Theaetetus (198)

SOC. Consider then what expressions are needed for the process of recapturing and taking and holding and letting go again whichever he please of the kinds of knowledge, whether they are the same expressions as those needed for the original acquisition, or others. But you will understand better by an illustration. You admit that there is an art of arithmetic?

THEAET. Yes.

SOC. Now suppose this to be a hunt after the kinds of knowledge, or sciences, of all odd and even numbers.

THEAET. I do so.

SOC. Now it is by this art, I imagine, that a man has the sciences of numbers under his own control and also that any man who transmits them to another does this.

THEAET. Yes.

SOC. And we say that when anyone transmits them he teaches, and when anyone receives them he learns, and when anyone, by having acquired them, has them in that aviary of ours, he knows them.

THEAET. Certainly.

SOC. Now pay attention to what follows from this. Does not the perfect arithmetician understand all numbers; for he has the sciences of all numbers in his mind?

THEAET. To be sure.

SOC. Then would such a man ever count anything—either any abstract numbers in his head, or any such external objects as possess number?

THEAET. Of course,

SOC. But we shall affirm that counting is the same thing as considering how great any number in question is.

THEAET. We shall.

SOC. Then he who by our previous admission knows all number is found to be considering that which he knows as if he did not know it. You have doubtless heard of such ambiguities.

THEAET. Yes, I have.

SOC. Continuing, then, our comparison with the acquisition and hunting of the pigeons, we shall say that the hunting is of two kinds, one before the acquisition for the sake of possessing, the other carried on by the possessor for the sake of taking and holding in his hands what he had acquired long before. And just so when a man long since by learning came to possess knowledge of certain things, and knew them, he may have these very things afresh by taking up again the knowledge of each of them separately and holding it—the knowledge which he had acquired long before, but had not at hand in his mind?

THEAET. That is true.

SOC. This, then, was my question just now: How should we express ourselves in speaking about them when an arithmetician undertakes to count or a man of letters to read something? In such a case shall we say that although he knows he sets himself to learn again from himself that which he knows?

THEAET. But that is extraordinary, Socrates.