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Metaphysics   


consist, heat and cold and the like are modifications of these, not
substances, and the body which is thus modified alone persists as
something real and as a substance. But, on the other hand, the body is
surely less of a substance than the surface, and the surface than
the line, and the line than the unit and the point. For the body is
bounded by these; and they are thought to be capable of existing
without body, but body incapable of existing without these. This is
why, while most of the philosophers and the earlier among them thought
that substance and being were identical with body, and that all
other things were modifications of this, so that the first
principles of the bodies were the first principles of being, the
more recent and those who were held to be wiser thought numbers were
the first principles. As we said, then, if these are not substance,
there is no substance and no being at all; for the accidents of
these it cannot be right to call beings.
But if this is admitted, that lines and points are substance
more than bodies, but we do not see to what sort of bodies these could
belong (for they cannot be in perceptible bodies), there can be no
substance.-Further, these are all evidently divisions of body,-one
in breadth, another in depth, another in length. Besides this, no sort
of shape is present in the solid more than any other; so that if the
Hermes is not in the stone, neither is the half of the cube in the
cube as something determinate; therefore the surface is not in it
either; for if any sort of surface were in it, the surface which marks
off the half of the cube would be in it too. And the same account
applies to the line and to the point and the unit. Therefore, if on
the one hand body is in the highest degree substance, and on the other
hand these things are so more than body, but these are not even
instances of substance, it baffles us to say what being is and what
the substance of things is.-For besides what has been said, the
questions of generation and instruction confront us with further
paradoxes. For if substance, not having existed before, now exists, or
having existed before, afterwards does not exist, this change is
thought to be accompanied by a process of becoming or perishing; but
points and lines and surfaces cannot be in process either of
becoming or of perishing, when they at one time exist and at another
do not. For when bodies come into contact or are divided, their
boundaries simultaneously become one in the one case when they
touch, and two in the other-when they are divided; so that when they
have been put together one boundary does not exist but has perished,
and when they have been divided the boundaries exist which before
did not exist (for it cannot be said that the point, which is
indivisible, was divided into two). And if the boundaries come into
being and cease to be, from what do they come into being? A similar
account may also be given of the 'now' in time; for this also cannot
be in process of coming into being or of ceasing to be, but yet
seems to be always different, which shows that it is not a
substance. And evidently the same is true of points and lines and
planes; for the same argument applies, since they are all alike either
limits or divisions.
6

In general one might raise the question why after all, besides
perceptible things and the intermediates, we have to look for
another class of things, i.e. the Forms which we posit. If it is for
this reason, because the objects of mathematics, while they differ
from the things in this world in some other respect, differ not at all
in that there are many of the same kind, so that their first
principles cannot be limited in number (just as the elements of all
the language in this sensible world are not limited in number, but
in kind, unless one takes the elements of this individual syllable
or of this individual articulate sound-whose elements will be
limited even in number; so is it also in the case of the
intermediates; for there also the members of the same kind are

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