150 ARISTOTLE
Now when we want to lead things back to their sources, we set down length as
being composed of the short and the long, a certain kind of small and large, and surface
of the wide and the narrow, and solid of the deep and the shallow. In what way, though,
will the surface have a line in it, or the solid have a line or a surface? For the wide and the
narrow are different kinds of thing from the deep and the shallow; so just as number is
not present in them either, because the many and the few differ from these, it is clear that
neither will any other of the higher things be present in the lower. But surely neither is
the wide a class of the deep, for then a solid would be a certain kind of surface. And from
what source will the points come to be present in them? Plato used to fight against this
class of things as a geometrical dogma, but he called the source of the line—and he set
this down often—indivisible lines. And yet there must necessarily be some limit of these;
so from the argument from which the line is deduced, the point too is deduced.
In general, though we are seeking wisdom about what is responsible for the
appearances, we have ignored this (for we say nothing about the cause from which the
source of change is), but supposing that we are speaking about the thinghood of them,
we say that there are other independent things, but as for how those are the thinghood of
these we speak in vain. For “participating,” as we said before, is no help. But on that
which we see to be a cause in the various kinds of knowledge, for the sake of which every
intellect and every nature produces things, and on that sort of cause which we say is one
of the sources of things, the forms do not even touch, but philosophy has turned into
mathematical things for people now, though they claim that it is for the sake of other
things that one ought to study them. But still, one might assume that the underlying being
which serves as material is too mathematical, and is something to be attributed to or be a
distinction within the being or material, rather than being material; for instance, the great
and the small are just the same as what the writers on nature call the rare and the dense,
claiming that these are the first distinctions within the underlying material, since they are
a certain kind of the more and less. And as for motion, if these are a process of moving,
it is clear that the forms would be moved; but if they are not, where does it come from?
For then the whole investigation about nature would be abolished.
And what seems to be easy, to show that all things are one, does not happen; for
from the premises set out, even if one grants them all, it does not come out that all
things are one, but that something is the one itself; and not even this comes out if one
will not grant that the universal is a genus, which in some cases is impossible. And there
is no explanation of the lengths, surfaces, and solids that are present with the numbers,
not of how they are or could be nor of what capacity they have; for it is not possible for
them to be forms (since they are not numbers), nor the in-between things (since those
are the mathematical ones), nor perishable things, but this seems in turn to be some
other fourth kind.
In general, to search for the elements of whatever iswithout distinguishing the
many ways this is meant, is to seek what is impossible to find, both for those inquiring
in other ways and those inquiring in this way about what sort of elements things are
made of. For out of what elements acting is made, or being acted upon, or the straight,
is just not there to be grasped, but if of anything, it is of independent things alone that it
can possibly be. Therefore to suppose that one is seeking or has the elements of all
beings is not true. And how could anyone learn the elements of all things? For it is clear
that it is not possible for someone to begin by knowing it beforehand. For just as it is
possible for the one who is learning to do geometry to know other things in advance,
though he does not already know any of the things of which geometry is the knowledge
and about which he is going to learn, so it is also with other things, so if there is any2030992 b
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