One of the company, though I do not exactly remember which of them, on hearing this, said : By Heaven, is not this the direct contrary of what was admitted before — that out of the greater came the less and out of the less the greater, and that opposites are simply generated from opposites ; whereas now this seems to be utterly denied.
Socrates inclined his head to the speaker and listened. I like your courage, he said, in reminding us of this. But you do not observe that there is a difference in the two cases. For then we were speaking of opposites in the concrete, and now of the essential opposite which, as is affirmed, neither in us nor in nature can ever be at variance with itself : then, my friend, we were speaking of things in which opposites are inherent and which are called after them, but now about the opposites which are inherent in them and which give their name to them ; these essential opposites will never, as we maintain, admit of generation into or out of one another. At the same time, turning to Cebes, he said : Were you at all disconcerted, Cebes, at our friend’s objection ?
That was not my feeling, said Cebes ; and yet I cannot deny that I am apt to be disconcerted.
Then we are agreed after all, said Socrates, that the opposite will never in any case be opposed to itself ?
To that we are quite agreed, he replied.
Yet once more let me ask you to consider the question from another point of view, and see whether you agree with me : There is a thing which you term heat, and another thing which you term cold ?
Certainly.
But are they the same as fire and snow ?
Most assuredly not.
Heat is not the same as fire, nor is cold the same as snow ?
No.
And yet you will surely admit that when snow, as before said, is under the influence of heat, they will not remain snow and heat ; but at the advance of the heat the snow will either retire or perish ?
Very true, he replied.
And the fire too at the advance of the cold will either retire or perish ; and when the fire is under the influence of the cold, they will not remain, as before, fire and cold.
That is true, he said.
And in some cases the name of the idea is not confined to the idea ; but anything else which, not being the idea, exists only in the form of the idea, may also lay claim to it. I will try to make this clearer by an example : The odd number is always called by the name of odd ?
Very true.
But is this the only thing which is called odd ? 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.