Bodies have bulk or volume, whereby they are said to occupy a certain place, and to fill it with their dimensions. Hence, to complete our task, we have now to consider space in relation with the volumes and places of bodies. To proceed orderly, we must first determine the proper definition of “place,” and its division; then we shall examine a few questions concerning the relation of each body to its place, and particularly the difficult and interesting one whether bodies can be really bilocated and multilocated.
Place.—Aristotle, in the fourth book of his Physics, defines the place of a body as “the surface by which the body is immediately surrounded and enveloped”—“Locus est extrema superficies corporis continentis immobilis.” This definition was accepted by nearly all the ancients. The best of their representatives, S. Thomas, says: “Locus est terminus corporis continentis”—viz., The place of a body is the surface of the body which contains it; and the Schoolmen very generally define place to be “the concave surface of the surrounding body: Superficies concava corporis ambientis.” Thus, according to the followers of Aristotle, no body can have place unless it is surrounded by some other body. Immobility was also believed to be necessarily included in the notion of place: Superficies immobilis. Cardinal de Lugo says: “the word place seems to be understood as meaning the real surface of a surrounding body, not, however, as simply having its extension all around, but as immovable—that is, as attached to a determinate imaginary space.”[179] We do not see what can be the meaning of this last phrase. For De Lugo holds that “real space” is the equivalent of “place,” and that space, as distinguished from place, is nothing real: Non est aliquid reale.[180] His imaginary space is, therefore, a mere nothing. How are we, then, to understand that a real surface can be “attached to a determinate imaginary space”? Can a real being be attached to a determinate nothing? Are there many nothings? or nothings possessing distinct determinations? We think that these questions must all be answered in the negative, and that neither Cardinal de Lugo, nor any one else who considers imaginary space as a mere nothing, can account for the immobility thus attributed to place.
The reason why Aristotle’s definition of place came to be generally adopted by the old Schoolmen is very plain. For, in the place occupied by any given body, two things can be considered, viz., the limiting surface, and the dimensive quantity which extends within the limiting surface. Now, as the ancients believed the matter of which bodies are composed to be endowed with continuity, it was natural that they should look upon the dimensive quantity included within the limiting surface as an appurtenance of the matter itself, and that they should consider it, not as an intrinsic constituent of the place occupied, but as a distinct reality through which the body could occupy a certain place. According to this notion of dimensive quantity, the limiting surface was retained as the sole constituent of the place occupied; and the dimensions within the surface being thus excluded from the notion of place, were attached to the matter of the body itself, as a special accident inhering in it.
This manner of conceiving things is still looked upon as unobjectionable by those philosophers who think that the old metaphysics has been carried to such a degree of perfection by the peripatetics as to have nothing or little to learn from the modern positive sciences. But whoever has once realized the fact that the dimensions of bodies are not continuous lines of matter, but intervals, or relations, in space, will agree that such dimensions do not inhere in the matter, but are extrinsic relations between material terms distinctly ubicated. What is called the volume of a body is nothing but the resultant of a system of relations in space. The matter of the body supplies nothing to its constitution except the extrinsic terms of the relations. The foundation of those relations is not to be found in the body, but in space alone, as we have proved in our last article; and the relations themselves do not inhere in the terms, but only intervene between them. Hence the dimensive quantity of the volume is intrinsically connected with the place it occupies, and must enter into the definition of place as its material constituent, as we are going to show.
As to the Aristotelic definition of place, we have the following objections: First, a good definition always consists of two notions, the one generic and determinable, as its material element, the other differential and determinant, as its formal element. Now, Aristotle’s definition of place exhibits at best only the formal or determinant, and omits entirely the material or determinable. It is evident, in fact, that the surface of any given body determines the limits and the figure of something involved in the notion of place. But what is this something? It cannot be a mere nothing; for nothing does not receive limits and figure, as real limits and real figure must be settled upon something real. This something must therefore be either the quantity of the matter, or the quantity of the volume enclosed within the limiting surface. And as we cannot admit that the quantity of the place occupied by a body is the quantity of matter contained in the body (because bodies which have different quantities of matter can occupy equal places), we are bound to conclude that the quantity of the place occupied by a body is the quantity of the volume comprised within the limiting surface. This is the determinable or material constituent of place; for this, and this alone, is determined by the concave surface of the surrounding body. In the same manner as a cubic body contains dimensions within its cubic form, so also a cubic place contains dimensions under its cubic surface; hence the place of a body has volume, the same volume as the body; and therefore it cannot be defined as a mere limiting surface.
Secondly, the definition of a thing should express what every one understands the thing to be. But no one understands the word “place” as meaning the exterior limit of the body which occupies it, therefore the exterior limit of the body is not the true definition of place. The minor of this syllogism is manifest. For we predicate of place many things which cannot be predicated of the exterior limit of the body. We say, for instance, that a place is full, half-full, or empty; that it is capable of so many objects, persons, etc.; and it is plain that these predicates cannot appertain to the exterior limit of the body, but they exclusively belong to the capacity within the limiting boundary. Hence a definition of place which overlooks such a capacity is defective.
Thirdly, to equal quantities of limiting surfaces do not necessarily correspond equal quantities of place. Therefore, the limiting surface is not synonymous with place, and cannot be its definition. The antecedent is well known. Take two cylinders having equal surfaces, but whose bases and altitudes are to one another in different ratios. It is evident by geometry that such cylinders will have different capacities—that is, there will be more occupable or occupied room in the one than in the other. The consequence, too, is plain; for, if the room, or place, can be greater or less while the limiting surface does not become greater or less, it is clear that the place is not the limiting surface.
Fourthly, what Aristotle and his school called “the surface of the surrounding body,” is now admitted to be formed by an assemblage of unextended material points, perfectly isolated; and therefore such a surface does not constitute a continuous material envelope, as it was believed in earlier times. Now, since those isolated points have no dimensions, but are simply terms of the dimensions in space, the so-called “surface” owes its own dimensions to the free intervals between those points, just as the dimensions also of the volume enclosed owe their existence to similar intervals between the same points. Therefore the same terms which mark in space the limit of place, mark also its volume; and thus the volume under the surface belongs to the place itself no less than does the limiting surface.
Fifthly, a body in vacuum would have its absolute place; and yet in vacuum there is no surface of surrounding bodies. Therefore an exterior surrounding body is not needed to constitute place. In fact, the body itself determines its own place by the extreme terms of its own bodily dimensions. This the philosophers of the peripatetic school could not admit, because they thought that the place of the body could not move with the body, but ought to remain “attached to a determinate imaginary space.” But, in so reasoning, they confounded the absolute place with the relative, as will be shown hereafter. Yet they conceded that a body in vacuum would have its place; and, when asked to point out there the surface of a surrounding body, they could not answer, except by abandoning the Aristotelic definition and by resorting to the centre and the poles of the world, thus exchanging the absolute place (locus) for the relative (situs), without reflecting that they had no right to admit a relative place where, according to their definition, the absolute was wanting.
Sixthly, the true definition of place must be so general as to be applicable to all possible places. But the Aristotelic definition does not apply to all places. Therefore such a definition is not true. The major of our argument needs no proof. The minor is proved thus: There are places not only within surfaces, but also within lines, and on the lines themselves; for, if on the surface of a body we describe a circle or a triangle, it is evident that a place will be marked and determined on that surface. Its limiting boundary, however, will be, not the surface of a surrounding body, but simply the circumference of the circle, or the perimeter of the triangle.