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.