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Metaphysics   


one, just as there is the same interval from one to two as from two to
one, and as the steep ascent and the steep descent are one, but the
being of them is not one; the case of the mover and the moved is
similar.
10

The infinite is either that which is incapable of being
traversed because it is not its nature to be traversed (this
corresponds to the sense in which the voice is 'invisible'), or that
which admits only of incomplete traverse or scarcely admits of
traverse, or that which, though it naturally admits of traverse, is
not traversed or limited; further, a thing may be infinite in
respect of addition or of subtraction, or both. The infinite cannot be
a separate, independent thing. For if it is neither a spatial
magnitude nor a plurality, but infinity itself is its substance and
not an accident of it, it will be indivisible; for the divisible is
either magnitude or plurality. But if indivisible, it is not infinite,
except as the voice is invisible; but people do not mean this, nor are
we examining this sort of infinite, but the infinite as untraversable.
Further, how can an infinite exist by itself, unless number and
magnitude also exist by themselvess-since infinity is an attribute
of these? Further, if the infinite is an accident of something else,
it cannot be qua infinite an element in things, as the invisible is
not an element in speech, though the voice is invisible. And evidently
the infinite cannot exist actually. For then any part of it that might
be taken would be infinite (for 'to be infinite' and 'the infinite'
are the same, if the infinite is substance and not predicated of a
subject). Therefore it is either indivisible, or if it is partible, it
is divisible into infinites; but the same thing cannot be many
infinites (as a part of air is air, so a part of the infinite would be
infinite, if the infinite is substance and a principle). Therefore
it must be impartible and indivisible. But the actually infinite
cannot be indivisible; for it must be of a certain quantity. Therefore
infinity belongs to its subject incidentally. But if so, then (as we
have said) it cannot be it that is a principle, but that of which it
is an accident-the air or the even number.
This inquiry is universal; but that the infinite is not among
sensible things, is evident from the following argument. If the
definition of a body is 'that which is bounded by planes', there
cannot be an infinite body either sensible or intelligible; nor a
separate and infinite number, for number or that which has a number is
numerable. Concretely, the truth is evident from the following
argument. The infinite can neither be composite nor simple. For (a) it
cannot be a composite body, since the elements are limited in
multitude. For the contraries must be equal and no one of them must be
infinite; for if one of the two bodies falls at all short of the other
in potency, the finite will be destroyed by the infinite. And that
each should be infinite is impossible. For body is that which has
extension in all directions, and the infinite is the boundlessly
extended, so that if the infinite is a body it will be infinite in
every direction. Nor (b) can the infinite body be one and
simple-neither, as some say, something apart from the elements, from
which they generate these (for there is no such body apart from the
elements; for everything can be resolved into that of which it
consists, but no such product of analysis is observed except the
simple bodies), nor fire nor any other of the elements. For apart from
the question how any of them could be infinite, the All, even if it is
finite, cannot either be or become any one of them, as Heraclitus says
all things sometime become fire. The same argument applies to this
as to the One which the natural philosophers posit besides the
elements. For everything changes from contrary to contrary, e.g.
from hot to cold.
Further, a sensible body is somewhere, and whole and part have the
same proper place, e.g. the whole earth and part of the earth.

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