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Of course.

And when we put them together shortly, and say 'One is,' that is equivalent to saying, 'partakes of being'?

Quite true.

Once more then let us ask, if one is what will follow. Does not this hypothesis necessarily imply that one is of such a nature as to have parts?

How so?

In this way:—If being is predicated of the one, if the one is, and one of being, if being is one; and if being and one are not the same; and since the one, which we have assumed, is, must not the whole, if it is one, itself be, and have for its parts, one and being?

Certainly.

And is each of these parts—one and being—to be simply called a part, or must the word 'part' be relative to the word 'whole'?

The latter.

Then that which is one is both a whole and has a part?

Certainly.

Again, of the parts of the one, if it is—I mean being and one—does either fail to imply the other? is the one wanting to being, or being to the one?

Impossible.

Thus, each of the parts also has in turn both one and being, and is at the least made up of two parts; and the same principle goes on for ever, and every part whatever has always these two parts; for being always involves one, and one being; so that one is always disappearing, and becoming two.

Certainly.

And so the one, if it is, must be infinite in multiplicity?

Clearly.

Let us take another direction.

What direction?

We say that the one partakes of being and therefore it is?

Yes.

And in this way, the one, if it has being, has turned out to be many?

True.

But now, let us abstract the one which, as we say, partakes of being, and try to imagine it apart from that of which, as we say, it partakes—will this abstract one be one only or many?

One, I think.

Let us see:—Must not the being of one be other than one? for the one is not being, but, considered as one, only partook of being?

Certainly.

If being and the one be two different things, it is not because the one is one that it is other than being; nor because being is being that it is other than the one; but they differ from one another in virtue of otherness and difference.

Certainly.

So that the other is not the same—either with the one or with being?

Certainly not.

And therefore whether we take being and the other, or being and the one, or the one and the other, in every such case we take two things, which may be rightly called both.

How so.

In this way—you may speak of being?

Yes.

And also of one?

Yes.

Then now we have spoken of either of them?

Yes.

Well, and when I speak of being and one, I speak of them both?

Certainly.

And if I speak of being and the other, or of the one and the other,—in any such case do I not speak of both?

Yes.

And must not that which is correctly called both, be also two?

Undoubtedly.

And of two things how can either by any possibility not be one?

It cannot.

Then, if the individuals of the pair are together two, they must be severally one?

Clearly.

And if each of them is one, then by the addition of any one to any pair, the whole becomes three?

Yes.

And three are odd, and two are even?

Of course.

And if there are two there must also be twice, and if there are three there must be thrice; that is, if twice one makes two, and thrice one three?

Certainly.

There are two, and twice, and therefore there must be twice two; and there are three, and there is thrice, and therefore there must be thrice three?

Of course.

If there are three and twice, there is twice three; and if there are two and thrice, there is thrice two?

Undoubtedly.

Here, then, we have even taken even times, and odd taken odd times, and even taken odd times, and odd taken even times.

True.

And if this is so, does any number remain which has no necessity to be?

None whatever.

Then if one is, number must also be?

It must.

But if there is number, there must also be many, and infinite multiplicity of being; for number is infinite in multiplicity, and partakes also of being: am I not right?

Certainly.

And if all number participates in being, every part of number will also participate?

Yes.

Then being is distributed over the whole multitude of things, and nothing that is, however small or however great, is devoid of it? And, indeed, the very supposition of this is absurd, for how can that which is, be devoid of being?

In no way.

And it is divided into the greatest and into the smallest, and into being of all sizes, and is broken up more than all things; the divisions of it have no limit.

True.

Then it has the greatest number of parts?

Yes, the greatest number.

Is there any of these which is a part of being, and yet no part?

Impossible.

But if it is at all and so long as it is, it must be one, and cannot be none?

Certainly.

Then the one attaches to every single part of being, and does not fail in any part, whether great or small, or whatever may be the size of it?

True.

But reflect:—Can one, in its entirety, be in many places at the same time?

No; I see the impossibility of that.

And if not in its entirety, then it is divided; for it cannot be present with all the parts of being, unless divided.

True.

And that which has parts will be as many as the parts are?

Certainly.

Then we were wrong in saying just now, that being was distributed into the greatest number of parts. For it is not distributed into parts more than the one, into parts equal to the one; the one is never wanting to being, or being to the one, but being two they are co-equal and co-extensive.

Certainly that is true.

The one itself, then, having been broken up into parts by being, is many and infinite?

True.

Then not only the one which has being is many, but the one itself distributed by being, must also be many?