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THE
CATHOLIC WORLD.
VOL. XXI., No. 124.—JULY, 1875.
Entered according to Act of Congress, in the year 1875. by Rev. I. T. Hecker, in the Office of the Librarian of Congress, at Washington, D. C.
SPACE.
I.
Mathematicians admit three kinds of continuous quantities, viz., the quantity of space measured by local movement, the quantity of time employed in the movement, and the quantity of change in the intensity of the movement. Thus all continuity, according to them, depends on movement; so that, if there were no continuous movement, nothing could be conceived as continuous. The ancient philosophers generally admitted, and many still admit, a fourth kind of continuous quantity, viz., the quantity of matter; but it is now fully demonstrated that bodies of matter are not, and cannot be, materially continuous, even in their primitive molecules, and that therefore the quantity of matter is not continuous, but consists of a discrete number of primitive material units. Hence, matter is not divisible in infinitum, and gives no occasion to infinitesimal quantities, except inasmuch as the volumes, or quantities of space, occupied (not filled) by matter are conceived to keep within infinitesimal dimensions. We may, therefore, be satisfied that space, time, and movement alone are continuous and infinitely divisible, and that the continuity of space and time, as viewed by the mathematicians, is essentially connected with the continuity of movement. But space measured by movement is a relative space, and time—that is, the duration of movement—is a relative duration; and since everything relative presupposes something absolute which is the source of its relativity, we are naturally brought to inquire what is absolute space and absolute duration; for, without the knowledge of the absolute, the relative can be only imperfectly understood. Men of course daily speak of time and of space, and understand what they say, and are understood by others; but this does not show that they know the intimate nature, or can give the essential definition, of either time or space. S. Augustine asks: “What is time?” and he answers: “When no one asks me, I know what it is; but when you ask me, I know not.” The same is true of space. We know what it is; but it would be hard to give its true definition. As, however, a true notion of space and time and movement cannot but be of great service in the elucidation of some important questions of philosophy, we will venture to investigate the subject, in the hope that by so doing we may contribute in some manner to the development of philosophical knowledge concerning the nature of those mysterious realities which form the conditions of the existence and vicissitudes of the material world.
Opinions of Philosophers about Space.—Space is usually defined “a capacity of bodies,” and is styled “full” when a body actually occupies that capacity, “void,” or “empty,” when no body is actually present in it. Again, a space which is determined by the presence of a body, and limited by its limits, is called “real,” whilst the space which is conceived to extend beyond the limits of all existing bodies is called “imaginary.”
Whether this definition and division of space is as correct as it is common, we shall examine hereafter. Meanwhile, we must notice that there is a great disagreement among philosophers in regard to the reality and the essence of space. Some hold, with Descartes and with Leibnitz, that space is nothing else than the extension of bodies. Others hold that space is something real, and really distinct from the bodies by which it is occupied. Some, as Clarke, said that space is nothing but God’s immensity, and considered the parts of space as parts of divine immensity. Fénelon taught that space is virtually contained in God’s immensity, and that immensity is nothing but unlimited extension—which last proposition is much criticised by Balmes[115] on the ground that extension cannot be conceived without parts, whereas no parts can be conceived in God’s immensity.
Lessius, in his much-esteemed work on God’s perfections, after having shown (contrary to the opinion of some of his contemporaries) that God by his immensity exists not only within but also without the world, puts to himself the following objection: “Some will say, How can God be in those spaces outside the skies, since no spaces are to be found there which are not fictitious and imaginary?” To which he answers thus: “We deny that there are not outside of the whole world any true intervals or spaces. If air or light were diffused throughout immensity outside of the existing world, there would certainly be true spaces everywhere; and in the same manner, if there is a Spirit filling everything outside of this world, there will be true and real spaces, not corporeal but spiritual, which, however, will not be really distinct from one another, because a Spirit does not extend through space by a distribution of parts, but fills it, so to say, by its totalities.… Hence, when we say that God is outside of the existing world, and filling infinite spaces, or that God exists in imaginary spaces, we do not mean that God exists in a fictitious and chimerical thing, nor do we mean that he exists in a space really distinct from his own being; but we mean that he exists in the space which his immensity formally extends, and to which an infinite created space may correspond.… We may therefore distinguish space into created, uncreated, and imaginary. Created space embraces the whole corporeal extension of the material world. Uncreated space is nothing less than divine immensity itself, which is the primitive, intrinsic, and fundamental space, on the existence of which all other spaces depend, and which by reason of its extension is equivalent to all possible corporeal spaces, and eminently contains them all. Imaginary space is that which our imagination suggests to us as a substitute for God’s immensity, which we are unable to conceive in any other wise. For, just as we cannot conceive God’s eternity without imagining infinite time, so neither can we conceive God’s immensity without imagining infinite space.”[116]
Boscovich, in his Theory of Natural Philosophy, defines space as “an infinite possibility of ubications,” but he does not say anything in regard to the manner of accounting for such a possibility. Others, as Charleton, were of opinion that real space is constituted by the real ubication of material things, and imaginary space by the actual negation of real ubications.
Among the modern authors, Balmes, with whom a number of other philosophers agree on this subject, gives us his theory of space in the following propositions:
“1st. Space is nothing but the extension of bodies themselves.
“2d. Space and extension are identical notions.
“3d. The parts which we conceive in space are particular extensions, considered as existing under their own limits.
“4th. The notion of infinite space is the notion of extension in all its generality—that is, as conceived by the abstraction of all limits.
“5th. Indefinite space is a figment of our imagination, which strives to follow the intellectual process of generalization by destroying all limits.
“6th. Where no body exists, there is no space.
“7th. Distance is the interposition of a body, and nothing more.
“8th. If the body interposed vanishes, all distance vanishes, and contiguity, or absolute contact, will be the result.
“9th. If there were two bodies only, they would not be distant; at least, we could not intellectually conceive them as distant.
“10th. A vacuum, whether of a large or of a small extent, whether accumulated or scattered, is an absolute impossibility.”[117]
These assertions form the substance of Balmes’ theory of space. But he wisely adds: “The apparent absurdity of some of these conclusions, and of others which I shall mention hereafter, leads me to believe either that the principle on which my reasonings rest is not altogether free from error, or that there is some latent blunder in the process of the deduction.”[118]
Lastly, to omit other suppositions which do not much differ from the ones we have mentioned, Kant and his followers are of opinion that space is nothing but a subjective form of our mind, and an intuition a priori. Hence, according to them, no real and objective space can be admitted.
Amid this variety and discord of opinions, we can hardly hope to ascertain the truth, and satisfy ourselves of its reality, unless we settle a few preliminary questions. It is necessary for us to know, first, whether any vacuum is or is not to be admitted in nature; then, we must know whether such a vacuum is or is not an objective reality. For, if it can be established that vacuum is mere nothingness, the consequence will be that all real space is necessarily and essentially filled with matter, as Balmes and others teach; if, on the contrary, it can be established that vacuum exists in nature, and has an objective reality, then it will follow that the reality of space does not arise from the presence of bodies, and cannot be confounded with their extension. In this case, Balmes’ theory will fall to the ground, and we shall have to borrow from Lessius and Fénelon, if not the whole solution of the question, at least the main conceptions on which it rests.
Existence of Void Space.—The first thing we must ascertain is the existence or non-existence of vacuum in nature. Is there any space in the world not occupied by matter?
Our answer must be affirmative, for many reasons. First, because without vacuum local movement would be impossible. In fact, since matter does not compenetrate matter, no movement can take place in a space full of matter unless the matter which lies on the way gives room to the advancing body. But such a matter cannot give room without moving; and it cannot move unless some other portion of matter near it vacates its place to make room for it. This other portion of matter, however, cannot make room without moving; and it cannot move unless another portion of matter makes room for it; and so on without end, or at least till we reach the outward limits of the material world. Hence, if there is no vacuum, a body cannot begin to move before it has shaken the whole material world throughout and compelled it to make room for its movement. Now, to make the movement of a body dependent on such a condition is absurd; for the condition can never be fulfilled. In fact, whilst the movement of the body cannot begin before room is made for it, no room is made for it before the movement has begun; for it is by moving that the body would compel the neighboring matter to give way. The condition is therefore contradictory, and can never be fulfilled, and therefore, if there is no vacuum, no local movement is possible.
Secondly, it has been proved in one of our articles on matter[119] that there is no such thing in the world as material continuity, and that therefore all natural bodies ultimately consist of simple and unextended elements. It is therefore necessary to admit that bodies owe their extension to the intervals of space intercepted between their primitive elements, and therefore there is a vacuum between all the material elements. This reason is very plain and cannot be questioned, as the impossibility of continuous matter has been established by such evident arguments as defy cavil.
Thirdly, bodies are compressible, and, when compressed, occupy less space—that is, their matter or mass is reduced to a less volume. Now, such a reduction in the volume of a body does not arise from material compenetration. It must therefore depend on a diminution of the distances, or void intervals, between the neighboring particles of matter.
Fourthly, it is well known that equal masses can exist under unequal volumes, and vice versa—that is, equal quantities of matter may occupy unequal spaces, and unequal quantities of matter may occupy equal spaces. This shows that one and the same space can be more or less occupied, according as the density of the body is greater or less. But the same space cannot be more or less occupied if there is no vacuum. For, if there is no vacuum, the space is entirely occupied by the matter, and does not admit of different degrees of occupation. It is therefore evident that without vacuum it is impossible to account for the specific weights and unequal densities of bodies.
Against this, some may object that what we call “vacuum” may be full of imponderable matter, say, of ether, the presence of which cannot indeed be detected by the balance, but is well proved by the phenomena of heat, electricity, etc. To which we answer, that the presence of ether between the molecules of bodies does not exclude vacuum; for ether itself is subject to condensation and rarefaction, as is manifest by its undulatory movements; and no condensation or rarefaction is possible without vacuum, as we have already explained.
Another objection against our conclusion may be the following: Simple elements, if they be attractive, can penetrate through one another, as we infer from the Newtonian law of action. Hence, the possibility of movement does not depend on the existence of vacuum. We answer, that the objection destroys itself; for whoever admits simple and unextended elements, must admit the existence of vacuum, it being evident that no space can be filled by unextended matter. We may add, that natural bodies and their molecules do not exclusively consist of attractive elements, but contain a great number of repulsive elements, to which they owe their impenetrability.
The ancients made against the existence of a vacuum another objection, drawn from the presumed necessity of a true material contact for the communication of movement. Vacuum, they said, is contra bonum naturæ—that is, incompatible with the requirements of natural order, for it prevents the interaction of bodies. This objection need hardly be answered, as it has long since been disposed of by the discovery of universal gravitation and of other physical truths. As we have proved in another place that “distance is an essential condition of the action of matter upon matter,”[120] we shall say nothing more on this point.
Objective Reality of Vacuum.—The second thing we must ascertain is whether space void of matter be a mere nothing, or an objective reality. Though Balmes and most modern philosophers hold that vacuum is mere nothingness, we think with other writers that the contrary can be rigorously demonstrated. Here are our reasons.
First, nothingness is not a region of movement. But vacuum is a region of movement. Therefore, vacuum is not mere nothingness. The minor of this syllogism is manifest from what we have just said about the impossibility of movement without vacuum, and the major can be easily proved. For, the interval of space which is measured by movement may be greater or less, whilst it would be absurd to talk of a greater or a less nothing; which shows that vacuum cannot be identified with nothingness. Again, void space can be really occupied, whilst it would be absurd to say that nothingness is really occupied, for occupation implies the presence of that which occupies in that which is occupied; hence, the occupation of nothingness would be the presence of a thing to nothing. But presence to nothing is no presence at all, just as relation to nothing is no relation. And therefore, the occupation of void space, if vacuum were a mere nothing, would be an evident contradiction. Moreover, nothingness has no real attributes, whereas real attributes are predicated of void space. We find no difficulty in conceiving void space as infinite, immovable, and virtually extended in all directions; whilst the conception of an extended nothing and of an infinite nothing is an utter impossibility. Whence we conclude that space void of matter is not a mere nothing.
Secondly, a mere nothing cannot be the foundation of a real relation: space void of matter is the foundation of a real relation; therefore, space void of matter is not a mere nothing. In this syllogism the major is quite certain; for all real relation has a real foundation, from which the correlated terms receive their relativity. Now, all real foundation is something real. On the other hand, nothingness is nothing real. Therefore, a mere nothing cannot be the foundation of a real relation. The minor proposition is no less certain, because space founds the relation of distance between any two material points, which relation is certainly real. In fact, that on account of which a distant term is related to another distant term, is the possibility of movement from the one to the other—that is, the possibility of a series of successive ubications between the two terms, without which no distance is conceivable. But the possibility of successive ubications is nothing else than the successive occupability of space, or space as occupable. And therefore, occupable space, or space void of matter, is the foundation of a real relation, and accordingly is an objective reality.
Thirdly, if vacuum were mere nothingness, no real extension could be conceived as possible. For, since all bodies are ultimately composed of elements destitute of extension, as has been demonstrated at length in our articles on matter, and since the primitive elements cannot touch one another mathematically without compenetration, the extension of bodies cannot be accounted for except by the existence of void intervals of space between neighboring elements. But, if vacuum is a mere nothing, all void intervals of space are nothing, and nothing remains between the neighboring elements; and if nothing remains between them, all the elements must be in mathematical contact, and therefore unite in a single indivisible point, as even Balmes concedes. Whence it is evident that the existence of real extension implies the objective reality of vacuum. We conclude, therefore, that space void of matter is not a mere nothing, but an objective reality.
Against this proposition some objections are made by the upholders of a different doctrine. In the first place, distance, they say, is a mere negation of contact; and since a mere negation is nothing, there is no need of assuming that vacuum is a reality.
We answer, that, if distance were a mere negation of contact, there would be no different distances; for the negation of contact does not admit of degrees, and cannot be greater or less. Distances may be, and are, greater or less. Therefore, distance is not a mere negation of contact. The negation of contact shows that the terms of the relation are distinct in space; for distinction in space is the negation of a common ubication. But the distinction of the terms, though a necessary condition for the existence of the relation, does not constitute it. Hence, the relation of distance presupposes, indeed, the distinction of the terms and the negation of contact, but formally it results from a positive foundation by which the terms are linked together in this or that determinate manner. If the interval between two material points were nothing, a greater interval would be a greater nothing, and a less interval a less nothing. We presume that no philosopher can safely admit a doctrine which leads to such a conclusion.
A second objection is as follows: It is possible to have distance without any vacuum between the distant terms. For, if the whole space between those terms were full of matter, their distance would be all the more real, without implying the reality of vacuum.
We answer, first, that, to fill space, continuous matter would be needed; and, as continuous matter has no existence in nature, no space can be filled with matter so as to exclude real vacuum. We answer, secondly, that, were it possible to admit continuous matter, filling the whole interval of space between two distant terms, the reality of that interval would still remain independent of the matter by which it is assumed to be filled; for matter is not space; and, on the other hand, if all the matter which is supposed to fill the interval be removed, the distance between the terms will not vanish; which shows that the filling of space, even if it were not an impossible task, would not in the least contribute to the constitution of real distances. Hence, space, even if it were assumed to be full of matter, would not found the relation of distance by its fulness, but only by its being terminated to distinct terms, so as to leave room between them for a certain extension of local movement.
A third objection may be the following: True though it is that real attributes are predicated of void space, it does not follow that void space is an objective reality. For, when we say that space, as such, is infinite, immovable, etc., we must bear in mind that we speak of a potential nature, and that those predicates are only potential. Again, though we must admit that void space can be measured by movement, we know that such a mensuration is not made by terms of space, but by terms of matter. Lastly, although space is the capacity of receiving bodies, it does not follow that there is in space any receptive reality; for its capacity is sufficiently accounted for by admitting that space becomes real by its very occupation.[121]
To the first point of this objection we answer, that space may, perhaps, be called a “potential nature” in this sense, that it is susceptible of new extrinsic denominations; but if by “potential nature” the objector means to express a potency of being, and to convey the idea that such a nature is not real, then it is absolutely wrong to say that void space is a potential nature. Space is not in a state of possibility, and never has been, as we shall presently show. Hence the predicates, infinite, immovable, etc., by which the nature of space is explained, express the actual attributes of an actual reality. The author from whom we have transcribed this objection says that such predicates of space are real, not objectively, but only subjectively. He means, if we understand him aright, that the reality of such predicates must be traced to the bodies which occupy space, not to space itself, and that, though we conceive those predicates to be real owing to the real bodies we see in space, yet they are not real in space itself. As for us, we cannot understand how “to be infinite, to be immovable, to be occupable, etc.,” can be the property of any body which occupies space, or be the property of space, by reason of its occupation and not by reason of its own intrinsic nature. Space must be really occupable before it is really occupied; and nothing is really occupable which is not real, as we have already established. Whence we conclude that this part of the objection, as confounding the possibility of occupation with the possibility of being, has no weight.
To the second point we answer, that the thing mensurable should not be confounded with that by which it can be measured. Whatever may be the nature of the measure to be employed in measuring, no mensuration is possible unless the mensurable is really mensurable. Hence, no matter by what measure space is to be measured, it is always necessary to concede that, if it is really measured, it is something real. The assertion that space is measured “by terms of matter” can scarcely have a meaning. Terms, in fact, measure nothing, but are merely the beginning and the end of the thing measured. Space is measured by continuous movement, not by terms of matter; but before it is thus measured, it is mensurable; and its mensurability sufficiently shows its objective reality.[122]
To the third point of the objection we reply, that space is not a subject destined to receive bodies; and therefore it is not to be called “a capacity of receiving bodies.” Hence, we admit that space has no “receptive” reality. But there are realities which are not receptive, because they are not intrinsically potential; and such is the reality of space, as we shall hereafter explain. With regard to the assertion that “space becomes real by its very occupation,” we observe that, if space void of matter is nothing, as the objection assumes, it is utterly impossible that it become a reality by the presence of bodies in it. The presence of a body in space is a real relation of the body to the space occupied; and such a relation presupposes two real terms—that is, a real body and a real space. If space, as such, is nothing, bodies were created in nothing, and occupy nothing. Their volumes will be nothings of different sizes, their dimensions nothings of different lengths, and their movements the measurement of nothing. It is manifest that real occupation presupposes real occupability, and real mensuration real mensurability; and, since mensurability implies quantity (virtual quantity, at least), to say that occupable and mensurable space is nothing, is to pretend that nothingness implies quantity—a thing which we, at least, cannot understand. Moreover, to consider void space as a potency of being, destined to become a reality through the presence of bodies, is no less a blunder than to admit that the absolute is nothing until it becomes relative, or to admit the relative without the absolute. In fact, the space occupied by a body is a relative space, as its determination depends on the relative dimensions of the body. On the other hand, the relative dimensions of the body are themselves dependent on space, for without space there are no dimensions; and the space on which such relative dimensions depend must be a reality in itself, independently of the same dimensions, it being evident that the dimensions of the body cannot bestow reality upon that which is the source of their own reality. To say the contrary is to destroy the principle of causality, by making the absolute reality of the cause dependent on the reality of its effects. The assertion that “the absolute is nothing until it becomes relative,” leads straight to Pantheism. If you say that absolute space is nothing until it is occupied by bodies, and thus actuated and exhibited under determinate figures, the Pantheist will say, with as much reason, that the absolute being is nothing until it is evolved in nature, and thus actuated and manifested under different aspects. If you say that absolute space, as such, is but an imaginary conception, he will draw the inference that absolute being, as such, is similarly a mere figment of our brains. If you say that the only reality of space arises from its figuration and occupation, he will claim the right of concluding, in like manner, that the only reality of the absolute arises from its evolution and manifestation. We might dilate a great deal more on this parallel; for everything that the deniers of the reality of void space can say in support of their view can be turned to account by the deniers of a personal God, and be made to serve the cause of German Pantheism—the manner of reasoning of the latter being exactly similar to that of the former. This is a point of great importance, and to which philosophers would do well to pay a greater attention than was done in other times, if they admit, in the case of space, that “the absolute is nothing until it becomes relative,” they will have no right to complain of the Pantheistic applications of their own theory.
Vacuum unmade.—The third thing we have to ascertain is, whether void space, absolutely considered as to its reality, be created or uncreated. This point can be easily settled. Those who say that vacuum has no objective reality have, of course, no alternative. For them, vacuum must be uncreated. But they are probably not prepared to hear that we too, who defend the reality of void space, do not differ from them in the solution of this question.
To prove that space void of matter is not created, the following plain reasons may be adduced. First, space void of matter is neither a material nor a spiritual creature. It is no material creature; for it excludes matter. It is no spiritual creature; for, whether there be spiritual creatures or not, it is necessary to admit occupable space.
Secondly, no created thing is immovable, unchangeable, and unlimited. Absolute space is evidently immovable, unchangeable, and unlimited. Therefore, absolute space is not a product of creation.
Thirdly, space considered absolutely as it is in itself, exhibits an infinite and inexhaustible possibility of real ubications. But such a possibility is to be found nowhere but in God alone, in whom all possible things have their formal possibility. And therefore, the reality of absolute space is all in God alone; and accordingly, such a reality not only is not, but could never be, created.
Fourthly, whatever is necessary, is uncreated and eternal. Space considered absolutely as it is in itself is something necessary. Therefore, absolute space is uncreated and eternal. The major of this syllogism is evident; the minor is thus proved: Space absolutely considered is nothing else than the formal possibility of real ubications; but the possibility of things contingent is necessary, uncreated, and eternal; for all contingent things are possible before any free act of the creator, since their intrinsic possibility does not depend on God’s volition, as Descartes imagined, but only on his essence as distinctly and comprehensively understood by the divine intellect.
Our next proposition will afford a fifth proof of this conclusion. Meanwhile, we beg of our reader not to forget the restriction by which we have limited our present question. We have spoken of space absolutely considered as it is in itself—that is, of absolute space. Our conclusion, if applied to relative space, would not be entirely true; for relative space implies the existence of at least two contingent terms, and therefore involves something created. We make this remark because men are apt to confound relative with absolute space, owing to the sensible representations which always accompany our intellectual operations, and also because we think that the philosophical difficulties encountered by many writers in their investigation of the nature of space originated in the latent and unconscious assumption that their imagination of relative space was an intellectual concept of absolute space. It is thus that they were led to consider all space void of matter as imaginary and chimerical.
Quiddity of Absolute Space.—It now remains for us to ascertain the true nature of absolute space, and to point out its essential definition. Our task will not be difficult after the preceding conclusions. If absolute space is an uncreated, infinite, eternal, and unchangeable reality, it must be implied in some of the attributes of Godhead. Now, the divine attribute in which the reason of all possible ubications is contained, is immensity. Hence, absolute space is implied in God’s immensity, and we shall see that it is nothing else than the virtuality or the extrinsic terminability of immensity itself.
Before we prove this proposition, we must define the terms virtuality and terminability. “Virtuality” comes from virtus as formality from forma. Things that are actual owe their being to their form; hence, whatever expresses some actual degree of entity is styled “a formality.” Thus, personality, animality, rationality, etc., are formalities exhibiting the actual being of man under different aspects. Things, on the contrary, that have no formal existence, but which may be made to exist, owe the possibility of their existence to the power (virtus) of the efficient cause of which they can be the effect, or to the nature of the sufficient reason from which they may formally result. In both cases, the things in question are said to exist virtually, inasmuch as they are virtually contained in their efficient cause or in their sufficient reason. Hence, every efficient cause or sufficient reason, as compared with the effects which it can produce or with the results of which it may be the foundation, is said to have “virtuality”; for, the virtuality of all producible effects, as of all resultable relations, is to be found nowhere but in their efficient cause and in their formal reason. Thus all active power has a virtuality extending to all the acts of which it may be the causality, and all formal reason has a virtuality extending to all the results of which it may be the foundation. God’s omnipotence, for instance, virtually contains in itself the reality of all possible creatures, and therefore possesses an infinite virtuality. In a similar manner, God’s immensity has an infinite virtuality, as it virtually contains all possible ubications, and is the reason of their formal resultability. Omnipotence has an infinite virtuality as an efficient principle; immensity has an infinite virtuality as a formal source only.
These remarks about virtuality go far to explain the word “terminability.” Whenever an efficient cause produces an effect, its action is terminated to an actuable term; hence, so long as the effect is not produced, the power of the efficient cause is merely terminable. In the same manner, whenever a formal reason gives rise to an actual result, and whenever a formal principle gives being to a potential term, there is a formal termination; and therefore, so long as the result, or the actual being, has no existence, its formal reason is merely terminable. Hence, terminability has the same range as virtuality; for nothing that is virtually contained in an efficient or in a formal principle can pass from the virtual to the actual state except by the termination of an efficient or a formal act to a potential term.
We have said that absolute space is nothing else than the virtuality, or extrinsic terminability, of God’s immensity. The first proof of this conclusion is as follows. Absolute space is the possibility of all real ubications. But such a possibility is nothing else than the infinite virtuality of God’s immensity. Hence our conclusion. The major of our syllogism is obviously true, and is admitted by all, either in the same or in equivalent terms. The minor needs but little explanation; for we have already seen that absolute space is an uncreated reality, and therefore is something connected with some divine attribute; but the only attribute in which the possibility of all real ubications is contained, is God’s immensity. Hence, the possibility of real ubications is evidently nothing else than the extrinsic terminability of divine immensity. In other terms, God’s immensity, like other divine attributes, is not only an immanent perfection of the divine nature, by which God has his infinite ubication in himself, but also the source and the eminent reason of all possible ubications, because it contains them all virtually in its boundless expanse. Hence, the infinite virtuality of God’s immensity is one and the same thing with the possibility of infinite ubications. And, therefore, absolute space is nothing but the virtuality of divine immensity.
Let the reader take notice that divine immensity is, with regard to absolute space, the remote principle, or, as the Schoolmen would say, the principium quod, whilst the virtuality or extrinsic terminability of divine immensity is the proximate principle, or the principium quo. Hence, it would not be altogether correct to say that absolute space is nothing but God’s immensity; for, as we call “space” that in which contingent beings can be ubicated, it is evident that the formal notion of space essentially involves the connotation of something exterior to God; and such a connotation is not included in divine immensity as such, but only inasmuch as it virtually pre-contains all possible ubications. And for this reason the infinite virtuality of God’s immensity constitutes the formal ratio of absolute space. It is in this sense that we should understand Lessius when he says: “The immensity of the divine substance is to itself and to the world a sufficient space: it is an expanse capable of all producible nature, whether corporeal or spiritual. For, as the divine essence is the first essence, the origin of all essences and of all conceivable beings, so is the divine immensity the first and self-supporting expanse or space, the origin of all expanse, and the space of all spaces, the place of all places, and the primordial seat and basis of all place and space.”[123]
The second proof of our conclusion may be the following. Let us imagine that all created things be annihilated. In such a case, there will remain nothing in space, and there will be an end of all contingent occupation, presence, or ubication. Yet, since God will remain in his immensity, there will remain that infinite reality which contains in its expanse the possibility of infinite contingent ubications; for there will remain God’s immensity with all its extrinsic terminability. In fact, God would not cease to be in those places where the creatures were located; the only change would be this, that those places, by the annihilation of creatures, would lose the contingent denominations which they borrowed from the actual presence of creatures in them, and thus all those ubications would cease to be formal, and would become virtual. It is plain, therefore, that the reality of void space must be accounted for by the fact that, after the annihilation of all creatures, there remains God’s immensity, whose infinite virtuality is equivalent to infinite virtual ubications. Hence, space void of matter, but filled with God’s substance, can be nothing else than the infinite virtuality of divine immensity.
A third proof of our conclusion, and a very plain one, can be drawn from God’s creative power. Wherever God is, he can create a material point; and wherever a material point can be placed, there is space; for space is the region where material things can be ubicated. Now, God is everywhere by his immensity; and therefore, everywhere there is the possibility of ubicating a material point—that is, absolute space has the same range as God’s immensity. On the other hand, there is no doubt that a material point, by being ubicated in absolute space, is constituted in God’s presence, and is thus related to God’s immensity; and this relation implies the extrinsic termination of God’s immensity. Therefore, the ubication of a material point in space is the extrinsic termination of divine immensity; whence it follows that the possibility of ubications is nothing but the extrinsic terminability of the same immensity.
The fourth proof of our conclusion consists in showing that none of the other known opinions about space can be admitted. First, as to the subjective form imagined by Kant, we cannot believe that it has any philosophical claim to adoption, as it evidently defies common sense, and is supported by no reasons. “Kant,” says Balmes, “seems to have overlooked all distinction between the imagination of space and the notion of space; and much as he labored in analyzing the subject, he did not succeed in framing a theory worthy of the name. While he considers space as a receptacle of natural phenomena, he at the same time despoils it of its objectivity, and says that space is nothing but a merely subjective condition, … an imaginary capacity in which we can scatter and arrange the phenomena.”[124] “To say that space is a thing merely subjective,” continues Balmes, “is either not to solve the problems of the outward world, or to deny them, inasmuch as their reality is thereby denied. What have we gained in philosophy by affirming that space is a merely subjective condition? Did we not know, even before this German philosopher uttered a word, that we had the perception of exterior phenomena? Does not consciousness itself bear witness to the existence of such a perception? It was not this, therefore, that we wished to know, but this only: whether such a perception be a sufficient ground for affirming the existence of the outward world, and what are the relations by which our perception is connected with the same outward world. This is the whole question. He who answers that in our perception there is nothing but a merely subjective condition, Alexander-like, cuts the knot, and denies, instead of explaining, the possibility of experimental knowledge.”[125]
As to Descartes’ and Leibnitz’ opinion, which makes the reality of space dependent on material occupation, we need only observe that such an opinion, even as modified by Balmes, leads to numerous absurdities, presupposes the material continuity of bodies, which we have shown to be intrinsically repugnant,[126] and assumes, by an evident petitio principii, that space void of matter is nothing. The same opinion is beset by another very great difficulty, inasmuch as it assumes that the reality of space lies in something relative, whilst it recognizes nothing absolute which may be pointed out as the foundation of the relativity. This difficulty will never be answered. In all kind and degree of reality, before anything relative can be conceived, something absolute is to be found from which the relative borrows its relativity. On the other hand, it is obvious that real space, as understood by Descartes, and by Balmes too, is something purely relative; for “space,” says Balmes, “is nothing but the extension of bodies themselves”; to which Descartes adds, that such a space “constitutes the essence of bodies.” But the extension of bodies is evidently relative, since it arises from the relations intervening between the material terms of bodies. The three dimensions of bodies—length, breadth, and depth—are nothing but distances, and distances are relations in space. Hence, no dimension is conceivable but through relations in space; and therefore, before we can have real dimensions in bodies, we must have, as their foundation, real space independent of bodies. Finally, since the opinion of which we are speaking affirms that relative space is a reality, while it denies that space without bodies is real, the same opinion lays down the foundation of real and of ideal Pantheism, as we have already remarked. This suffices to show that such an opinion must be absolutely rejected.
Nothing therefore remains but to accept the doctrine of those who account for the reality of absolute space either by divine immensity or by the possibility of real ubications. But these authors, as a little reflection will show, though employing a different phraseology, teach substantially the same thing; for it would be absurd to imagine the possibility of infinite real ubications as extraneous to God, in whom alone all things have their possibility. We must, therefore, conclude that space, considered absolutely as to its quiddity, may be defined to be the infinite virtuality, or extrinsic terminability, of divine immensity.
A Corollary.—Absolute space is infinite, eternal, immovable, immutable, indivisible, and formally simple, though virtually extended without limits—that is, equivalent to infinite length, breadth, and depth.
Solution of Objections.—It may be objected that absolute space, being only a virtuality, can have no formal existence. In fact, the virtuality of divine immensity is the mere possibility of real ubications; and possibilities have no formal existence. Hence, to affirm that absolute space has formal being in the order of realities, is to give body to a shadow. It would be more reasonable to say that space is contained in divine immensity just as the velocity which a body may acquire is contained in the power of an agent; and that, as the power of the agent is no velocity, so the virtuality of immensity is no space.
This objection may be answered thus: Granted that the virtuality of divine immensity is the mere possibility of real ubications, it does not follow that absolute space has only a virtual existence, but, on the contrary, that, as the virtuality of divine immensity is altogether actual, so also is absolute space. The reason alleged, that “possibilities have no formal existence,” is sophistic. A term which is only possible, say, another world, has of course no formal existence; but its possibility—that is, the extrinsic terminability of God’s omnipotence—is evidently as actual as omnipotence itself. And in the same manner, an ubication which is only possible has no formal existence; but its possibility—that is, the extrinsic terminability of God’s immensity—is evidently as actual as immensity itself. If absolute space were conceived as an array of actual ubications, we would readily concede that to give it a reality not grounded on actual ubications would be to give a body to a shadow; but, since absolute space must be conceived as the mere possibility of actual ubications, it is manifest that we need nothing but the actual terminability of God’s immensity to be justified in admitting the actual existence of absolute space.
Would it be “more reasonable” to say, as the objection infers, that space is contained in divine immensity just as velocity is contained in the power of the agent? Certainly not, because what is contained in divine immensity is the virtuality of contingent ubications, not the virtuality of absolute space. There is no virtuality of absolute space; for there is no virtuality of possibility of ubications; as the virtuality of a possibility would be nothing else than the possibility of a possibility—that is, a chimera. Hence, the words of the objection should be altered as follows: “Contingent ubications are contained in divine immensity just as velocity is contained in the power of an agent; for, as the power of the agent is no actual velocity, so the virtuality of immensity is no actual contingent ubication.” And we may go further in the comparison by adding, that, as the formal possibility of actual velocity lies wholly in the power of the agent, so the possibility of actual ubications—that is, absolute space—lies in the virtuality of divine immensity.
Thus the objection is solved. It will not be superfluous, however, to point out the false assumption which underlies it, viz., the notion that the extrinsic terminability of divine immensity has only a virtual, not a formal, reality. This assumption is false. The terminability is the formality under which God’s immensity presents itself to our thought, when it is regarded as the source of some extrinsic relation, ut habens ordinem ad extra. Such a formality is not a mere concept of our reason; for God’s immensity is not only conceptually, but also really, terminable ad extra; whence it follows that such a terminability is an objective reality in the divine substance. Terminability, of course, implies virtuality; but this does not mean that such a terminability has only a virtual reality; for the virtuality it implies is the virtuality of the extrinsic terms which it connotes, and not the virtuality of its own being. Were we to admit that the extrinsic terminability of God’s immensity is only a virtual entity, we would be compelled to say also that omnipotence itself is only a virtual entity; for omnipotence is the extrinsic terminability of God’s act. But it is manifest that omnipotence is in God formally, not virtually. In like manner, then, immensity is in God not only as an actual attribute, but also as an attribute having an actual terminability ad extra, which shows that its terminability is not a virtual, but a formal, reality.
A second objection may be made. Would it not be better to define space as the virtuality of all ubications, rather than the virtuality of God’s immensity? For when we think of space, we conceive it as something immediately connected with the ubication of creatures, without need of rising to the consideration of God’s immensity.
We answer that absolute space may indeed be styled “the virtuality of all ubications;” for all possible ubications are in fact virtually contained in it. But such a phrase does not express the quiddity of absolute space; for it does not tell us what reality is that in which all ubications are virtually contained. On the contrary, when we say that absolute space is “the virtuality of divine immensity,” we point out the very quiddity of space; for we point out its constituent formality which connects divine immensity with all possible ubications.
True it is that we are wont to think of space as connected with contingent ubications; for it is from such ubications that our knowledge of place and of space arises. But this space thus immediately connected with existing creatures is relative space, and its representation mostly depends on our imaginative faculty. Hence, this manner of representing space cannot be alleged as a proof that absolute space can be intellectually conceived without referring to divine immensity.
A third objection may be the following. Whatever has existence is either a substance or an accident. But absolute space is neither a substance nor an accident. Therefore, absolute space has no existence, and is nothing. The major of this argument is well known, and the minor is proved thus: Absolute space does not exist in any subject, of which it might be predicated; hence, absolute space is not an accident. Nor is it a substance; for then it would be the substance of God himself—an inference too preposterous to be admitted.
This objection will soon disappear by observing that, although everything existing may be reduced either to the category of substance or to some of the categories of accident, nevertheless, it is not true that every existing reality is formally a substance or an accident. There are a great many realities which cannot be styled “substances,” though they are not accidents. Thus, rationality, activity, substantiality, existence, and all the essential attributes and constituents of things, are not substances, and yet they are not accidents; for they either enter into the constitution, or flow from the essence, of substance, and are identified with it, though not formally nor adequately. Applying this distinction to our subject, we say that absolute space cannot be styled simply “God’s substance,” notwithstanding the fact that the virtuality of divine immensity identifies itself with immensity, and immensity with the divine substance. The reason of this is, that one thing is not said simply to be another, unless they be the same not only as to their reality, but also as to their conceptual notion. Hence, we do not say that the possibility of creatures is “God’s substance,” though such a possibility is in God alone; and in the same manner, we cannot say that the possibility of ubication is “God’s substance,” though such a possibility has the reason of its being in God alone. For the same reason, we cannot say simply that God’s eternity is his omnipotence, nor that his intellect is his immensity, nor that God understands by his will or by his goodness, though these attributes identify themselves really with the divine substance and with one another, as is shown in natural theology. It is plain, therefore, that absolute space is not precisely “God’s substance”; and yet it is not an accident; for it is the virtuality or extrinsic terminability of divine immensity itself.
A fourth objection arises from the opinion of those who consider God’s immensity as the foundation of absolute space, but in such a manner as to imply the existence of a real distinction between the two. Immensity, they say, has no formal extension, as it has no parts outside of parts; whereas, absolute space is formally extended, and has parts outside of parts; for when a body occupies one part of space, it does not occupy any other—which shows that the parts of space are really distinct from one another; and therefore absolute space, though it has the reason of its being in God’s immensity, is something really distinct from God’s immensity.
To this we answer, that it is impossible to admit a real distinction between absolute space and divine immensity. When divine immensity is said to be the foundation, or the reason of being, of absolute space, the phrase must not be taken to mean that absolute space is anything made, or extrinsic to God’s immensity; its meaning is that God’s immensity contains in itself virtually, as we have explained, all possible ubications of exterior things, just as God’s omnipotence contains in itself virtually all possible creatures. And as we cannot affirm without error that there is a real distinction between divine omnipotence and the possibility of creatures which it contains, so we cannot affirm without error that there is a real distinction between divine immensity and the possibility of ubications which it contains.
That immensity has no parts outside of parts we fully admit, though we maintain at the same time that God is everywhere formally by his immensity. But we deny that absolute space has parts outside of parts; for it is impossible to have parts where there are no distinct entities. Absolute space is one simple virtuality containing in itself the reason of distinct ubications, but not made up of them; just as the divine essence contains in itself the reason of all producible essences, but is not made up of them.
As to the formal extension of immensity, Lessius seems to admit it when he says that “God exists in the space which his immensity formally extends.” Fénelon also holds that “immensity is infinite extension”; whilst Balmes does not admit that extension can be conceived where there are no parts. The question, so far as we can judge, is one of words. That God is everywhere formally is a plain truth; on the other hand, to say that he is formally extended, taking “extension” in the ordinary signification, would be to imply parts and composition; which cannot be in God. It seems to us that the right manner of expressing the infinite range of God’s immensity would be this: “God through his immensity is formally everywhere, though by a virtual, not a formal, extension.” In the same manner, space is formally everywhere, though it is only virtually, not formally, extended. And very likely this, and nothing more, is what Lessius meant when saying that immensity “formally extends” space. This phrase may, in fact, be understood in two ways; first, as meaning that immensity causes space to be formally extended—which is wrong; secondly, as meaning that immensity is the formal, not the efficient, reason of the extension of space. This second meaning, which is philosophically correct, does not imply the formal extension of space, as is evident, unless by “formal extension” we understand the “formal reason of its extending”; in which case the word “extension” would be taken in an unusual sense.
Lastly, when it is objected that “bodies occupying one part of space do not occupy another,” and that therefore “space is composed of distinct parts,” a confusion is made of absolute space, as such, and space extrinsically terminated, or occupied by matter, and receiving from such a termination an extrinsic denomination. Distinct bodies give distinct names to the places occupied by them; but absolute space is not intrinsically affected by the presence of bodies, as we shall see in our next article; and, therefore, the distinct denominations of different places refer to the distinct ubications of matter, not to distinct parts of absolute space. As we cannot say that the sun and the planets are parts of divine omnipotence, so we cannot say that their places are parts of divine immensity or of its terminability; for as the sun and the planets are only extrinsic terms of omnipotence, so are their places only extrinsic terms of immensity. Such places, therefore, may be distinct from one another, but their possibility (that is, absolute space) is one, and has no parts. But this subject will receive a greater development in our next article, in which we intend to investigate the nature of relative space.
TO BE CONTINUED.