Part 11

SOCRATES: Then he who does not know what science or knowledge is, has no knowledge of the art or science of making shoes?

THEAETETUS: None.

SOCRATES: Nor of any other science?

THEAETETUS: No.

SOCRATES: And when a man is asked what science or knowledge is, to give in answer the name of some art or science is ridiculous; for the question is, 'What is knowledge?' and he replies, 'A knowledge of this or that.'

THEAETETUS: True.

SOCRATES: Moreover, he might answer shortly and simply, but he makes an enormous circuit. For example, when asked about the clay, he might have said simply, that clay is moistened earth--what sort of clay is not to the point.

THEAETETUS: Yes, Socrates, there is no difficulty as you put the question. You mean, if I am not mistaken, something like what occurred to me and to my friend here, your namesake Socrates, in a recent discussion.

SOCRATES: What was that, Theaetetus?

THEAETETUS: Theodorus was writing out for us something about roots, such as the roots of three or five, showing that they are incommensurable by the unit: he selected other examples up to seventeen--there he stopped. Now as there are innumerable roots, the notion occurred to us of attempting to include them all under one name or class.

SOCRATES: And did you find such a class?

THEAETETUS: I think that we did; but I should like to have your opinion.

SOCRATES: Let me hear.

THEAETETUS: We divided all numbers into two classes: those which are made up of equal factors multiplying into one another, which we compared to square figures and called square or equilateral numbers;--that was one class.

SOCRATES: Very good.

THEAETETUS: The intermediate numbers, such as three and five, and every other number which is made up of unequal factors, either of a greater multiplied by a less, or of a less multiplied by a greater, and when regarded as a figure, is contained in unequal sides;--all these we compared to oblong figures, and called them oblong numbers.

SOCRATES: Capital; and what followed?

THEAETETUS: The lines, or sides, which have for their squares the equilateral plane numbers, were called by us lengths or magnitudes; and the lines which are the roots of (or whose squares are equal to) the oblong numbers, were called powers or roots; the reason of this latter name being, that they are commensurable with the former [i.e., with the so-called lengths or magnitudes] not in linear measurement, but in the value of the superficial content of their squares; and the same about solids.

SOCRATES: Excellent, my boys; I think that you fully justify the praises of Theodorus, and that he will not be found guilty of false witness.

THEAETETUS: But I am unable, Socrates, to give you a similar answer about knowledge, which is what you appear to want; and therefore Theodorus is a deceiver after all.

SOCRATES: Well, but if some one were to praise you for running, and to say that he never met your equal among boys, and afterwards you were beaten in a race by a grown-up man, who was a great runner--would the praise be any the less true?

THEAETETUS: Certainly not.

SOCRATES: And is the discovery of the nature of knowledge so small a matter, as just now said? Is it not one which would task the powers of men perfect in every way?

THEAETETUS: By heaven, they should be the top of all perfection!

SOCRATES: Well, then, be of good cheer; do not say that Theodorus was mistaken about you, but do your best to ascertain the true nature of knowledge, as well as of other things.

THEAETETUS: I am eager enough, Socrates, if that would bring to light the truth.

SOCRATES: Come, you made a good beginning just now; let your own answer about roots be your model, and as you comprehended them all in one class, try and bring the many sorts of knowledge under one definition.

THEAETETUS: I can assure you, Socrates, that I have tried very often, when the report of questions asked by you was brought to me; but I can neither persuade myself that I have a satisfactory answer to give, nor hear of any one who answers as you would have him; and I cannot shake off a feeling of anxiety.