[1002a]
[1]
their heat and cold
and the like are modifications, not substances; and it is only the
body which undergoes these modifications that persists as something
real and a kind of substance.Again, the body is less truly substance than
the plane, and the plane than the line, and the line than the unit or
point; for it is by these that the body is defined, and it seems that
they are possible without the body, but that the body cannot exist
without them.This is why
the vulgar and the earlier thinkers supposed that substance and Being
are Body, and everything else the modifications of Body; and hence
also that the first principles of bodies are the first principles of
existing things; whereas later thinkers with a greater reputation for
wisdom supposed that substance and Being are numbers.As we
have said, then, if these things are not substance, there is no
substance or Being at all; for the attributes of these things surely
have no right to be called existent things. On the other hand, if it
be agreed that lines and points are more truly substance than bodies
are, yet unless we can see to what kind of bodies they
belong (for they cannot be in sensible bodies) there will still be no
substance.Further,
it is apparent that all these lines are divisions of Body, either in
breadth
[20]
or in depth or
in length. Moreover every kind of shape is equally present in a solid,
so that if "Hermes is not in the stone,"1
neither is the half-cube in the cube as a determinate shape.Hence neither is the plane; for
if any kind of plane were in it, so would that plane be which defines
the half-cube. The same argument applies to the line and to the point
or unit. Hence however true it may be that body is substance, if
planes, lines and points are more truly substance than Body is, and
these are not substance in any sense, the question of what Being is
and what is the substance of things baffles us.Because, in addition to the above
arguments, absurd results follow from a consideration of generation
and destruction; for it seems that if substance, not having existed
before, now exists, or having existed before, subsequently does not
exist it suffers these changes in the process of generation and
destruction. But points, lines and planes, although they exist at one
time and at another do not, cannot be in process of being either
generated or destroyed;for
whenever bodies are joined or divided,
1 Apparently a proverbial expression.
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