SOCRATES: Ever, as we say, into the hotter and the colder there enters a more and a less.
PROTARCHUS: Yes.
SOCRATES: Then, says the argument, there is never any end of them, and being endless they must also be infinite.
PROTARCHUS: Yes, Socrates, that is exceedingly true.
SOCRATES: Yes, my dear Protarchus, and your answer reminds me that such an expression as "exceedingly," which you have just uttered, and also the term "gently," have the same significance as more or less; for whenever they occur they do not allow of the existence of quant.i.ty--they are always introducing degrees into actions, inst.i.tuting a comparison of a more or a less excessive or a more or a less gentle, and at each creation of more or less, quant.i.ty disappears. For, as I was just now saying, if quant.i.ty and measure did not disappear, but were allowed to intrude in the sphere of more and less and the other comparatives, these last would be driven out of their own domain. When definite quant.i.ty is once admitted, there can be no longer a "hotter" or a "colder" (for these are always progressing, and are never in one stay); but definite quant.i.ty is at rest, and has ceased to progress. Which proves that comparatives, such as the hotter and the colder, are to be ranked in the cla.s.s of the infinite.
PROTARCHUS: Your remark certainly has the look of truth, Socrates; but these subjects, as you were saying, are difficult to follow at first. I think however, that if I could hear the argument repeated by you once or twice, there would be a substantial agreement between us.
SOCRATES: Yes, and I will try to meet your wish; but, as I would rather not waste time in the enumeration of endless particulars, let me know whether I may not a.s.sume as a note of the infinite--
PROTARCHUS: What?
SOCRATES: I want to know whether such things as appear to us to admit of more or less, or are denoted by the words "exceedingly," "gently,"
"extremely," and the like, may not be referred to the cla.s.s of the infinite, which is their unity, for, as was a.s.serted in the previous argument, all things that were divided and dispersed should be brought together, and have the mark or seal of some one nature, if possible, set upon them--do you remember?
PROTARCHUS: Yes.
SOCRATES: And all things which do not admit of more or less, but admit their opposites, that is to say, first of all, equality, and the equal, or again, the double, or any other ratio of number and measure--all these may, I think, be rightly reckoned by us in the cla.s.s of the limited or finite; what do you say?
PROTARCHUS: Excellent, Socrates.
SOCRATES: And now what nature shall we ascribe to the third or compound kind?
PROTARCHUS: You, I think, will have to tell me that.
SOCRATES: Rather G.o.d will tell you, if there be any G.o.d who will listen to my prayers.
PROTARCHUS: Offer up a prayer, then, and think.
SOCRATES: I am thinking, Protarchus, and I believe that some G.o.d has befriended us.
PROTARCHUS: What do you mean, and what proof have you to offer of what you are saying?
SOCRATES: I will tell you, and do you listen to my words.
PROTARCHUS: Proceed.
SOCRATES: Were we not speaking just now of hotter and colder?
PROTARCHUS: True.
SOCRATES: Add to them drier, wetter, more, less, swifter, slower, greater, smaller, and all that in the preceding argument we placed under the unity of more and less.
PROTARCHUS: In the cla.s.s of the infinite, you mean?
SOCRATES: Yes; and now mingle this with the other.
PROTARCHUS: What is the other.
SOCRATES: The cla.s.s of the finite which we ought to have brought together as we did the infinite; but, perhaps, it will come to the same thing if we do so now;--when the two are combined, a third will appear.
PROTARCHUS: What do you mean by the cla.s.s of the finite?
SOCRATES: The cla.s.s of the equal and the double, and any cla.s.s which puts an end to difference and opposition, and by introducing number creates harmony and proportion among the different elements.
PROTARCHUS: I understand; you seem to me to mean that the various opposites, when you mingle with them the cla.s.s of the finite, takes certain forms.
SOCRATES: Yes, that is my meaning.
PROTARCHUS: Proceed.
SOCRATES: Does not the right partic.i.p.ation in the finite give health--in disease, for instance?
PROTARCHUS: Certainly.
SOCRATES: And whereas the high and low, the swift and the slow are infinite or unlimited, does not the addition of the principles aforesaid introduce a limit, and perfect the whole frame of music?
PROTARCHUS: Yes, certainly.
SOCRATES: Or, again, when cold and heat prevail, does not the introduction of them take away excess and indefiniteness, and infuse moderation and harmony?
PROTARCHUS: Certainly.
SOCRATES: And from a like admixture of the finite and infinite come the seasons, and all the delights of life?
PROTARCHUS: Most true.
SOCRATES: I omit ten thousand other things, such as beauty and health and strength, and the many beauties and high perfections of the soul: O my beautiful Philebus, the G.o.ddess, methinks, seeing the universal wantonness and wickedness of all things, and that there was in them no limit to pleasures and self-indulgence, devised the limit of law and order, whereby, as you say, Philebus, she torments, or as I maintain, delivers the soul.--What think you, Protarchus?
PROTARCHUS: Her ways are much to my mind, Socrates.
SOCRATES: You will observe that I have spoken of three cla.s.ses?
PROTARCHUS: Yes, I think that I understand you: you mean to say that the infinite is one cla.s.s, and that the finite is a second cla.s.s of existences; but what you would make the third I am not so certain.
SOCRATES: That is because the amazing variety of the third cla.s.s is too much for you, my dear friend; but there was not this difficulty with the infinite, which also comprehended many cla.s.ses, for all of them were sealed with the note of more and less, and therefore appeared one.
PROTARCHUS: True.
SOCRATES: And the finite or limit had not many divisions, and we readily acknowledged it to be by nature one?
PROTARCHUS: Yes.
SOCRATES: Yes, indeed; and when I speak of the third cla.s.s, understand me to mean any offspring of these, being a birth into true being, effected by the measure which the limit introduces.