“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. Stargazing 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 embroidery 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 drawn 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 pervades 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 strings 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 prelude 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 mere 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 hymn of dialectic which is the music of the intellectual world, and which was by us compared to the effort of sight, when from beholding 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 contemplate 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 elevation 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 thither?” 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 attained 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 slough 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,
