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The Republic by Plato

2. The number of the interval which separates the king from the tyrant,

442 words  |  Chapter 26

and royal from tyrannical pleasures, is 729, the cube of 9. Which Plato characteristically designates as a number concerned with human life, because NEARLY equivalent to the number of days and nights in the year. He is desirous of proclaiming that the interval between them is immeasurable, and invents a formula to give expression to his idea. Those who spoke of justice as a cube, of virtue as an art of measuring (Prot.), saw no inappropriateness in conceiving the soul under the figure of a line, or the pleasure of the tyrant as separated from the pleasure of the king by the numerical interval of 729. And in modern times we sometimes use metaphorically what Plato employed as a philosophical formula. ‘It is not easy to estimate the loss of the tyrant, except perhaps in this way,’ says Plato. So we might say, that although the life of a good man is not to be compared to that of a bad man, yet you may measure the difference between them by valuing one minute of the one at an hour of the other (‘One day in thy courts is better than a thousand’), or you might say that ‘there is an infinite difference.’ But this is not so much as saying, in homely phrase, ‘They are a thousand miles asunder.’ And accordingly Plato finds the natural vehicle of his thoughts in a progression of numbers; this arithmetical formula he draws out with the utmost seriousness, and both here and in the number of generation seems to find an additional proof of the truth of his speculation in forming the number into a geometrical figure; just as persons in our own day are apt to fancy that a statement is verified when it has been only thrown into an abstract form. In speaking of the number 729 as proper to human life, he probably intended to intimate that one year of the tyrannical = 12 hours of the royal life. The simple observation that the comparison of two similar solids is effected by the comparison of the cubes of their sides, is the mathematical groundwork of this fanciful expression. There is some difficulty in explaining the steps by which the number 729 is obtained; the oligarch is removed in the third degree from the royal and aristocratical, and the tyrant in the third degree from the oligarchical; but we have to arrange the terms as the sides of a square and to count the oligarch twice over, thus reckoning them not as = 5 but as = 9. The square of 9 is passed lightly over as only a step towards the cube.
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Chapters

1. Chapter 1 2. INTRODUCTION AND ANALYSIS. 3. INTRODUCTION AND ANALYSIS. 4. Introduction to the Phaedrus). 5. BOOK I. The Republic opens with a truly Greek scene—a festival in 6. BOOK II. Thrasymachus is pacified, but the intrepid Glaucon insists on 7. BOOK III. There is another motive in purifying religion, which is to 8. 1. The constant appeal to the authority of Homer, whom, with grave 9. 2. ‘The style is to conform to the subject and the metre to the style.’ 10. 3. In the third book of the Republic a nearer approach is made to a 11. 4. Plato makes the true and subtle remark that the physician had better 12. 5. One of the most remarkable conceptions of Plato, because un-Greek 13. 6. Two paradoxes which strike the modern reader as in the highest 14. 7. Lesser matters of style may be remarked. 15. BOOK IV. Adeimantus said: ‘Suppose a person to argue, Socrates, that 16. BOOK V. I was going to enumerate the four forms of vice or decline in 17. Book IV, which fall unperceived on the reader’s mind, as they are 18. BOOK VI. Having determined that the many have no knowledge of true 19. 1. Of the higher method of knowledge in Plato we have only a glimpse. 20. 2. Plato supposes that when the tablet has been made blank the artist 21. 3. There is no difficulty in seeing that Plato’s divisions of knowledge 22. BOOK VII. And now I will describe in a figure the enlightenment or 23. BOOK VIII. And so we have arrived at the conclusion, that in the 24. BOOK IX. Last of all comes the tyrannical man, about whom we have to 25. 1. Plato’s account of pleasure is remarkable for moderation, and in 26. 2. The number of the interval which separates the king from the tyrant, 27. 3. Towards the close of the Republic, Plato seems to be more and more 28. BOOK X. Many things pleased me in the order of our State, but there was 29. 1. Plato expressly says that he is intending to found an Hellenic State 30. 2. The idea of the perfect State is full of paradox when judged of 31. introduction of the mere conception of law or design or final cause, 32. 3. Plato’s views of education are in several respects remarkable; like 33. 4. We remark with surprise that the progress of nations or the natural 34. 5. For the relation of the Republic to the Statesman and the Laws, and 35. 6. Others as well as Plato have chosen an ideal Republic to be the 36. 7. Human life and conduct are affected by ideals in the same way that 37. 8. Two other ideals, which never appeared above the horizon in Greek 38. BOOK I. 39. part I openly declare that I am not convinced, and that I do not 40. BOOK II. 41. BOOK III. 42. BOOK IV. 43. BOOK V. 44. BOOK VI. 45. BOOK VII. 46. BOOK VIII. 47. Introduction.) two perfect squares of irrational diameters (of a square 48. BOOK IX. 49. BOOK X.

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