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theaetetus   


Soc. Perhaps nothing. I will endeavour, however, to explain what I
believe to be my meaning: When you speak of cobbling, you mean the art
or science of making shoes?
Theaet. Just so.
Soc. And when you speak of carpentering, you mean the art of
making wooden implements?
Theaet. I do.
Soc. In both cases you define the subject matter of each of the
two arts?
Theaet. True.
Soc. But that, Theaetetus, was not the point of my question: we
wanted to know not the subjects, nor yet the number of the arts or
sciences, for we were not going to count them, but we wanted to know
the nature of knowledge in the abstract. Am I not right?
Theaet. Perfectly right.
Soc. Let me offer an illustration: Suppose that a person were to ask
about some very trivial and obvious thing-for example, What is clay?
and we were to reply, that there is a clay of potters, there is a clay
of oven-makers, there is a clay of brick-makers; would not the
answer be ridiculous?
Theaet. Truly.
Soc. In the first place, there would be an absurdity in assuming
that he who asked the question would understand from our answer the
nature of "clay," merely because we added "of the image-makers," or of
any other workers. How can a man understand the name of anything, when
he does not know the nature of it?
Theaet. He cannot.
Soc. Then he who does not know what science or knowledge is, has
no knowledge of the art or science of making shoes?
Theaet. None.
Soc. Nor of any other science?
Theaet. No.
Soc. 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."
Theaet. True.
Soc. Moreover, he might answer shortly and simply, but he makes an
enormous circuit. For example, when asked about the day, he might have
said simply, that clay is moistened earth-what sort of clay is not
to the point.
Theaet. 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.
Soc. What was that, Theaetetus?
Theaet. 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.
Soc. And did you find such a class?
Theaet. I think that we did; but I should like to have your opinion.
Soc. Let me hear.
Theaet. 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.
Soc. Very good.
Theaet. 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.

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