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. 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
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