Parmenides (158)

And the same reasoning applies to each part for the part must partake of the one. For if each of the parts is a part, the word each implies that it is one, separated from the rest, and existing by itself; otherwise it will not be each.

True.

But its participation in the one clearly implies that it is other than the one, for if not, it would not partake of the one, but would actually be one; but really it is impossible for anything except one itself to be one.

Yes, it is impossible.

And both the whole and the part must necessarily participate in the one; for the one will be a whole of which the parts are parts, and again each individual one which is a part of a whole will be a part of the whole.

Yes.

And will not the things which participate in the one be other than the one while participating in it?

Of course.

But the things which are other than the one will be many; for if they were neither one nor more than one, they would not be anything.

No.

But since the things which participate in the one as a part and the one as a whole are more than one, must not those participants in the one be infinite in number?

How so?

Let us look at the question in this way. Is it not true that at the moment when they begin to participate in the one they are not one and do not participate in one?

Clearly.

Then they are multitudes, in which the one is not, are they not?

Yes, they are multitudes.

Well, then, if we should subtract from them in thought the smallest possible quantity, must not that which is subtracted, if it has no participation in one, be also a multitude, and not one?

It must.

And always when we consider the nature of the class, which makes it other than one, whatever we see of it at any time will be unlimited in number, will it not?

Certainly.

And, further, when each part becomes a part, straightway the parts are limited in relation to each other and to the whole, and the whole in relation to the parts.

Undoubtedly.

The result, then, to the things which are other than one, that from the one and the union of themselves with it there arises, as it appears, something different within themselves which gives them a limitation in relation to one another; but their own nature, when they are left to themselves, gives them no limits.

So it appears.

Then the things which are other than one, both as wholes and as parts, are both unlimited and partake of limitation.

Certainly.

And are they also both like and unlike one another and themselves?

How is that?

Inasmuch as they are all by their own nature unlimited, they are all in that respect affected in the same way.

Certainly.

And surely inasmuch as they all partake of limitation, they are all affected in the same way in that respect also.

Obviously.