assumption
of the existence of the many, and the counter-argument of what follows
from the denial of the existence of the many: and similarly of likeness
and unlikeness, motion, rest, generation, corruption, being and not
being. And the consequences must include consequences to the things
supposed and to other things, in themselves and in relation to one
another, to individuals whom you select, to the many, and to the all;
these must be drawn out both on the affirmative and on the negative
hypothesis,--that is, if you are to train yourself perfectly to the
intelligence of the truth.' 'What you are suggesting seems to be a
tremendous process, and one of which I do not quite understand the
nature,' said Socrates; 'will you give me an example?' 'You must not
impose such a task on a man of my years,' said Parmenides. 'Then will
you, Zeno?' 'Let us rather,' said Zeno, with a smile, 'ask Parmenides,
for the undertaking is a serious one, as he truly says; nor could I urge
him to make the attempt, except in a select audience of persons who will
understand him.' The whole party joined in the request.

Here we have, first of all, an unmistakable attack made by the youthful
Socrates on the paradoxes of Zeno. He perfectly understands their drift,
and Zeno himself is supposed to admit this. But they appear to him, as
he says in the Philebus also, to be rather truisms than paradoxes. For
every one must acknowledge the obvious fact, that the body being one
has many members, and that, in a thousand ways, the like partakes of
the unlike, the many of the one. The real difficulty begins with the
relations of ideas in themselves, whether of the one and many, or of
any other ideas, to one another and to the mind. But this was a problem
which the Eleatic philosophers had never considered; their thoughts had
not gone beyond the contradictions of matter, motion, space, and the
like.

It was no wonder that Parmenides and Zeno should hear the novel
speculations of Socrates with mixed feelings of admiration and
displeasure. He was going out of the received circle of disputation into
a region in which they could hardly follow him. From the crude idea of
Being in the abstract, he was about to proceed to universals or general
notions. There is no contradiction in material things partaking of the
ideas of one and many; neither is there any contradiction in the ideas
of one and many, like and unlike, in themselves. But the contradiction
arises when