Dialogues of Plato - MobileReference [423]
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?
Certainly.
Further, inasmuch as the parts are parts of a whole, the one, as a whole, will be limited; for are not the parts contained by the whole?
Certainly.
And that which contains, is a limit?
Of course.
Then the one if it has being is one and many, whole and parts, having limits and yet unlimited in number?
Clearly.
And because having limits, also having extremes?
Certainly.
And if a whole, having beginning and middle and end. For can anything be a whole without these three? And if any one of them is wanting to anything, will that any longer be a whole?
No.
Then the one, as appears, will have beginning, middle, and end.
It will.
But, again, the middle will be equidistant from the extremes; or it would not be in the middle?
Yes.
Then the one will partake of figure, either rectilinear or round, or a union of the two?
True.
And if this is the case, it will be both in itself and in another too.
How?
Every part is in the whole, and none is outside the whole.
True.
And all the parts are contained by the whole?
Yes.
And the one is all its parts, and neither more nor less than all?
No.
And the one is the whole?
Of course.
But if all the parts are in the whole, and the one is all of them and the whole, and they are all contained by the whole, the one will be contained by the one; and thus the one will be in itself.
That is true.
But then, again, the whole is not in the parts--neither in all the parts, nor in some one of them. For if it is in all, it must be in one; for if there were any one in which it was not, it could not be in all the parts; for the part in which it is wanting is one of all, and if the whole is not in this, how can it be in them all?
It cannot.
Nor can the whole be in some