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[104a] 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 [104b] 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, [104c] 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.”


“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.” [104d] “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.”


“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?”


“And the opposite of this is the idea [104e] of the even?”


“Then the idea of the even will never be admitted by the number three.”


“Then three has no part in the even.”

“No, it has none.”

“Then the number three is uneven.”


“Now I propose to determine what things, without being the opposites of something, nevertheless refuse to admit it, as the number three, though it is not the opposite of the idea of even, nevertheless refuses to admit it, but always brings forward its opposite against it, and

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