"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 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."