Dialogues of Plato - MobileReference [511]
SOCRATES: Not, I think, at present; but if I want a fifth at some future time you shall allow me to have it.
PROTARCHUS: Certainly.
SOCRATES: Let us begin with the first three; and as we find two out of the three greatly divided and dispersed, let us endeavour to reunite them, and see how in each of them there is a one and many.
PROTARCHUS: If you would explain to me a little more about them, perhaps I might be able to follow you.
SOCRATES: Well, the two classes are the same which I mentioned before, one the finite, and the other the infinite; I will first show that the infinite is in a certain sense many, and the finite may be hereafter discussed.
PROTARCHUS: I agree.
SOCRATES: And now consider well; for the question to which I invite your attention is difficult and controverted. When you speak of hotter and colder, can you conceive any limit in those qualities? Does not the more and less, which dwells in their very nature, prevent their having any end? for if they had an end, the more and less would themselves have an end.
PROTARCHUS: That is most true.
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 quantity--they are always introducing degrees into actions, instituting a comparison of a more or a less excessive or a more or a less gentle, and at each creation of more or less, quantity disappears. For, as I was just now saying, if quantity 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 quantity 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 quantity 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 class 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 assume 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 class of the infinite, which is their unity, for, as was asserted 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 class 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 God will tell you, if there be any God who will listen to my prayers.
PROTARCHUS: Offer up a prayer, then, and think.
SOCRATES: I am thinking, Protarchus, and I believe that some God has befriended us.
PROTARCHUS: