The Catholic World, Vol. 21, April, 1875, to September, 1875 / A Monthly Magazine of General Literature and Science

by Various

In the present question, it is evident that the possibility of movement cannot be understood either in the first or in the second of these three manners; for our question does not regard the relation of the agent to the patient, or of the patient to the agent, but merely the relation of one ubication to another, and the freedom for movement between them. If the possibility of movement were taken here as originating in a motive power, such a possibility would be greater or less according to the greater or less power; and thus the relativity of two given ubications would be changed without altering their relation in space; which is absurd. And if the possibility of movement were taken as resulting from the passivity of the term moved, then, since this passivity is a mere indifference to receive the motion, and since indifference has no degrees, it would follow that the possibility of movement would be always the same; and therefore the relativity of the ubications would remain the same, even though the ubications were relatively changed; which is another absurdity. Accordingly, the possibility of movement which is involved in the conception of relative space is that which arises from space itself, whose virtual extension virtually contains all possible lines of movement, and allows any such lines to be formally drawn through it by actual movement.

From this it follows that relative space is nothing else than absolute space as extrinsically terminated by distinct terms, and affording room for movement between them. It follows, further, that this space is relative, not because it is itself related, but because it is that through which the extrinsic terms are related. It is actively, not passively, relative; it is the ratio, not the rationatum, the foundation, not the result, of the relativities. It follows, also, that the foundation of the relation of distance is nothing else than space as terminated by two extrinsic terms, and affording room for movement from the one to the other. This space is at the same time absolute and relative; absolute as to its entity, relative as to the extrinsic denomination derived from the relation of which it is the formal reason.

The distinction between absolute and relative space is therefore to be taken, not from space itself, but from its comparison with absolute or with relative ubications. Space, as absolute, exhibits the possibility of all absolute ubications; as relative, it exhibits the possibility of all ubicational changes. Absolute space may therefore be styled simply “the region of ubications,” whilst relative space maybe defined as “the region of movement.”

This notion of relative space will not fail to be opposed by those who think that all real space results from the dimensions of bodies. Their objections, however, need not detain us here, as we have already shown that the grounds of their argumentation are inadmissible. The same notion will be opposed with greater plausibility by those who confound the formal reason of local relations with the relations themselves, under the common name of relative space. Their objections are based on the popular language, as used, even by philosophers, in connection with relative space. We will reduce these objections to two heads, and answer them, together with two others drawn from other sources, that our reader may thus form a clearer judgment of the doctrine we have developed.

First difficulty. The entity of a relation is the entity of its foundation. If, then, the foundation of the relation of distance is absolute space, or the virtuality of God’s immensity, it follows that the entity of distance is an uncreated entity. But this cannot be admitted, except by Pantheists. Therefore the relation of distance is not founded on the virtuality of God’s immensity.

This difficulty arises from a false supposition. The entity of the relation is not the entity of its foundation, but it is the entity of the connotation (respectus) which arises from the existence of the terms under such a foundation. Likeness, for instance, is a relation resulting between two bodies, say, white, on account of their common property, say, whiteness. Whiteness is therefore the foundation of their likeness; but whiteness it not likeness. On the contrary, the whiteness which founds this relation is still competent to found innumerable other relations; a thing which would be impossible if the entity of the foundation were not infinitely superior to the entity of the relation which results from it.

This is even more evident in our case; for the foundation of the relation between two ubications is an entity altogether extrinsic to the ubications themselves, as we have already shown. Evidently, such an entity cannot be the relativity of those ubications. The relation of distance is neither absolute nor relative space, but only the mode of being of one term in space with respect to another term in space. Now, surely no one who has any knowledge of things will maintain that space, either absolute or relative, is a mode of being. The moon is distant from the earth; and therefore there is space, and possibility of movement, between the moon and the earth. But is this space the relation of distance? No. It is the ground of the relation. The relation itself consists in the mode of being of the moon with respect to the earth; and, evidently, this mode is not space.

The assumption that the entity of the relation is the entity of its foundation may be admitted in the case of transcendental relations, inasmuch as the actuality of beings, which results from the conspiration of their essential principles, identifies itself in concreto with the beings themselves. But the same cannot be said of predicamental relations. It would be absurd to say that the dependence of the world on its Creator is the creative act; nor would it be less absurd to say that the relativity of a son to his father is the act of generation, or that the fraternity of James and John is the same thing as the identity of Zebedee, their father, with himself. And yet these absurdities, and many others, must be admitted, if we admit the assumption that the entity of predicamental relations is the entity of their foundation. Hence the assumption must be discarded as false; and the objection, which rested entirely on this assumption, needs no further discussion.

We must, however, take this opportunity to again warn the student of the necessity of not confounding under one and the same name the relative space with the relations of things existing in space. This confusion is very frequent, as we often hear of distances, surfaces, and volumes of bodies spoken of as “relative spaces,” which, properly speaking, they are not. We ourselves are now and then obliged to use this inaccurate language, owing to the difficulty of conveying our thoughts to common readers without employing common phrases. But we would suggest that, to avoid all misconstruction of such phrases, the relative space, of which we have determined the notion, might be called “fundamental relative space,” whilst the relations of things as existing in space might receive the name of “resultant relative spaces.” At any rate, without some epithets of this sort, we cannot turn to good account the popular phraseology on the subject. Such a phraseology expresses things as they are represented in our imagination, not as they are defined by our reason. Distances are intervals between certain points in space, surfaces are intervals between certain lines in space, volumes are intervals between certain surfaces in spaces; but these intervals are no parts of space, though they are very frequently so called, but only relations in space. Space is one, not many; it has no parts, and, whether you call it absolute or relative, it cannot be cut to pieces. What is called an interval of space should rather be called an interval in space; for it is not a portion of space, but a relation of things in space; it is not a length of space, but the length of the movement possible between the extrinsic terms of space; it is not a divisible extension, but the ground on which movement can extend with its divisible extension. In the smallest conceivable interval of space there is God, with all his immensity. To affirm that intervals of space are distinct spaces would be to cut God’s immensity into pieces, by giving it a distinct being in really distinct intervals. It is therefore necessary to concede that, whilst the intervals are distinct, the space on which they have their foundation is one and the same.

Pantheists have taken advantage of the confusion of fundamental space with the resulting relations in space, to spread their absurd theories. If we grant them that distance is space, how can we refute their assertion that distance is a form under which divine substance, or the Absolute, makes an apparition? For, if distance is space, and space is no creature, distance consists of something uncreated (and therefore divine) under a contingent form. This is not the place for us to refute Pantheism; what we aim at is simply to point out the need we have of expressing our thoughts on space with philosophical accuracy, lest the Pantheists may shield themselves with our own loose phraseology.