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?
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.