Section 1f

But in music there was nothing which tended to that good which you are now seeking. You are most accurate, I said, in your recollection; in music there certainly was nothing of the kind. But what branch of knowledge is there, my dear Glaucon, which is of the desired nature; since all the useful arts were reckoned mean by us? Undoubtedly; and yet if music and gymnastic are excluded, and the arts are also excluded, what remains? Well, I said, there may be nothing left of our special subjects; and then we shall have to take something which is not special, but of universal application. What may that be? A something which all arts and sciences and intelligences use in common, and which every one first has to learn among the elements of education. What is that? The little matter of distinguishing one, two, and three--in a word, number and calculation:--do not all arts and sciences necessarily partake of them? Yes. Then the art of war partakes of them? To the sure. Then Palamedes, whenever he appears in tragedy, proves Agamemnon ridiculously unfit to be a general. Did you never remark how he declares that he had invented number, and had numbered the ships 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 general must he have been? I should say a very strange one, if this was as you say. Can we deny that a warrior should have a knowledge of arithmetic? Certainly he should, if he is to have the smallest understanding 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 your notion? It appears to me to be a study of the kind which we are seeking, and which leads naturally to reflection, but never to have been rightly used; for the true use of it is simply to draw the soul towards being. Will you explain your meaning? he said. I will try, I said; and I wish you would share the enquiry with me, and say `yes' or `no' when I attempt to distinguish in my own mind what branches of knowledge have this attracting power, in order that we may have clearer proof that arithmetic is, as I suspect, one of them. Explain, he said. I mean to say that objects of sense are of two kinds; some of them do not invite thought because the sense is an adequate judge of them; while in the case of other objects sense is so untrustworthy that further enquiry is imperatively demanded. You are clearly referring, he said, to the manner in which the senses are imposed upon by distance, and by painting in light and shade. No, I said, that is not at all my meaning. Then what is your meaning? When speaking of uninviting objects, I mean those which do not pass from one sensation to the opposite; inviting objects are those which do; in this latter case the sense coming upon the object, whether at a distance or near, gives no more vivid idea of anything in particular than of its opposite. An illustration will make my meaning clearer:-- here are three fingers--a little finger, a second finger, and a middle finger. Very good. You may suppose that they are seen quite close: And here comes the point. What is it? Each of them equally appears a finger, whether seen in the middle or at the extremity, whether white or black, or thick or thin-- it makes no difference; a finger is a finger all the same.