Phaedrus — Plato

p. 327What quality? Usefulness in war. Yes, if possible. There were two parts in our former scheme of education, were there not ? True. There was gymnastic which presided over the growth and decay of the body, and may therefore be regarded as having to do with generation and corruption ? True. Then that is not the knowledge which we are seeking to discover ? ^^^ No. But what do you say of music, as far as that entered into our scheme ? That, he said, as you will remember, was the counterpart of gymnastic, and trained the guardians by the influences of habit, giving them, not science, but a sort of harmonical composition, and a kind of rhythmical movementy-and the words, whether true or false, had kindred elements of rhythm and harmony in them ; but musical knowledge was not of a kind which tended to that good which you are now seeking. You are most acciu*ate, I said, in your recollection; for there certainly was nothing of that kind in our previous education. But then what branch of knowledge is there, my dear friend, which is of the desired nature ? For the useful arts were rejected by us as mean. Undoubtedly ; and yet if music and g)niinastic are excluded, and the arts are also excluded, what remains? Well, I said, there may be nothing left ; and then we shall have to take something which is of universal application. What is that ? A something which all arts and sciences and intelligences use in common, and which 6very one ought to learn among the elements of education. What is that ? The little matter of distinguishing one, two, and three, which I may sum up under the name of i^umber and calculatio»,— of that all arts and sciences are necessarily partakers. Very true. Then the art of war partakes of them ?

V.

-V

p. 328To be sure. Then Palamedes,^ when he appears in the play, proves Agamemnon* ridiculously unfit to be a general.

Did you never remark how he declares that he had invented number, and had numbered and set in array the ranks of the army at Troy ; which implies that they had never been numbered before, and Agamemnon must be supposed literally to have been incapable of counting his own feet — how could he, if he was ignorant of number ? And if that is true, what sort of a general must he have been ? I should say a very strange one, certainly.

Must not a warrior then, I said, in addition to his military skill, have a knowledge of arithmetic ? Certainly he must, if he is to have the slightest knowledge of military tactics, or indeed, I should rather say, if he is to be a man at all. I should like to know whether you have the same notion which I have of this study ? What is that ?

I am of opinion that this is 'a study of the kind which we are seeking, and which leads naturally to reflection, 5^3- but one which has never been rightly used as simply ^ conducting towards being. Will you explain your meaning ? he said.

I will try, I said ; and I wish you would consider and help me, and say *' yes*' or ** no " when I attempt to distinguish in my own mind what branches of knowledge have this conducting power, in order that we may have clearer proof that this is one of them. [Some objects we seem able to know sufficiently with the senses alone. Others demand further investigation. In making this investigation we find it profitable to count and calculate.

But besides this practical value, ** arithmetic has a very great and elevating effect, compelling the soul to reason about abstract number, and if visible or tangible objects are obtruding upon the argument, refusing to be satisfied."] That is very true. Now, suppose a person were to say to the arithmeticians : • See Apology, note 55. * See Apology, note ai.

p. 329O my friends, what are these wonderful numbers about which you are reasoning, in which, as you say, there is a unity such as you require, and each unit is equal, invariable, indi- ^ visible, what would they answer ? ^ They would answer, as I suppose, that they are speaking of those numbers which are only realized in thought.

Then you see that this knowledge may be truly called necessary, as necessitating the use of the pure intelligence in the attainment of pure truth ? Yes ; that is a marked characteristic. And have you further remarked that those who have a natural talent for calculation are generally quick at every other kind of knowledge ; and even the dull, if they have had an arithmetical training, gain in quickness, if not in any other way?

That is true, he said. And indeed, you will not easily find a more difficult study, and not many as difficult. You will not. And, for all these reasons, arithmetic must not be given up ; and this is a kind of knowledge in which the best natures should be trained. I agree. Let this then be made one of our subjects of education. And next, shall we inquire whether the kindred science also concerns us ? You mean geometry ? Yes.

Certainly, he said ; that part of geometry which relates to war is clearly our concern ; for in pitching a camp, or taking up a position, or closing or extending the lines of an army, or any other military manoeuvre, whether in actual battle or on a march, there will be a great difference in a general, according as he is or is not a geometrician.

Yes, I said, but for that purpose a very little of either geometry or calculation will be enough ; the question is ratiier of the higher and greater part of geometry, whether that tends towards the great end — I mean towards die vision of the idea of good ; and thither, as I was saying, all things tend which compel the soul to turn her gaze towards that place, where is the full perfection of being, of which she ought, by all means, to attain the vision.