YOUNG SOCRATES: They appear to do so.
VISITOR: So if we divided off two parts of theoretical knowledge as a whole, referring to one as directive and the other as making judgments, would we say that it had been divided suitably?
YOUNG SOCRATES: Yes, at least according to my view.
VISITOR: But if people are doing something together, it is enough if they agree with one another.
YOUNG SOCRATES: Quite.
VISITOR: So for as long as we are sharing in the present task, we should say goodbye to what everybody else may think.
YOUNG SOCRATES: Of course.
[c] VISITOR: So tell me: in which of these two sorts of expertise should we locate the expert in kingship? In the one concerned with making judgments, as if he were some sort of spectator, or shall we rather locate him as belonging to the directive sort of expertise, seeing that he is master of others?
YOUNG SOCRATES: In the second, of course.
VISITOR: Then we should need to look at directive expertise in its turn, to see if it divides somewhere. And to me it seems that it does so somewhere in this direction: in the way that the expertise of the retail-dealer is distinguished from that of the ‘self-seller’ or producer who sells [d] his own products, so the class of kings appears set apart from the class of heralds.
YOUNG SOCRATES: How so?
VISITOR: The retailer, I think, takes over someone else’s products, which have previously been sold, and sells them on, for a second time.
YOUNG SOCRATES: Absolutely.
VISITOR: Well then, the class of heralds takes over directions that have been thought up by someone else, and itself issues them for a second time to another group.
YOUNG SOCRATES: Very true.
VISITOR: So—shall we mix together the expertise of the king with that [e] of the interpreter, the person who gives the time to the rowers, the seer, the herald, and many other sorts of expertise related to these, just because they all have the feature of issuing directions? Or do you want us to make up a name in line with the analogy we were using just now, since in fact the class of ‘self-directors’ happens pretty much to be without a name of its own? Should we divide these things this way, locating the class of kings as belonging to the ‘self-directing’ sort of expertise, and taking no notice of all the rest, leaving someone else to propose another name for them? [261] For we set up our investigation in order to find the person who rules, not his opposite.
YOUNG SOCRATES: Absolutely.
VISITOR: Well then, since this11 is at a certain distance from those others, distinguished by difference in relation to kinship, we must in turn divide it too, if we still find some cut yielding to us in it?
YOUNG SOCRATES: Certainly.
VISITOR: And what’s more, we seem to have one: follow on and make the cut with me.
YOUNG SOCRATES: Where?
VISITOR: All those in control of others that we can think of as employing [b] directions—we shall find them issuing their directions, won’t we, for the sake of something’s coming into being?
YOUNG SOCRATES: Of course.
VISITOR: And it’s not at all difficult to separate into two all of those things that come into being.
YOUNG SOCRATES: How?
VISITOR: I imagine that, of all of them taken together, some are inanimate and some are animate.
YOUNG SOCRATES: Yes.
VISITOR: And it’s by these very things that we’ll cut the part of the theoretical which is directive, if indeed we wish to cut it.
YOUNG SOCRATES: How?
VISITOR: By assigning part of it to the production of inanimate things, [c] part to that of animate things; and in this way it will all immediately be divided into two.
YOUNG SOCRATES: I agree absolutely.
VISITOR: So then let’s leave one of these parts to one side, and take up the other; and then let’s divide the whole of it into two parts.
YOUNG SOCRATES: Which of the two parts do you say we should take up?
VISITOR: I suppose it must be the one that issues directions in relation to living creatures. For surely it is not the case that the expert knowledge that belongs to a king is ever something that oversees inanimate things, as if it were the knowledge of the master-builder; it is something nobler, which always has its power among living creatures and in relation to [d] just these.
YOUNG SOCRATES: Correct.
VISITOR: Now, as one can observe, either the production and rearing of living creatures is done singly, or it is a caring for creatures together12 in herds.
YOUNG SOCRATES: Correct.
VISITOR: But we’ll certainly not find the statesman rearing individual creatures, like some ox-driver or groom, but rather resembling a horse-breeder or cowherd.
YOUNG SOCRATES: It certainly seems so, now you say it.
VISITOR: Well then: when it comes to rearing living creatures, are we to [e] call13 the shared rearing of many creatures together a sort of ‘herd-rearing’ or ‘collective rearing’?
YOUNG SOCRATES: Whichever turns out to fit, in the course of the argument.
VISITOR: Well said, Socrates; and if you persevere in not paying serious attention to names, you will be seen to be richer in wisdom as you advance to old age. But now we must do just as you instruct. Do you see how by [262] showing the collective rearing of herds to be twin in form one will make what is now being sought in double the field then be sought in half of that?
YOUNG SOCRATES: I shall try my hardest. It seems to me that there is a different sort of rearing of human beings, and in turn another sort where animals are concerned.
VISITOR: Yes, absolutely, you’ve made a very keen and courageous division! But let’s try to avoid this happening to us again.
YOUNG SOCRATES: What sort of thing?
[b] VISITOR: Let’s not take off one small part on its own, leaving many large ones behind, and without reference to real classes; let the part bring a real class along with it. It’s a really fine thing to separate off immediately what one is searching for from the rest, if one gets it right—as you thought you had the right division, just before, and hurried the argument on, seeing it leading to human beings; but in fact, my friend, it’s not safe to make thin cuts; it’s safer to go along cutting through the middle of things, and that way one will be more likely to encounter real classes. This makes all the [c] difference in relation to philosophical investigations.
YOUNG SOCRATES: What do you mean by this, visitor?
VISITOR: I must try to tell you still more clearly, Socrates, out of good will towards your natural endowments. In the present circumstances, I have to say, it is impossible to show what I mean with absolute completeness; but I must bring it just a little further forward for the sake of clarity.
YOUNG SOCRATES: Well then, what sort of thing are you saying we weren’t doing right just now in our divisions?
VISITOR: This sort of thing: it’s as if someone tried to divide the human [d] race into two and made the cut in the way that most people here carve things up, taking the Greek race away as one, separate from all the rest, and to all the other races together, which are unlimited in number, which don’t mix with one another, and don’t share the same language—calling this collection by the single appellation ‘barbarian’. Because of this single appellation, they expect it to be a single family or class too. Another example would be if someone thought that he was dividing number into [e] two real classes by cutting off the number ten-thousand from all the rest, separating it off as a single class, and in positing a single name for all the rest supposed here too that through getting the name this class too came into existence, a second single one apart from the other. But I imagine the division would be done better, more by real classes and more into two, if one cut number by means of even and odd, and the human race in its turn by means of male and female, and only split off Lydians or Phrygians or anyone else and ranged them against all the rest when one was at a [263] loss as to how to split in such a way that each of the halves split off was sim
ultaneously a real class and a part.
YOUNG SOCRATES: Quite right; but this very thing—how is one to see it more plainly, that class and part are not the same but different from each other?
VISITOR: An excellent response, Socrates, but what you demand is no light thing. We have already wandered far away from the discussion we proposed, and you are telling us to wander even more. Well, as for now, let’s go back to where we were, which seems the reasonable thing to do; [b] and these other things we’ll pursue like trackers on another occasion, when we have the time. However, there is one thing you must absolutely guard against, and that is ever to suppose that you have heard from me a plain account of the matter.
YOUNG SOCRATES: Which?
VISITOR: That class and part are different from each other.
YOUNG SOCRATES: What should I say I have heard from you?
VISITOR: That whenever there is a class of something, it is necessarily also a part of whatever thing it is called a class of, but it is not at all necessary that a part is a class. You must always assert, Socrates, that this is what I say rather than the other way round.14
YOUNG SOCRATES: I shall do just that.
VISITOR: Tell me, then, about the next thing. [c]
YOUNG SOCRATES: What’s that?
VISITOR: The point from which our digression brought us to where we are now. I think it was pretty much the point at which you were asked how to divide herd-rearing, and you said with great keenness that there were two classes of living creatures, one human, and a second single one consisting of all the rest—the animals—together.
YOUNG SOCRATES: True.
VISITOR: And to me you appeared then to think that in taking away a part you had left behind the rest as in its turn a single class, consisting of all of them, because you had the same name, ‘animals’, to apply to them all. [d]
YOUNG SOCRATES: This too was as you say.
VISITOR: And yet, my courageous friend, maybe, if by chance there is some other animal which is rational, as for example the crane seems to be, or some other such creature, and which perhaps distributes names on the same principles as you, it might oppose cranes as one class to all other living creatures and give itself airs, taking all the rest together with human beings and putting them into the same category, which it would call by no other name except—perhaps—‘animals’. So let’s try to be very wary [e] of everything of this sort.
YOUNG SOCRATES: How?
VISITOR: By not dividing the class of living creatures as a whole, in order to lessen the risk of its happening to us.
YOUNG SOCRATES: Yes, we must certainly avoid it.
VISITOR: Yes; and we were going wrong in this way just at that point.
YOUNG SOCRATES: How so?
VISITOR: Of that theoretical knowledge which was directive we had a part, I think, of the class concerned with rearing living creatures, one which was concerned with creatures living in herds. True?
YOUNG SOCRATES: Yes.
[264] VISITOR: Well then, living creatures as a whole together had in effect already at that point been divided by the categories of domesticated and wild; for those that have a nature amenable to domestication are called tame, and those who do not15 are called wild.
YOUNG SOCRATES: Right.
VISITOR: But the knowledge we are hunting had to be and still is concerned with tame things, and must be looked for with reference to herd animals.
YOUNG SOCRATES: Yes.
[b] VISITOR: Well then, let’s not divide in the way we did then, looking at everything, or in a hurry, just in order to get quickly to statesmanship. It has already put us in the proverbial situation.
YOUNG SOCRATES: What situation is that?
VISITOR: That by not quietly getting on with dividing properly we have got to our destination more slowly.
YOUNG SOCRATES: Yes, visitor, and a fine situation it is!
VISITOR: If you say so. In any case, let’s go back and try again from the beginning to divide collective rearing; perhaps, as we go through it in detail, the argument itself will be better able to reveal to you what you are so keen to find. Tell me this.
YOUNG SOCRATES: What?
VISITOR: This—I wonder if perhaps you’ve heard about it from others? [c] You certainly haven’t yourself any direct acquaintance, I know, with the instances of domesticated fish-rearing in the Nile and in the King’s16 ponds. In ornamental fountains, at any rate, you may perhaps have seen them.
YOUNG SOCRATES: Absolutely—I’ve both seen these and heard about the others from many people.
VISITOR: And again, examples of goose-rearing and crane-rearing—even if you haven’t travelled over the plains of Thessaly, you’ve certainly heard about these and believe that they exist.
YOUNG SOCRATES: Of course.
[d] VISITOR: Look, it’s for this purpose that I’ve asked you all this: of the rearing of herd animals, some has to do with creatures living in water, some also with creatures that live on dry land.
YOUNG SOCRATES: It does.
VISITOR: Do you agree, then, that we must split the expert knowledge of collective rearing into two in this way, allocating one of its two parts to each of these, calling one aquatic rearing, the other dry-land rearing?
YOUNG SOCRATES: I do.
VISITOR: And we certainly shan’t ask, in this case, to which of the two sorts of expertise kingship belongs; it’s quite clear17 to anyone. [e]
YOUNG SOCRATES: Quite.
VISITOR: Everybody would divide the dry-land rearing sort of herd-rearing.
YOUNG SOCRATES: How?
VISITOR: By separating it by reference to the winged and what goes on foot.
YOUNG SOCRATES: Very true.
VISITOR: Well then—mustn’t we18 look for statesmanship in relation to what goes on foot? Or don’t you think that practically even the simplest of minds supposes so?
YOUNG SOCRATES: I do.
VISITOR: And the expertise to do with the management of creatures that go on foot—we must show it being cut into two, like an even19 number.
YOUNG SOCRATES: Clearly.
VISITOR: Now it seems that there are two routes to be seen stretching [265] out in the direction of the part towards which our argument has hurried, one of them quicker, dividing a small part off against a large one, while the other more closely observes the principle we were talking about earlier, that one should cut in the middle as much as possible, but is longer. We can go down whichever of the two routes we like.
YOUNG SOCRATES: What if I were to ask if it is impossible to follow both?
VISITOR: An extraordinary suggestion, if you mean both at once; but clearly it is possible to take each in turn.
YOUNG SOCRATES: Then I opt for taking both, in turn. [b]
VISITOR: That’s easy, since the part that remains is short; if we had been at the beginning or in the middle of our journey, the instruction would have been difficult to carry out. As it is, since you think we should take this option, let’s go down the longer route first; while we are fresher we’ll travel it more easily. Observe the division.
YOUNG SOCRATES: Tell me what it is.
VISITOR: Of tame things that live in herds, we find those that go on foot naturally divided into two.
YOUNG SOCRATES: By what?
VISITOR: By the fact that some of them come into being without horns, some with horns.
YOUNG SOCRATES: Evidently. [c]
VISITOR: Well then, divide the management of creatures that go on foot by assigning it to each of these two parts, using a descriptive phrase for the results of the division. For if you want to give them names, it will be more complicated than necessary.
YOUNG SOCRATES: How then should it be put?
VISITOR: Like this: by saying that when the knowledge that has to do with the management of creatures that go by foot is divided into two, one part is allocated to the horned part of the herd, the other to the hornless part.
[d] YOUNG SOCRATES: Let it be put like that; in any case it’s sufficient
ly clear.
VISITOR: Now, as for the next step, it’s perfectly obvious to us that the king tends a sort of docked herd—of hornless creatures.20
YOUNG SOCRATES: How couldn’t it be clear?
VISITOR: So by breaking this up let’s try to assign what falls to him.
YOUNG SOCRATES: Yes, certainly.
VISITOR: Well, do you want to divide it by the split-hooved and the so-called ‘single-hooved’, or by interbreeding and non-interbreeding? I think you grasp the point.
YOUNG SOCRATES: What’s that?
[e] VISITOR: That horses and donkeys are naturally such as to breed from one another.
YOUNG SOCRATES: Yes.
VISITOR: Whereas what is still left of the smooth-headed herd of tame creatures is unmixed in breeding, one with another.
YOUNG SOCRATES: Quite.
VISITOR: So: does the statesman, then, seem to take care of an interbreeding or of some non-interbreeding sort?
YOUNG SOCRATES: Clearly, of the non-mixing sort.
VISITOR: This, then, it seems, we must separate into two, as we did in the previous cases.
YOUNG SOCRATES: Indeed we must.
[266] VISITOR: Now those creatures that are tame and live in herds have pretty well all now been cut into their pieces, except for two classes. For it is not worth our while to count the class of dogs as among creatures living in herds.
YOUNG SOCRATES: No indeed. But what are we to use to divide21 the two classes?
VISITOR: Something that is absolutely appropriate for Theaetetus and you to use in your distributions, since it’s geometry the two of you engage in.22
YOUNG SOCRATES: What is it?
VISITOR: The diagonal, one could say, and then again the diagonal of the diagonal.
YOUNG SOCRATES: What do you mean?
VISITOR: The nature which the family or class of us humans possesses [b] surely isn’t endowed for the purpose of going from place to place any differently from the diagonal that has the power of two feet?23
YOUNG SOCRATES: No.
VISITOR: And what’s more the nature of the remaining class has in its turn the power of the diagonal of our power, if indeed it is endowed with two times two feet.
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