Such is the substance of the reasons adduced by Suarez to prove that the space occupied by bodies is nothing real. Had he, like Lessius, turned his thought to the extrinsic terminability of God’s immensity, he would have easily discovered that, to establish the reality of space, none of those old hypotheses which he refuted were needed. As we have already settled this point in a preceding article, we will not return to it. It may, however, be remarked that what Suarez says regarding the incompenetrability of the quantity of space with the quantity of the body is based entirely on the assumption that bodies have their own volume independently of space—an assumption which, though plausibly maintained by the ancients, can by no means be reconciled with the true notion of the volume of bodies as now established by physical science and accepted by all philosophers. As all dimensive quantity arises from relations in space, so it is owing to space itself that bodies have volume; and therefore there are not, as the ancients imagined, two volumes compenetrated, the one of space, and the other of matter; but there is one volume alone determined by the material terms related through space. And thus there is no ground left for the compenetration of two quantities.
S. Thomas also, in his Commentary to the Physics of Aristotle (4 Phys. lect. 6), and in the opuscule, De Natura Loci, argues that there is no space within the limiting surface of the body, for two reasons. The first is, that such a quantity of space would be an accident without a subject: Sequitur quod esset aliquod accidens absque subjecto; quod est impossibile. The second is, that if there is space within the surface of the body, as all the parts of the body are in the volume of the same, so will the places of all the parts be in the place of the whole; and consequently, there will be as many places compenetrated with one another as there can be divisions in the dimensions of the body. But these dimensions admit of an infinite division. Therefore, infinite places will be compenetrated together: Sequitur quod sint infinita loca simul; quod est impossibile.
These two reasons could not but have considerable weight in a time when material continuity formed the base of the physical theory of quantity, and when space without matter was considered a chimera; but in our time the case is quite different. To the first reason we answer, that the space within the surface of the body will not be “an accident without a subject.” In fact, such a space can be understood in two manners, viz., either as the foundation of the intervals, or as the intervals themselves; and in neither case will there be an accident without a subject. For, the space which is the foundation of the intervals is no accident; it is the virtuality of God’s immensity, as we have proved; and, therefore, there can be no question about its subject. Moreover, such a space is indeed within the limits of the body, but it is also without, as it is not limited by them. These limits, as compared with space, are extrinsic terms; and therefore they do not belong to space, but to the body alone. Lastly, although without space there can be no place, yet space is neither the material nor the formal constituent of place, but only the extrinsic ground of local relations, just as eternity is not an intrinsic constituent of time, but only the extrinsic ground of successive duration. Whence it is manifest that the entity of space is not the dimensive quantity of the body, but the eminent reason of its dimensions.
If, on the other hand, space is understood in the popular sense as meaning the accidental intervals between the limits of the body, then it is evident that such intervals will not be without their proportionate subject. Relations have a subject of predication, not of inhesion; for relation is a thing whose entity, according to the scholastic definition, consists entirely of a mere connotation; cuius totum esse est ad aliud se habere. Hence all relation is merely ad aliud, and cannot be in alio. Accordingly, the intervals between the terms of the body are between them, but do not inhere in them; and they have a sufficient subject—the only subject, indeed, which they require, for the very reason that they exist between real terms, with a real foundation. Thus the first reason objected is radically solved.
To the second reason we answer, that it is impossible to conceive an infinite multitude of places in one total place, unless we admit the existence of an infinite multitude of limiting terms—that is, unless we assume that matter is mathematically continuous. But, since material continuity is now justly considered as a baseless and irrational hypothesis, as our readers know, the compenetration of infinite places with one another becomes an impossibility.
Yet, as all bodies contain a very great number of material terms, it may be asked: Would the existence of space within the limits of place prove the compenetration of a finite number of places? Would it prove, for instance, that the places of different bodies existing in a given room compenetrate the place of the room? The answer depends wholly on the meaning attached to the word “space.” If we take “space” as the foundation of the relations between the terms of a place, then different places will certainly be compenetrated, inasmuch as the entity of space is the same, though differently terminated, in every one of them. But, if we take “space” as meaning the system of relative intervals between the terms of a body, then the place of a room will not be compenetrated with the places of the bodies it contains; because neither the intervals nor the terms of one place are the intervals or the terms of another, nor have they anything common except the absolute entity of their extrinsic foundation. Now, since place is not space properly, but only a system of correlations between ubications marking out the limits of the body in space, it follows that no compenetration of one place with another is possible so long as the terms of the one do not coincide with the terms of the other.
S. Thomas remarks also, in the same place, that if a recipient full of water contains space, then, besides the dimensions of the water, there would be in the same recipient the dimensions of space, and these latter would therefore be compenetrated with the former. Quum aqua est in vase, præter dimensiones aquæ sunt ibi aliæ dimensiones spatii penetrantes dimensiones aquæ. This would certainly be the case were it true that the dimensions of the body are materially continuous, as S. Thomas with all his contemporaries believed. But the truth is that the dimensions of bodies do not consist in the extension of continuous matter, but in the extension of the intervals between the limits of the bodies, which is greater or less according as it requires a greater or less extension of movement to be measured. The volume of a body—that is, the quantity of the place it occupies—is exactly the same whether it be full or empty, provided the limiting terms remain the same and in the same relation to one another. It is not the matter, therefore, that constitutes its dimensions. And then there are, and can be, no distinct dimensions of matter compenetrating the dimensions of place. But enough about the nature of place. Let us proceed to its division.
Division of Place.—Place in general may be divided into real and imaginary, according as its limiting terms exist in nature or are only imagined by us. This division is so clear that it needs no explanation. It might be asked whether there are not also ideal places. We answer, that strictly ideal places there are none; for the ideal is the object of our intellect, whilst place is the object of our senses and imagination. Hence the so-called “ideal” places are nothing but “imaginary” places.
Place, whether real or imaginary, is again divided by geometers into linear, superficial, and cubic or solid, according to the nature of their limiting boundaries. A place limited by surfaces is the place of a volume or geometric solid. A place limited by lines is the place of a surface. A place limited by mere points is the place of a line.
The ancients, when defining place as “the surface of the surrounding body,” connected the notion of place with the quantity of volume, without taking notice of the other two kinds just mentioned. This, too, was a necessary consequence of their assumption of continuous matter. For, if matter is intrinsically extended in length, breadth, and depth, all places must be extended in a similar manner. But it is a known fact that the word “place” (locus) is used now, and was used in all times, in connection not only with geometric volumes, but also with geometric surfaces and with geometric lines; and as the geometric quantities have their counterpart in the physical order, it is manifest that such geometric places cannot be excluded from the division of place. Can we not on any surface draw a line circumscribing a circle or any other close figure? And can we not point out the “place” where the circle or figure is marked out? There are therefore places of which the boundaries are lines, not surfaces. And again, can we not fix two points on a given line, and consider the interval between them as one of the many places which can be designated along the line? The word “place” in its generality applies to any kind of dimensive quantity in space. Those who pretend to limit it to “the surface of a volume” should tell us what other term is to be used when we have to mention the place of a plane figure on a wall, or of a linear length on the intersection of two surfaces. It will be said that the ancients in this case used the word Ubi. But we reply that Ubi and Locus were taken by them as synonymous. The quantities bounded by lines, or terminated by points, were therefore equivalently admitted to have their own “places”; which proves that the definition of place which philosophers left us in their books, did not express all that they themselves meant when using the word, and therefore it was not practically insisted upon. With us the case is different. The Ubi, as defined by us, designates a single point in space, and is distinct from locus; hence we do not admit that our ubi is a place; for there is no place within a point. But the philosophers of the old school could not limit the real ubication of matter to a mere point, owing to their opinion that matter was continuous.