ONE:Nothing can be more unreasonable than to expect an apprentice engineer to begin by an inductive course in learning and reasoning [3] about mechanics. Even if the mind were capable of such a course, which can not be assumed in so intricate and extensive a subject as mechanics, there would be a want of interest and an absence of apparent purpose which would hinder or prevent progress. Any rational view of the matter, together with as many facts as can be cited, will all point to the conclusion that apprentices must learn deductively, and that some practice should accompany or precede theoretical studies. How dull and objectless it seems to a young man when he toils through "the sum of the squares of the base and perpendicular of a right-angle triangle," without knowing a purpose to which this problem is to be applied; he generally wonders why such puzzling theorems were ever invented, and what they can have to do with the practical affairs of life. But if the same learner were to happen upon a builder squaring a foundation by means of the rule "six, eight, and ten," and should in this operation detect the application of that tiresome problem of "the sum of the squares," he would at once awake to a new interest in the matter; what was before tedious and without object, would now appear useful and interesting. The subject would become fascinating, and the learner would go on with a new zeal to trace out the connection between practice and other problems of the kind. Nothing inspires a learner so much as contact with practice; the natural tendency, as before said, is to proceed deductively.
TWO:We have next the disposition of individuals, no longer to interfere in making the law, but to override it, or to bend it into an instrument for their own purposes. Doubtless there existed such a tendency in Platos time, and his polity was very largely designed to hold it in check. But such unprincipled ambition was nothing new in Greece, however the mode of its manifestations might vary. What had formerly been seized by armed violence was now sought after with the more subtle weapons of rhetorical skill; just as at the present moment, among these same Greeks, it is the prize of parliamentary intrigue. The Cretan and Spartan institutions may very possibly have been designed with a view to checking this spirit of selfish lawlessness, by reducing private interests to a minimum; and Plato most certainly had them in his mind when he pushed the same method still further; but those institutions were not types of Hellenism as a whole, they only represented one, and that a very abnormal, side of it. Plato borrowed some elements from this quarter, but, as we shall presently show, he incorporated them with others of a widely different character. Sparta was, indeed, on any high theory of government, not a State at all, but a robber-clan established among a plundered population whom they never tried or cared to conciliate. How little weight her rulers attributed to the interests of the State as such, was well exhibited during the Peloponnesian War, when political advantages of the utmost importance were surrendered in deference to the noble families whose kinsmen had been captured at Sphactria, and whose sole object was to rescue them from the fate with which they were threatened by the Athenians as a means of extorting concessions;conduct with which the refusal of Rome to ransom the soldiers who had surrendered at Cannae may be instructively contrasted.Both the Theaettus 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 priori position was turned, a hundred years ago, by Kant. The philosopher of K?nigsberg 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 a212 dead deposit in consciousness or memory, but a living energy whereby phenomena are, to use Kants 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.
