Chapter XVI: Book VII: Argument (1)

In the _seventh book_, which opens with a beautiful description of the
nature of man confined in a dark cave, Plato proceeds to show the
means and plan for learning true philosophy, and how we may attain
to the serious and sober practice of social life and politics. That
moral discipline, argues he, which I require in my guardian, is not
mere vacant contemplation, but a profound and practical knowledge of
all matters nearly or more remotely concerning the duties of life
and the social relations of mankind,—that is, the state in its most
broad and general sense: in fact, that he should be a philosophic
ruler acquainted with divine and human things,—in other words, with
true and primary philosophy. This he terms _dialectic_, the
subordinates of which are _physics_, the science which considers the
origin and formation of matter, and _mathematics_, which is halfway
between the two others, engaged indeed in contemplating abstract and
purely argumentative, but not on that higher eternal truth;
emphatically, τὸ ὄν, that primarily exists in the mind of God: of
these matters he treats, particularly the first, at very
considerable length: which, as Ritter says, is a regulating
superintendent, which, from the knowledge of the eternally true, may
indicate to each special science its proper object.

CHAP. I.—After this then, said I, compare our nature as respects education, or the want thereof, to a condition such as follows:—Behold men, as it were, in an underground cave-like dwelling, having its entrance open towards the light and extending through the whole cave,—and within it persons, who from childhood upwards have had chains on their legs and their necks, so as, while abiding there, to have the power of looking forward only, but not to turn round their heads by reason of their chains, their light coming from a fire that burns above and afar off, and behind them; and between the fire and those in chains is a road above, along which one may see a little wall built along, just as the stages of conjurers are built before the people in whose presence they show their tricks. I see, said he. Behold then by the side of this little wall men carrying all sorts of machines rising above the wall, and statues of men and other animals wrought in stone, wood, and other materials, some of the bearers probably speaking, others proceeding in silence.[212] You are proposing, said he, a most absurd comparison and absurd captives also. Such as resemble ourselves, said I;—for think you that such as these would have seen anything else of themselves or one another except the shadows that fall from the fire on the opposite side of the cave? How can they, said he, if indeed they be through life compelled to keep their heads unmoved? But what respecting the things carried by them:—is not this the same? Of course. If then they had been able to talk with each other, do you not suppose they would think it right to give names to what they saw before them? Of course they would. But if the prison had an echo on its opposite side, when any person present were to speak, think you they would imagine anything else addressed to them, except the shadow before them? No, by Zeus, not I, said he. At all events then, said I, such persons would deem truth to be nothing else but the shadows of exhibitions. Of course they would. Let us inquire then, said I, as to their liberation from captivity, and their cure from insanity, such as it may be, and whether such will naturally fall to their lot;—were a person let loose and obliged immediately to rise up, and turn round his neck and walk, and look upwards to the light, and doing all this still feel pained, and be disabled by the dazzling from seeing those things of which he formerly saw the shadows;—what would he say, think you, if any one were to tell him that he formerly saw mere empty visions, but now saw more correctly, as being nearer to the real thing, and turned towards what was more real, and then, specially pointing out to him every individual passing thing, should question him, and oblige him, to answer respecting its nature:—think you not he would be embarrassed, and consider that what he before saw was truer than what was just exhibited? Quite so, said he.

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Footnote 212:

Allusion is here made to puppets which are made to perform on a
moveable stage by means of strings pulled from behind. See Ruhnken’s
Lexicon to the Timæus, on the word θαύματα, which he explains by the
compound word νευροσπάσματα.

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CHAP. II.—Therefore, even if a person should compel him to look to the light itself, would he not have pain in his eyes and shun it, and then, turning to what he really could behold, reckon these as really more clear than what had been previously pointed out? Just so, replied he. But if, said I, a person should forcibly drag him thence through a rugged and steep ascent without stopping, till he dragged him to the light of the sun, would he not while thus drawn be in pain and indignation, and when he came to the light, having his eyes dazzled with the splendour, be unable to behold even any one thing of what he had just alleged as true? No, he could not, at the moment at least, said he. He would require, at least then, to get some degree of practice, if he would see things above him:—and first, indeed, he would most easily perceive the shadows, and then the images of men and other animals in the water, and after that the things themselves;—and after this he would more easily behold the things in heaven, and heaven itself, by night, looking to the light of the stars and the moon, than after daylight to the sun and the light of the sun. How else? Last of all, then, methinks, he might be able to perceive and contemplate the nature of the sun, not as respects its images in water or any other place, but itself by itself in its own proper station? Necessarily so, said he. And after this, he might reason with himself concerning the sun, that it is the body which gives us the seasons and years and administers everything in its stated place, being the cause also in a certain manner of all natural events. It is evident, said he, after what has been formerly stated, that one must arrive at this conclusion. What then,—when a man remembers his first habitation and the wisdom therein residing, and his fellow captives also,—think you not, that he would congratulate himself on the change and pity the rest? Quite so. And whatever honours and praises and rewards were assigned by mutual consent to him that had the most acute perception of the present, and the best recollection both of long past and recent events, and from such observations was best able to conjecture the future,—think you that he would desire such honours, or envy those honoured by these, or possessing influence, or would not he rather experience what Homer says, and ardently desire

As labourer, for some ignoble man
To work for hire,[213]—

and rather endure anything than entertain such opinions and live in such a manner? I think, said he, that he would choose to suffer anything rather than live in that way. And consider this, said I, whether, in the case of such an one going down and again sitting in the same place, his eyes would not be blinded in consequence of coming so suddenly from the sun? Quite so, replied he. As for those shadows again, if he were compelled to split straws and dispute about them with those persons who had been in constant captivity, while yet he was in darkness before the establishment of his sight,—(and this time of getting habituated would not be short,)—would he not excite ridicule; and would it not be said of him, that after having once ascended he had come back with his eyesight destroyed, and should not even try to ascend again; and as for any one that attempted to liberate him and lead him up, they ought to put him to death, if they could get him into their hands? Especially so, said he.

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Footnote 213:

Comp. Hom. Odyss. x. 428.

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CHAP. III.—As respects this image then, we must apply the whole of it to our preceding discourse; comparing the region that is seen by the eyes to the prison-habitation, and the light of the fire therein to the power of the sun;—and if you were to consider the ascent above, and the contemplation of things above as the soul’s ascent into the region of intellect, you would not disappoint my expectations, since this it is which you desire to hear;—but God knows whether it be true. As respects appearances then, it thus seems, that in the subjects of human knowledge the idea of the good is the last object of vision, and hard to be seen; and when beheld it must be inferred from reason to be the cause of what is right and beautiful in all things, generating in what is visible, both light and its parent also, [viz. the sun,] while in that which is intelligible, it is itself the sovereign producing truth and intelligence; and it must be seen too by him that would act with judgment, either privately or in public. I too, said he, am quite of your opinion, as far indeed as I can be. Come then, said I, agree on this point also;—and be not surprised that those who come here are unwilling to act in human affairs, but have their souls ever urged to dwell on things above; for it is surely reasonable it should be so, since these things take place according to the above-mentioned image. Aye, quite reasonable, replied he. But what, said I;—think you it at all surprising, that a man coming from divine contemplations to mere human woes, should appear awkward and extremely ridiculous, while he is yet dazzled,[214]—and when, ere being used to the present darkness, he is obliged to contend in courts of law or elsewhere about the shadows of justice, or the statues of which they are the shadows, and then to dispute how these matters are apprehended by those who have never contemplated justice itself? No wonder this, replied he. Nay, said I, if a man has intelligence, he will be conscious, that there are two disturbances of vision arising from two causes,—viz., when we turn from light into darkness and from darkness into light;—and when a man thinks that the same takes place with reference to the soul likewise, when it beholds him disturbed and unable to realize its perceptions, he will not laugh immoderately, but rather consider whether the soul has come out of a more brilliant existence and is now darkened by ignorance, or else emerging out of gross ignorance into a more luminous existence, be overpowered by dazzling splendour;—and thus he will congratulate the former on its life and destiny, while he pities the life and destiny of the other; and even if he wished to laugh at it, his laughter will be less ridiculous than if it were directed to the soul which comes from light into darkness. Your remark is perfectly reasonable, he replied.

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Footnote 214:

This refers to the reproach made to philosophers on the unpractical
nature of their pursuits, and elsewhere alluded to in the preceding
book, ch. 3, and likewise in the Gorgias, p. 484 c.

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CHAP. IV.—It is fit then, said I, if these things be true, that we form such an opinion as this respecting them,—that education is not of that character which some persons announce it to be, when they somehow assert that, there is no science in the soul, but that they can implant it just as if they implanted sight in the eyes of the blind. Aye, they say so, he replied.[215] Our present argument however, said I, shows this power to reside in the soul of every person, and to be the organ by which every one learns.—Just as the eye cannot turn otherwise than with the whole body from darkness to the light, so also one must turn with the whole soul from sensible objects until it has become able to endure the contemplation of what is real, and what is most apparent of the real, and this we term _the good_: do we not? Yes. It will be the art then of this very person, said I, in turning about, to contrive this; namely, how he may turn with the greatest ease and advantage, not for the sake of implanting sight in him, but viewing him as already possessing it, though not rightly turned, and not looking in the right direction? It seems so, said he. The other virtues of the soul, as they are called, seem to me somewhat like those of the body; for in fact those not before contained therein are afterwards engendered by custom and practice:—but the faculty of intellect possesses, it seems, a nature somewhat more god-like than all the rest;—never losing its power, but by exertion becoming useful and profitable,—by the opposite, useless and hurtful. Have you never yet observed of those that are termed wicked yet clever,—how sharply the little soul looks, acutely distinguishing all to which it is turned, having indeed no contemptible power of vision, but compelled to be so far the servant of wickedness, that in proportion as its vision is more acute, the more crime it perpetrates? Quite so, of course, observed he. As regards this part of such a disposition, if from childhood upwards it should be stripped and cut off from what belongs to human production, as from leaden weights,—which have a relation to feastings, and pleasures, and lusts, that turn the sight of the soul to things downward;—if the soul can free itself and turn towards truth, the very same principle in the same individuals would as acutely see those things as the objects to which it is now turned. Certainly, he replied. What then, is not this probable, said I, and a necessary consequence of what has just been stated, that those who are untaught and inexperienced in truth can never exercise a sufficient superintendence over the state, nor yet those who are allowed to spend the whole of their time in philosophical pursuits,—the former, because they have no single object in life, towards which they should direct all their actions both private and public,—and the latter, because, as far as their will is concerned, they will not engage in public life, from the idea that even while yet living they have been transported to the islands of the blessed? True, said he. It is our business then, said I, to compel those of the inhabitants, who possess the greatest talent, to devote themselves to that learning which we formerly considered most important, both to contemplate the good and go in search of it;—and when they have gained it, and taken a sufficient view thereof, yet they are not to be allowed what is now allowed them. What is that? To abide there, said I, and show an unwillingness to descend again to those captives of whom we were speaking, or share with them, both their labours and honours, whether trifling or more important. In that case, said he, are we to do them injustice, and make them live a worse life, when they could have lived a better?

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Footnote 215:

Euripides alludes to the same false notion in the Hippolytus, v. 917.

ὦ πόλλ’ ἁμαρτάνοντες ἄνθρωποι μάτην,
τί δὴ τέχνας μὲν μυρίας διδάσκετε
καὶ πάντα μηχανᾶσθε κἀξευρίσκετε,
ἓν δ’ οὐκ ἐπίστασθ’ οὐδ’ ἐθηράσασθέ πω
φρονεῖν διδάσκειν οἷσιν οὐκ ἔνεστι νοῦς;

Pindar has a similar sentiment in Olymp. ix. 152-5.

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CHAP. V.—You have forgotten again, said I, that this is not the lawgiver’s concern, how any one class in a state may be especially happy, but to contrive rather that happiness shall be generated throughout the state, uniting the citizens both by persuasion and compulsion, making them share each other’s services, such as they can confer on the community at large; and when he introduces such men as these into the state, he does so, not that he may dismiss them and let them turn whichever way each likes, but that he may employ them as a bond of the state. True indeed, said he, for I had forgotten that. Anxiously consider then, Glaucon, that we must do no injustice to the philosophers born among us, but tell them what is just, when we compel them to take charge of and guard the remainder:—for we will assert, that those who in all other states become such [philosophers,] do not probably take a share in the labours going on therein, as they spring up of their own accord without the consent of the government in each; and it is just that what is voluntary, inasmuch as it owes its nurture to none, should willingly pay no one the price of its nurture;—but as for you, we brought into being both yourselves and the rest of the state, as leaders and kings in beehives, brought up better and more perfectly than the others, and better able to take a share in both [public life and philosophical pursuits]. Each must then in turn descend to the dwelling of the rest, and accustom himself to behold obscure objects; for, when once used to them, you will perceive the individual images of each, what they are and whence sprung, ten thousand times better from having already seen the truth concerning what is beautiful, and just, and good:—and thus the state will be settled as a real vision, both by us and yourselves, and not as a dream, like most of those inhabited by persons fighting about shadows, and quarrelling about government, as if it were some great good.—The truth, however, is as follows: in whatever state those about to rule are least anxious to take the government, this must necessarily be the best and most peacefully governed, while one that has governors of an opposite character, must of course be the opposite. Certainly, said he. Think you then, that those under our charge, when they hear these things, will disobey us, and be unwilling to take their individual share in the labours of the state, and spend the greater part of their time with one another in a state of leisure? Impossible, said he;—for we will prescribe what is just to just men, and each of them will enter on his office from this consideration above all others, that he should act in a manner directly contrary from those who now govern individual states. Yes, for so it is, my friend;—if you find the life of those appointed to official stations superior to the dignity of their office, then your state may possibly be well settled; as in that alone will the really wealthy govern,—not those rich in gold, but as happy men should be rich, in a life of virtue and good sense;—whereas, should they be poor, and destitute of property of their own, and then come into public life, thinking that they ought to plunder the public of its property, it is not possible [that such a state can be rightly settled]:—for as the contest is about the possession of the ruling power, such a war being domestic and intestine, is destructive to themselves as well as the rest of the state. Most true, he replied. Do you conceive then that any other kind of life despises political offices except that of true philosophy? No, by Zeus, said he. But still it is fitting, at least, that those should enter upon it who are not fond of governing, otherwise the rivals will fight about it. Of course, it cannot be otherwise. Whom else, then, would you compel to enter on the guardianship of a state, except such as are most intelligent in what concerns the best establishment of a state, and possess other honours, and a mode of life superior to that of a mere politician? None other, he replied.

CHAP. VI.—Do you wish, then, that we should now consider this,—in what manner such persons will be produced and how any one can draw them upward into light, just as some are said to have ascended from Hades to the gods? Of course that is my wish, he replied. This then, as it seems, is not a mere turning of a die,[216] but a movement of the soul, which ascends from some half-night kind of day to the true light of existence, which we will term true philosophy. Certainly. Ought we not, then, to inquire what branch of learning possesses this influence? Of course. What then, Glaucon, may that training of the soul be, which draws it from what is generated and unstable towards that which has a positive existence? And talking of this, I am reminded:—did we not say that it is necessary for these persons even while young to engage in warlike exercises? We did say so. We should add this, then, to the training which we are now seeking. What is that? That of not being useless to military men. Aye, we must indeed, said he, if it be possible. Moreover, in our former discourse, we somewhere said we would have them taught gymnastics and music. We did so, said he. The art of gymnastics has to do, I think, with what is unstable and perishable; for it presides over corporeal growth and decrease. It appears so. This then cannot be the branch of study, of which we are in pursuit. It cannot. Is it music then, such as we have previously described? That, said he, if you remember, corresponded to gymnastics, as it trains the habits of the guardians, giving them a sort of concord founded on harmony—not science,—and good rhythm on the principles of rhythm, and other things in discourses which are akin to these both in such as are fabulous and such as more resemble truth; but as to its being a branch of science that refers to a good such as you are now investigating, music had no such character. Most correctly, said I, do you remind me; for it is in reality no such thing: but, excellent Glaucon, what branch of science is it, that possesses this character?—for all the arts somehow seem to be mechanical and illiberal. Of course;—and moreover what other branch of science is there, that is distinct from music, gymnastics, and the arts? Come, said I, if we cannot conceive any except these, let us take one of those which extends over all. Of what kind is that? Such as this common idea which all arts, and intellects, and sciences employ, and which every person must learn at the outset. What is that? said he. This trifling matter, said I;—how to distinguish one, and two, and three, which I call in general terms arithmetic and computation:—is it not thus as regards these, that every art and science must necessarily have a share in these? Surely, he replied. Must not then the art of war? said I. Necessarily, he replied. What a ridiculous general then, said I, does Palamedes in his tragedies constantly represent Agamemnon to be.[217]—And have you not observed how he says, that after inventing numeration he adjusted the ranks at Ilium, and numbered the ships and the rest of the forces, as if they had never been numbered before, even when Agamemnon, as it seems, did not know how many feet he had, since he did not know how to count;—what kind of a general would you think him to be? I should think him a mighty absurd one, he replied, if this be true.

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Footnote 216:

This alludes to a game of chance,—ἡ ὀστρακίνδα, fully described in the
Onomast. of Pollux, lib. ix. ch. 7 § 110-112.

Footnote 217:

This passage refers, no doubt, to some one or more lost tragedies in
which Palamedes is made to accuse Agamemnon of an utter ignorance of
arithmetic.

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CHAP. VII.—Shall we not say, then, said I, that the power of computing and reckoning is a necessary attainment for a military man? Most certainly, he replied, if he intends to understand anything at all about marshalling troops,—or rather, if he means to be a man. Do you then understand, said I, about this branch of learning just what I do? What is that? It seems in its nature to be among the number of those things which lead to pure reason—of which indeed we are in search; but no one seems rightly to employ it, as evidently leading the mind to the consideration of true being. How say you? inquired he. I will at least, try, said I, to explain what is my opinion.—As to what I distinguish in my own mind as leading or not leading whither we are saying, [viz., to true being,] do you assist me in contemplating them, and either agree or dissent, so that we may more distinctly see whether they be such as I conjecture. Pray show me, said he. I will show you then, said I, if you will observe that some things relating to the perceptions do not invite intellect to the inquiry, as being sufficiently determined by perception; while there are other things which by all means bid its interference, as perception alone does nothing correct. You are evidently speaking, said he, of objects seen at a distance, and things sketched in a picture. You have not quite comprehended my meaning, said I. What are you speaking of then? asked he. There are some things, replied I, which do not appeal [to the intellect], and yet do not issue at once into a contrary perception; while those that do so issue I consider as so appealing, when the perceptive faculty takes cognizance of one thing more than another, on meeting it either near or afar off.—And you will thus more clearly know what I mean: these we say are three fingers, the little finger, the next to it, and the middle finger. Just so, observed he. Consider me then to speak of them as seen only from a short distance, and consider this also, respecting them. What? Each of them appears equally to be a finger, and so far it makes no difference whether one looks at the middle one or the last, whether it be white or black, thick or slender, or anything of the kind; for in all these the soul of man is not compelled to ask the intellect what of many things a finger is,[218] for sight itself never at the same time indicates a finger to be a finger, and its contrary. Of course not, replied he. It is probable, then, said I, that such a case as this would neither appeal to nor rouse the intellect. Probably. But what then;—does the sight sufficiently distinguish their large or small size, and does it make no difference to it whether one of them be placed in the middle or at the end?—And so in like manner does the sense of touch take cognizance of thickness and slenderness, softness and hardness?—And as for the other perceptions, are they not defective in showing such things, or rather does not each of them so act; and first of all, is not the sense which is affected by hardness necessarily also affected by softness, and does it not, when it perceives this, announce to the soul, that hard and soft are one and the same thing? Just so. he replied. It must necessarily follow then, said I, that in such matters, the soul will be in doubt as to what the perception indicates as hard, since it calls the same thing soft also;—and so also as regards the sense referring to light and heavy, the soul must be in doubt what is light and what is heavy, if the sense intimates heavy to be light, and light heavy? These at least, said he, are truly absurd reports made to the soul, and require investigation. Probably then, said I, in such cases as these the soul would first call in reason and intelligence to investigate the question whether the things reported be one or whether they be two. Of course. If then they appeared to be two, each of them will appear to be one and distinct from the other? Yes. If then each of them be one and both of them two, he will understand them to be two distinct; for, were they not distinct, he would not perceive two, but only one. Right. The sight, moreover, we say, could contemplate what is great and small, though not as distinct from each other, but as somewhat confused:—could it not? Yes. But for the sake of clearness in this matter, the intellect is once more obliged to consider great and small, not as confused, but as distinct in an opposite way from the other,—viz., the sense of sight. True. And is it not hence somehow, that it first sets on questioning us, as to what is the great and what is the small? Assuredly. And thus then we call the one intelligible, and the other visible. Very right, he replied.

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Footnote 218:

Gr. ἐν πᾶσι γὰρ τούτοις οὐκ ἀναγκάζεται τῶν πολλῶν ἡ ψυχὴ τὴν νόησιν
ἐπέρεσθαι τί ποτ’ ἔστι δάκτυλος. The words τῶν πολλῶν are usually
taken with τί ποτε, as above translated. Schleiermacher, however,
takes it with ἡ ψυχὴ, _the souls of people generally_. Ast thinks the
words an interpolation.

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CHAP. VIII.—This then is what I just now attempted to express, that some things appeal to the intellect and others not; defining those that make such an appeal, as what affect the senses at the same time as their opposites, while such as do not, do not excite the intellect. I quite understand now, said he; and I am of the same opinion. What then;—to which of them, think you, do number and unity belong? I do not understand, replied he. But let us reason by analogy, said I, from what we have already said:—for if unity can be sufficiently seen of itself, or comprehended by any other sense, it still would not lead to true being, just as we remarked about the finger:—but if there be always seen at the same time an exact opposite thereto, so that it shall no more appear unity than it does the contrary, some one would then be wanted to judge respecting it; and in that very matter the soul would necessarily be in difficulty, exciting reflection within itself, and would inquire into the nature of this same unity, and thus that branch of science which concerns unity would be among those which lead and turn the soul to the contemplation of real being. Ah, said he;—this is what the very sight of it does in no small degree; for we at once behold the same thing, both as one and as an infinite multitude. If then, said I, unity be thus affected, will not number generally be so likewise? Of course. Yet, again, all computation and arithmetic concern number? Quite so. But these at least seem to lead towards truth? Especially so, of course. They belong then, it seems, to the branches of learning which we are now investigating;—for a military man must necessarily learn them with a view to the marshalling of his troops, and so must a philosopher with the view of understanding real being, after having emerged from the unstable condition of becoming, or else he can never become an apt reasoner. That is the fact, he replied. But that guardian of ours happens to be both a military man and a philosopher? Unquestionably so. It would be proper then, Glaucon, to lay down laws for this branch of science and persuade those about to engage in the most important state-matters to apply themselves to computation, and study it, not in the common vulgar fashion, but with the view of arriving at the contemplation of the nature of numbers by the intellect itself,—not for the sake of buying and selling as anxious merchants and retailers, but for war also, and that the soul may acquire a facility of turning itself from what is in course of generation to truth and real being. A capital remark, he replied. And, moreover, I now observe, said I, respecting that branch of science which concerns computation, how refined it is, and in many ways useful to us as respects our wishes, if we will apply thereto for the sake of getting knowledge, and not with a view of traffic. In what way? inquired he. Just what we now said—that it powerfully leads the soul upwards, and compels it to reason on abstract numbers, without in any way allowing a person in his reasoning to advance numbers which are visible and tangible bodies;[219]—for perhaps you know of some persons skilled in these matters, who, if one were in argument to attempt dividing unity itself, would at once both ridicule him and not allow it; though, were _you_ to divide it into parts, they would multiply them, lest unity should somehow seem not to be unity, but numerous parts. A very true remark, he replied. What think you then, Glaucon, if a person should ask them—You wonderfully clever men, about what kind of numbers are you reasoning;—in which unity, such as you deem it, is equal, each whole to the whole, without any difference whatever, and having no parts in itself?—what think you they would reply? This, as far as I think;—that they speak of such numbers only—as can be comprehended by the intellect alone, but in no other way. You see then, my friend, I observed, that our real need of this branch of science, is probably because it seems to compel the soul to use pure intelligence in the search after pure truth. Aye, remarked he, it does this to a remarkable extent. Have you yet considered this,—that persons naturally skilled in computation seem clever in all branches of science,—whereas those naturally slow, if instructed and exercised in this, will yet all of them, if they derive no other advantage, make such progress, as to become cleverer than they were before? Exactly so, he replied. And, moreover, I think you will not easily find that many things give the learner and student more trouble than this. Of course not. On all these accounts, then, we must not omit this branch of science, but those with the best of talents should be instructed therein? I agree with you, he replied.

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Footnote 219:

_Abstract_, ideal numbers, Plato terms αὐτοὶ οἱ ἀριθμοί; and these
only are the subject of _scientific_ calculation. The _concrete_
numbers (ἀριθμοὶ σώματα ἔχοντες) are the subjects only of every-day
practical numeration and computation. The monad is the idea of unity,
abstract, indivisible unity (αὐτὸ τὸ ἕν), the duad of abstract
duality, &c.

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CHAP. IX.—Let this one thing then, said I, [that has just been discussed,] be settled between us; and now let us consider, in the second place, with respect to what follows from it,—whether and how far it concerns ourselves. What is it, said he;—is it geometry you mean? That very thing, said I. So far, observed he, as it bears a relation to the concerns of war, it evidently does concern us;—for in pitching encampments, occupying positions, contracting and extending a line of troops, and as respects all the varied forms in which they draw up armies, either in battle itself or during a march, it would make a vast difference, whether a general were a geometrician or not. Of course, rejoined I, for such purposes as these a very slender knowledge of geometry, and a small portion of arithmetic would suffice;—but as for any considerable amount thereof, and great progress in it, we must inquire how far they tend to this,—namely, to make us apprehend more easily the idea of the good:—and we say that all things contribute thereto, which compel the soul to turn itself to that region in which is the happiest portion of true being, which it must by all means perceive. Your remark is correct, said he. If then it compels the soul to contemplate true being, it is suitable,—but if only what is sensible and evanescent, it is not suitable. Aye, truly, we say so. This point then, at least, said I, those who have but little acquaintance with geometry, will not argue with us,—that this science has an entirely opposite nature to the words employed in it by those who practise it. How? said he. They speak somehow most absurdly, and necessarily so, since all the terms they use seem to be with a view to operation and practice,[220]—such as squaring, producing, adding, and such-like sounds; whereas on the other hand, the whole science should be studied for the sake of real knowledge. Assuredly, said he. Is this, then, further to be agreed on? What? That [it be studied] with a view to the knowledge of eternal being, and not of that which is subject to generation and destruction? We may well grant that, said he; for it is the business of geometry to concern itself with eternal being. It would have a tendency, therefore, gentle sir, to draw the soul to truth, and to cause a philosophic intelligence to direct upwards [the thoughts] which we now improperly cast downwards. As much as possible, he replied. As far as possible, then, said I, we must give special orders, that the inhabitants of that fine state[221] of yours should by no means omit the study of geometry, since even its by-works are not inconsiderable. What are they? inquired he. Those which you have just mentioned that concern war;—and indeed with reference to all branches of science, for the better understanding thereof, we are some how sure that it makes an entire difference every way, whether a man be acquainted with geometry or not. Every way, indeed, by Zeus, observed he. Let us fix on this then, as the second branch of learning for youth. Let us so fix it, he replied.

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Footnote 220:

Gr. ὡς πράττοντές τε καὶ πραξέως ἕνεκα.

Footnote 221:

The use of the ironical compound καλλίπολις gives a force and beauty
to the passage which is wholly lost in translation. It is the reading,
too, of all the best MSS., and altogether preferable to the old
reading.—ἐν τῇ καλλίστῃ πόλει σου.

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CHAP. X.—But what; shall we fix upon astronomy, as the third, or think you otherwise? I quite think we should, said he; for to have unusually acute perceptions respecting the times of months and years, is suitable not only for agriculture and navigation, but not less so for the art of war. You are jesting, said I, when you seem to be afraid that the multitude will charge you with enjoining useless objects of study:—yet it is not altogether a trifle, but rather difficult to persuade that by these branches of study some organ of the soul in each individual, is purified and rekindled like fire, after having been destroyed and blinded by other kinds of study,—an organ, indeed, better worth saving than ten thousand eyes, since by that alone can truth be seen. Among such, then, as join me in this opinion, you will have the reputation of reasoning admirably well; though such as never had any perception of this will think perhaps that you say nothing to the purpose, as they see no advantage therefrom accruing that is worthy of notice. Consider, then, from this point, against which of the parties you are arguing,—or whether against neither, but chiefly for your own sake you are carrying on the discussion; moreover, do not envy any other, if therefrom any one could derive any possible advantage. Thus, said he, do I choose, on my own account chiefly, to argue and ask questions, and make replies. Let us go a little back then, in our argument, for just now, indeed, we did not rightly take what is next in order after geometry. How then did we act? asked he. After a plain surface, said I, we took a solid in a state of revolution, without first considering it by itself, in the abstract; but the correct plan is to take the third in order, after the second dimension:—and this, probably, refers to the dimension of cubes, and what has to do with depth. Aye, it is so, said he: but these matters, Socrates, do not seem yet to have been investigated. Aye, there are two causes for this: because no state holds them in honour, they are only slightly investigated, as being difficult; and those that do so investigate them require a guide, without whom they cannot discover them,—one whom, first of all, it would be hard to get, and, when he is got, as things are at present, the investigators of these matters having lofty notions of themselves, would not obey him; whereas, if the whole state were to hold such pursuits in honour, and superintend them, these persons would be obedient, and the investigations being conducted with assiduity and vigour, would exhibit their true character; whereas now, despised and mutilated by the multitude, as well as by those who study them without being able to account for their usefulness, they still, in spite of all things, increase through their native grace; and it is no wonder that they should appear so to do. Aye, indeed, said he, this gracefulness is especially remarkable; but tell me more plainly what you were just now saying,—for you somehow defined geometry to be a study that concerns plane surfaces. I did, said I. Then next in order you mentioned astronomy; but afterwards you drew back. Yes, replied I, because when I am in a hurry to get quickly over the discussion, I get on the more slowly; for as regards the mode of measuring depth, which is next in order, that I passed over, as a hopeless investigation, and proceeded, after geometry, to speak about astronomy, which is the motion of solids. You say rightly, observed he. Let us fix on astronomy then, said he, as a fourth branch of science; as if that which we now omit, [viz. solid geometry,] may have an existence, whenever the state enters on that pursuit. Probably, said he: and as to what you just now urged on me, Socrates, about astronomy, as having needlessly praised it, I now praise it in accordance with your notions: for I think it is clear to every one, that it is this which compels the soul to look upwards, and from what is here conducts it thither. Perhaps, rejoined I, it may be clear to all except myself;—to me it does not seem so. Ah! how is that? said he. As those who introduce it into philosophy, nowadays pursue it, it makes the soul look altogether downwards. How say you? inquired he. I am of opinion, replied I, that you are not ungenerous in forming your mental estimate of the real nature of that branch of science which concerns things above; for you seem to be of opinion, that if a person were to look up and discover some of the heavenly bodies in an enclosed space, he would contemplate them with his intellect and not his eyes. Perhaps, then, you judge rightly, and I am wrong; though I, on the other hand, cannot hold the opinion that any other branch of science can make the soul look upwards, except that which concerns real being and the invisible,—whether one were to gape upwards, or try by peering downwards to get acquainted with those matters:—and if any one were to gape upwards and so try to get acquainted with any perceptible object, I think that he never would get acquainted with it; as his soul has no scientific knowledge of such things,—nor would his soul look upwards, but downwards,—even though he were to try to learn, swimming on his back at sea or lying so on the ground.

CHAP. XI.—I am punished, rejoined he;—for you have rightly reproved me:—but in what manner did you say we ought to learn astronomy different from that in which they now teach it, if people are to be taught advantageously for the purposes of which we now speak? Thus, said I:—these various bright bodies in the heaven,—since indeed they are so variously placed in visible space,—ought to be deemed very beautiful and most perfect in their kind, though much inferior to the true magnificence of movement, with which real velocity and real retardation mutually bear along those bodies with all that belongs to them, in their true number and in all their true shapes;[222]—which things, indeed, can be apprehended only by reason and intelligence, not by sight:—do you think they can? By no means, said he. Must we not then, said I, use the various heavenly phenomena, as an exhibition for the purpose of instructing us in those [real] concerns,—just as one might meet with sketches, capitally well drawn and elaborated by Dædalus, or some other artist or painter?—For one skilled in geometry, on seeing such drawings, would, perhaps, think them to be exceedingly well wrought, and nevertheless deem it absurd to give them a serious consideration,—as if he were thence to get his conception of truth about equals, or doubles, or any other proportion, Of course, it would be absurd, he replied. And think you not then, that the true astronomer will feel just the same, when he looks up to the orbits of the stars,—reckoning, indeed, that the heavens and all in them are established by the heavenly architect in the most beautiful manner possible for the formation of such works; and would not one deem it absurd of a man to conceive that this proportion of night with day, and of both these to a month, and of a month to a year, and of other stars to both of these, and towards each other has existed always in the same manner, and without experiencing any change, because they have a body, and are visible, and so to take all possible means to apprehend the truth of these things? So I think, he replied, whilst I listen to you. Let us then, said I, make use of problems, [or hypotheses,] in astronomy, as in geometry, and dismiss the heavenly bodies,—if we intend really to get acquainted with astronomy, and render useful instead of useless that portion of the soul which is naturally intelligent. You really impose, said he, a far harder task on astronomers than is enjoined them at present. I think, however, replied I, that we must enjoin other duties likewise, according to the same fashion, if we would be of any service as lawgivers.

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Footnote 222:

Gr. τῶν δὲ ἀληθινῶν πολὺ ἐνδεῖν, ἃς τὸ ὂν τάχος καὶ ἡ οὖσα βραδυτὴς ἐν
τῷ ἀληθινῷ ἀριθμῷ καὶ πᾶσι τοῖς ἀληθέσι σχήμασι φοράς τε πρὸς ἄλληλα
φέρεται καὶ τὰ ἐνόντα φέρει. The passage is evidently corrupt,—and, as
it now stands, is almost incapable of translation. That given above
closely resembles that given by Victor Cousin, a far better one than
Schleiermacher’s.

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CHAP. XII.—But have you anything to suggest about the fitting branches of study? I have not, he replied,—at present at least. Motion, moreover, said I, affords us, I think, not one indeed, but many species thereof;—all of which any wise man can probably tell; but those which occur to me are two. What are they? In addition to this, said I, there is its counterpart. Which? As the eyes, said I, seem formed for studying astronomy, so do the ears seem formed for harmonious motions; and these seem to be twin sciences to one another, as also the Pythagoreans[223] say; and we too, Glaucon, agree with them:—how shall we do? Just so, replied he. Shall we not, then, said I, since it is a matter of high importance, inquire of them how they speak concerning them, and whether they have anything else to say besides this; but we, notwithstanding all this, shall defend our own conclusion? What is that? That those whom we educate should never attempt to learn these things imperfectly, nor without always aiming at the object, to which all ought to be directed,—as we just stated with reference to astronomy:—and do not you know that they do some such thing with regard to harmony?—for, while they measure one with another the symphonies and sounds which are heard, they go through a fruitless toil, like the astronomers. Aye, by the gods, said he,—and absurdly too, when they make very frequent trials of the notes, lending their ears to catch the sound as from a neighbour’s voice,—some indeed saying that they hear some middle note, with the smallest appreciable interval, and others again doubtingly saying that the notes are just what were sounded before,—both parties placing the ears above the intellect. But you are now speaking, said I, of those thrifty, money-making musicians, who are ever harassing and tormenting their strings, turning them on the pegs:—but, that the comparison may not be too tedious, I refrain from speaking of their complaints about the refusal and stubbornness of the strings, and at once give up the simile, saying that we do not mean to speak of these, but of those true musicians whom we before mentioned:—for these do here just what the others did in astronomy; for they search for numbers, in the symphonies which they hear, but do not go on to the inquiry proposed,—what numbers are symphonious, what not, and the reason why they are either the one or the other. You speak, said he, of a noble undertaking. It is serviceable, of course, said I, in the search for the beautiful and good,—but, if pursued in another manner, it is quite useless. Aye, probably so, said he. Still, methinks, said I, the plan of inquiry into all these matters that we have described, if it touches on their mutual communion and alliance, and proves how they are mutually related, will contribute something to what we require, and our labour will not be fruitless; but otherwise it will. I likewise, said he, guess the very same thing:—but you are speaking, Socrates, of a most laborious undertaking. Mean you the introduction, or what else? said I:—what,—know we not, that all these things are introductory to the strain itself;[224] which we ought to learn?—for even persons clever in these things you perhaps do not think skilled in dialectics. No, by Zeus, said he, only some very few of such as I have met. But supposing some of them not able, said I, to offer and admit reasoning, will they ever be able to get acquainted with what we say they ought to know? They will never be able to do this, he replied. Is not this then the very strain, Glaucon, said I, which dialectic science executes,—which also, being cognizable by the intellect, may be said to be imitated by the power of sight,—which faculty seeks, first, as we observed, to gaze at animals, then at the stars, and last of all at the sun himself:—so when a man attempts to discuss a subject without the aid of his perceptive faculties, he is impelled by reason to what is individual and real being; and if he stops not, till he apprehends by intelligence what is the good itself, then, indeed, he arrives at the end of the intelligible, as the other does at the end of the visible. Assuredly, he replied. What then;—do not you call this the dialectic process? What else?

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Footnote 223:

It is here alleged that there are two species of motion (φορά),—one
affecting the eyes, and including the motion of the heavenly bodies,
which are the subject-matter of astronomical science,—the other
affecting the ears, and comprising that harmony of the heavenly
motions which the Pythagoreans conceived to have given the first
notion of music.

Footnote 224:

Glaucon is here complaining of the difficulty of the task proposed;
and Socrates replies, that is a mere introduction or prelude to the
main composition or piece of music (meaning dialectics) that is to
follow. The word νόμος often means _a strain_ or _piece of music_.

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