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26 - The Republic - Plato · The Philosophy Insights Collection

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  Book seven, Part two. Who then, are those whom we shall compel
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  to be guardians? Surely they will be the men who are wisest about affairs
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  of state, and by whom the state is best administered, and who at
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  the same time have other honors and another in a better life than that of
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  politics. They are the men, and I will choose them, he replied.
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  And now shall we consider in what way such guardians will be produced,
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  and how they are to be brought from darkness to light, as some are
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  said to have ascended from the world below to the gods by all means,
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  he replied. The process, I said, is not the turning over of
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  an oyster shell, but the turning round of a soul, passing from a
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  day which is little better than night to the true day of being. That
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  is the ascent from below, which we affirm to be true philosophy. Quite
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  so, and should we not inquire what sort of nne has the power of
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  effecting such a change? Certainly, what sort of knowledge is there which would
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  draw the soul from becoming to being? And another consideration has just occurred to
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  me. You will remember that our young men are to be warrior athletes.
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  Yes, that was said, then this new kind of knowledge must have an
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  additional quality? What quality? Usefulness? In war? Yes, if possible?
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  There were two parts in our former scheme of education, were there?
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  Not? Just so? There was gymnastic, which presided over the growth and
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  decay of the body, and may therefore be regarded as having to do with
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  generation and corruption. True, then that is not the knowledge which we are
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  seeking to discover. No, but what do you say of music, which
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  also entered to a certain extent into our former scheme? Music, he said,
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  as you will remember, was the counterpart of gymnastic, and trained the
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  guardians by the influences of habit by harmony, making them harmonious by rhythm rhythmical,
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  but not giving them science. And the words, whether fabulous or possibly
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  true, had kindred elements of rhythm and harmony in them. But in music
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  there was nothing which tended to that good which you are now seeking. You
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  are most accurate, I said, in your recollection. In music there certainly
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  was nothing of the kind. But what branch of knowledge is there, my
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  dear Glaucan, which is of the desired nature? Since all the useful arts
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  were reckoned mean by us? Undoubtedly? And yet if music and gymnastic are
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  excluded, and the arts are also excluded. What remains well? I said,
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  there may be nothing left of our special subjects, And then we shall
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  have to take something which is not special but of universal application. What may
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  that be? A something which all arts and sciences and intelligences use in common,
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  and which every one first has to learn among the elements of education.
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  What is that the little matter of distinguishing one, two, and three in
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  a word? Number and calculation? Do not all arts and sciences necessarily partake
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  of them? Yes? Then the art of war partakes of them? To
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  be sure? Then Palamedes, whenever he appears in tragedy, proves Agamemnon ridiculously
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  unfit to be a general. Did you never remark? How he declares that
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  he had invented number, and had numbered the ships and set in array the
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  ranks of the army at Troy, which implies that they had never been numbered
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  before. And Agamemnon must be supposed literally to have been incapable of counting his
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  own feet. How could he if he was ignorant of number? And if
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  that is true, what sort of general must he have been? I should
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  say, a very strange one? If this was, as you say,
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  can we deny that a warrior should have a knowledge of arithmetic? Certainly he
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  should if he is to have the smallest understanding of military tactics, or indeed,
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  I should rather say, if he is to be a man at all.
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  I should like to know whether you have the same notion which I have
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  of this study. What is your notion? It appears to me to be
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  a study of the kind which we are seeking, and which leads naturally to
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  reflection, but never to have been rightly used. For the true use of
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  it is simply to draw the soul towards being. Will you explain your meaning?
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  He said? I will try, I said, and I wish you
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  would share the enquiry with me. Say yes or no? When I attempt
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  to distinguish in my own mind, what branches of knowledge have this attracting power
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  in order that we may have clearer proof that arithmetic is as I suspect,
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  one of them, explain, he said, I mean to say that objects
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  of sense are of two kinds. Some of them do not invite thought,
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  because the sense is an adequate judge of them, while in the case of
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  other objects, sense is so untrustworthy that further enquiry is imperatively demanded. You
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  are clearly referring, he said, to the manner in which the senses are
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  imposed upon by distance and by painting in light and shade. No, I
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  said, that is not at all my meaning. Then what is your meaning?
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  When speaking of uninviting objects? I mean those which do not pass from
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  one sensation to the opposite. Inviting objects are those which do. In this
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  latter case, the sense coming upon the object, whether at a distance or
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  near, gives no more vivid idea of anything in particular than of its opposite.
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  An illustration will make my meaning clearer. Here are three fingers, a
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  little finger, a second finger, and a middle finger. Very good.
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  You may suppose that they are seen quite close. And here comes the point,
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  what is it? Each of them equally appears a finger, whether seen
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  in the middle or at the extremity, Whether white or black, or thick
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  or thin, it makes no difference. A finger is a finger all the
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  same. In these cases a man is not compelled to ask a thought the
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  question what is a finger? For the sight never intimates to the mind that
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  a finger is other than a finger. True, And therefore I said,
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  as we might expect, there is nothing here which invites or excites intelligence?
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  There is not, he said, But is this equally true of the greatness
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  and smallness of the fingers? Can sight adequately perceive them? And is no
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  difference made by the circumstance that one of the fingers is in the middle and
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  another at the extremity? And in like manner. Thus the touch adequately perceives
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  the qualities of thickness or thinness, of softness or hardness. And so of
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  the other senses do they give perfect intimations of such matters? Is not their
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  mode of operation? On this wise? The sense which is concerned with the
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  quality of hardness is necessarily concerned also with the quality of softness, and only
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  intimates to the soul that the same thing is felt to be both hard and
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  soft. You are quite right, he said, And must not the soul
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  be perplexed at this intimation which the sense gives of a heart which is also
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  soft? What again, is the meaning of light and heavy? If that
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  which is light is also heavy, and that which is heavy light, Yes,
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  he said, These intimations which the soul receives are very curious and required
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  to be explained. Yes, I said, And in these perplexities. The
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  soul naturally summons to her aid calculation and intelligence, that she may see whether
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  the several objects announced to her are one or two? True, And if
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  they turn out to be two, is not each of them one and different?
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  Certainly? And if each is one and both are two, she will
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  conceive the two as in a state of division, for if they were undivided,
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  they could only be conceived of as one. True. The eye certainly
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  did see both small and gray, but only in a confused manner. They
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  were not distinguished. Yes, whereas the thinking mind, intending to light up
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  the chaos, was compelled to reverse the process and look as small and great,
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  as separate and not confused. Very true? Was not this the beginning
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  of the enquiry what is great and what is small? Exactly so? And
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  thus arose a distinction of the visible and the intelligible? Most true? This
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  was what I meant when I spoke of impressions which invited the intellect or the
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  reverse. Those which are simultaneous with opposite impressions invite thought. Those which are
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  not simultaneous do not I understand, he said? And agree with you?
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  And to which class do unity and number belong? I do not know,
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  he replied, Think a little, and you will see that what has preceded
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  will supply the answer. For if simple unity could be adequately perceived by the
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  side, or by any other sense, then as we were saying in the
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  case of the finger, there would be nothing to attract towards being. But
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  when there is some contradiction always present, and one is the reverse of one
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  and involves the conception of plurality, then thought begins to be aroused within us,
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  and the soul, perplexed and wanting to arrive at the decision, asks
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  what is absolute unity? This is the way in which the study of the
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  one has the power of drawing and converting the mind to the contemplation of true
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  being. And surely, he said, this occurs notably in the case of
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  one, for we see the same thing to be both one and infinite in
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  multitude, Yes, I said, And this being true of one, must
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  be equally true of all number. Certainly, And all arithmetic and calculation have
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  to do with number. Yes, and they appear to lead the mind towards
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  truth. Yes, in a very remarkable manner. Then this is knowledge of
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  the kind for which we are seeking. Having a double use military and philosophical.
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  For the men of war must learn the art of number, or he
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  will not know how to array his troops. And the philosopher also because he
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  has to rise out of the sea of change and lay hold of true being,
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  And therefore he must be an arithmetician, that is true. And our
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  guardian is both warrior and philosopher. Certainly, then this is a kind of
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  knowledge which legislation may fitly prescribe. And we must endeavor to persuade those who
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  are to be the principal man of our state to go and learn arithmetic,
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  not as amateurs, but they must carry on the study until they see the
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  nature of numbers with the mind only, nor again like merchants or retail traders
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  with a view to buying or selling, but for the sake of their military
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  use and of the soul herself, and because this will be the easiest way
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  for her to pass from becoming to truth and being. That is excellent,
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  he said, yes, I said, And now having spoken of it,
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  I must add how charming the science is, and in how many ways it
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  conduces to our desired end, if pursued in the spirit of a philosopher and
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  not of a shopkeeper, How do you mean? I mean, as I
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  was saying that arithmetic has a very great and elevating effect, compelling the soul
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  to reason about abstract number and rebelling against the introduction of visible or tangible objects
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  into the argument. You know how steadily the masters of the art repel and
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  ridicule any one who attempts to divide absolute unity. When he is calculating any
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  few, they multiply, taking care that one shall continue one and not become
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  lost in fractions. That is very true. Now, suppose a person were
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  to say to them, oh, my friends, what are these wonderful numbers
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  about which you are reasoning, in which, as you say, there is
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  a unity such as you demand, and each unit is equal, invariable,
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  and the visible. What would they answer? They would answer, as I
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  should conceive that they were speaking of those numbers which can only be realized in
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  thought. Then you see that this knowledge may be truly called necessary, necessitating,
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  as it clearly does the use of the pure intelligence in the attainment of
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  pure truth. Yes, that is a marked characteristic of it. And have
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  you further observed that those who have a natural talent for calculation are generally quick
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  at every other kind of knowledge, and even the dull, if they have
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  had an arithmetical training, although they may derive no other advantage from it,
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  always become much quicker than they would otherwise have been. Very true, he
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  said, And indeed it will not easily find a more difficult study, and
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  not many as difficult you will not. And for all these reasons, arithmetic
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  is a kind of knowledge in which the best natures should be trained, and
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  which must not be given up. I agree, let this then be made
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  one of our subjects of education. End of Book seven, Part two,