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, and their labour, like that of the astronomers, is in vain.
Yes, by heaven! he said; and 'tis as good as a play to hear them talking about their condensed notes, as they call them; they put their ears close alongside of the strings like persons catching a sound from their neighbour's wall--one set 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 rack them on the pegs of the instrument: I might 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 enquire 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 and 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 speaking, 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?
Assuredly 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 will have the knowledge which we require of them?
Neither can this be supposed.
And so, Glaucon, 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 light 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 you call 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 (which are divine), and are the shadows of true existence (not shadows of images cast by a light of fire, which compared with the sun is only an image)--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 study 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.