Part 125

Theæ. What mean you by this, Socrates?

Socr. Perhaps nothing: but I will tell you what I think. When you speak of the shoemaker’s art, do you mean any thing else than the science of making shoes?

Theæ. Nothing.

12. Socr. But what of the carpenter’s art? Do you mean any thing else than the science of making implements in wood?

Theæ. Still nothing else.

Socr. In both, then, do you not define that of which each is the science?

Theæ. Yes.

Socr. But the question asked, Theætetus, was not this, of what things there is science, nor how many sciences there are; for we did not enquire, with a view to enumerate them, but to know what science itself is. Do I say nothing to the purpose?

Theæ. You speak very correctly.

Socr. Consider this too. If any one should ask us about any mean and obvious thing, as, for instance, clay, what it is, if we were to answer him, there is the potters’ clay, the oven-builders’ clay, and the brick-makers’ clay, should we not be ridiculous?

Theæ. Probably.

Socr. In the first place, we should be ridiculous for thinking that he who asks the question can understand from our answer, when we say Clay, adding, image-makers, or any other artizans whatever. Do you think that any one can understand the name of a thing when he does not know what that thing is?

Theæ. By no means.

13. Socr. Neither does he understand the science of shoes who does not know what science is?

Theæ. He does not.

Socr. He then does not understand what is the art of shoe-making, or any other art, who is ignorant of what science is?

Theæ. It is so.

Socr. It is, therefore, a ridiculous answer for one to give who is asked what science is, when he answers the name of some art. For he answers, of what there is a science, though this is not what he was asked.

Theæ. It seems so.

Socr. In the next place, when he might have answered plainly and briefly he goes round an endless way. As for instance to the question about clay, it is a plain and simple answer to give, that clay is earth mixed with moisture, without mentioning what use is made of it.

Theæ. It appears easy now, in this way, Socrates; for you appear to ask just such a question as lately occurred to me when we were conversing together, I and your namesake here, Socrates.

Socr. What was that, Theætetus?

14. Theæ. Theodorus here was describing to us something about powers, with respect to magnitudes of three and five feet, shewing that they are not commensurate in length to a magnitude of one foot, and thus proceeding through every number as far as to a magnitude of seventeen feet; at this he stopped. Since then powers appeared to be infinite in multitude, something of the following kind occurred to us, to endeavour to comprehend them in one name, by which we might denominate all these powers.

Socr. And did you discover any thing of the kind?

Theæ. I think we did. But do you also consider.

Socr. Say on.

Theæ. We divided all number into two classes; then comparing that in which the factors are the same to a square figure, we called it square and equilateral.

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