When the training in music and gymnastic is completed, there follows the first stage of active and public life. But soon education is to begin again from a new point of view. In the interval between the Fourth and Seventh Books we have discussed the nature of knowledge, and have thence been led to form a higher conception of what was required of us. For true knowledge, according to Plato, is of abstractions, and has to do, not with particulars or individuals, but with universals only; not with the beauties of poetry, but with the ideas of philosophy. And the great aim of education is the cultivation of the habit of abstraction. This is to be acquired through the study of the mathematical sciences. They alone are capable of giving ideas of relation, and of arousing the dormant energies of thought.
Mathematics in the age of Plato comprehended a very small part of that which is now included in them; but they bore a much larger proportion to the sum of human knowledge. They were the only organon of thought which the human mind at that time possessed, and the only measure by which the chaos of particulars could be reduced to rule and order. The faculty which they trained was naturally at war with the poetical or imaginative; and hence to Plato, who is everywhere seeking for abstractions and trying to get rid of the illusions of sense, nearly the whole of education is contained in them. They seemed to have an inexhaustible application, partly because their true limits were not yet understood. These Plato himself is beginning to investigate; though not aware that number and figure are mere abstractions of sense, he recognizes that the forms used by geometry are borrowed from the sensible world. He seeks to find the ultimate ground of mathematical ideas in the idea of good, though he does not satisfactorily explain the connexion between them; and in his conception of the relation of ideas to numbers, he falls very far short of the definiteness attributed to him by Aristotle (Met.). But if he fails to recognize the true limits of mathematics, he also reaches a point beyond them; in his view, ideas of number become secondary to a higher conception of knowledge. The dialectician is as much above the mathematician as the mathematician is above the ordinary man. The one, the self-proving, the good which is the higher sphere of dialectic, is the perfect truth to which all things ascend, and in which they finally repose.
This self-proving unity or idea of good is a mere vision of which no distinct explanation can be given, relative only to a particular stage in Greek philosophy. It is an abstraction under which no individuals are comprehended, a whole which has no parts (Arist., Nic. Eth.). The vacancy of such a form was perceived by Aristotle, but not by Plato. Nor did he recognize that in the dialectical process are included two or more methods of investigation which are at variance with each other. He did not see that whether he took the longer or the shorter road, no advance could be made in this way. And yet such visions often have an immense effect; for although the method of science cannot anticipate science, the idea of science, not as it is, but as it will be in the future, is a great and inspiring principle. In the pursuit of knowledge we are always pressing forward to something beyond us; and as a false conception of knowledge, for example the scholastic philosophy, may lead men astray during many ages, so the true ideal, though vacant, may draw all their thoughts in a right direction. It makes a great difference whether the general expectation of knowledge, as this indefinite feeling may be termed, is based upon a sound judgment. For mankind may often entertain a true conception of what knowledge ought to be when they have but a slender experience of facts. The correlation of the sciences, the consciousness of the unity of nature, the idea of classification, the sense of proportion, the unwillingness to stop short of certainty or to confound probability with truth, are important principles of the higher education. Although Plato could tell us nothing, and perhaps knew that he could tell us nothing, of the absolute truth, he has exercised an influence on the human mind which even at the present day is not exhausted; and political and social questions may yet arise in which the thoughts of Plato may be read anew and receive a fresh meaning.
The Idea of good is so called only in the Republic, but there are traces of it in other dialogues of Plato. It is a cause as well as an idea, and from this point of view may be compared with the creator of the Timaeus, who out of his goodness created all things. It corresponds to a certain extent with the modern conception of a law of nature, or of a final cause, or of both in one, and in this regard may be connected with the measure and symmetry of the Philebus. It is represented in the Symposium under the aspect of beauty, and is supposed to be attained there by stages of initiation, as here by regular gradations of knowledge. Viewed subjectively, it is the process or science of dialectic. This is the science which, according to the Phaedrus, is the true basis of rhetoric, which alone is able to distinguish the natures and classes of men and things; which divides a whole into the natural parts, and reunites the scattered parts into a natural or organized whole; which defines the abstract essences or universal ideas of all things, and connects them; which pierces the veil of hypotheses and reaches the final cause or first principle of all; which regards the sciences in relation to the idea of good. This ideal science is the highest process of thought, and may be described as the soul conversing with herself or holding communion with eternal truth and beauty, and in another form is the everlasting question and answer — the ceaseless interrogative of Socrates. The dialogues of Plato are themselves examples of the nature and method of dialectic. Viewed objectively, the idea of good is a power or cause which makes the world without us correspond with the world within. Yet this world without us is still a world of ideas. With Plato the investigation of nature is another department of knowledge, and in this he seeks to attain only probable conclusions (Timaeus).
If we ask whether this science of dialectic which Plato only half explains to us is more akin to logic or to metaphysics, the answer is that in his mind the two sciences are not as yet distinguished, any more than the subjective and objective aspects of the world and of man, which German philosophy has revealed to us. Nor has he determined whether his science of dialectic is at rest or in motion, concerned with the contemplation of absolute being, or with a process of development and evolution. Modern metaphysics may be described as the science of abstractions, or as the science of the evolution of thought; modern logic, when passing beyond the bounds of mere Aristotelian forms, may be defined as the science of method. The germ of both of them is contained in the Platonic dialectic; all metaphysicians have something in common with the ideas of Plato; all logicians have derived something from the method of Plato. The nearest approach in modern philosophy to the universal science of Plato, is to be found in the Hegelian ‘succession of moments in the unity of the idea.’ Plato and Hegel alike seem to have conceived the world as the correlation of abstractions; and not impossibly they would have understood one another better than any of their commentators understand them (Swift’s Voyage to Laputa. ‘Having a desire to see those ancients who were most renowned for wit and learning, I set apart one day on purpose. I proposed that Homer and Aristotle might appear at the head of all their commentators; but these were so numerous that some hundreds were forced to attend in the court and outward rooms of the palace. I knew, and could distinguish these two heroes, at first sight, not only from the crowd, but from each other. Homer was the taller and comelier person of the two, walked very erect for one of his age, and his eyes were the most quick and piercing I ever beheld. Aristotle stooped much, and made use of a staff. His visage was meagre, his hair lank and thin, and his voice hollow. I soon discovered that both of them were perfect strangers to the rest of the company, and had never seen or heard of them before. And I had a whisper from a ghost, who shall be nameless, “That these commentators always kept in the most distant quarters from their principals, in the lower world, through a consciousness of shame and guilt, because they had so horribly misrepresented the meaning of these authors to posterity.” I introduced Didymus and Eustathius to Homer, and prevailed on