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The subject of gymnastic leads Plato to the sister subject of medicine, which he further illustrates by the parallel of law. The modern disbelief in medicine has led in this, as in some other departments of knowledge, to a demand for greater simplicity; physicians are becoming aware that they often make diseases 'greater and more complicated' by their treatment of them (Rep.). In two thousand years their art has made but slender progress; what they have gained in the analysis of the parts is in a great degree lost by their feebler conception of the human frame as a whole. They have attended more to the cure of diseases than to the conditions of health; and the improvements in medicine have been more than counterbalanced by the disuse of regular training. Until lately they have hardly thought of air and water, the importance of which was well understood by the ancients; as Aristotle remarks, 'Air and water, being the elements which we most use, have the greatest effect upon health' (Polit.). For ages physicians have been under the dominion of prejudices which have only recently given way; and now there are as many opinions in medicine as in theology, and an equal degree of scepticism and some want of toleration about both. Plato has several good notions about medicine; according to him, 'the eye cannot be cured without the rest of the body, nor the body without the mind' (Charm.). No man of sense, he says in the Timaeus, would take physic; and we heartily sympathize with him in the Laws when he declares that 'the limbs of the rustic worn with toil will derive more benefit from warm baths than from the prescriptions of a not over wise doctor.' But we can hardly praise him when, in obedience to the authority of Homer, he depreciates diet, or approve of the inhuman spirit in which he would get rid of invalid and useless lives by leaving them to die. He does not seem to have considered that the 'bridle of Theages' might be accompanied by qualities which were of far more value to the State than the health or strength of the citizens; or that the duty of taking care of the helpless might be an important element of education in a State. The physician himself (this is a delicate and subtle observation) should not be a man in robust health; he should have, in modern phraseology, a nervous temperament; he should have experience of disease in his own person, in order that his powers of observation may be quickened in the case of others.

The perplexity of medicine is paralleled by the perplexity of law; in which, again, Plato would have men follow the golden rule of simplicity. Greater matters are to be determined by the legislator or by the oracle of Delphi, lesser matters are to be left to the temporary regulation of the citizens themselves. Plato is aware that laissez faire is an important element of government. The diseases of a State are like the heads of a hydra; they multiply when they are cut off. The true remedy for them is not extirpation but prevention. And the way to prevent them is to take care of education, and education will take care of all the rest. So in modern times men have often felt that the only political measure worth having—the only one which would produce any certain or lasting effect, was a measure of national education. And in our own more than in any previous age the necessity has been recognized of restoring the ever-increasing confusion of law to simplicity and common sense.

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.