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?