Then now comes the question — How shall we create our rulers; what way is there from darkness to light? The change is effected by philosophy; it is not the turning over of an oyster-shell, but the conversion of a soul from night to day, from becoming to being. And what training will draw the soul upwards? Our former education had two branches, gymnastic, which was occupied with the body, and music, the sister art, which infused a natural harmony into mind and literature; but neither of these sciences gave any promise of doing what we want. Nothing remains25 to us but that universal or primary science of which all the arts and sciences are partakers, I mean number or calculation. ‘Very true.’ Including the art of war? ‘Yes, certainly.’ Then there is something ludicrous about Palamedes in the tragedy, coming in and saying that he had invented number, and had counted the ranks and set them in order. For if Agamemnon could not count his feet (and without number how could he?) he must have been a pretty sort of general indeed. No man should be a soldier who cannot count, and indeed he is hardly to be called a man. But I am not speaking of these practical applications of arithmetic, for number, in my view, is rather to be regarded as a conductor to thought and being. I will explain what I mean by the last expression:— Things sensible are of two kinds; the one class invite or stimulate27 the mind, while in the other the mind acquiesces28. Now the stimulating29 class are the things which suggest contrast and relation. For example, suppose that I hold up to the eyes three fingers — a fore7 finger, a middle finger, a little finger — the sight equally recognizes all three fingers, but without number cannot further distinguish them. Or again, suppose two objects to be relatively30 great and small, these ideas of greatness and smallness are supplied not by the sense, but by the mind. And the perception of their contrast or relation quickens and sets in motion the mind, which is puzzled by the confused intimations of sense, and has recourse to number in order to find out whether the things indicated are one or more than one. Number replies that they are two and not one, and are to be distinguished31 from one another. Again, the sight beholds32 great and small, but only in a confused chaos33, and not until they are distinguished does the question arise of their respective natures; we are thus led on to the distinction between the visible and intelligible34. That was what I meant when I spoke35 of stimulants36 to the intellect; I was thinking of the contradictions which arise in perception. The idea of unity37, for example, like that of a finger, does not arouse thought unless involving some conception of plurality; but when the one is also the opposite of one, the contradiction gives rise to reflection; an example of this is afforded by any object of sight. All number has also an elevating effect; it raises the mind out of the foam38 and flux39 of generation to the contemplation of being, having lesser40 military and retail41 uses also. The retail use is not required by us; but as our guardian42 is to be a soldier as well as a philosopher, the military one may be retained. And to our higher purpose no science can be better adapted; but it must be pursued in the spirit of a philosopher, not of a shopkeeper. It is concerned, not with visible objects, but with abstract truth; for numbers are pure abstractions — the true arithmetician indignantly denies that his unit is capable of division. When you divide, he insists that you are only multiplying; his ‘one’ is not material or resolvable into fractions, but an unvarying and absolute equality; and this proves the purely43 intellectual character of his study. Note also the great power which arithmetic has of sharpening the wits; no other discipline is equally severe, or an equal test of general ability, or equally improving to a stupid person.
Let our second branch of education be geometry. ‘I can easily see,’ replied Glaucon, ‘that the skill of the general will be doubled by his knowledge of geometry.’ That is a small matter; the use of geometry, to which I refer, is the assistance given by it in the contemplation of the idea of good, and the compelling the mind to look at true being, and not at generation only. Yet the present mode of pursuing these studies, as any one who is the least of a mathematician44 is aware, is mean and ridiculous; they are made to look downwards45 to the arts, and not upwards to eternal existence. The geometer is always talking of squaring, subtending, apposing, as if he had in view action; whereas knowledge is the real object of the study. It should elevate the soul, and create the mind of philosophy; it should raise up what has fallen down, not to speak of lesser uses in war and military tactics, and in the improvement of the faculties46.
Shall we propose, as a third branch of our education, astronomy? ‘Very good,’ replied Glaucon; ‘the knowledge of the heavens is necessary at once for husbandry, navigation, military tactics.’ I like your way of giving useful reasons for everything in order to make friends of the world. And there is a difficulty in proving to mankind that education is not only useful information but a purification of the eye of the soul, which is better than the bodily eye, for by this alone is truth seen. Now, will you appeal to mankind in general or to the philosopher? or would you prefer to look to yourself only? ‘Every man is his own best friend.’ Then take a step backward, for we are out of order, and insert the third dimension which is of solids, after the second which is of planes, and then you may proceed to solids in motion. But solid geometry is not popular and has not the patronage47 of the State, nor is the use of it fully48 recognized; the difficulty is great, and the votaries49 of the study are conceited50 and impatient. Still the charm of the pursuit wins upon men, and, if government would lend a little assistance, there might be great progress made. ‘Very true,’ replied Glaucon; ‘but do I understand you now to begin with plane geometry, and to place next geometry of solids, and thirdly, astronomy, or the motion of solids?’ Yes, I said; my hastiness has only hindered us.
‘Very good, and now let us proceed to astronomy, about which I am willing to speak in your lofty strain. No one can fail to see that the contemplation of the heavens draws the soul upwards.’ I am an exception, then; astronomy as studied at present appears to me to draw the soul not upwards, but downwards. Star-gazing is just looking up at the ceiling — no better; a man may lie on his back on land or on water — he may look up or look down, but there is no science in that. The vision of knowledge of which I speak is seen not with the eyes, but with the mind. All the magnificence of the heavens is but the embroidery51 of a copy which falls far short of the divine Original, and teaches nothing about the absolute harmonies or motions of things. Their beauty is like the beauty of figures drawn52 by the hand of Daedalus or any other great artist, which may be used for illustration, but no mathematician would seek to obtain from them true conceptions of equality or numerical relations. How ridiculous then to look for these in the map of the heavens, in which the imperfection of matter comes in everywhere as a disturbing element, marring the symmetry of day and night, of months and years, of the sun and stars in their courses. Only by problems can we place astronomy on a truly scientific basis. Let the heavens alone, and exert the intellect.
Still, mathematics admit of other applications, as the Pythagoreans say, and we agree. There is a sister science of harmonical motion, adapted to the ear as astronomy is to the eye, and there may be other applications also. Let us inquire of the Pythagoreans about them, not forgetting that we have an aim higher than theirs, which is the relation of these sciences to the idea of good. The error which pervades53 astronomy also pervades harmonics. The musicians put their ears in the place of their minds. ‘Yes,’ replied Glaucon, ‘I like to see them laying their ears alongside of their neighbours’ faces — some saying, “That’s a new note,” others declaring that the two notes are the same.’ Yes, I said; but you mean the empirics who are always twisting and torturing the strings54 of the lyre, and quarrelling about the tempers of the strings; I am referring rather to the Pythagorean harmonists, who are almost equally in error. For they investigate only the numbers of the consonances which are heard, and ascend no higher — of the true numerical harmony which is unheard, and is only to be found in problems, they have not even a conception. ‘That last,’ he said, ‘must be a marvellous thing.’ A thing, I replied, which is only useful if pursued with a view to the good.
All these sciences are the prelude56 of the strain, and are profitable if they are regarded in their natural relations to one another. ‘I dare say, Socrates,’ said Glaucon; ‘but such a study will be an endless business.’ What study do you mean — of the prelude, or what? For all these things are only the prelude, and you surely do not suppose that a mere57 mathematician is also a dialectician? ‘Certainly not. I have hardly ever known a mathematician who could reason.’ And yet, Glaucon, is not true reasoning that hymn58 of dialectic which is the music of the intellectual world, and which was by us compared to the effort of sight, when from beholding59 the shadows on the wall we arrived at last at the images which gave the shadows? Even so the dialectical faculty withdrawing from sense arrives by the pure intellect at the contemplation of the idea of good, and never rests but at the very end of the intellectual world. And the royal road out of the cave into the light, and the blinking of the eyes at the sun and turning to contemplate60 the shadows of reality, not the shadows of an image only — this progress and gradual acquisition of a new faculty of sight by the help of the mathematical sciences, is the elevation61 of the soul to the contemplation of the highest ideal of being.
‘So far, I agree with you. But now, leaving the prelude, let us proceed to the hymn. What, then, is the nature of dialectic, and what are the paths which lead thither62?’ Dear Glaucon, you cannot follow me here. There can be no revelation of the absolute truth to one who has not been disciplined in the previous sciences. But that there is a science of absolute truth, which is attained63 in some way very different from those now practised, I am confident. For all other arts or sciences are relative to human needs and opinions; and the mathematical sciences are but a dream or hypothesis of true being, and never analyse their own principles. Dialectic alone rises to the principle which is above hypotheses, converting and gently leading the eye of the soul out of the barbarous slough64 of ignorance into the light of the upper world, with the help of the sciences which we have been describing — sciences, as they are often termed, although they require some other name, implying greater clearness than opinion and less clearness than science, and this in our previous sketch65 was understanding. And so we get four names — two for intellect, and two for opinion — reason or mind, understanding, faith, perception of shadows — which make a proportion — being:becoming::intellect:opinion — and science:belief::understanding: perception of shadows. Dialectic may be further described as that science which defines and explains the essence or being of each nature, which distinguishes and abstracts the good, and is ready to do battle against all opponents in the cause of good. To him who is not a dialectician life is but a sleepy dream; and many a man is in his grave before his is well waked up. And would you have the future rulers of your ideal State intelligent beings, or stupid as posts? ‘Certainly not the latter.’ Then you must train them in dialectic, which will teach them to ask and answer questions, and is the coping-stone of the sciences.
I dare say that you have not forgotten how our rulers were chosen; and the process of selection may be carried a step further:— As before, they must be constant and valiant66, good-looking, and of noble manners, but now they must also have natural ability which education will improve; that is to say, they must be quick at learning, capable of mental toil67, retentive68, solid, diligent69 natures, who combine intellectual with moral virtues; not lame26 and one-sided, diligent in bodily exercise and indolent in mind, or conversely; not a maimed soul, which hates falsehood and yet unintentionally is always wallowing in the mire70 of ignorance; not a bastard71 or feeble person, but sound in wind and limb, and in perfect condition for the great gymnastic trial of the mind. Justice herself can find no fault with natures such as these; and they will be the saviours72 of our State; disciples73 of another sort would only make philosophy more ridiculous than she is at present. Forgive my enthusiasm; I am becoming excited; but when I see her trampled75 underfoot, I am angry at the authors of her disgrace. ‘I did not notice that you were more excited than you ought to have been.’ But I felt that I was. Now do not let us forget another point in the selection of our disciples — that they must be young and not old. For Solon is mistaken in saying that an old man can be always learning; youth is the time of study, and here we must remember that the mind is free and dainty, and, unlike the body, must not be made to work against the grain. Learning should be at first a sort of play, in which the natural bent76 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 promising77 disciples, with whom a new epoch78 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 speculative79 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 illustrated80 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 doctrines81 which he learnt at home and which exercised a parental82 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 vice83 and vice virtue, and his mind becomes unsettled, and he ceases to love, honour, and obey them as he has hitherto done. He is seduced84 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 discredit85. 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 oracle86 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 aspiration87, 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 proceeding88 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 onward89 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 derive90 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 warrior91 athlete, and a good servant of the mind; — and thirdly, after an interval92 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; secondly93, 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 correlation94 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 opposition95 or proportion are suggestive of reflection. The mere impression of sense evokes96 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 Ethics97 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 depreciate98 their application to the arts. He will observe that Plato has a conception of geometry, in which figures are to be dispensed99 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, alas100! 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 allusion101 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 simplicity102 and certainty of astronomy and harmonics seemed to contrast with the variation and complexity103 of the world of sense; hence the circumstance that there was some elementary basis of fact, some measurement of distance or time or vibrations104 on which they must ultimately rest, was overlooked by him. The modern predecessors105 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 dynamics106, by the help of which most astronomical107 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 quantitative108 differences of physical phenomena109. 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, repel110 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 fixedness111 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 erring55 lives according to them.’ It is worthy112 of remark that the old Pythagorean ethical113 symbols still exist as figures of speech among ourselves. And those who in modern times see the world pervaded114 by universal law, may also see an anticipation115 of this last word of modern philosophy in the Platonic116 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 prevailing117 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 blurred118 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 deficient119 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 intervals120 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 philosophical121 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 variance122 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 derided123 and persecuted124 by them; but after a while they see the things below in far truer proportions than those who have never ascended125 into the upper world. The difference between the politician turned into a philosopher and the philosopher turned into a politician, is symbolized126 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 descends128 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 disciple74 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 Imperialism129, 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 Commonwealth130 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 today. They have been intoxicated131 with great ideas, such as liberty, or equality, or the greatest happiness of the greatest number, or the brotherhood132 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 luminous133 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 disorder127 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 sect134 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 disorders135.
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 ‘aufklarung.’ We too observe that when young men begin to criticise136 customary beliefs, or to analyse the constitution of human nature, they are apt to lose hold of solid principle (Greek). 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 paradoxes137 respecting morality, some fancy about art, some novelty or eccentricity138 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 discourse139 to any one about a new philosophy. They are generally the disciples of some eminent140 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 beset141 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 quaint142 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.)
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marionette
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parable
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behold
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rugged
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ascent
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fore
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descend
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dwelling
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upwards
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attains
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| （通常经过努力）实现( attain的第三人称单数 )； 达到； 获得； 达到（某年龄、水平、状况） | |
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beatific
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13
unwilling
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| adj.不情愿的 | |
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faculty
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| n.才能；学院，系；(学院或系的)全体教学人员 | |
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15
conversion
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| n.转化，转换，转变 | |
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16
virtue
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| n.德行，美德；贞操；优点；功效，效力 | |
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17
virtues
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| 美德( virtue的名词复数 )； 德行； 优点； 长处 | |
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18
rogue
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| n.流氓；v.游手好闲 | |
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19
bind
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| vt.捆，包扎；装订；约束；使凝固；vi.变硬 | |
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decided
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| adj.决定了的，坚决的；明显的，明确的 | |
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21
fixed
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| adj.固定的，不变的，准备好的；(计算机)固定的 | |
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22
ascend
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| vi.渐渐上升，升高；vt.攀登，登上 | |
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23
descending
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| n. 下行 adj. 下降的 | |
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24
salvation
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| n.（尤指基督）救世，超度，拯救，解困 | |
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25
remains
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| n.剩余物，残留物；遗体，遗迹 | |
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26
lame
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| adj.跛的，(辩解、论据等)无说服力的 | |
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27
stimulate
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| vt.刺激，使兴奋；激励，使…振奋 | |
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28
acquiesces
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| v.默认，默许( acquiesce的第三人称单数 ) | |
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29
stimulating
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| adj.有启发性的，能激发人思考的 | |
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30
relatively
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| adv.比较...地，相对地 | |
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31
distinguished
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| adj.卓越的，杰出的，著名的 | |
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32
beholds
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| v.看，注视( behold的第三人称单数 )；瞧；看呀；（叙述中用于引出某人意外的出现）哎哟 | |
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33
chaos
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| n.混乱，无秩序 | |
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34
intelligible
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| adj.可理解的，明白易懂的，清楚的 | |
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35
spoke
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| n.（车轮的）辐条；轮辐；破坏某人的计划；阻挠某人的行动 v.讲，谈（speak的过去式）；说；演说；从某种观点来说 | |
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36
stimulants
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| n.兴奋剂( stimulant的名词复数 )；含兴奋剂的饮料；刺激物；激励物 | |
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37
unity
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| n.团结，联合，统一；和睦，协调 | |
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38
foam
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| v./n.泡沫，起泡沫 | |
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39
flux
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| n.流动；不断的改变 | |
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40
lesser
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| adj.次要的，较小的；adv.较小地，较少地 | |
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41
retail
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| v./n.零售；adv.以零售价格 | |
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42
guardian
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| n.监护人；守卫者，保护者 | |
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43
purely
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| adv.纯粹地，完全地 | |
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44
mathematician
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| n.数学家 | |
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45
downwards
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| adj./adv.向下的（地），下行的（地） | |
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46
faculties
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| n.能力( faculty的名词复数 )；全体教职员；技巧；院 | |
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47
patronage
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| n.赞助，支援，援助；光顾，捧场 | |
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48
fully
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| adv.完全地，全部地，彻底地；充分地 | |
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49
votaries
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| n.信徒( votary的名词复数 )；追随者；（天主教）修士；修女 | |
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50
conceited
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| adj.自负的，骄傲自满的 | |
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51
embroidery
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| n.绣花，刺绣；绣制品 | |
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52
drawn
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| v.拖，拉，拔出；adj.憔悴的，紧张的 | |
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53
pervades
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| v.遍及，弥漫( pervade的第三人称单数 ) | |
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54
strings
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| n.弦 | |
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55
erring
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| 做错事的，错误的 | |
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56
prelude
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| n.序言，前兆，序曲 | |
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57
mere
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| adj.纯粹的；仅仅，只不过 | |
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58
hymn
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| n.赞美诗，圣歌，颂歌 | |
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59
beholding
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| v.看，注视( behold的现在分词 )；瞧；看呀；（叙述中用于引出某人意外的出现）哎哟 | |
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60
contemplate
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| vt.盘算，计议；周密考虑；注视，凝视 | |
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61
elevation
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| n.高度；海拔；高地；上升；提高 | |
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62
thither
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| adv.向那里；adj.在那边的，对岸的 | |
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63
attained
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| （通常经过努力）实现( attain的过去式和过去分词 )； 达到； 获得； 达到（某年龄、水平、状况） | |
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64
slough
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| v.蜕皮，脱落，抛弃 | |
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65
sketch
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| n.草图；梗概；素描；v.素描；概述 | |
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66
valiant
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| adj.勇敢的，英勇的；n.勇士，勇敢的人 | |
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67
toil
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| vi.辛劳工作，艰难地行动；n.苦工，难事 | |
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68
retentive
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| v.保留的，有记忆的；adv.有记性地，记性强地；n.保持力 | |
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69
diligent
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| adj.勤勉的，勤奋的 | |
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70
mire
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| n.泥沼，泥泞；v.使...陷于泥泞，使...陷入困境 | |
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71
bastard
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| n.坏蛋，混蛋；私生子 | |
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72
saviours
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| n.救助者( saviour的名词复数 )；救星；救世主；耶稣基督 | |
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73
disciples
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| n.信徒( disciple的名词复数 )；门徒；耶稣的信徒；（尤指）耶稣十二门徒之一 | |
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74
disciple
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| n.信徒，门徒，追随者 | |
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75
trampled
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| 踩( trample的过去式和过去分词 )； 践踏； 无视； 侵犯 | |
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76
bent
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| n.爱好，癖好；adj.弯的；决心的，一心的 | |
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77
promising
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| adj.有希望的，有前途的 | |
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78
epoch
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| n.(新)时代；历元 | |
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79
speculative
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| adj.思索性的，暝想性的，推理的 | |
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80
illustrated
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| adj. 有插图的，列举的 动词illustrate的过去式和过去分词 | |
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81
doctrines
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| n.教条( doctrine的名词复数 )；教义；学说；（政府政策的）正式声明 | |
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82
parental
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| adj.父母的；父的；母的 | |
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83
vice
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| n.坏事；恶习；[pl.]台钳，老虎钳；adj.副的 | |
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84
seduced
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| 诱奸( seduce的过去式和过去分词 )； 勾引； 诱使堕落； 使入迷 | |
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85
discredit
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| vt.使不可置信；n.丧失信义；不信，怀疑 | |
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86
oracle
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| n.神谕，神谕处，预言 | |
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87
aspiration
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| n.志向，志趣抱负；渴望；(语)送气音；吸出 | |
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88
proceeding
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| n.行动，进行，(pl.)会议录，学报 | |
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89
onward
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| adj.向前的，前进的；adv.向前，前进，在先 | |
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90
derive
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| v.取得；导出；引申；来自；源自；出自 | |
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91
warrior
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| n.勇士，武士，斗士 | |
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92
interval
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| n.间隔，间距；幕间休息，中场休息 | |
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93
secondly
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| adv.第二，其次 | |
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94
correlation
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| n.相互关系，相关，关连 | |
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95
opposition
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| n.反对，敌对 | |
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96
evokes
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| 产生，引起，唤起( evoke的第三人称单数 ) | |
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97
ethics
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| n.伦理学；伦理观，道德标准 | |
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98
depreciate
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| v.降价，贬值，折旧 | |
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99
dispensed
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| v.分配( dispense的过去式和过去分词 )；施与；配（药） | |
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100
alas
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| int.唉(表示悲伤、忧愁、恐惧等) | |
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101
allusion
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| n.暗示，间接提示 | |
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102
simplicity
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| n.简单，简易；朴素；直率，单纯 | |
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103
complexity
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| n.复杂(性)，复杂的事物 | |
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104
vibrations
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| n.摆动( vibration的名词复数 )；震动；感受；（偏离平衡位置的）一次性往复振动 | |
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105
predecessors
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| n.前任( predecessor的名词复数 )；前辈；（被取代的）原有事物；前身 | |
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106
dynamics
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| n.力学，动力学，动力，原动力；动态 | |
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107
astronomical
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| adj.天文学的，（数字）极大的 | |
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108
quantitative
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| adj.数量的，定量的 | |
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109
phenomena
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| n.现象 | |
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110
repel
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| v.击退，抵制，拒绝，排斥 | |
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111
fixedness
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| n.固定；稳定；稳固 | |
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112
worthy
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| adj.(of)值得的，配得上的；有价值的 | |
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113
ethical
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| adj.伦理的，道德的，合乎道德的 | |
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114
pervaded
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| v.遍及，弥漫( pervade的过去式和过去分词 ) | |
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115
anticipation
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| n.预期，预料，期望 | |
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116
platonic
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| adj.精神的；柏拉图（哲学）的 | |
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117
prevailing
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| adj.盛行的；占优势的；主要的 | |
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118
blurred
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| v.（使）变模糊( blur的过去式和过去分词 )；（使）难以区分；模模糊糊；迷离 | |
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119
deficient
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| adj.不足的，不充份的，有缺陷的 | |
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120
intervals
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| n.[军事]间隔( interval的名词复数 )；间隔时间；[数学]区间；（戏剧、电影或音乐会的）幕间休息 | |
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121
philosophical
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| adj.哲学家的，哲学上的，达观的 | |
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122
variance
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| n.矛盾，不同 | |
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123
derided
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| v.取笑，嘲笑( deride的过去式和过去分词 ) | |
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124
persecuted
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| （尤指宗教或政治信仰的）迫害(~sb. for sth.)( persecute的过去式和过去分词 )； 烦扰，困扰或骚扰某人 | |
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125
ascended
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| v.上升，攀登( ascend的过去式和过去分词 ) | |
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126
symbolized
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| v.象征，作为…的象征( symbolize的过去式和过去分词 ) | |
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127
disorder
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| n.紊乱，混乱；骚动，骚乱；疾病，失调 | |
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128
descends
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| v.下来( descend的第三人称单数 )；下去；下降；下斜 | |
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129
imperialism
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| n.帝国主义，帝国主义政策 | |
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130
commonwealth
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| n.共和国，联邦，共同体 | |
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131
intoxicated
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| 喝醉的，极其兴奋的 | |
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132
brotherhood
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| n.兄弟般的关系，手中情谊 | |
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133
luminous
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| adj.发光的，发亮的；光明的；明白易懂的；有启发的 | |
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134
sect
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| n.派别，宗教，学派，派系 | |
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135
disorders
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| n.混乱( disorder的名词复数 )；凌乱；骚乱；（身心、机能）失调 | |
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136
criticise
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| v.批评，评论；非难 | |
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137
paradoxes
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| n.似非而是的隽语，看似矛盾而实际却可能正确的说法( paradox的名词复数 )；用于语言文学中的上述隽语；有矛盾特点的人[事物，情况] | |
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138
eccentricity
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| n.古怪，反常，怪癖 | |
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139
discourse
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| n.论文，演说；谈话；话语；vi.讲述，著述 | |
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140
eminent
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| adj.显赫的，杰出的，有名的，优良的 | |
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beset
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| v.镶嵌；困扰，包围 | |
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quaint
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| adj.古雅的，离奇有趣的，奇怪的 | |
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