Dialogues

And if pleasure were deprived not only of the first but of the second place, she would be terribly damaged in the eyes of her admirers, for not even to them would she still appear as fair as before. Socrates Well, but had we not better leave her now, and not pain her by applying the crucial test, and finally detecting her? Protarchus Nonsense, Socrates. Socrates Why? because I said that we had better not pain pleasure, which is an impossibility? Protarchus Yes, and more than that, because you do not seem to be aware that none of us will let you go home until you have finished the argument. Socrates Heavens! Protarchus, that will be a tedious business, and just at present not at all an easy one. For in going to war in the cause of mind, who is aspiring to the second prize, I ought to have weapons of another make from those which I used before; some, however, of the old ones may do again. And must I then finish the argument? Protarchus Of course you must. Socrates Let us be very careful in laying the foundation. Protarchus What do you mean? Socrates Let us divide all existing things into two, or rather, if you do not object, into three classes. Protarchus Upon what principle would you make the division? Socrates Let us take some of our newly-found notions. Protarchus Which of them? Socrates Were we not saying that God revealed a finite element of existence, and also an infinite? Protarchus Certainly. Socrates Let us assume these two principles, and also a third, which is compounded out of them; but I fear that I am ridiculously clumsy at these processes of division and enumeration. Protarchus What do you mean, my good friend? Socrates I say that a fourth class is still wanted. Protarchus What will that be? Socrates Find the cause of the third or compound, and add this as a fourth class to the three others. Protarchus And would you like to have a fifth class or cause of resolution as well as a cause of composition? 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