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.-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
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