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TWO: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.
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