Part 34

“And again, that fire, when cold approaches it, must either depart or perish; but that it will never endure, when it has admitted coldness, to continue what it was, fire and cold?”

121. “You speak truly,” he said.

“It happens then,” he continued, “with respect to some of such things, that not only is the idea itself always thought worthy of the same appellation, but likewise something else which is not indeed that idea itself but constantly retains its form so long as it exists. What I mean will perhaps be clearer in the following examples. The odd in number must always possess the name by which we now call it; must it not?”

“Certainly.”

“Must it alone of all things, for this I ask, or is there any thing else, which is not the same as the odd, but yet which we must always call odd, together with its own name, because it is so constituted by nature, that it can never be without the odd? But this I say is the case with the number three, and many others. For consider with respect to the number three; does it not appear to you that it must always be called by its own name, as well as by that of the odd, which is not the same as the number three? Yet such is the nature of the number three, five, and the entire half of number, that though they are not the same as the odd, yet each of them is always odd. And again, two and four, and the whole other series of number, though not the same as the even, are nevertheless each of them always even: do you admit this or not?”

122. “How should I not?” he replied.

“Observe then,” said he, “what I wish to prove. It is this, that it appears, not only that these contraries do not admit each other, but that even such things as are not contrary to each other, and yet always possess contraries, do not appear to admit that idea which is contrary to the idea that exists in themselves, but, when it approaches, perish or depart. Shall we not allow that the number three would first perish, and suffer any thing whatever, rather than endure, while it is still three, to become even?”

“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 cannot.”

“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.”