The Republic — Plato
The text is shown on its own: no facing layer is held for this issue.
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 because this will be the easiest way for her to pass from becoming to truth and being. That is excellent, he said. Yes, I said, and now having spoken of it, I must add how charming the science is ! and in how many ways it conduces to our desired end, if pursued in the spirit of a philosopher, and not of a shopkeeper ! How do you mean ?
I mean, as I was saying, that arithmetic has a very great and elevating efifect, compelling the soul to reason about abstract number, and rebelling against the introduction of visible or tangible objects into the argument.
You know how steadily the masters of the art repel and ridicule anyone who attempts to divide absolute unity when he is calculating, and if you divide, they multiply,^ taking care that one shall continue one and not become lost in fractions. That is very true.
Now, suppose a person were to say to them : O my friends, what are these wonderful numbers about which you are reasoning, in which, as you say, there is a unity such as you demand, and each unit is equal, invariable, indivisible — what would they answer ? They would answer, as I should conceive, that they were speaking of those numbers which can only be realized in thought.
Then you see that this knowledge may be truly called necessary, necessitating as it clearly does the use of the pure intelligence in the attainment of pure truth? Yes ; that is a marked characteristic of it.
And have you further observed 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, although they may derive no other advantage from it, always become much quicker than they would otherwise have been? Very true, he said.
And indeed, you will not easily find a more difficult study, and not many as difficult. > Meaning eithor (i) that they integrate the number because they deny tlie possibility of fractions ; or (2) tliat division is regarded by them as.a process ol multiplication, for the fractions of one continue to be units.
You will not. And, for all these reasons, arithmetic is a kind of knowledge in which the best natures should be trained, and which must not be given up. 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 ? Exactly so. Clearly, he said, we are concerned with that part of geometry which relates to war; 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, it will make all the difference whether a general 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 relates rather to the greater and more advanced part of geometry — whether that tends in any degree to make more easy the vision of the idea of good ; and thither, as I was saying, all things tend which compel the soul to turn her gaze toward that place, where is the full perfection of being, which she ought, by all means, to behold. True, he said. Then if geometry compels us to view being, it concerns us ; if becoming only, it does not concern us? Yes, that is what we assert. Yet anybody who has the least acquaintance with geometry will not deny that such a conception of the science is in flat contradiction to the ordinary language of geometricians. How so? They have in view practice only, and are always speaking, in a narrow and ridiculous manner, of squaring and extending and applying and the like — they confuse the necessities of geometry with those of daily life ; whereas knowledge is the real object of th.e whole science. Certainly, he said. Then must not a further admission be made? What admission?
p. 224
PLATO
No commentary for this page under the selected tracks.
There is commentary on page 1.