Through all his criticisms on the popular sources of information-sense, language and public opinion-Plato refers to an ideal of perfect knowledge which he assumes without being able to define it. It must satisfy the negative condition of being free from self-contradiction, but further than this we cannot go. Yet, in the hands of a metaphysician, no more than this was required to reconstruct the world. The demand for consistency explains the practical philosophy of Socrates. It also explains, under another form, the philosophy, both practical and speculative, of his disciple. Identity and the correlative of identity, difference, gradually came to cover with their manifold combinations all knowledge, all life, and all existence.

It was from mathematical science that the light of certainty first broke. Socrates had not encouraged the study of mathematics, either pure or applied; nor, if we may judge from some disparaging allusions to Hippias and his lectures in the Protagoras, did Plato at first regard it with any particular favour. He may have acquired some notions of arithmetic and geometry at school; but the intimate acquaintance with, and deep interest in them, manifested throughout his later works, probably dates from his visits to Italy, Sicily, Cyrênê, and Egypt. In each of these places the exact sciences were cultivated with more assiduity than at Athens; in southern Italy they had been brought into close connexion with philosophy by a system of mystical interpretation. The glory of discovering their true speculative significance was reserved for Plato. Just as he had detected a profound analogy between the Socratic scepticism and the Heracleitean flux, so also, by another vivid intuition, he saw in the definitions and demonstrations of geometry a type of true reasoning, a particular application of the Socratic logic. Thus the two studies were brought into fruitful reaction, the one gaining a wider applicability, and the other an exacter method of proof. The mathematical spirit ultimately proved

too strong for Plato, and petrified his philosophy into a lifeless formalism; but no extraneous influence helped so much to bring about the complete maturity of his constructive powers, in no direction has he more profoundly influenced the thought of later ages.

Both the Theaetêtus and the Cratylus contain allusions to mathematical reasoning, but its full significance is first exhibited in the Meno. Here the old question, whether virtue can be taught, is again raised, to be discussed from an entirely new point of view, and resolved into the more general question, Can anything be taught? The answer is, Yes and No. You may stimulate the native activity of the intellect, but you cannot create it. Take a totally uneducated man, and, under proper guidance, he shall discover the truths of geometry for himself, by virtue of their self-evident clearness. Being independent of any traceable experience, the elementary principles of this science, of all science, must have been acquired in some antenatal period, or rather they were never acquired at all, they belong to the very nature of the soul herself. The doctrine here unfolded had a great future before it; and it has never, perhaps, been discussed with so much eagerness as during the last half-century among ourselves. The masters of English thought have placed the issue first raised by Plato in the very front of philosophical controversy; and the general public have been brought to feel that their dearest interests hang on its decision. The subject has, however, lost much of its adventitious interest to those. who know that the à priori position was turned, a hundred years ago, by Kant. The philosopher of Königsberg showed that, granting knowledge to be composed of two elements, mind adds nothing to outward experience but its own forms, the system of connexions according to which it groups phenomena. Deprive these forms of the content given to them by feeling, and the soul will be left beating her wings in a vacuum. The doctrine that knowledge is not a

dead deposit in consciousness or memory, but a living energy whereby phenomena are, to use Kant's words, gathered up into the synthetic unity of apperception, has since found a physiological basis in the theory of central innervation. And the experiential school of psychology have simultaneously come to recognise the existence of fixed conditions under which consciousness works and grows, and which, in the last analysis, resolve themselves into the apprehension of resemblance, difference, coexistence, and succession. The most complex cognition involves no more than these four categories; and it is probable that they all co-operate in the most elementary perception.

The truths here touched on seem to have been dimly present to the mind of Plato. He never doubts that all knowledge must, in some way or other, be derived from experience; and, accordingly, he assumes that what cannot have been learned in this world was learned in another. But he does not (in the Meno at least) suppose that the process ever had a beginning. It would seem that he is trying to express in figurative language the distinction, lost almost as soon as found, between intelligence and the facts on which intelligence is exercised. An examination of the steps by which Meno's slave is brought to perceive, without being directly told, the truth of the Pythagorean theorem, will show that his share in the demonstration is limited to the intuition of certain numerical equalities and inequalities. Now, to Plato, the perception of sameness and difference meant everything. He would have denied that the sensible world presented examples of these relations in their ideal absoluteness and purity. In tracing back their apprehension to the self-reflection of the soul, the consciousness of personal identity, he would not have transgressed the limits of a legitimate enquiry. But selfconsciousness involved a possible abstraction from disturbing influences, which he interpreted as a real separation between mind and matter; and, to make it more complete, an inde

pendent pre-existence of the former. Nor was this all. Since knowledge is of likeness in difference, then the central truth of things, the reality underlying all appearance, must be an abiding identity recognised by the soul through her previous communion with it in a purer world. The inevitable tendency of two identities, one subjective and the other objective, was to coalesce in an absolute unity where all distinctions of time and space would have disappeared, carrying the whole mythical machinery along with them; and Plato's logic is always hovering on the verge of such a consummation without being able fully to accept it. Still, the mystical tendency, which it was reserved for Plotinus to carry out in its entirety, is always present, though restrained by other motives, working for the ascertainment of uniformity in theory and for the enforcement of uniformity in practice.

We have accompanied Plato to a point where he begins to see his way towards a radical reconstruction of all existing beliefs and institutions. In the next chapter we shall attempt to show how far he succeeded in this great purpose, how much, in his positive contributions to thought is of permanent, and how much of merely biographical or literary value,

CHAPTER V.

PLATO AS A REFORMER.

I.

IN the last chapter we considered the philosophy of Plato chiefly under its critical and negative aspects. We saw how it was exclusively from that side that he at first apprehended and enlarged the dialectic of Socrates, how deeply his scepticism was coloured by the religious reaction of the age, and how he attempted, out of his master's mouth, to overturn the positive teaching of the master himself. We saw how, in the Protagoras, he sketched a theory of ethics, which was no sooner completed than it became the starting-point of a still more extended and arduous enquiry. We followed the widening horizon of his speculations until they embraced the whole contemporary life of Hellas, and involved it in a common condemnation as either hopelessly corrupt, or containing within itself the seeds of corruption. We then saw how, by a farther generalisation, he was led to look for the sources of error in the laws of man's sensuous nature and of the phenomenal world with which it holds communion; how, moreover, under the guidance of suggestions coming both from within and from without, he reverted to the earlier schools of Greek thought, and brought their results into parallelism with the main lines of Socratic dialectic. And finally, we watched him planting a firm foothold on the basis of mathematical demonstration; seeking in the very constitution of the soul itself for a derivation of the truths which sensuous experience could not impart, and winning back from