Jowett: demonstration

Nay, my good friend, said Socrates  , let us not boast, lest some evil eye should put to flight the word which I am about to speak. That, however, may be left in the hands of those above, while I draw near in Homeric fashion, and try the mettle of your words. Briefly, the sum of your objection is as follows : You want to have proven to you that the soul is imperishable and immortal, and you think that the philosopher who is confident in death has but a vain and foolish confidence, if he thinks that he will fare better than one who has led another sort of life, in the world below, unless he can prove this ; and you say that the demonstration of the strength and divinity of the soul, and of her existence prior to our becoming men, does not necessarily imply her immortality. Granting that the soul is longlived, and has known and done much in a former state, still she is not on that account immortal ; and her entrance into the human form may be a sort of disease which is the beginning of dissolution, and may at last, after the toils of life are over, end in that which is called death. And whether the soul enters into the body once only or many times, that, as you would say, makes no difference in the fears of individuals. For any man, who is not devoid of natural feeling, has reason to fear, if he has no knowledge or proof of the soul’s immortality. That is what I suppose you to say, Cebes, which I designedly repeat, in order that nothing may escape us, and that you may, if you wish, add or subtract anything. PHAEDO  

Soc. Why, my dear boy, you are young, and therefore your ear is quickly caught and your mind influenced by popular arguments. Protagoras, or some one speaking on his behalf, will doubtless say in reply, good people, young and old, you meet and harangue, and bring in the gods, whose existence of non-existence I banish from writing and speech, or you talk about the reason of man being degraded to the level of the brutes, which is a telling argument with the multitude, but not one word of proof or demonstration do you offer. All is probability with you, and yet surely you and Theodorus had better reflect whether you are disposed to admit of probability and figures of speech in matters of such importance. He or any other mathematician who argued from probabilities and likelihoods in geometry, would not be worth an ace. THEAETETUS  

Theaet. I see no reason why we should be ashamed of our demonstration, Socrates. THEAETETUS

There are many, but the greatest of all is this : — If an opponent argues that these ideas, being such as we say they ought to be, must remain unknown, no one can prove to him that he is wrong, unless he who denies their existence be a man of great ability and knowledge, and is willing to follow a long and laborious demonstration ; he will remain unconvinced, and still insist that they cannot be known. PARMENIDES  

Str. That we shall some day require this notion of a mean with a view to the demonstration of absolute truth ; meanwhile, the argument that the very existence of the arts must be held to depend on the possibility of measuring more or less, not only with one another, but also with a view to the attainment of the mean, seems to afford a grand support and satisfactory proof of the doctrine which we are maintaining ; for if there are arts, there is a standard of measure, and if there is a standard of measure, there are arts ; but if either is wanting, there is neither. STATESMAN

In the first place, then, as is evident to all, fire and earth and water and air are bodies. And every sort of body possesses solidity, and every solid must necessarily be contained in planes ; and every plane rectilinear figure is composed of triangles ; and all triangles are originally of two kinds, both of which are made up of one right and two acute angles ; one of them has at either end of the base the half of a divided right angle, having equal sides, while in the other the right angle is divided into unequal parts, having unequal sides. These, then, proceeding by a combination of probability with demonstration, we assume to be the original elements of fire and the other bodies ; but the principles which are prior to these God only knows, and he of men who is the friend God. And next we have to determine what are the four most beautiful bodies which are unlike one another, and of which some are capable of resolution into one another ; for having discovered thus much, we shall know the true origin of earth and fire and of the proportionate and intermediate elements. And then we shall not be willing to allow that there are any distinct kinds of visible bodies fairer than these. Wherefore we must endeavour to construct the four forms of bodies which excel in beauty, and then we shall be able to say that we have sufficiently apprehended their nature. Now of the two triangles, the isosceles has one form only ; the scalene or unequal-sided has an infinite number. Of the infinite forms we must select the most beautiful, if we are to proceed in due order, and any one who can point out a more beautiful form than ours for the construction of these bodies, shall carry off the palm, not as an enemy, but as a friend. Now, the one which we maintain to be the most beautiful of all the many triangles (and we need not speak of the others) is that of which the double forms a third triangle which is equilateral ; the reason of this would be long to tell ; he who disproves what we are saying, and shows that we are mistaken, may claim a friendly victory. Then let us choose two triangles, out of which fire and the other elements have been constructed, one isosceles, the other having the square of the longer side equal to three times the square of the lesser side. TIMAEUS  

Thus were created women and the female sex in general. But the race of birds was created out of innocent light-minded men, who, although their minds were directed toward heaven, imagined, in their simplicity, that the clearest demonstration of the things above was to be obtained by sight ; these were remodelled and transformed into birds, and they grew feathers instead of hair. The race of wild pedestrian animals, again, came from those who had no philosophy in any of their thoughts, and never considered at all about the nature of the heavens, because they had ceased to use the courses of the head, but followed the guidance of those parts of the soul which are in the breast. In consequence of these habits of theirs they had their front-legs and their heads resting upon the earth to which they were drawn by natural affinity ; and the crowns of their heads were elongated and of all sorts of shapes, into which the courses of the soul were crushed by reason of disuse. And this was the reason why they were created quadrupeds and polypods : God gave the more senseless of them the more support that they might be more attracted to the earth. And the most foolish of them, who trail their bodies entirely upon the ground and have no longer any need of feet, he made without feet to crawl upon the earth. The fourth class were the inhabitants of the water : these were made out of the most entirely senseless and ignorant of all, whom the transformers did not think any longer worthy of pure respiration, because they possessed a soul which was made impure by all sorts of transgression ; and instead of the subtle and pure medium of air, they gave them the deep and muddy sea to be their element of respiration ; and hence arose the race of fishes and oysters, and other aquatic animals, which have received the most remote habitations as a punishment of their outlandish ignorance. These are the laws by which animals pass into one another, now, as ever, changing as they lose or gain wisdom and folly. TIMAEUS

Cle. Yes, Stranger ; but then how often have we repeated already that on the present occasion there is no reason why brevity should be preferred to length ; who is "at our heels" ? — as the saying goes, and it would be paltry and ridiculous to prefer the shorter to the better. It is a matter of no small consequence, in some way or other to prove that there are Gods, and that they are good, and regard justice more than men do. The demonstration of this would be the best and noblest prelude of all our laws. And therefore, without impatience, and without hurry, let us unreservedly consider the whole matter, summoning up all the power of persuasion which we possess. LAWS BOOK X

Ath. Come, then, and if ever we are to call upon the Gods, let us call upon them now in all seriousness to come to the demonstration of their own existence. And so holding fast to the rope we will venture upon the depths of the argument. When questions of this sort are asked of me, my safest answer would appear to be as follows : — Some one says to me, "O Stranger, are all things at rest and nothing in motion, or is the exact opposite of this true, or are some things in motion and others at rest ? — To this I shall reply that some things are in motion and others at rest. "And do not things which move a place, and are not the things which are at rest at rest in a place ?" Certainly. "And some move or rest in one place and some in more places than one ?" You mean to say, we shall rejoin, that those things which rest at the centre move in one place, just as the circumference goes round of globes which are said to be at rest ? "Yes." And we observe that, in the revolution, the motion which carries round the larger and the lesser circle at the same time is proportionally distributed to greater and smaller, and is greater and smaller in a certain proportion. Here is a wonder which might be thought an impossibility, that the same motion should impart swiftness and slowness in due proportion to larger and lesser circles. "Very true." And when you speak of bodies moving in many places, you seem to me to mean those which move from one place to another, and sometimes have one centre of motion and sometimes more than one because they turn upon their axis ; and whenever they meet anything, if it be stationary, they are divided by it ; but if they get in the midst between bodies which are approaching and moving towards the same spot from opposite directions, they unite with them. "I admit the truth of what you are saying." Also when they unite they grow, and when they are divided they waste away — that is, supposing the constitution of each to remain, or if that fails, then there is a second reason of their dissolution. "And when are all things created and how ?" Clearly, they are created when the first principle receives increase and attains to the second dimension, and from this arrives at the one which is neighbour to this, and after reaching the third becomes perceptible to sense. Everything which is thus changing and moving is in process of generation ; only when at rest has it real existence, but when passing into another state it is destroyed utterly. Have we not mentioned all motions that there are, and comprehended them under their kinds and numbered them with the exception, my friends, of two ? LAWS BOOK X

Ath. One is the argument about the soul, which has been already mentioned — that it is the eldest, and most divine of all things, to which motion attaining generation gives perpetual existence ; the other was an argument from the order of the motion of the stars, and of all things under the dominion of the mind which ordered the universe. If a man look upon the world not lightly or ignorantly, there was never any one so godless who did not experience an effect opposite to that which the many imagine. For they think that those who handle these matters by the help of astronomy, and the accompanying arts of demonstration, may become godless, because they see, as far as they can see, things happening by necessity, and not by an intelligent will accomplishing good. LAWS BOOK XII

I hear from Archedemus that you think that not only I myself should keep quiet but my friends also from doing or saying anything bad about you ; and that "you except Dion only." [2.310c] Now your saying this, that Dion is excepted, implies that I have no control over my friends ; for had I had this control over you and Dion, as well as the rest, more blessings would have come to us all and to the rest of the Greeks also, as I affirm. But as it is, my greatness consists in making myself follow my own instructions. However, I do not say this as though what Cratistolus and Polyxenus have told you is to be trusted ; for it is said that [2.310d] one of these men declares that at Olympia he heard quite a number of my companions maligning you. No doubt his hearing is more acute than mine ; for I certainly heard no such thing. For the future, whenever anyone makes such a statement about any of us, what you ought, I think, to do is to send me a letter of inquiry ; for I shall tell the truth without scruple or shame. Now as for you and me, the relation in which we stand towards each other is really this. There is not a single Greek, one may say, to whom we are unknown, and our intercourse is a matter of common talk ; [2.310e] and you may be sure of this, that it will be common talk also in days to come, because so many have heard tell of it owing to its duration and its publicity. What, now, is the point of this remark ? I will go back to the beginning and tell you. It is natural for wisdom and great power to come together, and they are for ever pursuing and seeking each other and consorting together. Moreover, these are qualities which people delight in discussing themselves in private conversation and hearing others discuss [2.311a] in their poems. For example, when men talk about Hiero or about Pausanias the Lacedaemonian they delight to bring in their meeting with Simonides and what he did and said to them ; and they are wont to harp on Periander of Corinth and Thales of Miletus, and on Pericles and Anaxagoras, and on Croesus also and Solon as wise men with Cyrus as potentate. The poets, too, follow their example, and bring together Creon and Tiresias, [2.311b] Polyeidus and Minos  , Agamemnon and Nestor, Odysseus and Palamedes ; and so it was, I suppose, that the earliest men also brought together Prometheus and Zeus. And of these some were — as the poets tell — at feud with each other, and others were friends ; while others again were now friends and now foes, and partly in agreement and partly in disagreement. Now my object in saying all this is to make it clear, that when we ourselves die [2.311c] men’s talk about us will not likewise be silenced ; so that we must be careful about it. We must necessarily, it seems, have a care also for the future, seeing that, by some law of nature, the most slavish men pay no regard to it, whereas the most upright do all they can to ensure that they shall be well spoken of in the future. Now I count this as a proof that the dead have some perception of things here on earth ; for the best souls divine that this is so, [2.311d] while the worst deny it ; and the divinings of men who are godlike are of more authority than those of men who are not. I certainly think that, had it been in their power to rectify what was wrong in their intercourse, those men of the past whom I have mentioned would have striven to the utmost to ensure a better report of themselves than they now have. In our case, then — if God so grant — it still remains possible to put right whatever has been amiss in word or deed during our intercourse in the past. For I maintain that, as regards [2.311e] the true philosophy, men will think and speak well of it if we ourselves are upright, and ill if we are base. And in truth we could do nothing more pious than to give attention to this matter, nothing more impious than to disregard it. How this result should be brought about, and what is the just course to pursue, I will now explain. I came to Sicily with the reputation of being by far the most eminent of those engaged in philosophy ; and I desired, on my arrival [2.312a] in Syracuse, to gain your testimony as well, in order that I might get philosophy held in honor even by the multitude. In this, however, I was disappointed. But the reason I give for this is not that which is commonly given ; rather it was because you showed that you did not fully trust me but wished rather to get rid of me somehow and invite others in my place ; and owing, as I believe, to your distrust of me, you showed yourself inquisitive as to what my business was. Thereupon it was proclaimed aloud by many that you utterly despised me [2.312b] and were devoted to other affairs. This certainly was the story noised abroad. And now I will tell you what it is right to do after this, that so I may reply also to your question how you and I ought to behave towards each other. If you altogether despise philosophy, leave it alone. If, again, you have been taught by someone else or have yourself invented better doctrines than mine, hold them in honor. But if you are contented with my doctrines, then you should hold me also in special honor. So now, just as at the beginning, do you lead the way and I will follow. If I am honored [2.312c] by you, I will honor you ; but if I am not honored I will keep to myself. Moreover, if you honor me and take the lead in so doing, you will be thought to be honoring philosophy ; and the very fact that you have studied other systems as well will gain you the credit, in the eyes of many, of being a philosopher yourself. But if I honor you, while you do not honor me, I shall be deemed to be a man who worships and pursues after wealth ; and to such conduct everyone, we know, gives a bad name. So, to sum it all up, if you pay the honor, it will be a credit to both of us, but if I pay it a disgrace to both. [2.312d] So much, then, about this subject. As to the globe, there is something wrong with it ; and Archedemus will point it out to you when he arrives. There is also another matter — much more valuable and divine than the globe — which he most certainly must explain, as you were puzzled about it when you sent him. For, according to his report, you say that you have not had a sufficient demonstration of the doctrine concerning the nature of "the First." Now I must expound it to you in a riddling way in order that, should the tablet come to any harm "in folds of ocean or of earth," he that readeth may not understand. The matter stands thus : Related to [2.312e] the King of All are all things, and for his sake they are, and of all things fair He is the cause. And related to the Second are the second things and related to the Third the third. About these, then, the human soul strives to learn, looking to the things that are akin to itself, [2.313a] whereof none is fully perfect. But as to the King and the objects I have mentioned, they are of quite different quality. In the next place the soul inquires — "Well then, what quality have they ?" But the cause of all the mischief, O son of Dionysius and Doris, lies in this very question, or rather in the travail which this question creates in the soul ; and unless a man delivers himself from this he will never really attain the truth. You, however, declared to me in the garden, under the laurels, that you had formed this notion yourself and that it was a discovery of your own ; [2.313b] and I made answer that if it was plain to you that this was so, you would have saved me from a long discourse. I said, however, that I had never met with any other person who had made this discovery ; on the contrary most of the trouble I had was about this very problem. So then, after you had either, as is probable, got the true solution from someone else, or had possibly (by Heaven’s favor) hit on it yourself, you fancied you had a firm grip on the proofs of it, and so you omitted to make them fast ; thus your view of the truth sways now this way, now that, round about the apparent object ; whereas the true object is wholly different. [2.313c] Nor are you alone in this experience ; on the contrary, there has never yet been anyone, I assure you, who has not suffered the same confusion at the beginning, when he first learnt this doctrine from me ; and they all overcome it with difficulty, one man having more trouble and another less, but scarcely a single one of them escapes with but little. So now that this has occurred, and things are in this state, we have pretty well found an answer, as I think, to the question how we ought to behave towards each other. For seeing that you are testing my doctrines both by attending the lectures of other teachers and [2.313d] by examining my teaching side by side with theirs, as well as by itself, then, if the test you make is a true one, not only will these doctrines implant themselves now in your mind, but you also will be devoted both to them and to us. How, then, will this, and all that I have said, be brought to pass ? You have done right now in sending Archedemus ; and in the future also, after he returns to you and reports my answer, you will probably be beset later on with fresh perplexities. Then, if you are rightly advised, you will send Archedemus back to me, and he with his cargo will return to you again. [2.313e] And if you do this twice or thrice, and fully test the doctrines I send you, I shall be surprised if your present difficulties do not assume quite a new aspect. Do you, therefore, act so, and with confidence ; for there is no merchandise more fair than this or dearer to Heaven which you can ever dispatch or Archedemus transport. [2.314a] Beware, however, lest these doctrines be ever divulged to uneducated people. For there are hardly any doctrines, I believe, which sound more absurd than these to the vulgar, or, on the other hand, more admirable and inspired to men of fine disposition. For it is through being repeated and listened to frequently for many years that these doctrines are refined at length, like gold, with prolonged labor. But listen now to the most remarkable result of all. Quite a number of men there are [2.314b] who have listened to these doctrines — men capable of learning and capable also of holding them in mind and judging them by all sorts of tests — and who have been hearers of mine for no less than thirty years and are now quite old ; and these men now declare that the doctrines that they once held to be most incredible appear to them now the most credible, and what they then held most credible now appears the Opposite. So, bearing this in mind, have a care lest one day you should repent of what has now been divulged improperly. The greatest safeguard is to avoid writing and to learn by heart ; [2.314c] for it is not possible that what is written down should not get divulged. For this reason I myself have never yet written anything on these subjects, and no treatise by Plato exists or will exist, but those which now bear his name belong to a Socrates become fair and young. Fare thee well, and give me credence ; and now, to begin with, read this letter over repeatedly and then burn it up. LETTERS LETTER II

The second proof is derived from the nature of the soul : seeing that the individual soul, like the State, has been divided by us into three principles, the division may, I think, furnish a new demonstration. THE REPUBLIC   BOOK IX