The modern mathematician will readily sympathise with Plato’s delight in the properties of pure mathematics. He will not be disinclined to say with him:—Let alone the heavens, and study the beauties of number and figure in themselves. He too will be apt to depreciate their application to the arts. He will observe that Plato has a conception of geometry, in which figures are to be dispensed with; thus in a distant and shadowy way seeming to anticipate the possibility of working geometrical problems by a more general mode of analysis. He will remark with interest on the backward state of solid geometry, which, alas! was not encouraged by the aid of the State in the age of Plato; and he will recognize the grasp of Plato’s mind in his ability to conceive of one science of solids in motion including the earth as well as the heavens,—not forgetting to notice the intimation to which allusion has been already made, that besides astronomy and harmonics the science of solids in motion may have other applications. Still more will he be struck with the comprehensiveness of view which led Plato, at a time when these sciences hardly existed, to say that they must be studied in relation to one another, and to the idea of good, or common principle of truth and being. But he will also see (and perhaps without surprise) that in that stage of physical and mathematical knowledge, Plato has fallen into the error of supposing that he can construct the heavens a priori by mathematical problems, and determine the principles of harmony irrespective of the adaptation of sounds to the human ear. The illusion was a natural one in that age and country. The simplicity and certainty of astronomy and harmonics seemed to contrast with the variation and complexity of the world of sense; hence the circumstance that there was some elementary basis of fact, some measurement of distance or time or vibrations on which they must ultimately rest, was overlooked by him. The modern predecessors of Newton fell into errors equally great; and Plato can hardly be said to have been very far wrong, or may even claim a sort of prophetic insight into the subject, when we consider that the greater part of astronomy at the present day consists of abstract dynamics, cxi by the help of which most astronomical discoveries have been made.
The metaphysical philosopher from his point of view recognizes mathematics as an instrument of education,—which strengthens the power of attention, developes the sense of order and the faculty of construction, and enables the mind to grasp under simple formulae the quantitative differences of physical phenomena. But while acknowledging their value in education, he sees also that they have no connexion with our higher moral and intellectual ideas. In the attempt which Plato makes to connect them, we easily trace the influences of ancient Pythagorean notions. There is no reason to suppose that he is speaking of the ideal numbers at p. [525 E]; but he is describing numbers which are pure abstractions, to which he assigns a real and separate existence, which, as ‘the teachers of the art’ (meaning probably the Pythagoreans) would have affirmed, repel all attempts at subdivision, and in which unity and every other number are conceived of as absolute. The truth and certainty of numbers, when thus disengaged from phenomena, gave them a kind of sacredness in the eyes of an ancient philosopher. Nor is it easy to say how far ideas of order and fixedness may have had a moral and elevating influence on the minds of men, ‘who,’ in the words of the Timaeus, ‘might learn to regulate their erring lives according to them’ (47 C). It is worthy of remark that the old Pythagorean ethical symbols still exist as figures of speech among ourselves. And those who in modern times see the world pervaded by universal law, may also see an anticipation of this last word of modern philosophy in the Platonic idea of good, which is the source and measure of all things, and yet only an abstraction. (Cp. Philebus sub fin.).
Two passages seem to require more particular explanations. First, that which relates to the analysis of vision. The difficulty in this passage may be explained, like many others, from differences in the modes of conception prevailing among ancient and modern thinkers. To us, the perceptions of sense are inseparable from the act of the mind which accompanies them. The consciousness of form, colour, distance, is indistinguishable from the simple sensation, which is the medium of them. Whereas to Plato sense is the Heraclitean flux of sense, not cxii the vision of objects in the order in which they actually present themselves to the experienced sight, but as they may be imagined to appear confused and blurred to the half-awakened eye of the infant. The first action of the mind is aroused by the attempt to set in order this chaos, and the reason is required to frame distinct conceptions under which the confused impressions of sense may be arranged. Hence arises the question, ‘What is great, what is small?’ and thus begins the distinction of the visible and the intelligible.
The second difficulty relates to Plato’s conception of harmonics. Three classes of harmonists are distinguished by him:—first, the Pythagoreans, whom he proposes to consult as in the previous discussion on music he was to consult Damon—they are acknowledged to be masters in the art, but are altogether deficient in the knowledge of its higher import and relation to the good; secondly, the mere empirics, whom Glaucon appears to confuse with them, and whom both he and Socrates ludicrously describe as experimenting by mere auscultation on the intervals of sounds. Both of these fall short in different degrees of the Platonic idea of harmony, which must be studied in a purely abstract way, first by the method of problems, and secondly as a part of universal knowledge in relation to the idea of good.
The allegory has a political as well as a philosophical meaning. The den or cave represents the narrow sphere of politics or law (cp. the description of the philosopher and lawyer in the Theaetetus, 172–176), and the light of the eternal ideas is supposed to exercise a disturbing influence on the minds of those who return to this lower world. In other words, their principles are too wide for practical application; they are looking far away into the past and future, when their business is with the present. The ideal is not easily reduced to the conditions of actual life, and may often be at variance with them. And at first, those who return are unable to compete with the inhabitants of the den in the measurement of the shadows, and are derided and persecuted by them; but after a while they see the things below in far truer proportions than those who have never ascended into the upper world. The difference between the politician turned into a philosopher and the philosopher turned into a politician, is symbolized by the two kinds of disordered eyesight, cxiii the one which is experienced by the captive who is transferred from darkness to day, the other, of the heavenly messenger who voluntarily for the good of his fellow-men descends into the den. In what way the brighter light is to dawn on the inhabitants of the lower world, or how the idea of good is to become the guiding principle of politics, is left unexplained by Plato. Like the nature and divisions of dialectic, of which Glaucon impatiently demands to be informed, perhaps he would have said that the explanation could not be given except to a disciple of the previous sciences. (Compare Symposium 210 A.)
Many illustrations of this part of the Republic may be found in modern Politics and in daily life. For among ourselves, too, there have been two sorts of Politicians or Statesmen, whose eyesight has become disordered in two different ways. First, there have been great men who, in the language of Burke, ‘have been too much given to general maxims,’ who, like J. S. Mill or Burke himself, have been theorists or philosophers before they were politicians, or who, having been students of history, have allowed some great historical parallel, such as the English Revolution of 1688, or possibly Athenian democracy or Roman Imperialism, to be the medium through which they viewed contemporary events. Or perhaps the long projecting shadow of some existing institution may have darkened their vision. The Church of the future, the Commonwealth of the future, the Society of the future, have so absorbed their minds, that they are unable to see in their true proportions the Politics of to-day. They have been intoxicated with great ideas, such as liberty, or equality, or the greatest happiness of the greatest number, or the brotherhood of humanity, and they no longer care to consider how these ideas must be limited in practice or harmonized with the conditions of human life. They are full of light, but the light to them has become only a sort of luminous mist or blindness. Almost every one has known some enthusiastic half-educated person, who sees everything at false distances, and in erroneous proportions.
With this disorder of eyesight may be contrasted another—of those who see not far into the distance, but what is near only; who have been engaged all their lives in a trade or a profession; who are limited to a set or sect of their own. Men of this kind cxiv have no universal except their own interests or the interests of their class, no principle but the opinion of persons like themselves, no knowledge of affairs beyond what they pick up in the streets or at their club. Suppose them to be sent into a larger world, to undertake some higher calling, from being tradesmen to turn generals or politicians, from being schoolmasters to become philosophers:—or imagine them on a sudden to receive an inward light which reveals to them for the first time in their lives a higher idea of God and the existence of a spiritual world, by this sudden conversion or change is not their daily life likely to be upset; and on the other hand will not many of their old prejudices and narrownesses still adhere to them long after they have begun to take a more comprehensive view of human things? From familiar examples like these we may learn what Plato meant by the eyesight which is liable to two kinds of disorders.
Nor have we any difficulty in drawing a parallel between the young Athenian in the fifth century before Christ who became unsettled by new ideas, and the student of a modern University who has been the subject of a similar ‘aufklärung.’ We too observe that when young men begin to criticise customary beliefs, or to analyse the constitution of human nature, they are apt to lose hold of solid principle (ἅπαν τὸ βέβαιον αὐτῶν ἐξοίχεται). They are like trees which have been frequently transplanted. The earth about them is loose, and they have no roots reaching far into the soil. They ‘light upon every flower,’ following their own wayward wills, or because the wind blows them. They catch opinions, as diseases are caught—when they are in the air. Borne hither and thither, ‘they speedily fall into beliefs’ the opposite of those in which they were brought up. They hardly retain the distinction of right and wrong; they seem to think one thing as good as another. They suppose themselves to be searching after truth when they are playing the game of ‘follow my leader.’ They fall in love ‘at first sight’ with paradoxes respecting morality, some fancy about art, some novelty or eccentricity in religion, and like lovers they are so absorbed for a time in their new notion that they can think of nothing else. The resolution of some philosophical or theological question seems to them more interesting and important than any substantial knowledge of cxv literature or science or even than a good life. Like the youth in the Philebus, they are ready to discourse to any one about a new philosophy. They are generally the disciples of some eminent professor or sophist, whom they rather imitate than understand. They may be counted happy if in later years they retain some of the simple truths which they acquired in early education, and which they may, perhaps, find to be worth all the rest. Such is the picture which Plato draws and which we only reproduce, partly in his own words, of the dangers which beset youth in times of transition, when old opinions are fading away and the new are not yet firmly established. Their condition is ingeniously compared by him to that of a supposititious son, who has made the discovery that his reputed parents are not his real ones, and, in consequence, they have lost their authority over him.
The distinction between the mathematician and the dialectician is also noticeable. Plato is very well aware that the faculty of the mathematician is quite distinct from the higher philosophical sense which recognizes and combines first principles ([531 E]). The contempt which he expresses at p. [533] for distinctions of words, the danger of involuntary falsehood, the apology which Socrates makes for his earnestness of speech, are highly characteristic of the Platonic style and mode of thought. The quaint notion that if Palamedes was the inventor of number Agamemnon could not have counted his feet; the art by which we are made to believe that this State of ours is not a dream only; the gravity with which the first step is taken in the actual creation of the State, namely, the sending out of the city all who had arrived at ten years of age, in order to expedite the business of education by a generation, are also truly Platonic. (For the last, compare the passage at the end of the third book ([415 D]), in which he expects the lie about the earthborn men to be believed in the second generation.)
Republic VIII.
ANALYSIS. BOOK VIII. [543]And so we have arrived at the conclusion, that in the perfect State wives and children are to be in common; and the education and pursuits of men and women, both in war and peace, are to be common, and kings are to be philosophers and warriors, and the soldiers of the State are to live together, cxvi having all things in common; and they are to be warrior athletes, receiving no pay but only their food, from the other citizens. Now let us return to the point at which we digressed. ‘That is easily done,’ he replied: ‘You were speaking of the State which you had constructed, and of the individual who answered to this, both of whom you affirmed to be good; [544]and you said that of inferior States there were four forms and four individuals corresponding to them, which although deficient in various degrees, were all of them worth inspecting with a view to determining the relative happiness or misery of the best or worst man. Then Polemarchus and Adeimantus interrupted you, and this led to another argument,—and so here we are.’ Suppose that we put ourselves again in the same position, and do you repeat your question. ‘I should like to know of what constitutions you were speaking?’ Besides the perfect State there are only four of any note in Hellas:—first, the famous Lacedaemonian or Cretan commonwealth; secondly, oligarchy, a State full of evils; thirdly, democracy, which follows next in order; fourthly, tyranny, which is the disease or death of all government. Now, States are not made of ‘oak and rock,’ but of flesh and blood; and therefore as there are five States there must be five human natures in individuals, which correspond to them. And first, there is the ambitious nature, [545]which answers to the Lacedaemonian State; secondly, the oligarchical nature; thirdly, the democratical; and fourthly, the tyrannical. This last will have to be compared with the perfectly just, which is the fifth, that we may know which is the happier, and then we shall be able to determine whether the argument of Thrasymachus or our own is the more convincing. And as before we began with the State and went on to the individual, so now, beginning with timocracy, let us go on to the timocratical man, and then proceed to the other forms of government, and the individuals who answer to them.