The middle of the Republic, from the later part of Book V to the end of Book VII, is occupied mainly with questions of pure philosophy, as opposed to politics. These questions are introduced by a somewhat abrupt statement:

Until philosophers are kings, or the kings and princes of this world have the spirit and power of philosophy, and political greatness and wisdom meet in one, and those commoner natures who pursue either to the exclusion of the other are compelled to stand aside, cities will never have rest from these evils—no, nor the human race, as I believe—and then only will this our State have a possibility of life and behold the light of day.

If this is true, we must decide what constitutes a philosopher, and what we mean by 'philosophy'. The consequent discussion is the most famous part of the Republic, and has perhaps been the most influential. It has, in parts, extraordinary literary beauty; the reader may disagree (as I do) with what is said, but cannot help being moved by it.

Plato's philosophy rests on the distinction between reality and appearance, which was first set forth by Parmenides; throughout the discussion with which we are now concerned, Parmenidean phrases and arguments are constantly recurring. There is, however, a religious tone about reality, which is rather Pythagorean than Parmenidean; and there is much about mathematics and music which is directly traceable to the disciples of Pythagoras. This combination of the logic of Parmenides with the other-worldliness of Pythagoras and the Orphics produced a doctrine which was felt to be satisfying to both the intellect and the religious emotions; the result was a very powerful synthesis, which, with various modifications, influenced most of the great philosophers, down to and including Hegel. But not only philosophers were influenced by Plato. Why did the Puritans object to the music and painting and gorgeous ritual of the Catholic Church? You will find the answer in the tenth book of the Republic. Why are children in school compelled to learn arithmetic? The reasons are given in the seventh book.

The following paragraphs summarize Plato's theory of ideas.

Our question is: What is a philosopher? The first answer is in accordance with the etymology: a philosopher is a lover of wisdom. But this is not the same thing as a lover of knowledge, in the sense in which an inquisitive man may be said to love knowledge; vulgar curiosity does not make a philosopher. The definition is therefore amended: the philosopher is a man who loves the 'vision of truth'. But what is this vision?

Consider a man who loves beautiful things, who makes a point of being present at new tragedies, seeing new pictures, and hearing new music. Such a man is not a philosopher, because he loves only beautiful things, whereas the philosopher loves beauty in itself. The man who only loves beautiful things is dreaming, whereas the man who knows absolute beauty is wide awake. The former has only opinion; the latter has knowledge.

What is the difference between 'knowledge' and 'opinion'? The man who has knowledge has knowledge of something, that is to say, of something that exists, for what does not exist is nothing. (This is reminiscent of Parmenides.) Thus knowledge is infallible, since it is logically impossible for it to be mistaken. But opinion can be mistaken. How can this be? Opinion cannot be of what is not, for that is impossible; nor of what is, for then it would be knowledge. Therefore opinion must be of what both is and is not.

But how is this possible? The answer is that particular things always partake of opposite characters: what is beautiful is also, in some respects, ugly; what is just is, in some respects, unjust; and so on. All particular sensible objects, so Plato contends, have this contradictory character; they are thus intermediate between being and not-being, and are suitable as objects of opinion, but not of knowledge. 'But those who see the absolute and eternal and immutable may be said to know, and not to have opinion only.'

Thus we arrive at the conclusion that opinion is of the world presented to the senses, whereas knowledge is of a super-sensible eternal world; for instance, opinion is concerned with particular beautiful things, but knowledge is concerned with beauty in itself.

The only argument advanced is that it is self-contradictory to suppose that a thing can be both beautiful and not beautiful, or both just and not just, and that nevertheless particular things seem to combine such contradictory characters. Therefore particular things are not real. Heraclitus had said 'We step and do not step into the same rivers; we are and are not.' But combining this with Parmenides we arrive at Plato's result.

There is, however, something of great importance in Plato's doctrine which is not traceable to his predecessors, and that is the theory of 'ideas' or 'forms'. This theory is partly logical, partly metaphysical. The logical part has to do with the meaning of general words. There are many individual animals of whom we can truly say 'this is a cat'. What do we mean by the word 'cat'? Obviously something different from each particular cat. An animal is a cat, it would seem, because it participates in a general nature common to all cats. Language cannot get on without general words such as 'cat', and such words are evidently not meaningless. But if the word 'cat' means anything, it means something which is not this or that cat, but some kind of universal cattiness. This is not born when a particular cat is born, and does not die when it dies, In fact, it has no position in space or time; it is 'eternal'. This is the logical part of the doctrine. The arguments in its favour, whether ultimately valid or not, are strong, and quite independent of the metaphysical part of the doctrine.

According to the metaphysical part of the doctrine, the word 'cat' means a certain ideal cat, 'the cat', created by God, and unique. Particular cats partake of the nature of the cat, but more or less imperfectly; it is only owing to this imperfection that there can be many of them. The cat is real; particular cats are only apparent.

In the last book of the Republic, as a preliminary to a condemnation of painters, there is a very clear exposition of the doctrine of ideas or forms.

Here Plato explains that, whenever a number of individuals have a common name, they have also a common 'idea' or 'form'. For instance, though there are many beds, there is only one 'idea' or 'form' of a bed. Just as a reflection of a bed in a mirror is only apparent and not 'real', so the various particular beds are unreal, being only copies of the 'idea', which is the one real bed, and is made by God. Of this one bed, made by God, there can be knowledge, but in respect of the many beds made by carpenters there can be only opinion. The philosopher, as such, will be interested only in the one ideal bed, not in the many beds found in the sensible world. He will have a certain indifference to ordinary mundane affairs: 'how can he who has magnificence of mind and is the spectator of all time and all existence, think much of human life?' The youth who is capable of becoming a philosopher will be distinguished among his fellows as just and gentle, fond of learning, possessed of a good memory and a naturally harmonious mind. Such a one shall be educated into a philosopher and a guardian.

At this point Adeimantus breaks in with a protest. When he tries to argue with Socrates, he says, he feels himself led a little astray at each step, until, in the end, all his former notions are turned upside down. But whatever Socrates may say, it remains the case, as any one can see, that people who stick to philosophy become strange monsters, not to say utter rogues; even the best of them are made useless by philosophy.

Socrates admits that this is true in the world as it is, but maintains that it is the other people who are to blame, not the philosophers; in a wise community the philosophers would not seem foolish; it is only among fools that the wise are judged to be destitute of wisdom.

What are we to do in this dilemma? There were to have been two ways of inaugurating our Republic: by philosophers becoming rulers, or by rulers becoming philosophers. The first way seems impossible as a beginning, because in a city not already philosophic the philosophers are unpopular. But a born prince might be a philosopher, and 'one is enough; let there be one man who has a city obedient to his will, and he might bring into existence the ideal polity about which the world is so incredulous.' Plato hoped that he had found such a prince in the younger Dionysius, tyrant of Syracuse, but the young man turned out disappointingly.

In the sixth and seventh books of the Republic, Plato is concerned with two questions: First, what is philosophy? Second, how can a young man or woman, of suitable temperament, be so educated as to become a philosopher?

Philosophy, for Plato, is a kind of vision, the 'vision of truth'. It is not purely intellectual; it is not merely wisdom, but love of wisdom, Spinoza's 'intellectual love of God' is much the same intimate union of thought and feeling. Every one who has done any kind of creative work has experienced, in a greater or less degree, the state of mind in which, after long labour, truth or beauty appears, or seems to appear, in a sudden glory—it may be only about some small matter, or it may be about the universe. The experience is, at the moment, very convincing; doubt may come later, but at the time there is utter certainty. I think most of the best creative work, in art, in science, in literature, and in philosophy, has been the result of such a moment. Whether it comes to others as to me, I cannot say. For my part, I have found that, when I wish to write a book on some subject, I must first soak myself in detail, until all the separate parts of the subject-matter are familiar; then, some day, if I am fortunate, I perceive the whole, with all its parts duly interrelated. After that, I only have to write down what I have seen. The nearest analogy is first walking all over a mountain in a mist, until every path and ridge and valley is separately familiar, and then, from a distance, seeing the mountain whole and clear in bright sunshine.

This experience, I believe, is necessary to good creative work, but it is not sufficient; indeed the subjective certainty that it brings with it may be fatally misleading. William James describes a man who got the experience from laughing-gas; whenever he was under its influence, he knew the secret of the universe, but when he came to, he had forgotten it. At last, with immense effort, he wrote down the secret before the vision had faded. When completely recovered, he rushed to see what he had written. It was: 'A smell of petroleum prevails throughout.' What seems like sudden insight may be misleading, and must be tested soberly, when the divine intoxication has passed.

Plato's vision, which he completely trusted at the time when he wrote the Republic, needs ultimately the help of a parable, the parable of the cave, in order to convey its nature to the reader. But it is led up to by various preliminary discussions, designed to make the reader see the necessity of the world of ideas.

First, the world of the intellect is distinguished from the world of the senses; then intellect and sense-perception are in turn each divided into two kinds. The two kinds of sense-perception need not concern us; the two kinds of intellect are called, respectively, 'reason' and 'understanding'. Of these, reason is the higher kind; it is concerned with pure ideas, and its method is dialectic. Understanding is the kind of intellect that is used in mathematics; it is inferior to reason in that it uses hypotheses which it cannot test. In geometry, for example, we say: 'Let ABC be a rectilinear triangle.' It is against the rules to ask whether ABC really is a rectilinear triangle, although, if it is a figure that we have drawn, we may be sure that it is not, because we can't draw absolutely straight lines. Accordingly, mathematics can never tell us what is, but only what would be if…. There are no straight lines in the sensible world; therefore, if mathematics is to have more than hypothetical truth, we must find evidence for the existence of super-sensible straight lines in a super-sensible world. This cannot be done by the understanding, but according to Plato it can be done by reason, which shows that there is a rectilinear triangle in heaven, of which geometrical propositions can be affirmed categorically, not hypothetically.

There is, at this point, a difficulty which did not escape Plato's notice, and was evident to modern idealistic philosophers. We saw that God made only one bed, and it would be natural to suppose that he made only one straight line. But if there is a heavenly triangle, he must have made at least three straight lines. The objects of geometry, though ideal, must exist in many examples; we need the possibility of two intersecting circles, and so on. This suggests that geometry, on Plato's theory, should not be capable of ultimate truth, but should be condemned as part of the study of appearance. We will, however, ignore this point, as to which Plato's answer is somewhat obscure.

Plato seeks to explain the difference between clear intellectual vision and the confused vision of sense-perception by an analogy from the sense of sight. Sight, he says, differs from the other senses, since it requires not only the eye and the object, but also light. We see clearly objects on which the sun shines: in twilight we see confusedly, and in pitch-darkness not at all. Now the world of ideas is what we see when the object is illumined by the sun, while the world of passing things is a confused twilight world. The eye is compared to the soul, and the sun, as the source of light, to truth or goodness.

The soul is like an eye: when resting upon that on which truth and being shine, the soul perceives and understands, and is radiant with intelligence; but when turned towards the twilight of becoming and perishing, then she has opinion only, and goes blinking about, and is first of one opinion and then of another, and seems to have no intelligence…. Now what imparts truth to the known and the power of knowing to the knower is what I would have you term the idea of good, and this you will deem to be the cause of science.

This leads up to the famous simile of the cave or den, according to which those who are destitute of philosophy may be compared to prisoners in a cave, who are only able to look in one direction because they are bound, and who have a fire behind them and a wall in front. Between them and the wall there is nothing; all that they see are shadows of themselves, and of objects behind them, cast on the wall by the light of the fire. Inevitably they regard these shadows as real, and have no notion of the objects to which they are due. At last some man succeeds in escaping from the cave to the light of the sun; for the first time he sees real things, and becomes aware that he had hitherto been deceived by shadows. If he is the sort of philosopher who is fit to become a guardian, he will feel it is his duty to those who were formerly his fellow-prisoners to go down again into the cave, instruct them as to the truth, and show them the way up. But he will have difficulty in persuading them, because, coming out of the sunlight, he will see shadows less clearly than they do, and will seem to them stupider than before his escape.

'And now, I said, let me show in a figure how far our nature is enlightened or unenlightened:—Behold! human beings living in an underground den, which has a mouth open toward the light and reaching all along the den; here they have been from their childhood, and have their legs and necks chained so that they cannot move, and can only see before them, being prevented by the chains from turning round their heads. Above and behind them a fire is blazing at a distance, and between the fire and the prisoners there is a raised way; and you will see, if you look, a low wall built along the way, like the screen which marionette players have in front of them, over which they show the puppets.

'I see.

'And do you see, I said, men passing along the wall carrying all sorts of vessels, and statues and figures of animals made of wood and stone and various materials, which appear over the wall? Some of them are talking, others silent.

'You have shown me a strange image, and they are strange prisoners.

'Like ourselves, I replied; and they see only their own shadows, or the shadows of one another, which the fire throws on the opposite wall of the cave.'

The position of the good in Plato's philosophy is peculiar. Science and truth, he says, are like the good, but the good has a higher place. 'The good is not essence, but far exceeds essence in dignity and power.' Dialectic leads to the end of the intellectual world in the perception of the absolute good. It is by means of the good that dialectic is able to dispense with the hypotheses of the mathematician. The underlying assumption is that reality, as opposed to appearance, is completely and perfectly good; to perceive the good, therefore, is to perceive reality. Throughout Plato's philosophy there is the same fusion of intellect and mysticism as in Pythagoreanism, but at this final culmination mysticism clearly has the upper hand.

Plato's doctrine of ideas contains a number of obvious errors. But in spite of these it marks a very important advance in philosophy, since it is the first theory to emphasize the problem of universals, which, in varying forms, has persisted to the present day. Beginnings are apt to be crude, but their originality should not be overlooked on this account Something remains of what Plato had to say, even after all necessary corrections have been made. The absolute minimum of what remains, even in the view of those most hostile to Plato, is this: that we cannot express ourselves in a language composed wholly of proper names, but must have also general words such as 'man', 'dog', 'cat'; or, if not these, then relational words such as 'similar', 'before', and so on. Such words are not meaningless noises, and it is difficult to see how they can have meaning if the world consists entirely of particular things, such as are designated by proper names. There may be ways of getting round this argument, but at any rate it affords a prima facie case in favour of universals. I shall provisionally accept it as in some degree valid. But when so much is granted, the rest of what Plato says by no means follows.

In the first place, Plato has no understanding of philosophical syntax. I can say 'Socrates is human', 'Plato is human', and so on. In all these statements, it may be assumed that the word 'human' has exactly the same meaning. But whatever it means, it means something which is not of the same kind as Socrates, Plato, and the rest of the individuals who compose the human race. 'Human' is an adjective; it would be nonsense to say 'human is human'. Plato makes a mistake analogous to saying 'human is human'. He thinks that beauty is beautiful; he thinks that the universal 'man' is the name of a pattern man created by God, of whom actual men are imperfect and somewhat unreal copies. He fails altogether to realize how great is the gap between universals and particulars; his 'ideas' are really just other particulars, ethically and aesthetically superior to the ordinary kind. He himself, at a later date, began to see this difficulty, as appears in the Parmenides, which contains one of the most remarkable cases in history of self-criticism by a philosopher.

The Parmenides is supposed to be related by Antiphon (Plato's half-brother), who alone remembers the conversation, but is now only interested in horses. They find him carrying a bridle, and with difficulty persuade him to relate the famous discussion between Parmenides, Zeno, and Socrates. This, we are told, took place when Parmenides was old (about sixty-five), Zeno in middle life (about forty), and Socrates quite a young man. Socrates expounds the theory of ideas; he is sure that there are ideas of likeness, justice, beauty, and goodness; he is not sure that there is an idea of man; and he rejects with indignation the suggestion that there could be ideas of such things as hair and mud and dirt—though, he adds, there are times when he thinks that there is nothing without an idea. He runs away from this view because he is afraid of falling into a bottomless pit of nonsense.

'Yes, Socrates, said Parmenides; that is because you are still young; the time will come, if I am not mistaken, when philosophy will have a firmer grasp of you, and then you will not despise even the meanest things.'

Socrates agrees that, in his view, 'There are certain ideas of which all other things partake, and from which they derive their names; that similars, for example, become similar, because they partake of similarity; and great things become great, because they partake of greatness; and that just and beautiful things become just and beautiful, because they partake of justice and beauty.'

Parmenides proceeds to raise difficulties. (a) Does the individual partake of the whole idea, or only of a part? To either view there are objections. If the former, one thing is in many places at once; if the latter, the idea is divisible, and a thing which has a part of smallness will be smaller than absolute smallness, which is absurd. (b) When an individual partakes of an idea, the individual and the idea are similar; therefore there will have to be another idea, embracing both the particulars and the original idea. And there will have to be yet another, embracing the particulars and the two ideas, and so on ad infinitum. Thus every idea, instead of being one, becomes an infinited series of ideas. (This is the same as Aristotle's argument of the 'third man'.) (c) Socrates suggests that perhaps ideas are only thoughts; but Parmenides points out that thoughts must be of something. (d) Ideas cannot resemble the particulars that partake of them, for the reason given in (b) above. (e) Ideas, if there are any, must be unknown to us, because our knowledge is not absolute. (f) If God's knowledge is absolute, He will not know us, and therefore cannot rule us.

Nevertheless, the theory of ideas is not wholly abandoned. Without ideas, Socrates says, there will be nothing on which the mind can rest, and therefore reasoning will be destroyed. Parmenides tells him that his troubles come of lack of previous training, but no definite conclusion is reached.

I do not think that Plato's logical objections to the reality of sensible particulars will bear examination. He says, for example, that whatever is beautiful is also in some respects ugly; what is double is also half; and so on. But when we say of some work of art that it is beautiful in some respects and ugly in others, analysis will always (at least theoretically) enable us to say 'this part or aspect is beautiful, while that part or aspect is ugly.' And as regards 'double' and 'half', these are relative terms; there is no contradiction in the fact that 2 is double of 1 and half of 4. Plato is perpetually getting into trouble through not understanding relative terms. He thinks that if A is greater than B and less than C, then A is at once great and small, which seems to him a contradiction. Such troubles are among the infantile diseases of philosophy.

The distinction between reality and appearance cannot have the consequences attributed to it by Parmenides and Plato and Hegel. If appearance really appears, it is not nothing, and is therefore part of reality; this is an argument of the correct Parmenidean sort. If appearance does not really appear, why trouble our heads about it? But perhaps some one will say: 'Appearance does not really appear, but it appears to appear.' This will not help, for we shall ask again: 'Does it really appear to appear, or only apparently appear to appear?' Sooner or later, if appearance is even to appear to appear, we must reach something that really appears, and is therefore part of reality. Plato would not dream of denying that there appear to be many beds, although there is only one real bed, namely the one made by God. But he does not seem to have faced the implications of the fact that there are many appearances, and that this manyness is part of reality. Any attempt to divide the world into portions, of which one is more 'real' than the other, is doomed to failure.

Connected with this is another curious view of Plato's, that knowledge and opinion must be concerned with different subject-matters. We should say: If I think it is going to snow, that is opinion; if later I see it snowing, that is knowledge; but the subject-matter is the same on both occasions. Plato, however, thinks that what can at any time be a matter of opinion can never be a matter of knowledge. Knowledge is certain and infallible; opinion is not merely fallible, but is necessarily mistaken, since it assumes the reality of what is only appearance. All this repeats what had been said by Parmenides.

There is one respect in which Plato's metaphysic is apparently different from that of Parmenides. For Parmenides there is only the One; for Plato, there are many ideas. There are not only beauty, truth, and goodness, but, as we saw, there is the heavenly bed, created by God; there is a heavenly man, a heavenly dog, a heavenly cat, and so on through a whole Noah's ark. All this however, seems, in the Republic, to have been not adequately thought out. A Platonic idea or form is not a thought, though it may be the object of a thought. It is difficult to see how God can have created it, since its being is timeless, and he could not have decided to create a bed unless his thought, when he decided, had had for its object that very Platonic bed which we are told he brought into existence. What is timeless must be uncreated. We come here to a difficulty which has troubled many philosophic theologians. Only the contingent world, the world in space and time, can have been created; but this is the everyday world which has been condemned as illusory and also bad. Therefore the Creator, it would seem, created only illusion and evil. Some Gnostics were so consistent as to adopt this view; but in Plato the difficulty is still below the surface, and he seems, in the Republic, to have never become aware of it.

The philosopher who is to be a guardian must, according to Plato, return into the cave, and live among those who have never seen the sun of truth. It would seem that God Himself, if He wishes to amend His creation, must do likewise; a Christian Platonist might so interpret the Incarnation. But it remains completely impossible to explain why God was not content with the world of ideas. The philosopher finds the cave in existence, and is actuated by benevolence in returning to it; but the Creator, if He created everything, might, one would think, have avoided the cave altogether.

Perhaps this difficulty arises only from the Christian notion of a Creator, and is not chargeable to Plato, who says that God did not create everything, but only what is good. The multiplicity of the sensible world, on this view, would have some other source than God. And the ideas would, perhaps, be not so much created by God as constituents of His essence. The apparent pluralism involved in the multiplicity of ideas would thus not be ultimate. Ultimately there is only God, or the Good, to whom the ideas are adjectival. This, at any rate, is a possible interpretation of Plato.

Plato proceeds to an interesting sketch of the education proper to a young man who is to be a guardian. We saw that the young man is selected for this honour on the ground of a combination of intellectual and moral qualities; he must be just and gentle, fond of learning, with a good memory and a harmonious mind. The young man who has been chosen for these merits will spend the years from twenty to thirty on the four Pythagorean studies: arithmetic, geometry (plane and solid), astronomy, and harmony. These studies are not to be pursued in any utilitarian spirit, but in order to prepare his mind for the vision of eternal things. In astronomy, for example, he is not to trouble himself too much about the actual heavenly bodies, but rather with the mathematics of the motion of ideal heavenly bodies. This may sound absurd to modern ears, but strange to say, it proved to be a fruitful point of view in connection with empirical astronomy. The way this came about is curious, and worth considering.

The apparent motions of the planets, until they have been very profoundly analysed, appear to be irregular and complicated, and not at all such as a Pythagorean Creator would have chosen. It was obvious to every Greek that the heavens ought to exemplify mathematical beauty, which would only be the case if the planets moved in circles. This would be especially evident to Plato, owing to his emphasis on the good. The problem thus arose: is there any hypothesis which will reduce the apparent disorderliness of planetary motions to order and beauty and simplicity? If there is, the idea of the good will justify us in asserting this hypothesis. Aristarchus of Samos found such a hypothesis: that all the planets, including the earth, go round the sun in circles. This view was rejected for two thousand years, partly on the authority of Aristotle, who attributes a rather similar hypothesis to 'the Pythagoreans' (De Coelo, 293 a). It was revived by Copernicus, and its success might seem to justify Plato's aesthetic bias in astronomy. Unfortunately, however, Kepler discovered that the planets move in ellipses, not in circles, with the sun at a focus, not at the centre; then Newton discovered that they do not move even in exact ellipses. And so the geometrical simplicity sought by Plato, and apparently found by Aristarchus of Samos, proved in the end illusory.

This piece of scientific history illustrates a general maxim: that any hypothesis, however absurd, may be useful in science, if it enables a discoverer to conceive things in a new way; but that, when it has served this purpose by luck, it is likely to become an obstacle to further advance. The belief in the good as the key to the scientific understanding of the world was useful, at a certain stage, in astronomy, but at every later stage it was harmful. The ethical and aesthetic bias of Plato, and still more of Aristotle, did much to kill Greek science.

It is noteworthy that modern Platonists, with few exceptions, are ignorant of mathematics, in spite of the immense importance that Plato attached to arithmetic and geometry, and the immense influence that they had on his philosophy. This is an example of the evils of specialization: a man must not write on Plato unless he has spent so much of his youth on Greek as to have had no time for the things that Plato thought important.

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