tion, and we possess at the same time a key to the Platonic use of number and figure in the region of philosophy, and to the relation in which Plato stood to the Pythagorean school in this respect. Very remarkable also are the elucidations given with regard to the relation between the mathematical method and the dialectic, although they stand in no connection whatever with the former theory, unless by the introduction of a middle term, here not even alluded to, in so far, that is, as mathematical hypotheses can be considered also as types of real premises or first principles. Thus, at least, upon these arguments it would be quite consistent in Plato to distinguish himself from those who think themselves able to define the essence of things by means of number and figure, and fancy that they know, in the philosophical sense of the word, while they are only forming mathematical connections. But if already at an earlier period material things have been described as constituting the true in the sphere of the visible, and called also types of the ideas, still mathematical processes, as belonging to the province of the intelligible, have justly the precedence of them, and thus the four gradations that follow obtain among the objects of intellectual activity: corporeal vision has for its object the types; belief, real things; abstract intuition, mathematical subjects; and real knowledge, ideas. To this gradation, then, the whole series of studies of those intended for the government is to correspond; and that we may the better survey this, and learn to estimate the reciprocation between studies and practice, Socrates suddenly transports us out of the midst of these investigations into that cave, in which the tenor of life and condition of those who, because it is im

possible for them to turn themselves with their eyes to the spiritual sun, take external appearance, and the types, that is, visible objects, for reality and being, is represented in such vivid colours, that one scarcely sees, even though the illuminated were to give up their own happiness which they enjoy above, and to bestow it there, why it should be even worth while to lead such a destitute life, in which there is nothing to improve and nothing to lose; so that he is indeed no common patriot who, as is here demanded, applies to this point also that magnanimous sentiment, that it is not an object that any one part of the whole should be prosperous above the rest*. But if, notwithstanding all guidance, the great mass of the people ever continues what it was before—and Plato does not appear to conceive the existence of society upon any other principle, or to have an idea of a progressive improvement comprehending the people-then even the most magnanimous selfdevotion can only receive any compensation in so far as it is by this means alone possible, in the case of every rising generation, to discover the more honourable natures, and bring them to a better lot. And if to this we add the further consideration that the population in Plato's state, to which we are now again introduced, is not even to multiply itself, and that the relation between the producers and the consumers must appear to him confined within very narrow limits, we may say that the problem of the Platonic state, and consequently of collective human activity considered in the gross, is no other than to preserve human nature without deterioration in its once given relations. So that our philosopher appears in the character of the strictest and

most consistent champion of stability. In what manner, then, the small selection of more noble natures is to be tried, and by degrees practised in and accustomed to their better lot, is immediately developed by Plato by an elegant reference of this image of the cave to the original one of the sun, in which it is at once selfevident that the capability of gazing at the sun itself can only be acquired by manifold preparatory exercises. As then the common corporeal and mental exercises of the children were unavoidably much conversant with typical images, by reason of the mythical matter involved in them, and the world of real material things, and consequently of faith, is the scene of the whole development of infantine life, so also the preparatory exercises of the grown-up boys of distinguished powers are conversant exclusively with the world of intuition, subjective thought, which is constituted by the mathematical sciences in their natural order. Yet even here Plato draws a distinction between two different processes, separated by a couple of strictly gymnastic years. The first is the delivery of those sciences, according to his notions improperly so called, each for itself, though always setting aside all merely experimental proceeding, and all practical reference to material thingsexclusively bearing upon number in the abstract, figure in the abstract, and in like manner motions and relations in the abstract. The next is the setting up of these sciences in their connection with, and their relation to, the nature of absolute existence; and those only who can follow up to this point, and join in the contemplation of this, are recognised as dialectic and consequently regal natures. But it is not until a late period, and after they have been compelled to divide

their time very unequally between that enviable scientific life and the joyless service in the cave, that even these men attain to the pure contemplation of the idea of the good, and to government; to which last, however, they have only to devote intermittingly the smaller part of their time, dedicating the greater to contemplation, until at length in due time, and extolled by all, they close their mortal career.

And with this, Socrates, after having first given a cursory hint as to the manner in which, provided only first of all that true philosophers but once had the power in their hands, such a state might actually exist, has fully acquitted himself of the whole task which Adimantus had set him, and returns back at the beginning of the eighth book to the point at which this great digression was imposed upon him, and we now take our leave of this singular Republic. And if I may be allowed to say a few words upon the same, I would first call attention to the point, how little Plato deserves the accusation not unfrequently brought against him, of contempt for his own nation; how highly, on the contrary, he thought of the Hellenic nature, as he not only ascribes to it a pre-eminent development of the knowledge-seeking element in the human mind, but even in so contracted a population as population as we have to conceive his Republic capable of containing, he calculates upon finding that rare union of qualities, and these in sufficient strength, to engage successfully in all these exercises and trials, in so many individuals, including even the female sex, that he will never want rulers, although no one attains to the highest power before his fiftieth year, and then several are to relieve one another by turns.

Perhaps even in our own

populous states we would not undertake to effect this, though with the total difference in our method of education it can never be possible that the attempt should be made. Meanwhile, however, we have gone so far as to require from all those who would exercise great influence upon society, a combination of scientific accomplishments with those requisite for war, and vice versâ. And if we cannot desire that they who have to exercise the highest power should possess the most dialectic genius, with us the supreme power does not comprehend so much as in Plato; and we count moreover much upon the fact that they who live most in the kingdom of ideas, by exercising a manifold influence upon education, will also have a predominant influence in the formation of public opinion, which always, though unconsciously, regulates the exercise of the supreme power. Nay, even though temporary mischief might not always be avoidable in so doing, we might pretty confidently leave it to the emulous principle in our nature, in the development of which we are so far in advance of the ancients, to decide where self-seeking and counterfeit sophistry is endeavouring to play the part of the philosopher, and falsify the description of the good.

Now this perfect Republic being only constructed for the particular purpose of exhibiting justice in the gross, after those general outlines also have been sketched which do not stand in immediate connection with this object, a nearer approximation is now made to what was to have been done at the end of the fourth book, we mean, to answering the question as to what mode of life is the most desirable. And here the same method

of proceeding is adopted as that by which we were conducted to a definition of the idea of justice. For