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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.