“Most certainly,” said Cebes.

“And yet,” said he, “the number two is not contrary to three.”

“Surely not.”

“Not only, then, do ideas that are contrary never allow the approach of each other, but some other things also do not allow the approach of contraries.”

“You say very truly,” he replied.

“Do you wish, then,” he said, “that, if we are able, we should define what these things are?”

“Certainly.”

“Would they not then, Cebes,” he said, “be such things as, whatever they occupy, compel that thing not only to retain its own idea, but also that of something which is always a contrary?”

“How do you mean?”

123.  “As we just now said.  For you know, surely, that whatever things the idea of three occupies must of necessity not only be three, but also odd?”

“Certainly.”

“To such a thing, then, we assert, that the idea contrary to that form which constitutes this can never come.”

“It can not.”

“But did the odd make it so?”

“Yes.”

“And is the contrary to this the idea of the even?”

“Yes.”

“The idea of the even, then, will never come to the three?”

“No, surely.”

“Three, then, has no part in the even?”

“None whatever.”

“The number three is uneven?”

“Yes.”

“What, therefore, I said should be defined—­namely, what things they are which, though not contrary to some particular thing, yet do not admit of the contrary itself; as, in the present instance, the number three, though not contrary to the even, does not any the more admit it, for it always brings the contrary with it, just as the number two does to the odd, fire to cold, and many other particulars.  Consider, then, whether you would thus define, not only that a contrary does not admit a contrary, but also that that which brings with it a contrary to that to which it approaches will never admit the contrary of that which it brings with it. 124.  But call it to mind again, for it will not be useless to hear it often repeated.  Five will not admit the idea of the even, nor ten, its double, that of the odd.  This double, then, though it is itself contrary to something else,[38] yet will not admit the idea of the odd, nor will half as much again, nor other things of the kind, such as the half and the third part, admit the idea of the whole, if you follow me, and agree with me that it is so.”

“I entirely agree with you,” he said, “and follow you.”

“Tell me again, then,” he said, “from the beginning; and do not answer me in the terms in which I put the question, but in different ones, imitating my example.  For I say this because, besides that safe mode of answering which I mentioned at first,[39] from what has now been said, I see another no less safe one.  For if you should ask me what that is which, if it be in the body, will cause it to be hot,