Page - 881 - in The Complete Plato

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 881