In what way?
Because the others are other than the one inasmuch as they have parts; for if they had no parts they would be simply one.
Right.
And parts, as we affirm, have relation to a whole?
So we say.
And a whole must necessarily be one made up of many; and the parts will be parts of the one, for each of the parts is not a part of many, but of a whole.
How do you mean?
If anything were a part of many, being itself one of them, it will surely be a part of itself, which is impossible, and it will be a part of each one of the other parts, if of all; for if not a part of some one, it will be a part of all the others but this one, and thus will not be a part of each one; and if not a part of each, one it will not be a part of any one of the many; and not being a part of any one, it cannot be a part or anything else of all those things of none of which it is anything.
Clearly not.
Then the part is not a part of the many, nor of all, but is of a certain single form, which we call a whole, being one perfect unity framed out of all--of this the part will be a part.
Certainly.
If, then, the others have parts, they will partic.i.p.ate in the whole and in the one.
True.
Then the others than the one must be one perfect whole, having parts.
Certainly.
And the same argument holds of each part, for the part must partic.i.p.ate in the one; for if each of the parts is a part, this means, I suppose, that it is one separate from the rest and self-related; otherwise it is not each.
True.
But when we speak of the part partic.i.p.ating in the one, it must clearly be other than one; for if not, it would not merely have partic.i.p.ated, but would have been one; whereas only the itself can be one.
Very true.
Both the whole and the part must partic.i.p.ate in the one; for the whole will be one whole, of which the parts will be parts; and each part will be one part of the whole which is the whole of the part.
True.
And will not the things which partic.i.p.ate in the one, be other than it?
Of course.
And the things which are other than the one will be many; for if the things which are other than the one were neither one nor more than one, they would be nothing.
True.
But, seeing that the things which partic.i.p.ate in the one as a part, and in the one as a whole, are more than one, must not those very things which partic.i.p.ate in the one be infinite in number?
How so?
Let us look at the matter thus:--Is it not a fact that in partaking of the one they are not one, and do not partake of the one at the very time when they are partaking of it?
Clearly.
They do so then as mult.i.tudes in which the one is not present?
Very true.
And if we were to abstract from them in idea the very smallest fraction, must not that least fraction, if it does not partake of the one, be a mult.i.tude and not one?
It must.
And if we continue to look at the other side of their nature, regarded simply, and in itself, will not they, as far as we see them, be unlimited in number?
Certainly.
And yet, when each several part becomes a part, then the parts have a limit in relation to the whole and to each other, and the whole in relation to the parts.
Just so.
The result to the others than the one is that the union of themselves and the one appears to create a new element in them which gives to them limitation in relation to one another; whereas in their own nature they have no limit.
That is clear.
Then the others than the one, both as whole and parts, are infinite, and also partake of limit.
Certainly.
Then they are both like and unlike one another and themselves.
How is that?
Inasmuch as they are unlimited in their own nature, they are all affected in the same way.
True.
And inasmuch as they all partake of limit, they are all affected in the same way.
Of course.
But inasmuch as their state is both limited and unlimited, they are affected in opposite ways.
Yes.
And opposites are the most unlike of things.