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Objection 1: It would seem that an angel does not pass through
intermediate space. For everything that passes through a middle space
first travels along a place of its own dimensions, before passing
through a greater. But the place responding to an angel, who is
indivisible, is confined to a point. Therefore if the angel passes
through middle space, he must reckon infinite points in his movement:
which is not possible.
Objection 2: Further, an angel is of simpler substance than the
soul. But our soul by taking thought can pass from one extreme to
another without going through the middle: for I can think of France
and afterwards of Syria, without ever thinking of Italy, which
stands between them. Therefore much more can an angel pass from one
extreme to another without going through the middle.
On the contrary, If the angel be moved from one place to another,
then, when he is in the term "whither," he is no longer in motion,
but is changed. But a process of changing precedes every actual
change: consequently he was being moved while existing in some place.
But he was not moved so long as he was in the term "whence."
Therefore, he was moved while he was in mid-space: and so it was
necessary for him to pass through intervening space.
I answer that, As was observed above in the preceding article, the
local motion of an angel can be continuous, and non-continuous. If
it be continuous, the angel cannot pass from one extreme to another
without passing through the mid-space; because, as is said by the
Philosopher (Phys. v, text 22; vi, text 77), "The middle
is that into which a thing which is continually moved comes, before
arriving at the last into which it is moved"; because the order of
first and last in continuous movement, is according to the order of the
first and last in magnitude, as he says (Phys. iv, text 99).
But if an angel's movement be not continuous, it is possible for him
to pass from one extreme to another without going through the middle:
which is evident thus. Between the two extreme limits there are
infinite intermediate places; whether the places be taken as divisible
or as indivisible. This is clearly evident with regard to places which
are indivisible; because between every two points that are infinite
intermediate points, since no two points follow one another without a
middle, as is proved in Phys. vi, text. 1. And the same must of
necessity be said of divisible places: and this is shown from the
continuous movement of a body. For a body is not moved from place to
place except in time. But in the whole time which measures the
movement of a body, there are not two "nows" in which the body moved
is not in one place and in another; for if it were in one and the same
place in two "nows," it would follow that it would be at rest there;
since to be at rest is nothing else than to be in the same place now and
previously. Therefore since there are infinite "nows" between the
first and the last "now" of the time which measures the movement,
there must be infinite places between the first from which the movement
begins, and the last where the movement ceases. This again is made
evident from sensible experience. Let there be a body of a palm's
length, and let there be a plane measuring two palms, along which it
travels; it is evident that the first place from which the movement
starts is that of the one palm; and the place wherein the movement ends
is that of the other palm. Now it is clear that when it begins to
move, it gradually quits the first palm and enters the second.
According, then, as the magnitude of the palm is divided, even so
are the intermediate places multiplied; because every distinct point in
the magnitude of the first palm is the beginning of a place, and a
distinct point in the magnitude of the other palm is the limit of the
same. Accordingly, since magnitude is infinitely divisible and the
points in every magnitude are likewise infinite in potentiality, it
follows that between every two places there are infinite intermediate
places.
Now a movable body only exhausts the infinity of the intermediate
places by the continuity of its movement; because, as the intermediate
places are infinite in potentiality, so likewise must there be reckoned
some infinitudes in movement which is continuous. Consequently, if
the movement be not continuous, then all the parts of the movement will
be actually numbered. If, therefore, any movable body be moved, but
not by continuous movement, it follows, either that it does not pass
through all the intermediate places, or else that it actually numbers
infinite places: which is not possible. Accordingly, then, as the
angel's movement is not continuous, he does not pass through all
intermediate places.
Now, the actual passing from one extreme to the other, without going
through the mid-space, is quite in keeping with an angel's nature;
but not with that of a body, because a body is measured by and
contained under a place; hence it is bound to follow the laws of place
in its movement. But an angel's substance is not subject to place as
contained thereby, but is above it as containing it: hence it is under
his control to apply himself to a place just as he wills, either
through or without the intervening place.
Reply to Objection 1: The place of an angel is not taken as equal
to him according to magnitude, but according to contact of power: and
so the angel's place can be divisible, and is not always a mere
point. Yet even the intermediate divisible places are infinite, as
was said above: but they are consumed by the continuity of the
movement, as is evident from the foregoing.
Reply to Objection 2: While an angel is moved locally, his essence
is applied to various places: but the soul's essence is not applied to
the things thought of, but rather the things thought of are in it. So
there is no comparison.
Reply to Objection 3: In continuous movement the actual change is
not a part of the movement, but its conclusion; hence movement must
precede change. Accordingly such movement is through the mid-space.
But in movement which is not continuous, the change is a part, as a
unit is a part of number: hence the succession of the various places,
even without the mid-space, constitutes such movement.
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