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Plato... introduces two infinities, because both in increase and diminution there appears to be transcendency, and a progression to infinity. Though... he did not use them: for neither is there infinity in numbers by diminution or division; since unity is a minimum: nor by increase; for he extends number as far as to the decad.
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It is the mark of an educated man to look for precision in each class of things just so far as the nature of the subject admits; it is evidently equally foolish to accept probable reasoning from a mathematician and to demand from a rhetorician scientific proofs.
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If everything when it occupies an equal space is at rest, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless.
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That which is excellent endures.
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Every art and every inquiry, and similarly every action and pursuit, is thought to aim at some good; and for this reason the good has rightly been declared to be that at which all things aim.
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To let them share in the highest offices is to take a risk; inevitably, their unjust standards will cause them to commit injustice, and their lack of judgement will lead them into error. On the other hand there is a risk in not giving them a share, and in their non participation, for when there are many who have no property and no honours they inevitably constitute a huge hostile element in the state. But it can still remain open to them to participate in deliberating and judging.
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Young people are in a condition like permanent intoxication, because life is sweet and they are growing.
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The life of theoretical philosophy is the best and happiest a man can lead. Few men are capable of it and then only intermittently. For the rest there is a second-best way of life, that of moral virtue and practical wisdom.
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But voice is a certain sound of that which is animated; for nothing inanimate emits a voice; but they are said to emit a voice from similitude, as a pipe, and a lyre, and such other inanimate things, have extension, modulation, and dialect; for thus it appears, because voice, also, has these.
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If the consequences are the same it is always better to assume the more limited antecedent, since in things of nature the limited, as being better, is sure to be found, wherever possible, rather than the unlimited.
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Justice therefore demands that no one should do more ruling than being ruled, but that all should have their turn.
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Practical life is not necessarily directed toward other people, as some think; and it is not the case that practical thoughts are only those which result from action for the sake of what ensues. On the contrary, much more practical are those mental activities and reflections which have their goal in themselves and take place for their own sake.
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Those who merely possess the goods of fortune may be haughty and insolent; . . . they try to imitate the great-souled man without being really like him, and only copy him in what they can, reproducing his contempt for others but not his virtuous conduct. For the great-souled man is justified in despising other people - his estimates are correct; but most proud men have no good ground for their pride.
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Once more: there are three offices according to whose directions the highest magistrates are chosen in certain states - guardians of the law, probuli, councilors - of these, the guardians of the law are an aristocratical, the probuli an oligarchical, the council a democratical institution.
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That which is desirable on its own account and for the sake of knowing it is more of the nature of wisdom than that which is desirable on account of its results.
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The misanthrope, as an essentially solitary man, is not a man at all: he must be a beast or a god.
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Persuasion is effected through the medium of the hearers, when they shall have been brought to a state of excitement under the influence of speech; for we do not, when influenced by pain or joy, or partiality or dislike, award our decisions in the same way; about which means of persuasion alone, I declare that the system-mongers of the present day busy themselves.
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A democracy exists whenever those who are free and are not well-off, being in the majority, are in sovereign control of government, an oligarchy when control lies with the rich and better-born, these being few.
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When Pleasure is at the bar the jury is not impartial.
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Accordingly, the poet should prefer probable impossibilities to improbable possibilities. The tragic plot must not be composed of irrational parts.
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Again, men in general desire the good, and not merely what their fathers had.
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Hence both women and children must be educated with an eye to the constitution, if indeed it makes any difference to the virtue of a city-state that its children be virtuous, and its women too. And it must make a difference, since half the free population are women, and from children come those who participate in the constitution.
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For suppose that every tool we had could perform its task, either at our bidding or itself perceiving the need, and if-like the statues made by Dædalus or the tripods of Hephæstus, of which the poet says that "self-moved they enter the assembly of the gods" - shuttles in a loom could fly to and fro and a plectrum play a lyre all self-moved, then master-craftsmen would have no need of servants nor masters of slaves.
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We must not listen to those who advise us 'being men to think human thoughts, and being mortal to think mortal thoughts' but must put on immortality as much as possible and strain every nerve to live according to that best part of us, which, being small in bulk, yet much more in its power and honour surpasses all else.