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

by Various

Thus we have three supreme kinds of place—the linear, with one dimension, length; the superficial, with two dimensions, length and breadth; the cubic or solid, with three dimensions, length, breadth, and depth. The true characteristic difference between these kinds of place is drawn from their formal constituents, viz., from their boundaries. The cubic place is a place terminated by surfaces. The superficial place is a place terminated by lines. The linear place is a place terminated by two points.

These supreme species admit of further subdivision, owing to the different geometrical figures affected by their respective boundaries. Thus the place of a body may be tetrahedric, hexahedric, spherical, etc., and the place of a surface may be triangular, polygonal, circular, etc.

Place is also divided into absolute and relative. It is called absolute when it is considered secundum se—that is, as to its entity, or as consisting of a system of correlation within a definite limit. It is called relative when it is considered in connection with some other place or places, as more or less distant from them, or as having with respect to them this or that position or situation.

The absolute place of a body, whatever our imagination may suggest to the contrary, is always the same as long as the body remains under the same dimensions, be it at rest or in movement. In fact, whenever we speak of a change of place, we mean that the place of a body acquires a new relation to the place of some other body—that is, we mean the mere change of its relativity. When the world was believed to be a sphere of continuous matter with no real space outside of it, the absolute place of a body could be considered as corresponding to one or another definite portion of that sphere, and therefore as changeable; but since the reality of infinite space independent of matter has been established, it is manifest that absolute place has no relation to the limits of the material world, but only to the infinity of space, with respect to which bodies cannot change their place any more than a point can change its ubication. Hence, when a body moves, its relative place, or, better, the relativity of its place to the places of other bodies, is changed; but its absolute place remains the same. Thus the earth, in describing its orbit, takes different positions round the sun, and, while preserving its absolute place unchanged, it undergoes a continuous change of its relativity.

Lastly, place is also divided into intrinsic and extrinsic. Omitting the old explanations of this division, we may briefly state that the intrinsic place is that which is determined by the dimensions and boundary of the body, and therefore is coextensive with it. The extrinsic place of a body is a place greater than the body which is placed in it. Thus Rome is the extrinsic place of the Vatican Palace, and the Vatican Palace is the extrinsic place of the Pope; because the Vatican Palace is in Rome, and the Pope in the Vatican Palace.

Occupation of Place.—We have now to answer a few questions about the occupation of place. The first is, whether bodies fill the space they occupy. The second is, whether the same place can be simultaneously occupied by two bodies. The third is, whether the place limits and conserves the body it contains. The fourth is, whether the same body can be miraculously in two places or more at the same time.

That bodies fill place is a very common notion, because people do not make any marked distinction between filling and occupying. But to fill and to occupy are not synonymous. To fill a place is to leave no vacuum within it; and this is evidently impossible without continuous matter. As we have proved that continuous matter does not exist, we cannot admit that any part of place, however small, can be filled. Place, however, is occupied. In fact, the material elements of which bodies are ultimately composed, by their presence in space occupy distinct points in space—that is, take possession of them, maintain themselves in them, and from them direct their action all around, by which they manifest to us their existence, ubication, and other properties. This is the meaning of occupation. Hence the formal reason of occupation is the presence of material elements in space. Therefore, the place of a body is occupied by the presence in it of discrete material points, none of which fill space—that is to say, the place is occupied, not filled. The common expression, “a place filled with matter,” may, however, be admitted in this sense, that when the place is occupied by a body, it does not naturally allow the intrusion of another body. This amounts to saying, not that the place is really filled, but that the resistance offered by the body to the intrusion of another body prevents its passage as effectually as if there were left no occupable room. So much for the first question.

The second question may be answered thus: Since space is not filled by the occupying bodies, the reason why bodies exclude one another from their respective places must be traced not to a want of room in them, but only to their mutual opposite actions. These actions God can neutralize and overcome by an action of His own; and if this be done, nothing will remain that can prevent the compenetration of two bodies and of their respective places. It is therefore possible, at least supernaturally, for two bodies to occupy the same place. Nevertheless, we must bear in mind that, as the elements of the one body are not the elements of the other, so the ubications of the first set of elements are not the ubications of the second, and consequently the correlations of the first set are not identically the correlations of the second. Hence, if one body penetrates into the place of another body, their places will be intertwined, but distinct from each other.

The third question must be answered in the negative, notwithstanding the contrary opinion of all the Peripatetics. The place does not limit and conserve the body by which it is occupied; it is the body itself that limits and conserves its own place. For what is it that gives to a place its formal determination, and its specific and numeric distinction from all other places, but its extreme boundary? Now, this boundary is marked out by the very elements which constitute the limits of the body. It is, therefore, the body itself that by its own limits defines the limits of its own place, and constitutes the place formally such or such. There is the same connection between a body and its place as between movement and its duration. There is no movement without time, nor time without movement; but movement does not result from time, for it is time itself that results from movement. Hence, the duration of the movement is limited by the movement itself. In like manner, there is no body without place, and no place without a body; but the body does not result from the place, for it is the place itself that results from the presence of the body in space. Hence, the place of the body is formally determined by the body itself. Therefore, it is the body that limits and conserves its place, not the place that limits and conserves the body.

This conclusion is confirmed by the manner in which our knowledge of place is acquired. Our perception of the place of a body is caused, not by the place, but by the body, which acts upon our senses from different points of its surface, and depicts in our organs the figure of its limits. This figure, therefore, is the figure of the place only inasmuch as it is the figure of the body; or, in other terms, it is the body itself that by its limits determines the limits of its place.