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27 - The Republic - Plato · Logic Library

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Seven par three. And next shall we inquire whether the kindred science also concerns
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us? You mean geometry exactly so clearly, he said, we are concerned
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with that part of geometry which relates to war. For in pitching a camp,
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or taking up a position, or closing or extending the lines of an
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army, or any other military maneuver, whether in actual battle or in a
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march, it will make all the difference whether a general is or is not
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a geometrician. Yes, I said, But for that purpose a very little
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of either geometry or calculation will be enough. The question relates rather to the
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greater and more advanced part of geometry, whether that tends in any degree to
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make more easy the vision of the idea of good and thither, as I
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was saying, all things which compel the soul to turn her gaze towards that
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place where is the full perfection of being which she ought by all means to
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behold true, he said, then, if geometry compels us to view being,
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it concerns us. If becoming only it does not concern us. Yes,
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that is what we assert. Yet anybody who has the least acquaintance with
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geometry will not deny that such a conception of the science is in flat contradiction
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to the ordinary language of geometricians. How So they have in view practice only,
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and are always speaking in a narrow and ridiculous manner of squaring and extending
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and applying and the like. They confuse the necessities of geometry with those of
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daily life, whereas knowledge is the real object of the whole science. Certainly,
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he said, then must not a further admission be made? What admission
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that the knowledge at which geometry aims is knowledge of the eternal and not of
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aught, perishing and transient, that he replied, may be readily allowed?
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And it is true, then, my noble friend, geometry will draw the
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soul towards truth, and create the spirit of philosophy, and raise up that
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which is now unhappily allowed to fall down. Nothing will be more likely to
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have such an effect. Then, nothing should be more sternly laid down than
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that the inhabitants of your fair city should, by all means learn geometry.
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Moreover, the science has indirect effects which are not small. Of what kind
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he said. There are the military advantages of which he spoke, I said,
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And in all departments of knowledge, as experience proves any one who has
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studied geometry is infinitely quicker of apprehension than one who has not. Yes,
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indeed, he said, there is an infinite difference between them. Then shall
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we propose this as a second branch of knowledge which our youth will study.
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Let us do so, he replied, And suppose we make astronomy the third.
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What do you say, I am strongly inclined to it, he said.
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The observation of the seasons and of months and years is as essential to
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the general as it is to the farmer or sailor. I am amused,
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I said, at your fear of the world, which makes you guard against
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the appearance of insisting upon useless studies. And I quite admit the difficulty of
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believing that in every man there is an eye of the soul, which,
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when by other pursuits lost and dimmed, is by these purified and re illumined,
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and is more precious far than ten thousand bodily eyes, For by it
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alone is truth seen. Now there are two classes of persons, one class
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of those who will agree with you and will take your words as a revelation,
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another class to whom they will be utterly unmeaning and who will naturally deem
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them to be idle tales, for they see no sort of profit which is
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to be obtained from them. And therefore you had better decide at once with
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which of the two you are proposing to argue. You will very likely say
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with neither, and that your chief aim in carrying on the argument is your
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own improvement. At the same time, you do not grudge to others any
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benefit which they may receive. I think that I should prefer to carry on
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the argument mainly on my own behalf. Then take a step backward where we
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have gone wrong in the order of the sciences. What was the mistake?
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He said, After plain geometry, I said, we proceeded at once the
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solids in revolution, instead of taking solids in themselves. Whereas after the second
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dimension, the third, which is concerned with cubes and dimensions of depth,
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ought to have followed. That is true, Socrates. But so little seems
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to be known as yet about these subjects. Why yes, I said,
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And for two reasons. In the first place, no government patronizes them.
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This leads to a want of energy in the pursuit of them, and they
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are difficult. In the second place, students cannot learn them unless they have
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a director. But then a director can hardly be found, and even if
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he could, as matters now stand, the students, who are very conceited,
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would not attend to him. That, however, would be otherwise.
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If the whole state became the director of these studies and gave honor to them,
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then disciples would want to come, and there would be continuous and earnest
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search, and discoveries would be made. Since, even now, disregarded as
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they are by the world and maying of their fair proportions, and although none
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of their votaries can tell the use of them, still these studies forced their
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way by their natural charm, and very likely, if they had the help
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of the state, they would some day emerge into light. Yes, he
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said, there is a remarkable charm in them, But I do not clearly
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understand the change in the order. First, you began with the geometry of
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plain surfaces, yes, I said, And you placed astronomy next. And
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then you made a step backward. Yes, And I have delayed you by
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my hurry. The ludicrous state of solid geometry, which in natural order should
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have followed, made me pass over this branch and go on to astronomy or
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motion of solids. True, he said, then, assuming that the science
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now omitted would come into existence if encouraged by the state, let us go
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on to astronomy, which will be fourth the right order, he replied.
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And now, Socrates, as he rebuked the vulgar manner in which I praised
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astronomy before my praise shall be given in your own spirit. For every one,
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as I think, must see that astronomy compels the soul to look upwards
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and leads us from this world to another. Every one but myself, I
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said. To every one else, this may be clear, but not to
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me. And what then would you say? I should rather say that those
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who elevate astronomy into philoilosophy appear to me to make us look downwards and not
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upwards. What do you mean, he asked you, I replied, have
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in your mind a truly sublime conception of our knowledge of the things above.
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And I dare say that if a person were to throw his head back and
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study the fretted ceiling, you would still think that his mind was the percipient
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and not his eyes. And you are very likely right. And I may
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be a simpleton, but in my opinion, that knowledge only which is of
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being and of the unseen, can make the soul look upwards. And whether
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a man gains at the heavens or blinks on the ground seeking to learn ter
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particular of sense, I would deny that he can learn, for nothing of
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that sort is matter of science. His soul is looking downwards, not upwards,
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whether his way to knowledge is by water or by land, whether he
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floats or only lies on his back, I acknowledge, he said, the
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justice of your rebuke. Still, I should like to ascertain how astronomy can
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be learned in any manner more conducive to that knowledge of which we are speaking.
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I will tell you, I said, the starry heaven which we behold
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is wrought upon a visible ground. And therefore, although the fairest and most
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perfect of visible things must necessarily be deemed inferior far to the true motions of
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absolute swiftness and absolute slowness, which are relative to each other, and carry
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with them that which is contained in them, in the true number and in
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every true figure. Now these are to be apprehended by reason and intelligence,
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but not by sight. True, he replied, the spangled heavens should be
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used as a pattern and with a view to that higher knowledge. Their beauty
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is like the beauty of figures, or pictures excellent wrought by the hand of
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Daedalus or some other great artist, which we may chance to behold. Any
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geometrician who saw them would appreciate the exquisiteness of their workmanship. But he would
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never dream of thinking that in them he could find the true equal, or
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the true double, or the truth of any other proportion. No, he
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replied, such an idea would be ridiculous, And will not a true astronomer
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have the same feeling when he looks at the movements of the stars. Will
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he not think that heaven and the things in heaven are framed by the creature
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of them in the most perfect manner. But he will never imagine that the
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proportions of night and day, or of both, to the month, or
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of the month to the year, or of the stars, to these and
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to one another, and any other things that are material and visible, can
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also be eternal and subject to no deviation. That would be absurd, And
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it is equally absurd to take so much pains in investigating their exact truth.
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I quite agree, though I never thought of this before then. I said,
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in astronomy, as in geometry, we should employ problems and let the
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heavens alone, if we would approach the subject in the right way, and
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so make the natural gift of reason to be of any real use. That
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he said, is a work infinitely beyond our present astronomers. Yes, I
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said, And there are many other things which must also have a similar extension
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given to them, if our legislation is to be of any value. But
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can you tell me of any other suitable study, No, he said,
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not without thinking. Motion, I said, has many forms, and not
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one. Only two of them are obvious enough even to witsnow better than ours.
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And there are others, as I imagine, which may be left to
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wiser persons. But where are the two? There is a second, I
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said, which is the counterpart of the one already named. And what may
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that be? The second, I said, would seem relatively to the ears
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to be what the first is to the eyes. For I conceive that as
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the eyes are designed to look up at the stars, so are the ears
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to hear harmonious motions. And these are sister sciences, as the Pythagoreans say,
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and we glaucan agree with them. Yes, he replied, But this,
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I said, is a laborious study, and therefore we had better go
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and learn of em, and they will tell us whether there are any other
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applications of these sciences. At the same time, we must not lose sight
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of our own higher object. What is that there is a perfection which all
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knowledge ought to reach, and which our pupils ought also to attain, and
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not to fall short of, as I was saying that they did in astronomy.
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For in the science of harmony, as you probably know, the same
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thing happens. The teachers of harmony compare the sounds and consonances which are heard
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only, and their labor, like that of the astronomers, is in vain,
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Yes, by heaven, he said, and tis as good as a
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play to hear them talking about their condensed notes, as they call them.
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They put their ears close alongside of the strings, like persons catching a sound
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from their neighbor's wall. Once said of them, declaring that they distinguish an
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intermediate note and have found the least interval, which should be the unit of
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measurement. The others, insisting that the two sounds have passed into the same
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Either parties, setting their ears before their understanding. You mean, I said,
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those gentlemen who tease and torture the strings and reck them on the pegs
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of the instrument. I might carry on the metaphor and speak after their manner
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of the blows which the plectrum gives, and make accusations against the strings,
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both of backwardness and forwardness to sound. But this would be tedious, and
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therefore I will only say that these are not the men, and that I
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am referring to the Pythagoreans of whom I was just now proposing to inquire about
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harmony. For they too are in error. Like the astronomers. They investigate
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the numbers of the harmonies which are heard, but they never attain to problems,
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that is to say, they never reach the natural harmonies of number,
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or reflect why some numbers are harmonious and others not. That, he said,
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is a thing of more than mortal knowledge, a thing, I replied,
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which I would rather call useful, that is, if sought after with
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a view to the beautiful and good, but if pursued in any other spirit,
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useless. Very true, he said, Now, when all these studies
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reach the point of intercommunion and connection with one another, and come to be
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considered in their mutual affinities, then, I think, But not till then
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will the pursuit of them have a value for our objects. Otherwise there is
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no profit in them, I suspect so. But you are speaking, Socrates,
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of a vast work. What do you mean, I said, the
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prelude? Or what? Do you not know? That all this is but
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the prelude to the actual strain which we have to learn? For you surely
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would not regard the skilled mathematician as a dialectician. Assuredly not, he said,
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I have hardly ever known a mathematician who was capable of reasoning. But
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do you imagine that men who are unable to give and take a reason will
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have the knowledge which we require them? Neither can this be supposed? And
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so glaucon I said, we have at last arrived at the hymn of dialectic.
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This is that strain which is of the intellect only, but which the
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faculty of sight will nevertheless be found to imitate. For sight, as you
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may remember, was imagined by us after a while to behold the real animals
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and stars, and last of all the sun himself. And so with dialectic,
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when a person starts on the discovery of the absolute by the light of
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reason only and without any assistance of sense, and perseveres until by pure intelligence
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he arrives at the perception of the absolute good. He at last finds himself
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at the end of the intellectual world, as in the case of sight,
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at the end of the visible Exactly, he said, then, this is
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the progress which we call dialectic true. But the release of the prince listeners
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from chains, and their translation from the shadows to the images, and to
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the light, and the ascent from the underground then to the sun. While
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in his presence they are vainly trying to look on animals and plants and the
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light of the sun, but are able to perceive, even with their weak
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eyes, the images in the water and are the shadows of true existence.
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This power of elevating the highest principle in the soul to the contemplation of that
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which is best in existence, with which we may compare the raising of that
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faculty, which is the very light of the body, to the sight of
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that which is brightest in the material and visible world. This power is given,
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as I was saying, by all that steady and pursuit of the arts
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which has been described. I agree in what you are saying, he replied,
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which may be hard to believe. Yet from another point of view is
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harder still to deny. This, however, is not a theme to be
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treated of in passing only, but will have to be discussed again and again.
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And so, whether our conclusion be true or false, let us assume
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all this and proceed at once from the prelude or preamble to the chief strain,
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and describe that in like manner. Say, then, what is the
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nature and what are the divisions of dialectic? And what are the paths which
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lead thither? For these paths will also lead to our final rest. Dear
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Glaucan, I said, you will not be able to follow me here,
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though I would do my best, and you should behold not an image only,
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but the absolute truth, according to my notion. Whether what I told
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you would or would not have been a reality, I cannot venture to say.
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But you would have seen something like reality of that I am confident doubtless,
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he replied. But I must also remind you that the power of Dialectican
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can reveal this, and only to one who is a disciple of the previous
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sciences of that assertion, you may be as confident as of the last,
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and assuredly no one will argue that there is any other method of comprehending,
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by any regular process all true existence, or of ascertaining what each thing is
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in its own nature. For the arts in general are concerned with the desires
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or opinions of men, or are cultivated with a view to production and construction,
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or for the preservation of such productions and constructions. And as to the
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mathematical sciences, which, as we were saying, have some apprehension of true
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being, geometry and the like, they only dream about being. But never
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can they behold the waking reality, so long as they leave the hypotheses which
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they use unexamined, and are unable to give an account of them. For
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when a man knows not his own first principle, and when the conclusion and
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intermediate its steps are also constructed out of he knows not what how can he
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imagine that such a fabric of convention can ever become science? Impossible? He
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said, then dialectic and dialectic alone goes directly to the first principle, and
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is the only science which does away with hypotheses in order to make her ground
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secure. The eye of the soul, which is literally buried in an outlandish
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slew, is by her gentle aid lifted upwards, and she uses as handmaids
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and helpers in the work of conversion. The sciences which we have been discussing,
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custom terms them sciences, But they ought to have some other name,
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implying greater clearness than opinion, and less clearness than science. And this in
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our previous sketch was called understanding. But why should we dispute about names when
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we have realities of such importance to consider? Why? Indeed, he said,
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when any name will do which expresses the thought of the mind with clearness.
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At any rate, we are satisfied as before to have four divisions,
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two for intellect and two for opinion, and to call the first division science,
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the second understanding, the third belief, and the fourth perception of shadows.
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Opinion being concerned with becoming and intellect with being, And so to make
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a proportion. As being is to becoming, so is pure intellect to opinion.
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And as intellect is to opinion, so is science to believe, and
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understanding to the perception of shadows. End of Book seven, Part three