For these reasons we maintain that place cannot properly be defined as “the surface of the surrounding body.” As to the additional limitation, that such a surface should be considered as “immovable”—that is, affixed to a determinate space (imaginary, of course, according to the peripatetic theory, and therefore wholly fictitious)—we need only say that even if it were possible to attach the surface of a body to a determinate space, which is not the case, yet this condition could not be admitted in the definition of place, because the absolute place of a body is invariably the same, wherever it be, in absolute space, and does not change except as compared with other places. Absolute place, just as absolute ubication, has but one manner of existing in absolute space; for all places, considered in themselves, are extrinsic terminations of the same infinite virtuality, and are all equally in the centre, so to say, of its infinite expanse, whatever be their mutual relations.
True Notion of Place.—What is, then, the true definition of place? Webster describes it in his Dictionary as “a particular portion of space of indefinite extent, occupied, or intended to be occupied, by any person or thing, and considered as the space where a person or thing does or may rest, or has rested, as distinct from space in general.” This is in fact the meaning of the word “place” in the popular language. The philosophical definition of place, as gathered from this description, would be: “Place is a particular portion of space.” This is the very definition which all philosophers, before Aristotle, admitted, and which Aristotle endeavored to refute, on the ground that, when a body moves through space, its place remains intrinsically the same.
We have shown in our last article that space considered in itself has no parts; but those who admit portion of space, consider space as a reality dependent on the dimensions of the bodies by which it is occupied—that is, they call “space” those resultant relative intervals which have their foundation in space itself. If we were to take the word “space” in this popular sense, we might well say that “place is a portion of space,” because any given place is but one out of the many places determined by the presence of bodies in the whole world. On the other hand, since space, properly so called, is itself virtually extended—that is, equivalent in its absolute simplicity to infinite extension, and since virtual extension suggests the thought of virtual parts, we might admit that there are virtual portions of space in this sense, that space as the foundation of all local relations corresponds by its virtuality to all the dimensions and intervals mensurable between all terms ubicated, and receives from them distinct extrinsic denominations. Thus, space as occupied by the sun is virtually distinguished from itself as occupied by the moon, not because it has a distinct entity in the sun and another in the moon, but because it has two distinct extrinsic terminations. We might therefore admit that place is “a virtual portion of space determined by material limits”; and we might even omit the epithet “virtual” if it were understood that the word “space” was taken as synonymous with the dimensions of bodies, as is taken by those who deny the reality of vacuum. But, though this manner of speaking is and will always remain popular, owing to its agreement with our imagination and to its conciseness, which makes it preferable for our ordinary intercourse, we think that the place of a body, in proper philosophical language, should be defined as “a system of correlations between the terms which mark out the limits of the body in space”; and therefore place in general, whether really occupied or not, should be defined as “a system of correlations between ubications marking out the limits of dimensive quantity.”
This definition expresses all that we imply and that Webster includes in the description of place; but it changes the somewhat objectionable phrase “portion of space” into what people mean by it, viz., “a system of correlations between distinct ubications,” thereby showing that it is not the absolute entity of fundamental space, but only the resultant relations in space, that enter into the intrinsic constitution of place.
By “a system of correlations” we mean the adequate result of the combination of all the intervals from every single term to every other within the limits assumed, in every direction. Such a result will therefore represent either a volume, or a surface, or a line, according as the terms considered within the given limits are differently disposed in space. Thus a spherical place results from the mutual relations intervening between all the terms of its geometric surface; and therefore it implies all the intervals which can be measured, and all the lines that can be traced, in all directions, from any of those terms to any other within the given limits. In like manner, a triangular place results from the mutual relations intervening between all the terms forming its perimeter; and therefore it implies all the intervals and lines of movement which can be traced, in all directions, from any of those terms to any other within the given limits.
In the definition we have given, the material or determinable element is the system of correlations or intervals which are mensurable within the limiting terms; the formal or determinant is the disposition of the limiting terms themselves—that is, the definite boundary which determines the extent of those intervals, and gives to the place a definite shape.
Thus it appears that, although there is no place without space, nevertheless the entity of space does not enter into the constitution of place as an intrinsic constituent, but only as the extrinsic foundation. This is what we have endeavored to express as clearly as we could in our definition of place. As, however, in our ordinary intercourse we cannot well speak of place with such nice circumlocutions as are needed in philosophical treatises, we do not much object to the common notion that place is “space intercepted by a limiting boundary,” and we ourselves have no difficulty in using this expression, out of philosophy, owing to the loose meaning attached to the word “space” in common language; for all distances and intervals in space are called “spaces,” even in mechanics; and thus, when we hear of “space intercepted,” we know that the speakers do not refer to the absolute entity of space (which they have been taught to identify with nothingness), but merely to the intervals resulting from the extrinsic terminations of that entity.
Most of the Schoolmen (viz., all those who considered void space as imaginary and unreal) agreed, as we have intimated, with Aristotle, that the notion of place involves nothing but the surface of a surrounding body, and contended that within the limits of that surface there was no such chimerical thing as mere space, but only the quantity of the body itself. Suarez, in his Metaphysics (Disp. 51, sect. 1, n. 9), mentions the opinion of those who maintained that place is the space occupied by a body, and argues against it on the ground that no one can say what kind of being such a space is. Some have affirmed, says he, that such a space is a body indivisible and immaterial—which leads to an open contradiction—though they perhaps considered this body to be “indivisible,” not because it had no parts, but because its parts could not be separated. They also called it “immaterial,” on account of its permeability to all bodies. But this opinion, he justly adds, is against reason and even against faith; for, on the one hand this space should be eternal, uncreated, and infinite, whilst on the other no body can be admitted to have these attributes.
Others, Suarez continues, thought that the space which can be occupied by bodies is mere quantity extending all around without end. This opinion was refuted by Aristotle, and is inadmissible, because there cannot be quantitative dimensions without a substance, and because the bodies which would occupy such a space have already their own dimensions, which cannot be compenetrated with the dimensions of space. And moreover, such a quantity would be either eternal and uncreated—which is against faith—or created with all other things, and therefore created in space; which shows that space itself is not such a quantity.
Others finally opine, with greater probability, says he, that space, as distinct from the bodies that fill it, is nothing real and positive, but a mere emptiness, implying both the absence of bodies and the aptitude to be filled by bodies. Of this opinion Toletus says (4 Phys. q. 3) that it is probable, and that it cannot be demonstratively refuted. Yet, adds Suarez, it can be shown that such a space, as distinct from bodies, is in fact nothing; for it is neither a substance nor an accident, nor anything created or temporal, but eternal.