Plato, Republic

[587a] so far as such a thing is possible,¹ the truest.” “Precisely so.” “And so when one of the other two gets the mastery the result for it is that it does not find its own proper pleasure and constrains the others to pursue an alien pleasure and not the true.” “That is so,” he said. “And would not that which is furthest removed from philosophy and reason be most likely to produce this effect²?” “Quite so,” he said. “And is not that furthest removed from reason which is furthest from law and order?” “Obviously.” “And was it not made plain that the furthest removed are the erotic and tyrannical appetites?” “Quite so.” [587b] “And least so the royal and orderly?” “Yes.” “Then the tyrant's place, I think, will be fixed at the furthest remove³ from true and proper pleasure, and the king's at the least.” “Necessarily.” “Then the tyrant's life will be least pleasurable and the king's most.” “There is every necessity of that.” “Do you know, then,” said I, “how much less pleasurably the tyrant lives than the king?” “I’ll know if you tell me,⁴” he said. “There being as it appears three pleasures, one genuine and two spurious, [587c] the tyrant in his flight from law and reason crosses the border beyond⁵ the spurious, cohabits with certain slavish, mercenary pleasures, and the measure of his inferiority is not easy to express except perhaps thus.” “How?” he said. “The tyrant, I believe, we found at the third remove from the oligarch, for the democrat came between.” “Yes.” “And would he not also dwell with a phantom of pleasure in respect of reality three stages removed from that other, if all that we have said is true?” “That is so.” “And the oligarch in turn is at the third remove from the royal man [587d] if we assume the identity of the aristocrat and the king.⁶” “Yes, the third.” “Three times three, then, by numerical measure is the interval that separates the tyrant from true pleasure.” “Apparently.” “The phantom⁷ of the tyrant's pleasure is then by longitudinal mensuration a plane number.” “Quite so.” “But by squaring and cubing it is clear what the interval of this separation becomes.” “It is clear,” he said, “to a reckoner.” “Then taking it the other way about, [587e] if one tries to express the extent of the interval between the king and the tyrant in respect of true pleasure he will find on completion of the multiplication that he lives 729 times as happily and that the tyrant's life is more painful by the same distance.⁸” “An overwhelming⁹ and baffling calculation,” he said, “of the difference¹⁰ between the just and