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Start listening today at P-O-D-C-A-S-T-L-I-D-R-A-R-Y.org. Start listening today at P-O-D-C-A-S-T-L-I-D-R-A-R-Y.org. A-O-D-C-A-S-T-L-I-R-Y-R-Y-R-Y-R-Y-R-Y-R-Y-R-Y-R-Y-R-Y-R-Y-R-Y-R-Y-R-Y-R-Y-R-Y-R-Y-R-Y-G. Next, I asked Professor Yes, that is what be a zerd.
Yet, anybody who has the least acquaintance with geometry will not deny that such a conception of the science is in flat contradiction to the ordinary language of dual-matricians. How so? They have in view practice only, and are always speaking in a narrow and ridiculous manner of squaring and extending and applying and the like. They confuse the necessities of geometry with those of daily life, whereas knowledge is the real object of the whole science.
Certainly, he said. Then must not a further admission be made. Not admission. That the knowledge at which geometry aims is knowledge of the eternal, and not of art perishing and transient.
That, he replied, may be readily allowed, and is true. Then my noble friend, geometry will draw the soul towards truth and create the spirit of philosophy and raise up that which is now unhappily allowed to fall down. Nothing will be more likely to have such an effect. Then nothing should be more sternly laid down than that the inhabitants of your first city should by all means learn geometry.
Moreover, the science has indirect effects which are not small. Of what kind, he said. There are the military advantages of which he spoke, I said, and in all departments of knowledge as experienced groups, anyone who has studied geometry is infinitely quicker of apprehension than one who has not. Yes, indeed, he said, there is an infinite difference between them.
Then, shall we propose this as a second branch of knowledge which are youthful study? Let us do so, he replied. And suppose we make astronomy the third, what do you say? I am strongly inclined to it, he said.
The observation of the seasons and of months and years is as essential to the general as it is to the farmer or sailor. I am amused, I said, as your fear of the world which makes you guard against the appearance of insisting upon useless studies. And I quite admit the difficulty of believing that in every man there is an eye of the soul which, when by other pursuits lost and dimmed, is by these purified and re-illumined, and is more precious far than ten thousand bodily eyes, for by it alone is truth seen. Now, there are two classes of persons.
One class of those will agree with you and will take your words as a revelation, another class to whom they will be utterly unmeaning, and will naturally deem them to be idle tales, for they see no sort of profit which is to be obtained from them, and therefore you have better decide at once with which of the two you are proposing to argue. You will very likely say, with neither, and that your chief aim in carrying on the argument is your own improvement. At the same time, you do not grudge to others any benefits which they may receive. I think that I should prefer to carry on the argument mainly on my own behalf.
Then, take a step backward, for we have gone wrong in the order of the sciences. What was the mistake, he said? After plain geometry, I said, we proceeded at once the solids in revolution, instead of taking solids in themselves, whereas after the second dimension, the third, which is concerned with cubes and dimensions of depth, ought to have followed. That is true, Socrates, but so little seems to be known as yet about these subjects.
Why, yes, I said, and for two reasons, in the first place no government patronizes them, this leads to a want of energy in the pursuit of them, and they are difficult. In the second place, students cannot learn them unless they have a director, but then a director can hardly be found, and even if he could, as matters now stand, the students, who are very conceited, would not attend to him. That however, would be otherwise if the whole state became the director of these studies and gave honor to them. Then disciples would want to come, and there would be continues and earnest search, and discoveries would be made.
This even now, disregarded as they are by the world, and made of their fair proportions, and although none of their votaries can tell the use of them, steal these studies forced their way by their natural charm, and very likely, if they had the help of the state, they would someday emerge into light. Yes, he said, there is a remarkable charm in them, but I do not clearly understand the change in the order. First you began with the geometry of plain surfaces. Yes, I said, and you placed astronomy next, and then you made a step backward.
Yes, and I have delayed you by my hurry. The liticrous state of solid geometry, which, in natural order, should have followed, made me pass over this branch and go on to astronomy or motion of solids. True, he said. Then, assuming that the science now omitted would come into existence, if encouraged by the state, let us go on to astronomy, which will be forth.
The right order, he replied, and now Socrates, as he rebuked the vulgar manner in which I praised astronomy before, my praise shall be given in your own spirit. For every one, as I think, must see that astronomy compels the soul to look upwards and leads this from this world to another. Everyone but myself, I said, to everyone else this may be clear, but not to me. And what then would you say?
I should rather say that those who elevate astronomy into philosophy appeared to me to make us look downwards and not upwards. What do you mean, he asked? You, I replied, having your mind a truly sublime conception of our knowledge of the things above, and I dare say that if a person were to throw his head back and study the fretted ceiling, you would still think that his mind was the Percipient, and not his eyes. And you are very likely right, and I may be a simpleton.
But in my opinion, that knowledge, only which is of being and of the unseen, can make the soul look upwards, and whether men gape at the heavens or blinks on the ground, seeking to learn some particular sense, I will deny that he can learn, for nothing of that sort is matter of science. His soul is looking downwards, not upwards, whether his way to knowledge is by water or by land, whether he flows or only lies on his back. I acknowledge, he said, the justice of your rebuke. Still, I should like to a certain, how astronomy can be learned in any manner more conducive to that knowledge of which we are seeking.
I will tell you, I said, the starry heaven which we behold is wrought upon a visible ground, and therefore, although the fairest and most perfect of visible things, must necessarily be deemed inferior far to the true motions of absolute swiftness and absolute slowness which are relative to each other, and carry with them that which is contained in them in the true number and in every true figure. Now, these are to be apprehended by reason and intelligence, but not by sight. True, he replied, the spangled heavens should be used as a pattern, and with a view to that higher knowledge, their beauty is like the beauty of figures or pictures, excellently brought by the hand of Daedalus, or some other great artist, which we may chance to behold, any geometrician who saw them would appreciate the exquisiteness of their workmanship, but he would never dream of thinking that in them he could find the true equal or the true double or the truth of any other proportion. No, he replied, such an idea would be ridiculous, and will not a true astronomer have the same feeling when he looks at the movements of the stars, who cannot think that heaven and the things in heaven are framed by the creator of them in the most perfect manner, but he will never imagine that the proportions of night and day, or of both to the month, or of the month to the year, or of the stars to these into one another, and any other things that are material and visible, can also be eternal and subject to no deviation.
That would be absurd, and it is equally absurd to take so much pains in investigating their exact truth. I quite agree, though I never thought of this before. Then I said, in astronomy, as in geometry, we should employ problems, in that the heavens alone, if we would approach the subject in the right way, and so make the natural gift of reason to be of any real use. He said, is a work infinitely beyond our present astronomers.
Yes, I said, and there are many other things which must also have a similar extension given to them, if our legislation is to be of any value. But can you tell me of any other suitable study? No, he said, not without thinking. Motion, I said, has many forms, and not one only.
Two of them are obvious enough even to which snow better than ours, and there are others, as I imagine, which may be left to wiser persons. But when are the two? There is a second, I said, which is the counterpart of the one already named. And what may that be?
The second, I said, would seem relatively to the ears to be what the first is to the eyes, for I can see that as the eyes are designed to look up at the stars, so are the ears to hear harmonious motions. And these are sister sciences, as the Pythagorean say, and we, Glauken, agree with them? Yes, he replied. But this, I said, is a laborious study, and therefore we had better go and learn of them.
And they will tell us whether there are any other applications of these sciences. At the same time, we must not lose sight of our own higher object. What is that? There is a perfection which all knowledge ought to reach, and which our pupils ought also to attain, and not to fall short of, as I was saying that they did in astronomy.
For in the science of harmony, as you probably know, the same thing happens. The teachers of harmony compare the sounds and consonances which are heard only in their labor like that of the astronomers, is in vain. Yes, by heaven, he said, and it is as good as a play to hear them talking about their condensed notes as they call them. They put their ears closed alongside of the streams, like persons sketching a sound from their neighbor's wall, once out of them declaring that they distinguish an intermediate note and have found the least interval which should be the unit of measurement.
The others insisting that the two sounds have passed into the same, either party setting their ears before their understanding. You mean, I said, those gentlemen who tease and torture the strings and wreck them on the pads of the instrument. I would carry on the metaphor and speak after their manner of the blows which the plectrum gives and make accusations against the strings, both of backwardness and forwardness to sound. But this would be tedious, and therefore I will only say that these are not the men, and that I am referring to the Pythagoreans, of whom I was just now proposing to inquire about harmony, for they too are in error, like the astronomers.
They investigate the numbers of the harmonies which are heard, but they never attain to problems, that is to say, they never reach the natural harmonies of number, or reflect why some numbers are harmonious and others not. That he said, is a thing of more than mortal knowledge. A thing, I replied, which I would rather call useful, that is, if sought after with a view to the beautiful and good, but if pursued in any other spirit, useless. Very true, he said.
Now, when all these studies reach the point of inter-communion in connection with one another, and come to be considered in their mutual affinities, then, I think, but not till then, will the pursuit of them have a value for our objects, otherwise there is no profit in them. I suspect so, but you are seeking Socrates of a vast work. What do you mean, I said? The prelude or what?
Do you not know that all this is but the prelude to the actual strain which we have to learn? For you surely would not regard the skilled mathematician as a dialectician. A shrewdly not, he said. I have hardly ever known a mathematician who was capable of reasoning.
But do you imagine that men who are unable to give and take a reason who have the knowledge which we require of them? Neither can this be supposed. And so, Galkon, I said, we have at last arrived at the hymn of dialectic. This is that strain which is of the intellect only, but which the faculty of sight will nevertheless be found to imitate.
For sight, as you may remember, was imagined by us after a while to behold the real animals and stars, and last of all the sun himself. And so with dialectic, when a person starts on the discovery of the absolute by the life of reason only, and without any assistance of sense, and perseveres until by pure intelligence he arrives at the perception of the absolute good, he at last finds himself at the end of the intellectual world, as in the case of sight at the end of the visible. Exactly, he said. Then this is the progress which are called dialectic.
True. But the release of the prisoners from chains, and their translation from the shadows to the images and to the light, and the ascent from the underground den to the sun, while in his presence they are vainly trying to look on animals and plants and the light of the sun, but are able to perceive even with their weak eyes the images in the water, and are the shadows of true existence. This power of elevating the highest principle in the soul, to the contemplation of that which is best in existence, with which we may compare the raising of that faculty which is the very light of the body to the sight of that which is brightest in the material and visible world, this power is given, as I was saying, by all that steady and pursuit of the arts which has been described. I agree in what you are saying, he replied, which may be hard to believe, yet from another point of view is harder still to deny.
This however is not a theme to be treated of in passing only, but will have to be discussed again and again. And so, whether our conclusion be true or false, let us assume all this, and proceed at once from the prelude or preamble to the chief strain, and describe that in like manner. Say then, what is the nature and what are the divisions of dialectic, and what are the paths which lead thither, for these paths will also lead to our final rest. Dear Glauken, I said, you will not be able to follow me here, though I would do my best, and you should behold not an image only but the absolute truth according to my notion, whether what I told you would or would not have been a reality, I cannot venture to say, but you would have seen something like reality.
Of that I am confident. Douglass he replied, but I must also remind you that the power of dialectic alone can reveal this, and only to one who is a disciple of the previous sciences. Of that assertion you may be as confident as of the last. And assuredly no one will argue that there is any other method of comprehending by any regular process, all true existence, or are ascertaining what each thing is in its own nature, for the arts in general are concerned with the desires or opinions of men, or are cultivated with a view to production and construction, or for the preservation of such productions and constructions.
And after the mathematical sciences, which as we were saying, have some apprehension of true being, geometry and the like, they only dream about being, but never can they behold the waking reality so long as they leave the hypotheses which they use unexamined, and are unable to give an account of them. For when a man knows not his own first principle, and when the conclusion and intermediate steps are also constructed out of his knows not what, how can he imagine that such a fabric of convention can ever become science? Impossible, he said. Then dialectic, and dialectic alone goes directly to the first principle, and is the only science which does away with hypotheses in order to make her ground secure.
The eye of the soul, which is literally buried in an outlandish slew, is by her gentle aid lifted upwards, and she uses as hand-nades and helpers in the work of conversion the sciences which we have been discussing. And as we have been, we have been able to make a proportion, and as being is to be coming, so is pure intellect to opinion, and as intellect is to opinion, so is science to believe, and understanding to the perception of shadows. End of Book 7, Part 3.