second harmony is to be the cube of the number of which the former
harmony is the square, and therefore must be divided by the cube of 3.
In other words, the whole expression will be: (1), for the first
harmony, 400/9: (2), for the second harmony, 8000/27.’

The reasons which have inclined me to agree with Dr. Donaldson and also
with Schleiermacher in supposing that 216 is the Platonic number of
births are: (1) that it coincides with the description of the number
given in the first part of the passage (Greek...): (2) that the number