Phaedo (103-104)

Phaedo. That, said Cebes, seems to me quite evident. Then one of those present—I don’t just remember who it was—said: In Heaven’s name, is not this present doctrine the exact opposite of what was fitted in our earlier discussion, that the greater is generated from the less and the less from the greater and that opposites are always generated from their opposites? But now it seems to me we are saying, this can never happen. Socrates cocked his head on one side and listened. You have spoken up like a man, he said, but you do not observe the difference between the present doctrine and what we said before. We said before that in the case of concrete things opposites are generated from opposites; whereas now we say that the abstract concept of an opposite can never become its own opposite, either in us or in the world about us. Then we were talking about things which possess opposite qualities and are called after them, but now about those very opposites the immanence of which gives the things their names. We say that these latter can never be generated from each other. At the same time he looked at Cebes and said: And you—are you troubled by any of our friends’ objections? No, said Cebes, not this time; though I confess that objections often do trouble me. Well, we are quite agreed, said Socrates, upon this, that an opposite can never be its own opposite. Entirely agreed, said Cebes. Now, said he, see if you agree with me in what follows: Is there something that you call heat and something you call cold? Yes. Are they the same as snow and fire? No, not at all. But heat is a different thing from fire and cold differs from snow? Yes. Yet I fancy you believe that snow, if (to employ the form of phrase we used before) it admits heat, will no longer be what it was, namely snow, and also warm, but will either withdraw when heat approaches it or will cease to exist. Certainly. And similarly fire, when cold approaches it, will either withdraw or perish. It will never succeed in admitting cold and being still fire, as it was before, and also cold. That is true, said he. The fact is, said he, in some such cases, that not only the abstract idea itself has a right to the same name through all time, but also something else, which is not the idea, but which always, whenever it exists, has the form of the idea. But perhaps I can make my meaning clearer by some examples. In numbers, the odd must always have the name of odd, must it not? Certainly.

Phaedo. But is this the only thing so called (for this is what I mean to ask), or is there something else, which is not identical with the odd but nevertheless has a right to the name of odd in addition to its own name, because it is of such a nature that it is never separated from the odd? I mean, for instance, the number three, and there are many other examples. Take the case of three; do you not think it may always be called by its own name and also be called odd, which is not the same as three? Yet the number three and the number five and half of numbers in general are so constituted, that each of them is odd though not identified with the idea of odd. And in the same way two and four and all the other series of numbers are even, each of them, though not identical with evenness. Do you agree, or not? Of course, he replied. Now see what I want to make plain. This is my point, that not only abstract opposites exclude each other, but all things which, although not opposites one to another, always contain opposites; these also, we find, exclude the idea which is opposed to the idea contained in them, and when it approaches they either perish or withdraw. We must certainly agree that the number three will endure destruction or anything else rather than submit to becoming even, while still remaining three, must we not? Certainly, said Cebes. But the number two is not the opposite of the number three. No. Then not only opposite ideas refuse to admit each other when they come near, but certain other things refuse to admit the approach of opposites. Very true, he said. Shall we then, said Socrates, determine if we can, what these are? Certainly. Then, Cebes, will they be those which always compel anything of which they take possession not only to take their form but also that of some opposite? What do you mean? Such things as we were speaking of just now. You know of course that those things in which the number three is an essential element must be not only three but also odd. Certainly. Now such a thing can never admit the idea which is the opposite of the concept which produces this result. No, it cannot. But the result was produced by the concept of the odd? Yes. And the opposite of this is the idea of the even? Yes. Then the idea of the even will never be admitted by the number three. No. Then three has no part in the even. No, it has none. Then the number three is uneven. Yes.