Dialogues of Plato - MobileReference [894]
YOUNG SOCRATES: Yes.
STRANGER: There is surely no need to ask which of these two contains the royal art, for it is evident to everybody.
YOUNG SOCRATES: Certainly.
STRANGER: Any one can divide the herds which feed on dry land?
YOUNG SOCRATES: How would you divide them?
STRANGER: I should distinguish between those which fly and those which walk.
YOUNG SOCRATES: Most true.
STRANGER: And where shall we look for the political animal? Might not an idiot, so to speak, know that he is a pedestrian?
YOUNG SOCRATES: Certainly.
STRANGER: The art of managing the walking animal has to be further divided, just as you might halve an even number.
YOUNG SOCRATES: Clearly.
STRANGER: Let me note that here appear in view two ways to that part or class which the argument aims at reaching,--the one a speedier way, which cuts off a small portion and leaves a large; the other agrees better with the principle which we were laying down, that as far as we can we should divide in the middle; but it is longer. We can take either of them, whichever we please.
YOUNG SOCRATES: Cannot we have both ways?
STRANGER: Together? What a thing to ask! but, if you take them in turn, you clearly may.
YOUNG SOCRATES: Then I should like to have them in turn.
STRANGER: There will be no difficulty, as we are near the end; if we had been at the beginning, or in the middle, I should have demurred to your request; but now, in accordance with your desire, let us begin with the longer way; while we are fresh, we shall get on better. And now attend to the division.
YOUNG SOCRATES: Let me hear.
STRANGER: The tame walking herding animals are distributed by nature into two classes.
YOUNG SOCRATES: Upon what principle?
STRANGER: The one grows horns; and the other is without horns.
YOUNG SOCRATES: Clearly.
STRANGER: Suppose that you divide the science which manages pedestrian animals into two corresponding parts, and define them; for if you try to invent names for them, you will find the intricacy too great.
YOUNG SOCRATES: How must I speak of them, then?
STRANGER: In this way: let the science of managing pedestrian animals be divided into two parts, and one part assigned to the horned herd, and the other to the herd that has no horns.
YOUNG SOCRATES: All that you say has been abundantly proved, and may therefore be assumed.
STRANGER: The king is clearly the shepherd of a polled herd, who have no horns.
YOUNG SOCRATES: That is evident.
STRANGER: Shall we break up this hornless herd into sections, and endeavour to assign to him what is his?
YOUNG SOCRATES: By all means.
STRANGER: Shall we distinguish them by their having or not having cloven feet, or by their mixing or not mixing the breed? You know what I mean.
YOUNG SOCRATES: What?
STRANGER: I mean that horses and asses naturally breed from one another.
YOUNG SOCRATES: Yes.
STRANGER: But the remainder of the hornless herd of tame animals will not mix the breed.
YOUNG SOCRATES: Very true.
STRANGER: And of which has the Statesman charge,--of the mixed or of the unmixed race?
YOUNG SOCRATES: Clearly of the unmixed.
STRANGER: I suppose that we must divide this again as before.
YOUNG SOCRATES: We must.
STRANGER: Every tame and herding animal has now been split up, with the exception of two species; for I hardly think that dogs should be reckoned among gregarious animals.
YOUNG SOCRATES: Certainly not; but how shall we divide the two remaining species?
STRANGER: There is a measure of difference which may be appropriately employed by you and Theaetetus, who are students of geometry.
YOUNG SOCRATES: What is that?
STRANGER: The diameter; and, again, the diameter of a diameter. (Compare Meno.)
YOUNG SOCRATES: What do you mean?
STRANGER: How does man walk, but as a diameter whose power is two feet?
YOUNG SOCRATES: Just so.
STRANGER: And the power of the remaining kind, being the power of twice two feet, may be said to be the diameter of our diameter.
YOUNG SOCRATES: