Section 1‚

Are there not other things which have their own name, and yet are called odd, because, although not the same as oddness, they are never without oddness?-that is what I mean to ask-whether numbers such as the number three are not of the class of odd. And there are many other examples: would you not say, for example, that three may be called by its proper name, and also be called odd, which is not the same with three? and this may be said not only of three but also of five, and every alternate number-each of them without being oddness is odd, and in the same way two and four, and the whole series of alternate numbers, has every number even, without being evenness. Do you admit that? Yes, he said, how can I deny that? Then now mark the point at which I am aiming: not only do essential opposites exclude one another, but also concrete things, which, although not in themselves opposed, contain opposites; these, I say, also reject the idea which is opposed to that which is contained in them, and at the advance of that they either perish or withdraw. There is the number three for example; will not that endure annihilation or anything sooner than be converted into an even number, remaining three? Very true, said Cebes. And yet, he said, the number two is certainly not opposed to the number three? It is not. Then not only do opposite ideas repel the advance of one another, but also there are other things which repel the approach of opposites. That is quite true, he said. Suppose, he said, that we endeavor, if possible, to determine what these are. By all means. Are they not, Cebes, such as compel the things of which they have possession, not only to take their own form, but also the form of some opposite? What do you mean? I mean, as I was just now saying, and have no need to repeat to you, that those things which are possessed by the number three must not only be three in number, but must also be odd. Quite true. And on this oddness, of which the number three has the impress, the opposite idea will never intrude? No. And this impress was given by the odd principle? Yes. And to the odd is opposed the even? True. Then the idea of the even number will never arrive at three? No. Then three has no part in the even? None. Then the triad or number three is uneven? Very true. To return then to my distinction of natures which are not opposites, and yet do not admit opposites: as, in this instance, three, although not opposed to the even, does not any the more admit of the even, but always brings the opposite into play on the other side; or as two does not receive the odd, or fire the cold-from these examples (and there are many more of them) perhaps you may be able to arrive at the general conclusion that not only opposites will not receive opposites, but also that nothing which brings the opposite will admit the opposite of that which it brings in that to which it is brought. And here let me recapitulate-for there is no harm in repetition. The number five will not admit the nature of the even, any more than ten, which is the double of five, will admit the nature of the odd-the double, though not strictly opposed to the odd, rejects the odd altogether. Nor again will parts in the ratio of 3:2, nor any fraction in which there is a half, nor again in which there is a third, admit the notion of the whole, although they are not opposed to the whole. You will agree to that? Yes, he said, I entirely agree and go along with you in that.