Soc. All things which appear to us to become more or less, or to admit of emphatic and gentle and excessive and the like, are to be put in the class of the infinite as their unity, in accordance with what we said a while ago, if you remember, that we ought to collect all things that are scattered and split up and impress upon them to the best of our ability the seal of some single nature.

Pro. I remember.

Soc. And the things which do not admit of more and less and the like, but do admit of all that is opposed to them—first equality and the equal, then the double, and anything which is a definite number or measure in relation to such a number or measure— all these might properly be assigned to the class of the finite. What do you say to that?

Pro. Excellent, Socrates.

Soc. Well, what shall we say is the nature of the third class, made by combining these two?

Pro. You will tell me, I fancy, by answering your own question.

Soc. Nay, a god will do so, if any god will give ear to my prayers.

Pro. Pray, then, and watch.

Soc. I am watching; and I think, Protarchus, one of the gods has this moment been gracious unto me.

Pro. What do you mean, and what evidence have you?

Soc. I will tell you, of course. Just follow what I say.

Pro. Say on.

Soc. We spoke just now of hotter and colder, did we not?

Pro. Yes.

Soc. Add to them drier and wetter, more and less, quicker and slower, greater and smaller, and all that we assigned before to the class which unites more and less.

Pro. You mean the class of the infinite?

Soc. Yes. Mix with that the second class, the offspring of the limit.

Pro. What class do you mean?

Soc. The class of the finite, which we ought just now to have reduced to unity, as we did that of the infinite. We have not done that, but perhaps we shall even now accomplish the same end, if these two are both unified and then the third class is revealed.

Pro. What third class, and what do you mean?

Soc. The class of the equal and double and everything which puts an end to the differences between opposites and makes them commensurable and harmonious by the introduction of number.

Pro. I understand. I think you mean that by mixture of these elements certain results are produced in each instance.

Soc. Yes, you are right.

Pro. Go on.