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THREE:On the other hand, this substitution of the social for the personal integer involves a corresponding change in the398 valuation of individual happiness. What the passions had been to later Greek philosophy, that the individual soul became to Hobbes, something essentially infinite and insatiable, whose desires grow as they are gratified, whose happiness, if such it can be called, is not a condition of stable repose but of perpetual movement and unrest.556 Here, again, the analogy between physics and ethics obtains. In both, there was an original opposition between the idea of a limit and the idea of infinite expansion. Just as, among the earlier Greek thinkers, there was a physical philosophy of the infinite or, as its impugners called it, the indefinite, so also there was, corresponding to it, a philosophy of the infinite or indefinite in ethics, represented, not indeed by professional moralists, but by rhetoricians and men of the world. Their ideal was not the contented man, but the popular orator or the despot who revels in the consciousness of power��the ability to satisfy his desires, whatever they may be. And the extreme consequence of this principle is drawn by Plato��s Callicles when he declares that true happiness consists in nursing one��s desires up to the highest point at which they can be freely indulged; while his ideal of character is the superior individual who sets at naught whatever restraints have been devised by a weak and timid majority to protect themselves against him.

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THREE:3. Two elevations taken at right angles to each other, fix all points, and give all dimensions of parts that have their axis parallel to the planes on which the views are taken; but when a machine is complex, or when several parts lie in the same plane, three and sometimes four views are required to display all the parts in a comprehensive manner.Both the Theaet��tus 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 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.

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THREE:36On the other hand, a theory of reasoning based on the relations of concepts, instead of on the relations of judgments, necessarily leaves out of account the whole doctrine of hypothetical and disjunctive propositions, together with that of the syllogisms based on them; since the elements of which they are composed are themselves propositions. And this inevitable omission is the more remarkable because alterna381tive and, to a less extent, hypothetical arguments form the staple of Aristotle��s own dialectic; while categorical reasoning never occurs in it at all. His constant method is to enumerate all possible views of a subject, and examine them one after the other, rejecting those which are untenable, and resting content with the remainder. In other words, he reaches his positive conclusions through a series of negative premises representing a process of gradual elimination. The First Analytics is itself an admirable instance of his favourite method. Every possible combination of terms is discussed, and the valid moods are sifted out from a much greater number of illegitimate syllogisms. The dialectic of Socrates and Plato followed the same procedure. It was essentially experimental��a method of trial, elimination, and selection. On going back still further, we find that when there is any reasoning at all in Homer, it is conducted after the same fashion. Hector, in his soliloquy before the Scaean Gate, imagines three alternative courses, together exhausting the possibilities of the situation. He may either retreat within the walls, or offer terms of peace to Achilles, or fight. The first two alternatives being rejected, nothing remains but the third. This is the most elaborate example; but on many other occasions Homer��s actors are represented as hesitating between two courses, and finally deciding on one of them.

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