And now, I said, let me show in a figure how far our nature is enlightened
or unenlightened:--Behold! human beings living in a underground den, which
has a mouth open towards the light and reaching all along the den; here
they have been from their childhood, and have their legs and necks chained
so that they cannot move, and can only see before them, being prevented by
the chains from turning round their heads. Above and behind them a fire is
blazing at a distance, and between the fire and the prisoners there is a
raised way; and you will see, if you look, a low wall built along the way,
like the screen which marionette players have in front of them, over which
they show the puppets.
And do you see, I said, men passing along the wall carrying all sorts of
vessels, and statues and figures of animals made of wood and stone and
various materials, which appear over the wall? Some of them are talking,
You have shown me a strange image, and they are strange prisoners.
Like ourselves, I replied; and they see only their own shadows, or the
shadows of one another, which the fire throws on the opposite wall of the
True, he said; how could they see anything but the shadows if they were
never allowed to move their heads?
And of the objects which are being carried in like manner they would only
see the shadows?
Yes, he said.
And if they were able to converse with one another, would they not suppose
that they were naming what was actually before them?
And suppose further that the prison had an echo which came from the other
side, would they not be sure to fancy when one of the passers-by spoke that
the voice which they heard came from the passing shadow?
No question, he replied.
To them, I said, the truth would be literally nothing but the shadows of
That is certain.
And now look again, and see what will naturally follow if the prisoners are
released and disabused of their error. At first, when any of them is
liberated and compelled suddenly to stand up and turn his neck round and
walk and look towards the light, he will suffer sharp pains; the glare will
distress him, and he will be unable to see the realities of which in his
former state he had seen the shadows; and then conceive some one saying to
him, that what he saw before was an illusion, but that now, when he is
approaching nearer to being and his eye is turned towards more real
existence, he has a clearer vision,--what will be his reply? And you may
further imagine that his instructor is pointing to the objects as they pass
and requiring him to name them,--will he not be perplexed? Will he not
fancy that the shadows which he formerly saw are truer than the objects
which are now shown to him?
And if he is compelled to look straight at the light, will he not have a
pain in his eyes which will make him turn away to take refuge in the
objects of vision which he can see, and which he will conceive to be in
reality clearer than the things which are now being shown to him?
True, he said.
And suppose once more, that he is reluctantly dragged up a steep and rugged
ascent, and held fast until he is forced into the presence of the sun
himself, is he not likely to be pained and irritated? When he approaches
the light his eyes will be dazzled, and he will not be able to see anything
at all of what are now called realities.
Not all in a moment, he said.
He will require to grow accustomed to the sight of the upper world. And
first he will see the shadows best, next the reflections of men and other
objects in the water, and then the objects themselves; then he will gaze
upon the light of the moon and the stars and the spangled heaven; and he
will see the sky and the stars by night better than the sun or the light of
the sun by day?
Last of all he will be able to see the sun, and not mere reflections of him
in the water, but he will see him in his own proper place, and not in
another; and he will contemplate him as he is.
He will then proceed to argue that this is he who gives the season and the
years, and is the guardian of all that is in the visible world, and in a
certain way the cause of all things which he and his fellows have been
accustomed to behold?
Clearly, he said, he would first see the sun and then reason about him.
And when he remembered his old habitation, and the wisdom of the den and
his fellow-prisoners, do you not suppose that he would felicitate himself
on the change, and pity them?
Certainly, he would.
And if they were in the habit of conferring honours among themselves on
those who were quickest to observe the passing shadows and to remark which
of them went before, and which followed after, and which were together; and
who were therefore best able to draw conclusions as to the future, do you
think that he would care for such honours and glories, or envy the
possessors of them? Would he not say with Homer,
'Better to be the poor servant of a poor master,'
and to endure anything, rather than think as they do and live after their
Yes, he said, I think that he would rather suffer anything than entertain
these false notions and live in this miserable manner.
Imagine once more, I said, such an one coming suddenly out of the sun to be
replaced in his old situation; would he not be certain to have his eyes
full of darkness?
To be sure, he said.
And if there were a contest, and he had to compete in measuring the shadows
with the prisoners who had never moved out of the den, while his sight was
still weak, and before his eyes had become steady (and the time which would
be needed to acquire this new habit of sight might be very considerable),
would he not be ridiculous? Men would say of him that up he went and down
he came without his eyes; and that it was better not even to think of
ascending; and if any one tried to loose another and lead him up to the
light, let them only catch the offender, and they would put him to death.
No question, he said.
This entire allegory, I said, you may now append, dear Glaucon, to the
previous argument; the prison-house is the world of sight, the light of the
fire is the sun, and you will not misapprehend me if you interpret the
journey upwards to be the ascent of the soul into the intellectual world
according to my poor belief, which, at your desire, I have expressed--
whether rightly or wrongly God knows. But, whether true or false, my
opinion is that in the world of knowledge the idea of good appears last of
all, and is seen only with an effort; and, when seen, is also inferred to
be the universal author of all things beautiful and right, parent of light
and of the lord of light in this visible world, and the immediate source of
reason and truth in the intellectual; and that this is the power upon which
he who would act rationally either in public or private life must have his
I agree, he said, as far as I am able to understand you.
Moreover, I said, you must not wonder that those who attain to this
beatific vision are unwilling to descend to human affairs; for their souls
are ever hastening into the upper world where they desire to dwell; which
desire of theirs is very natural, if our allegory may be trusted.
Yes, very natural.
And is there anything surprising in one who passes from divine
contemplations to the evil state of man, misbehaving himself in a
ridiculous manner; if, while his eyes are blinking and before he has become
accustomed to the surrounding darkness, he is compelled to fight in courts
of law, or in other places, about the images or the shadows of images of
justice, and is endeavouring to meet the conceptions of those who have
never yet seen absolute justice?
Anything but surprising, he replied.
Any one who has common sense will remember that the bewilderments of the
eyes are of two kinds, and arise from two causes, either from coming out of
the light or from going into the light, which is true of the mind's eye,
quite as much as of the bodily eye; and he who remembers this when he sees
any one whose vision is perplexed and weak, will not be too ready to laugh;
he will first ask whether that soul of man has come out of the brighter
life, and is unable to see because unaccustomed to the dark, or having
turned from darkness to the day is dazzled by excess of light. And he will
count the one happy in his condition and state of being, and he will pity
the other; or, if he have a mind to laugh at the soul which comes from
below into the light, there will be more reason in this than in the laugh
which greets him who returns from above out of the light into the den.
That, he said, is a very just distinction.
But then, if I am right, certain professors of education must be wrong when
they say that they can put a knowledge into the soul which was not there
before, like sight into blind eyes.
They undoubtedly say this, he replied.
Whereas, our argument shows that the power and capacity of learning exists
in the soul already; and that just as the eye was unable to turn from
darkness to light without the whole body, so too the instrument of
knowledge can only by the movement of the whole soul be turned from the
world of becoming into that of being, and learn by degrees to endure the
sight of being, and of the brightest and best of being, or in other words,
of the good.
And must there not be some art which will effect conversion in the easiest
and quickest manner; not implanting the faculty of sight, for that exists
already, but has been turned in the wrong direction, and is looking away
from the truth?
Yes, he said, such an art may be presumed.
And whereas the other so-called virtues of the soul seem to be akin to
bodily qualities, for even when they are not originally innate they can be
implanted later by habit and exercise, the virtue of wisdom more than
anything else contains a divine element which always remains, and by this
conversion is rendered useful and profitable; or, on the other hand,
hurtful and useless. Did you never observe the narrow intelligence
flashing from the keen eye of a clever rogue--how eager he is, how clearly
his paltry soul sees the way to his end; he is the reverse of blind, but
his keen eye-sight is forced into the service of evil, and he is
mischievous in proportion to his cleverness?
Very true, he said.
But what if there had been a circumcision of such natures in the days of
their youth; and they had been severed from those sensual pleasures, such
as eating and drinking, which, like leaden weights, were attached to them
at their birth, and which drag them down and turn the vision of their souls
upon the things that are below--if, I say, they had been released from
these impediments and turned in the opposite direction, the very same
faculty in them would have seen the truth as keenly as they see what their
eyes are turned to now.
Yes, I said; and there is another thing which is likely, or rather a
necessary inference from what has preceded, that neither the uneducated and
uninformed of the truth, nor yet those who never make an end of their
education, will be able ministers of State; not the former, because they
have no single aim of duty which is the rule of all their actions, private
as well as public; nor the latter, because they will not act at all except
upon compulsion, fancying that they are already dwelling apart in the
islands of the blest.
Very true, he replied.
Then, I said, the business of us who are the founders of the State will be
to compel the best minds to attain that knowledge which we have already
shown to be the greatest of all--they must continue to ascend until they
arrive at the good; but when they have ascended and seen enough we must not
allow them to do as they do now.
What do you mean?
I mean that they remain in the upper world: but this must not be allowed;
they must be made to descend again among the prisoners in the den, and
partake of their labours and honours, whether they are worth having or not.
But is not this unjust? he said; ought we to give them a worse life, when
they might have a better?
You have again forgotten, my friend, I said, the intention of the
legislator, who did not aim at making any one class in the State happy
above the rest; the happiness was to be in the whole State, and he held the
citizens together by persuasion and necessity, making them benefactors of
the State, and therefore benefactors of one another; to this end he created
them, not to please themselves, but to be his instruments in binding up the
True, he said, I had forgotten.
Observe, Glaucon, that there will be no injustice in compelling our
philosophers to have a care and providence of others; we shall explain to
them that in other States, men of their class are not obliged to share in
the toils of politics: and this is reasonable, for they grow up at their
own sweet will, and the government would rather not have them. Being
self-taught, they cannot be expected to show any gratitude for a culture
which they have never received. But we have brought you into the world to
be rulers of the hive, kings of yourselves and of the other citizens, and
have educated you far better and more perfectly than they have been
educated, and you are better able to share in the double duty. Wherefore
each of you, when his turn comes, must go down to the general underground
abode, and get the habit of seeing in the dark. When you have acquired the
habit, you will see ten thousand times better than the inhabitants of the
den, and you will know what the several images are, and what they
represent, because you have seen the beautiful and just and good in their
truth. And thus our State, which is also yours, will be a reality, and not
a dream only, and will be administered in a spirit unlike that of other
States, in which men fight with one another about shadows only and are
distracted in the struggle for power, which in their eyes is a great good.
Whereas the truth is that the State in which the rulers are most reluctant
to govern is always the best and most quietly governed, and the State in
which they are most eager, the worst.
Quite true, he replied.
And will our pupils, when they hear this, refuse to take their turn at the
toils of State, when they are allowed to spend the greater part of their
time with one another in the heavenly light?
Impossible, he answered; for they are just men, and the commands which we
impose upon them are just; there can be no doubt that every one of them
will take office as a stern necessity, and not after the fashion of our
present rulers of State.
Yes, my friend, I said; and there lies the point. You must contrive for
your future rulers another and a better life than that of a ruler, and then
you may have a well-ordered State; for only in the State which offers this,
will they rule who are truly rich, not in silver and gold, but in virtue
and wisdom, which are the true blessings of life. Whereas if they go to
the administration of public affairs, poor and hungering after their own
private advantage, thinking that hence they are to snatch the chief good,
order there can never be; for they will be fighting about office, and the
civil and domestic broils which thus arise will be the ruin of the rulers
themselves and of the whole State.
Most true, he replied.
And the only life which looks down upon the life of political ambition is
that of true philosophy. Do you know of any other?
Indeed, I do not, he said.
And those who govern ought not to be lovers of the task? For, if they are,
there will be rival lovers, and they will fight.
Who then are those whom we shall compel to be guardians? Surely they will
be the men who are wisest about affairs of State, and by whom the State is
best administered, and who at the same time have other honours and another
and a better life than that of politics?
They are the men, and I will choose them, he replied.
And now shall we consider in what way such guardians will be produced, and
how they are to be brought from darkness to light,--as some are said to
have ascended from the world below to the gods?
By all means, he replied.
The process, I said, is not the turning over of an oyster-shell (In
allusion to a game in which two parties fled or pursued according as an
oyster-shell which was thrown into the air fell with the dark or light side
uppermost.), but the turning round of a soul passing from a day which is
little better than night to the true day of being, that is, the ascent from
below, which we affirm to be true philosophy?
And should we not enquire what sort of knowledge has the power of effecting
such a change?
What sort of knowledge is there which would draw the soul from becoming to
being? And another consideration has just occurred to me: You will
remember that our young men are to be warrior athletes?
Yes, that was said.
Then this new kind of knowledge must have an additional quality?
Usefulness in war.
Yes, if possible.
There were two parts in our former scheme of education, were there not?
There was gymnastic which presided over the growth and decay of the body,
and may therefore be regarded as having to do with generation and
Then that is not the knowledge which we are seeking to discover?
But what do you say of music, which also entered to a certain extent into
our former scheme?
Music, he said, as you will remember, was the counterpart of gymnastic, and
trained the guardians by the influences of habit, by harmony making them
harmonious, by rhythm rhythmical, but not giving them science; and the
words, whether fabulous or possibly true, had kindred elements of rhythm
and harmony in them. But in music there was nothing which tended to that
good which you are now seeking.
You are most accurate, I said, in your recollection; in music there
certainly was nothing of the kind. But what branch of knowledge is there,
my dear Glaucon, which is of the desired nature; since all the useful arts
were reckoned mean by us?
Undoubtedly; and yet if music and gymnastic are excluded, and the arts are
also excluded, what remains?
Well, I said, there may be nothing left of our special subjects; and then
we shall have to take something which is not special, but of universal
What may that be?
A something which all arts and sciences and intelligences use in common,
and which every one first has to learn among the elements of education.
What is that?
The little matter of distinguishing one, two, and three--in a word, number
and calculation:--do not all arts and sciences necessarily partake of them?
Then the art of war partakes of them?
To be sure.
Then Palamedes, whenever he appears in tragedy, proves Agamemnon
ridiculously unfit to be a general. Did you never remark how he declares
that he had invented number, and had numbered the ships and set in array
the ranks of the army at Troy; which implies that they had never been
numbered before, and Agamemnon must be supposed literally to have been
incapable of counting his own feet--how could he if he was ignorant of
number? And if that is true, what sort of general must he have been?
I should say a very strange one, if this was as you say.
Can we deny that a warrior should have a knowledge of arithmetic?
Certainly he should, if he is to have the smallest understanding of
military tactics, or indeed, I should rather say, if he is to be a man at
I should like to know whether you have the same notion which I have of this
What is your notion?
It appears to me to be a study of the kind which we are seeking, and which
leads naturally to reflection, but never to have been rightly used; for the
true use of it is simply to draw the soul towards being.
Will you explain your meaning? he said.
I will try, I said; and I wish you would share the enquiry with me, and say
'yes' or 'no' when I attempt to distinguish in my own mind what branches of
knowledge have this attracting power, in order that we may have clearer
proof that arithmetic is, as I suspect, one of them.
Explain, he said.
I mean to say that objects of sense are of two kinds; some of them do not
invite thought because the sense is an adequate judge of them; while in the
case of other objects sense is so untrustworthy that further enquiry is
You are clearly referring, he said, to the manner in which the senses are
imposed upon by distance, and by painting in light and shade.
No, I said, that is not at all my meaning.
Then what is your meaning?
When speaking of uninviting objects, I mean those which do not pass from
one sensation to the opposite; inviting objects are those which do; in this
latter case the sense coming upon the object, whether at a distance or
near, gives no more vivid idea of anything in particular than of its
opposite. An illustration will make my meaning clearer:--here are three
fingers--a little finger, a second finger, and a middle finger.
You may suppose that they are seen quite close: And here comes the point.
What is it?
Each of them equally appears a finger, whether seen in the middle or at the
extremity, whether white or black, or thick or thin--it makes no
difference; a finger is a finger all the same. In these cases a man is not
compelled to ask of thought the question what is a finger? for the sight
never intimates to the mind that a finger is other than a finger.
And therefore, I said, as we might expect, there is nothing here which
invites or excites intelligence.
There is not, he said.
But is this equally true of the greatness and smallness of the fingers?
Can sight adequately perceive them? and is no difference made by the
circumstance that one of the fingers is in the middle and another at the
extremity? And in like manner does the touch adequately perceive the
qualities of thickness or thinness, of softness or hardness? And so of the
other senses; do they give perfect intimations of such matters? Is not
their mode of operation on this wise--the sense which is concerned with the
quality of hardness is necessarily concerned also with the quality of
softness, and only intimates to the soul that the same thing is felt to be
both hard and soft?
You are quite right, he said.
And must not the soul be perplexed at this intimation which the sense gives
of a hard which is also soft? What, again, is the meaning of light and
heavy, if that which is light is also heavy, and that which is heavy,
Yes, he said, these intimations which the soul receives are very curious
and require to be explained.
Yes, I said, and in these perplexities the soul naturally summons to her
aid calculation and intelligence, that she may see whether the several
objects announced to her are one or two.
And if they turn out to be two, is not each of them one and different?
And if each is one, and both are two, she will conceive the two as in a
state of division, for if there were undivided they could only be conceived
of as one?
The eye certainly did see both small and great, but only in a confused
manner; they were not distinguished.
Whereas the thinking mind, intending to light up the chaos, was compelled
to reverse the process, and look at small and great as separate and not
Was not this the beginning of the enquiry 'What is great?' and 'What is
And thus arose the distinction of the visible and the intelligible.
This was what I meant when I spoke of impressions which invited the
intellect, or the reverse--those which are simultaneous with opposite
impressions, invite thought; those which are not simultaneous do not.
I understand, he said, and agree with you.
And to which class do unity and number belong?
I do not know, he replied.
Think a little and you will see that what has preceded will supply the
answer; for if simple unity could be adequately perceived by the sight or
by any other sense, then, as we were saying in the case of the finger,
there would be nothing to attract towards being; but when there is some
contradiction always present, and one is the reverse of one and involves
the conception of plurality, then thought begins to be aroused within us,
and the soul perplexed and wanting to arrive at a decision asks 'What is
absolute unity?' This is the way in which the study of the one has a power
of drawing and converting the mind to the contemplation of true being.
And surely, he said, this occurs notably in the case of one; for we see the
same thing to be both one and infinite in multitude?
Yes, I said; and this being true of one must be equally true of all number?
And all arithmetic and calculation have to do with number?
And they appear to lead the mind towards truth?
Yes, in a very remarkable manner.
Then this is knowledge of the kind for which we are seeking, having a
double use, military and philosophical; for the man of war must learn the
art of number or he will not know how to array his troops, and the
philosopher also, because he has to rise out of the sea of change and lay
hold of true being, and therefore he must be an arithmetician.
That is true.
And our guardian is both warrior and philosopher?
Then this is a kind of knowledge which legislation may fitly prescribe; and
we must endeavour to persuade those who are to be the principal men of our
State to go and learn arithmetic, not as amateurs, but they must carry on
the study until they see the nature of numbers with the mind only; nor
again, like merchants or retail-traders, with a view to buying or selling,
but for the sake of their military use, and of the soul herself; and
because this will be the easiest way for her to pass from becoming to truth
That is excellent, he said.
Yes, I said, and now having spoken of it, I must add how charming the
science is! and in how many ways it conduces to our desired end, if pursued
in the spirit of a philosopher, and not of a shopkeeper!
How do you mean?
I mean, as I was saying, that arithmetic has a very great and elevating
effect, compelling the soul to reason about abstract number, and rebelling
against the introduction of visible or tangible objects into the argument.
You know how steadily the masters of the art repel and ridicule any one who
attempts to divide absolute unity when he is calculating, and if you
divide, they multiply (Meaning either (1) that they integrate the number
because they deny the possibility of fractions; or (2) that division is
regarded by them as a process of multiplication, for the fractions of one
continue to be units.), taking care that one shall continue one and not
become lost in fractions.
That is very true.
Now, suppose a person were to say to them: O my friends, what are these
wonderful numbers about which you are reasoning, in which, as you say,
there is a unity such as you demand, and each unit is equal, invariable,
indivisible,--what would they answer?
They would answer, as I should conceive, that they were speaking of those
numbers which can only be realized in thought.
Then you see that this knowledge may be truly called necessary,
necessitating as it clearly does the use of the pure intelligence in the
attainment of pure truth?
Yes; that is a marked characteristic of it.
And have you further observed, that those who have a natural talent for
calculation are generally quick at every other kind of knowledge; and even
the dull, if they have had an arithmetical training, although they may
derive no other advantage from it, always become much quicker than they
would otherwise have been.
Very true, he said.
And indeed, you will not easily find a more difficult study, and not many
You will not.
And, for all these reasons, arithmetic is a kind of knowledge in which the
best natures should be trained, and which must not be given up.
Let this then be made one of our subjects of education. And next, shall we
enquire whether the kindred science also concerns us?
You mean geometry?
Clearly, he said, we are concerned with that part of geometry which relates
to war; for in pitching a camp, or taking up a position, or closing or
extending the lines of an army, or any other military manoeuvre, whether in
actual battle or on a march, it will make all the difference whether a
general is or is not a geometrician.
Yes, I said, but for that purpose a very little of either geometry or
calculation will be enough; the question relates rather to the greater and
more advanced part of geometry--whether that tends in any degree to make
more easy the vision of the idea of good; and thither, as I was saying, all
things tend which compel the soul to turn her gaze towards that place,
where is the full perfection of being, which she ought, by all means, to
True, he said.
Then if geometry compels us to view being, it concerns us; if becoming
only, it does not concern us?
Yes, that is what we assert.
Yet anybody who has the least acquaintance with geometry will not deny that
such a conception of the science is in flat contradiction to the ordinary
language of geometricians.
They have in view practice only, and are always speaking, in a narrow and
ridiculous manner, of squaring and extending and applying and the like--
they confuse the necessities of geometry with those of daily life; whereas
knowledge is the real object of the whole science.
Certainly, he said.
Then must not a further admission be made?
That the knowledge at which geometry aims is knowledge of the eternal, and
not of aught perishing and transient.
That, he replied, may be readily allowed, and is true.
Then, my noble friend, geometry will draw the soul towards truth, and
create the spirit of philosophy, and raise up that which is now unhappily
allowed to fall down.
Nothing will be more likely to have such an effect.