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