[
1085b]
[1]
If on the other hand
there is more than one kind of matter—one of the line,
another of the plane, and another of the solid—either the
kinds are associated with each other, or they are not. Thus the same
result will follow in this case also; for either the plane will not
contain a line, or it will be a line.
Further, no
attempt is made to explain how number can be generated from unity and
plurality; but howsoever they account for this, they have to meet the
same difficulties as those who generate number from unity and the
indeterminate dyad. The one school generates number not from a
particular plurality but from that which is universally predicated;
the other from a particular plurality, but the first; for they hold
that the dyad is the first plurality.
1 Thus there is practically no difference
between the two views; the same difficulties will be involved with
regard to mixture, position, blending, generation and the other
similar modes of combination.
2We might very well ask the further question: if
each unit is one, of what it is composed; for clearly each unit is not
absolute unity. It must be generated from absolute unity and either
plurality or a part of plurality.Now we cannot hold that the unit is a
plurality, because the unit is indivisible; but the view that it is
derived from a part of plurality involves many further difficulties,
because (a) each part must be indivisible; otherwise it will be a
plurality and the unit will be divisible,
[20]
and unity and plurality will not be its elements,
because each unit will not be generated from plurality
3 and unity.(b) The exponent of this theory merely
introduces another number; because plurality is a number of
indivisible parts.
4Again, we must
inquire from the exponent of this theory whether the number
5 is infinite or finite.There was, it appears, a finite
plurality from which, in combination with Unity, the finite units were
generated; and absolute plurality is different from finite plurality.
What sort of plurality is it, then, that is, in combination with
unity, an element of number?
We might
ask a similar question with regard to the point, i.e. the element out
of which they create spatial magnitudes.This is surely not the one and only point. At
least we may ask from what each of the other points comes; it is not,
certainly, from some interval and the Ideal point. Moreover, the parts
of the interval cannot be indivisible parts, any more than the parts
of the plurality of which the units are composed; because although
number is composed of indivisible parts, spatial magnitudes are
not.
All these and other similar considerations
make it clear that number and spatial magnitudes cannot exist
separately.