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of either limit, in which either A is not or B is. But for the generated
there must be such a time either actually or potentially, though not
for A and B in either way. C then will be, and also not be, for a
limited length of time, and this is true also of D, the destructible.
Therefore each is both generated and destructible. Therefore 'generated'
and 'destructible' are coincident. Now let E stand for the ungenerated,
F for the generated, G for the indestructible, and H for the destructible.
As for F and H, it has been shown that they are coincident. But when
terms stand to one another as these do, F and H coincident, E and
F never predicated of the same thing but one or other of everything,
and G and H likewise, then E and G must needs be coincident. For suppose
that E is not coincident with G, then F will be, since either E or
F is predictable of everything. But of that of which F is predicated
H will be predicable also. H will then be coincident with G, but this
we saw to be impossible. And the same argument shows that G is coincident
with E.
Now the relation of the ungenerated (E) to the generated (F) is the
same as that of the indestructible (G) to the destructible (H). To
say then that there is no reason why anything should not be generated
and yet indestructible or ungenerated and yet destroyed, to imagine
that in the one case generation and in the other case destruction
occurs once for all, is to destroy part of the data. For (1) everything
is capable of acting or being acted upon, of being or not being, either
for an infinite, or for a definitely limited space of time; and the
infinite time is only a possible alternative because it is after a
fashion defined, as a length of time which cannot be exceeded. But
infinity in one direction is neither infinite or finite. (2) Further,
why, after always existing, was the thing destroyed, why, after an
infinity of not being, was it generated, at one moment rather than
another? If every moment is alike and the moments are infinite in
number, it is clear that a generated or destructible thing existed
for an infinite time. It has therefore for an infinite time the capacity
of not being (since the capacity of being and the capacity of not
being will be present together), if destructible, in the time before
destruction, if generated, in the time after generation. If then we
assume the two capacities to be actualized, opposites will be present
together. (3) Further, this second capacity will be present like the
first at every moment, so that the thing will have for an infinite
time the capacity both of being and of not being; but this has been
shown to be impossible. (4) Again, if the capacity is present prior
to the activity, it will be present for all time, even while the thing
was as yet ungenerated and non-existent, throughout the infinite time
in which it was capable of being generated. At that time, then, when
it was not, at that same time it had the capacity of being, both of
being then and of being thereafter, and therefore for an infinity
of time.
It is clear also on other grounds that it is impossible that the destructible
should not at some time be destroyed. For otherwise it will always
be at once destructible and in actuality indestructible, so that it
will be at the same time capable of always existing and of not always
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ON THE HEAVENS 24
existing. Thus the destructible is at some time actually destroyed.
The generable, similarly, has been generated, for it is capable of
having been generated and thus also of not always existing.
We may also see in the following way how impossible it is either for
a thing which is generated to be thenceforward indestructible, or
for a thing which is ungenerated and has always hitherto existed to
be destroyed. Nothing that is by chance can be indestructible or ungenerated,
since the products of chance and fortune are opposed to what is, or
comes to be, always or usually, while anything which exists for a
time infinite either absolutely or in one direction, is in existence
either always or usually. That which is by chance, then, is by nature
such as to exist at one time and not at another. But in things of
that character the contradictory states proceed from one and the same
capacity, the matter of the thing being the cause equally of its existence
and of its non-existence. Hence contradictories would be present together
in actuality.
Further, it cannot truly be said of a thing now that it exists last
year, nor could it be said last year that it exists now. It is therefore
impossible for what once did not exist later to be eternal. For in
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