The Complete Aristotle (eng.)

elements infinite in number, as Anaxagoras and Democritus do,
say that the infinite is continuous by contact-compounded of the
homogeneous parts according to the one, of the seed-mass of the
atomic shapes according to the other.
    Further, Anaxagoras held that any part is a mixture in the same
way as the All, on the ground of the observed fact that anything
comes out of anything. For it is probably for this reason that he
maintains that once upon a time all things were together. (This
flesh and this bone were together, and so of any thing: therefore
all things: and at the same time too.) For there is a beginning of
separation, not only for each thing, but for all. Each thing that
comes to be comes from a similar body, and there is a coming to be
of all things, though not, it is true, at the same time. Hence
there must also be an origin of coming to be. One such source there
is which he calls Mind, and Mind begins its work of thinking from
some starting-point. So necessarily all things must have been
together at a certain time, and must have begun to be moved at a
certain time.
    Democritus, for his part, asserts the contrary, namely that no
element arises from another element. Nevertheless for him the
common body is a source of all things, differing from part to part
in size and in shape.
    It is clear then from these considerations that the inquiry
concerns the physicist. Nor is it without reason that they all make
it a principle or source. We cannot say that the infinite has no
effect, and the only effectiveness which we can ascribe to it is
that of a principle. Everything is either a source or derived from
a source. But there cannot be a source of the infinite or
limitless, for that would be a limit of it. Further, as it is a
beginning, it is both uncreatable and indestructible. For there
must be a point at which what has come to be reaches completion,
and also a termination of all passing away. That is why, as we say,
there is no principle of this, but it is this which is held to be
the principle of other things, and to encompass all and to steer
all, as those assert who do not recognize, alongside the infinite,
other causes, such as Mind or Friendship. Further they identify it
with the Divine, for it is ‘deathless and imperishable’ as
Anaximander says, with the majority of the physicists.
    Belief in the existence of the infinite comes mainly from five
considerations:
    (1) From the nature of time-for it is infinite.
    (2) From the division of magnitudes-for the mathematicians also
use the notion of the infinite.
    (3) If coming to be and passing away do not give out, it is only
because that from which things come to be is infinite.
    (4) Because the limited always finds its limit in something, so
that there must be no limit, if everything is always limited by
something different from itself.
    (5) Most of all, a reason which is peculiarly appropriate and
presents the difficulty that is felt by everybody-not only number
but also mathematical magnitudes and what is outside the heaven are
supposed to be infinite because they never give out in our
thought.
    The last fact (that what is outside is infinite) leads people to
suppose that body also is infinite, and that there is an infinite
number of worlds. Why should there be body in one part of the void
rather than in another? Grant only that mass is anywhere and it
follows that it must be everywhere. Also, if void and place are
infinite, there must be infinite body too, for in the case of
eternal things what may be must be. But the problem of the infinite
is difficult: many contradictions result whether we suppose it to
exist or not to exist. If it exists, we have still to ask how it
exists; as a substance or as the essential attribute of some
entity? Or in neither way, yet none the less is there something
which is infinite or some things which are infinitely many?
    The problem, however, which specially belongs to the physicist
is to investigate whether there is a sensible magnitude which is
infinite.
    We must begin by distinguishing the various senses in which the
term ‘infinite’ is used.
    (1) What is incapable of being gone through, because it is not
in its nature to be gone through (the sense in which the voice is
‘invisible’).
    (2) What admits of being gone through, the process however
having no termination, or what scarcely admits of being gone
through.
    (3) What naturally admits of being gone through, but is not
actually gone through or does not actually