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 partic.i.p.ates in being, every part of number will also partic.i.p.ate?
Yes.
Then being is distributed over the whole mult.i.tude 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?