Whether an angel passes through intermediate space?
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.