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[357a] or distant—what would save our life? Would it not be knowledge; a knowledge of measurement, since the art here is concerned with excess and defect, and of numeration, as it has to do with odd and even? People would admit this, would they not?

Protagoras agreed that they would.

Well then, my friends, since we have found that the salvation of our life depends on making a right choice of pleasure and pain—of the more and the fewer, [357b] the greater and the smaller, and the nearer and the remoter—is it not evident, in the first place, that measurement is a study of their excess and defect and equality in relation to each other?

This must needs be so.

And being measurement, I presume it must be an art or science?

They will assent to this.

Well, the nature of this art or science we shall consider some other time1; but the mere fact of its being a science will suffice for the proof which Protagoras and I [357c] are required to give in answer to the question you have put to us. You asked it, if you remember, when we were agreeing2 that there is nothing stronger than knowledge, and that knowledge, wherever it may be found, has always the upper hand of pleasure or anything else; and then you said that pleasure often masters even the man of knowledge, and on our refusing to agree with you, you went on to ask us: Protagoras and Socrates, if this experience is not “being overcome by pleasure,” [357d] whatever can it be, and what do you call it? Tell us. If on the spur of the moment we had replied, “Ignorance,” you would have laughed us to scorn: but now if you laugh at us you will be laughing at yourselves as well. For you have admitted that it is from defect of knowledge that men err, when they do err, in their choice of pleasures and pains—that is, in the choice of good and evil; and from defect not merely of knowledge but of the knowledge which you have now admitted also to be that of measurement. And surely you know well enough for yourselves [357e] that the erring act committed without knowledge is done through ignorance. Accordingly “to be overcome by pleasure” means just this—ignorance in the highest degree, which Protagoras here and Prodicus and Hippias profess to cure. But you, through supposing it to be something else than ignorance, will neither go yourselves nor send your children to these sophists, who are the teachers of those things—you say it cannot be taught; you are chary of your money and will give them none,

1 The intellectual control of our sense-perceptions, which differ as to the size or number of the same things when near and when distant, etc., has an important part in the educational scheme of the Republic. The measuring art is further considered in the Politicus (283 ff.).

2 cf. Plat. Prot. 352b ff.

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