Thomas Aquinas, Summa Theologiae

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.

Articulus 2

Argumentum 1

Ad secundum sic proceditur. Videtur quod Angelus non transeat per medium. Omne enim quod pertransit medium, prius pertransit locum sibi aequalem, quam maiorem. Locus autem aequalis Angeli, qui est indivisibilis, est locus punctalis. Si ergo Angelus in suo motu pertransit medium, oportet quod numeret puncta infinita suo motu, quod est impossibile.

Argumentum 2

Praeterea, Angelus est simplicioris substantiae quam anima nostra.

Sed anima nostra sua cogitatione potest transire de uno extremo in aliud, non pertranseundo medium, possum enim cogitare Galliam et postea syriam, nihil cogitando de Italia, quae est in medio.

Ergo multo magis Angelus potest de uno extremo transire ad aliud, non per medium.

Sed Contra

Sed contra, si Angelus movetur de uno loco ad alium, quando est in termino ad quem, non movetur, sed mutatus est. Sed ante omne mutatum esse praecedit mutari, ergo alicubi existens movebatur.

Sed non movebatur dum erat in termino a quo. Movebatur ergo dum erat in medio. Et ita oportet quod pertranseat medium.

Corpus

Respondeo dicendum quod, sicut supra dictum est, motus localis Angeli potest esse continuus, et non continuus.

Si ergo sit continuus, non potest Angelus moveri de uno extremo in alterum, quin transeat per medium, quia, ut dicitur in V physic., medium est in quod prius venit quod continue mutatur, quam in quod mutatur ultimum; ordo enim prioris et posterioris in motu continuo, est secundum ordinem prioris et posterioris in magnitudine, ut dicitur in IV physic..

Si autem motus Angeli non sit continuus, possibile est quod pertranseat de aliquo extremo in aliud, non pertransito medio.

Quod sic patet. Inter quaelibet enim duo extrema loca sunt infinita loca media; sive accipiantur loca divisibilia, sive indivisibilia. Et de indivisibilibus quidem manifestum est, quia inter quaelibet duo puncta sunt infinita puncta media, cum nulla duo puncta consequantur se invicem sine medio, ut in VI physic. Probatur.

De locis autem divisibilibus necesse est etiam hoc dicere. Et hoc demonstratur ex motu continuo alicuius corporis. Corpus enim non movetur de loco ad locum nisi in tempore. In toto autem tempore mensurante motum corporis, non est accipere duo nunc, in quibus corpus quod movetur non sit in alio et alio loco, quia si in uno et eodem loco esset in duobus nunc, sequeretur quod ibi quiesceret; cum nihil aliud sit quiescere quam in loco eodem esse nunc et prius. Cum igitur inter primum nunc et ultimum temporis mensurantis motum, sint infinita nunc, oportet quod inter primum locum, a quo incipit moveri, et ultimum locum, ad quem terminatur motus, sint infinita loca.

Et hoc sic etiam sensibiliter apparet. Sit enim unum corpus unius palmi, et sit via per quam transit, duorum palmorum, manifestum est quod locus primus, a quo incipit motus, est unius palmi; et locus, ad quem terminatur motus, est alterius palmi.

Manifestum est autem quod, quando incipit moveri, paulatim deserit primum palmum, et subintrat secundum. Secundum ergo quod dividitur magnitudo palmi, secundum hoc multiplicantur loca media, quia quodlibet punctum signatum in magnitudine primi palmi, est principium unius loci; et punctum signatum in magnitudine alterius palmi, est terminus eiusdem. Unde cum magnitudo sit divisibilis in infinitum, et puncta sint etiam infinita in potentia in qualibet magnitudine; sequitur quod inter quaelibet duo loca sint infinita loca media.

Mobile autem infinitatem mediorum locorum non consumit nisi per continuitatem motus, quia sicut loca media sunt infinita in potentia, ita et in motu continuo est accipere infinita quaedam in potentia. Si ergo motus non sit continuus, omnes partes motus erunt numeratae in actu. Si ergo mobile quodcumque moveatur motu non continuo, sequitur quod vel non transeat omnia media, vel quod actu numeret media infinita, quod est impossibile. Sic igitur secundum quod motus Angeli non est continuus, non pertransit omnia media.

Hoc autem, scilicet moveri de extremo in extremum et non per medium, potest convenire Angelo sed non corpori. Quia corpus mensuratur et continetur sub loco, unde oportet quod sequatur leges loci in suo motu. Sed substantia Angeli non est subdita loco ut contenta, sed est superior eo ut continens, unde in potestate eius est applicare se loco prout vult, vel per medium vel sine medio.

Ad 1

Ad primum ergo dicendum quod locus Angeli non accipitur ei aequalis secundum magnitudinem, sed secundum contactum virtutis, et sic locus Angeli potest esse divisibilis, et non semper punctalis. Sed tamen loca media etiam divisibilia, sunt infinita, ut dictum est, sed consumuntur per continuitatem motus, ut patet ex praedictis.

Ad 2

Ad secundum dicendum quod Angelus dum movetur localiter, applicatur eius essentia diversis locis, animae autem essentia non applicatur rebus quas cogitat, sed potius res cogitatae sunt in ipsa. Et ideo non est simile.

Ad 3

Ad tertium dicendum quod in motu continuo mutatum esse non est pars moveri, sed terminus unde oportet quod moveri sit ante mutatum esse. Et ideo oportet quod talis motus sit per medium.

Sed in motu non continuo mutatum esse est pars, sicut unitas est pars numeri, unde successio diversorum locorum, etiam sine medio, constituit talem motum.