I understand, he said, and agree with you.
And to which class do unity and number belong?
I do not know, he replied.
Think a little and you will see that what has preceded will supply the answer; for if simple unity could be adequately perceived by the sight or by any other sense, then, as we were saying in the case of the finger, there would be nothing to attract toward being; but when there is some contradiction always present, and one is the reverse of one and involves the conception of plurality, then thought begins to be aroused within us, and the soul perplexed and wanting to arrive at a decision asks, “What is absolute unity?” This is the way in which the study of the one has a power of drawing and converting the mind to the contemplation of true being.
And surely, he said, this occurs notably in the case of one; for we see the same thing to be both one and infinite in multitude?
Yes, I said; and this being true of one must be equally true of all number?
Certainly.
And all arithmetic and calculation have to do with number?
Yes.
And they appear to lead the mind toward truth?
Yes, in a very remarkable manner.
Then this is knowledge of the kind for which we are seeking, having a double use, military and philosophical; for the man of war must learn the art of number or he will not know how to array his troops, and the philosopher also, because he has to rise out of the sea of change and lay hold of true being, and therefore he must be an arithmetician.
That is true.
And our guardian is both warrior and philosopher?
Certainly.
Then this is a kind of knowledge which legislation may fitly prescribe; and we must endeavor to persuade those who are to be the principal men of our State to go and learn arithmetic, not as amateurs, but they must carry on the study until they see the nature of numbers with the mind only; nor again, like merchants or retail-traders, with a view to buying or selling, but for the sake of their military use, and of the soul herself; and
