Philebus (24-25)

Soc. I mean, then, that the two which I select are the same which I mentioned before, the infinite and the finite. I will try to show that the infinite is, in a certain sense, many; the finite can wait.

Pro. Yes.

Soc. Consider then. What I ask you to consider is difficult and debatable; but consider it all the same. In the first place, take hotter and colder and see whether you can conceive any limit of them, or whether the more and less which dwell in their very nature do not, so long as they continue to dwell therein, preclude the possibility of any end; for if there were any end of them, the more and less would themselves be ended.

Pro. Very true.

Soc. But always, we affirm, in the hotter and colder there is the more and less.

Pro. Certainly.

Soc. Always, then, the argument shows that these two have no end; and being endless, they are of course infinite.

Pro. Most emphatically, Socrates.

Soc. I am glad you responded, my dear Protarchus, and reminded me that the word emphatically which you have just used, and the word gently have the same force as more and less. For wherever they are present, they do not allow any definite quantity to exist; they always introduce in every instance a comparison—more emphatic than that which is quieter, or vice versa—and thus they create the relation of more and less, thereby doing away with fixed quantity. For, as I said just now, if they did not abolish quantity, but allowed it and measure to make their appearance in the abode of the more and less, the emphatically and gently, those latter would be banished from their own proper place. When once they had accepted definite quantity, they would no longer be hotter or colder; for hotter and colder are always progressing and never stationary; but quantity is at rest and does not progress. By this reasoning hotter and its opposite are shown to be infinite.

Pro. That appears to be the case, Socrates; but, as you said, these subjects are not easy to follow. Perhaps, however, continued repetition might lead to a satisfactory agreement between the questioner and him who is questioned.

Soc. That is a good suggestion, and I must try to carry it out. However, to avoid waste of time in discussing all the individual examples, see if we can accept this as a designation of the infinite.

Pro. Accept what?

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.