Jowett: calculation

Socrates   : Shall we, then, assume this also, [367b] that there is such a person as a man who is false about calculation and number ? LESSER HIPPIAS

Socrates : Who, then, becomes false in respect to calculation, Hippias, other than the good man ? For the same man is also powerful and he is also true. LESSER HIPPIAS

When Protagoras heard me say this, he replied : You ask questions fairly, and I like to answer a question which is fairly put. If Hippocrates comes to me he will not experience the sort of drudgery with which other Sophists are in the habit of insulting their pupils ; who, when they have just escaped from the arts, are taken and driven back into them by these teachers, and made to learn calculation, and astronomy, and geometry, and music (he gave a look at Hippias as he said this) ; but if he comes to me, he will learn that which he comes to learn. And this is prudence in affairs private as well as public ; he will learn to order his own house in the best manner, and he will be able to speak and act for the best in the affairs of the state. PROTAGORAS

Soc. From these premises I proceed to argue the question whether I ought or ought not to try to escape without the consent of the Athenians : and if I am clearly right in escaping, then I will make the attempt ; but if not, I will abstain. The other considerations which you mention, of money and loss of character, and the duty of educating children, are, as I hear, only the doctrines of the multitude, who would be as ready to call people to life, if they were able, as they are to put them to death — and with as little reason. But now, since the argument has thus far prevailed, the only question which remains to be considered is, whether we shall do rightly either in escaping or in suffering others to aid in our escape and paying them in money and thanks, or whether we shall not do rightly ; and if the latter, then death or any other calamity which may ensue on my remaining here must not be allowed to enter into the calculation. CRITO  

Soc. But there are other arts which work wholly through the medium of language, and require either no action or very little, as, for example, the arts of arithmetic, of calculation, of geometry, and of playing draughts ; in some of these speech is pretty nearly co-extensive with action, but in most of them the verbal element is greater — they depend wholly on words for their efficacy and power : and I take your meaning to be that rhetoric is an art of this latter sort ? GORGIAS

Soc. Well, then, let me now have the rest of my answer : — seeing that rhetoric is one of those arts which works mainly by the use of words, and there are other arts which also use words, tell me what is that quality in words with which rhetoric is concerned : — Suppose that a person asks me about some of the arts which I was mentioning just now ; he might say, "Socrates, what is arithmetic ?" and I should reply to him, as you replied to me, that arithmetic is one of those arts which take effect through words. And then he would proceed to ask : "Words about what ?" and I should reply, Words about and even numbers, and how many there are of each. And if he asked again : "What is the art of calculation ?" I should say, That also is one of the arts which is concerned wholly with words. And if he further said, "Concerned with what ?" I should say, like the clerks in the assembly, "as aforesaid" of arithmetic, but with a difference, the difference being that the art of calculation considers not only the quantities of odd and even numbers, but also their numerical relations to themselves and to one another. And suppose, again, I were to say that astronomy is only word — he would ask, "Words about what, Socrates ?" and I should answer, that astronomy tells us about the motions of the stars and sun and moon, and their relative swiftness. GORGIAS

Soc. At the Egyptian city of Naucratis, there was a famous old god, whose name was Theuth ; the bird which is called the Ibis is sacred to him, and he was the inventor of many arts, such as arithmetic and calculation and geometry and astronomy and draughts and dice, but his great discovery was the use of letters. Now in those days the god Thamus was the king of the whole country of Egypt ; and he dwelt in that great city of Upper Egypt which the Hellenes call Egyptian Thebes, and the god himself is called by them Ammon. To came Theuth and showed his inventions, desiring that the other Egyptians might be allowed to have the benefit of the he enumerated them, and Thamus enquired about their several uses, and praised some of them and censured others, as he approved or disapproved of them. It would take a long time to repeat all that Thamus said to Theuth in praise or blame of the various arts. But when they came to letters, This, said Theuth, will make the Egyptians wiser and give them better memories ; it is a specific both for the memory and for the wit. Thamus replied : O most ingenious Theuth, the parent or inventor of an art is not always the best judge of the utility or inutility of his own inventions to the users of them. And in this instance, you who are the father of letters, from a paternal love of your own children have been led to attribute to them a quality which they cannot have ; for this discovery of yours will create forgetfulness in the learners’ souls, because they will not use their memories ; they will trust to the external written characters and not remember of themselves. The specific which you have discovered is an aid not to memory, but to reminiscence, and you give your disciples not truth, but only the semblance of truth ; they will be hearers of many things and will have learned nothing ; they will appear to be omniscient and will generally know nothing ; they will be tiresome company, having the show of wisdom without the reality. PHAEDRUS  

Soc. And astronomy and harmony and calculation ? THEAETETUS  

Str. Such as this : You may remember that we made an art of calculation ? STATESMAN

Str. And to this art of calculation which discerns the differences of numbers shall we assign any other function except to pass judgment on their differences ? STATESMAN

Soc. And similarly, if you had no memory you would not recollect that you had ever been pleased, nor would the slightest recollection of the pleasure which you feel at any moment remain with you ; and if you had no true opinion you would not think that you were pleased when you were ; and if you had no power of calculation you would not be able to calculate on future pleasure, and your life would be the life, not of a man, but of an oyster or pulmo marinus. Could this be otherwise ? PHILEBUS  

Soc. And when we compare the art of mensuration which is used in building with philosophical geometry, or the art of computation which is used in trading with exact calculation, shall we say of either of the pairs that it is one or two ? PHILEBUS

Ath. Let us, then, in the first place declare and affirm that the citizen who does not know these things ought never to have any kind of authority entrusted to him : he must be stigmatized as ignorant, even though he be versed in calculation and skilled in all sorts of accomplishments, and feats of mental dexterity ; and the opposite are to be called wise, even although, in the words of the proverb, they know neither how to read nor how to swim ; and to them, as to men of sense, authority is to be committed. For, O my friends, how can there be the least shadow of wisdom when there is no harmony ? There is none ; but the noblest and greatest of harmonies may be truly said to be the greatest wisdom ; and of this he is a partaker who lives according to reason ; whereas he who is devoid of reason is the destroyer of his house and the very opposite of a saviour of the state : he is utterly ignorant of political wisdom. Let this, then, as I was saying, be laid down by us. LAWS BOOK III

But how can our law sufficiently train the director of education. himself ; for as yet all has been imperfect, and nothing has been said either clear or satisfactory ? Now, as far as possible, the law ought to leave nothing to him, but to explain everything, that he may be an interpreter and tutor to others. About dances and music and choral strains, I have already spoken both to the character of the selection of them, and the manner in which they are to be amended and consecrated. But we have not as yet spoken, O illustrious guardian of education, of the manner in which your pupils are to use those strains which are written in prose, although you have been informed what martial strains they are to learn and practise ; what relates in the first place to the learning of letters, and secondly, to the lyre, and also to calculation, which, as we were saying, is needful for them all to learn, and any other things which are required with a view to war and the management of house and city, and, looking to the same object, what is useful in the revolutions of the heavenly bodies — the stars and sun and moon, and the various regulations about these matters which are necessary for the whole state — I am speaking of the arrangements of ; days in periods of months, and of months in years, which are to be observed, in order that seasons and sacrifices and festivals may have their regular and natural order, and keep the city alive and awake, the Gods receiving the honours due to them, and men having a better understanding about them : all these things, O my friend, have not yet been sufficiently declared to you by the legislator. Attend, then, to what I am now going to say : — We were telling you, in the first place, that you were not sufficiently informed about letters, and the objection was to this effect — that you were never told whether he who was meant to be a respectable citizen should apply himself in detail to that sort of learning, or not apply himself at all ; and the same remark holds good of the study of the lyre. But now we say that he ought to attend to them. A fair time for a boy of ten years old to spend in letters is three years ; the age of thirteen is the proper time for him to begin to handle the lyre, and he may continue at this for another three years, neither more nor less, and whether his father or himself like or dislike the study, he is not to be allowed to spend more or less time in learning music than the law allows. And let him who disobeys the law be deprived of those youthful honours of which we shall hereafter speak. Hear, however, first of all, what the young ought to learn in the early years of life, and what their instructors ought to teach them. They ought to be occupied with their letters until they are to read and write ; but the acquisition of perfect beauty or quickness in writinig, if nature has not stimulated them to acquire these accomplishments in the given number of years, they should let alone. And as to the learning of compositions committed to writing which are not set to the lyre, whether metrical or without rhythmical divisions, compositions in prose, as they are termed, having no rhythm or harmony — seeing how dangerous are the writings handed down to us by many writers of this class — what will you do with them, O most excellent guardians of the law ? or how can the lawgiver rightly direct you about them ? I believe that he will be in great difficulty. LAWS BOOK VII

Ath. If, my friend, we say that the whole path and movement of heaven, and of all that is therein, is by nature akin to the movement and revolution and calculation of mind, and proceeds by kindred laws, then, as is plain, we must say that the best soul takes care of the world and guides it along the good pAth. LAWS BOOK X

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 ? THE REPUBLIC   BOOK VII

Yes, I said, and in these perplexities the soul naturally summons to her aid calculation and intelligence, that she may see whether the several objects announced to her are one or two. THE REPUBLIC BOOK VII

And all arithmetic and calculation have to do with number ? THE REPUBLIC BOOK VII

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 ? THE REPUBLIC BOOK VII

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. THE REPUBLIC BOOK VII

And, therefore, calculation and geometry and all the other elements of instruction, which are a preparation for dialectic, should be presented to the mind in childhood ; not, however, under any notion of forcing our system of education. THE REPUBLIC BOOK VII

What a wonderful calculation ! And how enormous is the distance which separates the just from the unjust in regard to pleasure and pain ! THE REPUBLIC BOOK IX

Yet a true calculation, I said, and a number which nearly concerns human life, if human beings are concerned with days and nights and months and years. THE REPUBLIC BOOK IX

And the arts of measuring and numbering and weighing come to the rescue of the human understanding — there is the beauty of them — and the apparent greater or less, or more or heavier, no longer have the mastery over us, but give way before calculation and measure and weight ? THE REPUBLIC BOOK X

And the better part of the soul is likely to be that which trusts to measure and calculation ? THE REPUBLIC BOOK X