Matter. IV.
To complete our investigation about the essential properties of matter, one great question remains to be answered, viz.: Is the matter of which bodies are made up intrinsically extended so as to fill a portion of space, or does it ultimately consist of unextended points? We call this a great question, not indeed because of any great difficulty to be encountered in its solution, but because it has a great importance in metaphysics, and because it has been at all times much ventilated by great philosophers.
That bodies do not fill with their matter the dimensions of their volume is conceded by all, as porosity is a general property of bodies. That the molecules, or chemical atoms, of which the mass of a body is composed, do not touch one another with their matter, but are separated by appreciable intervals of space, is also admitted by our best scientists, though many of them are of opinion that those intervals are filled with a subtle medium, by which calorific and luminous vibrations are supposed to be propagated. But with regard to the molecules themselves, the question, whether their constitution is continuous or discrete, has not yet been settled. Some teach, with the old physicists, that bodies are ultimately made up of particles materially continuous, filling with their mass the whole space occupied by their volume. These last particles they call atoms, because their mass is not susceptible of physical division, although their volume is infinitely divisible in a mathematical sense. Others, on the contrary, deny the material continuity of matter, and hold with Boscovich that, as all bodies are composed of discrete molecules, so are all molecules composed of discrete elements wholly destitute of material extension, occupying distinct mathematical points in space, and bound by mutual action in mechanical systems differently constituted, according to the different nature of the substances to which they belong.
Which of these two opinions is right? Although scientists more generally incline to the second, metaphysicians are still in favor of the first. Yet we do not hesitate to say, though it may appear presumptuous on our part, that it is not difficult to decide the question. Let the reader follow our reasoning upon the subject, and we confidently predict that he will soon be satisfied of the truth of our assertion.
Groundless assumption of continuous matter.—As the true metaphysics of matter must be grounded on real facts, we may first inquire what facts, if any, can be adduced in favor of the intrinsic extension and material continuity of molecules. Is there any sensible fact which directly or indirectly proves such a continuity?
We must answer in the negative. For sensible facts are perceived by us in consequence of the impressions [pg 273] which objects make on our senses; if, therefore, such impressions are not calculated to reveal anything concerning the question of material continuity, no sensible fact can be adduced as a proof of the continuity of matter. Now, the impressions made on our senses cannot reveal anything about our question. For we know that bodies contain not only millions of pores, which are invisible to the naked eye, but also millions of movable and separate particles, which are so minute that no microscope can make them visible, and which, though so extremely minute, are composed of millions of other particles still more minute, which have independent movements, and therefore possess an independent existence. There are many species of animalcules (infusoria) so small that millions together would not equal the bulk of a grain of sand, and thousands might swim at once through the eye of a needle. These almost infinitesimal animals are as well adapted to life as the largest beasts, and their movements display all the phenomena of life, sense, and instinct. They have nerves and muscles, organs of digestion and of propagation, liquids and solids of different kinds, etc. It is impossible to form a conception of the minute dimensions of these organic structures; and yet each separate organ of every animalcule is a compound of several organic substances, each in its turn comprising numberless atoms of carbon, oxygen, and hydrogen. It is plain from this and other examples that the actual magnitude of the ultimate molecules of any body is something completely beyond the reach of our senses to perceive or of our intellect to comprehend.[73] We must therefore concede that no impression received by our senses is calculated to make us perceive anything like a molecule or to give us a clue to its constitution. To say that molecules are so many pieces of continuous matter is therefore to assert what no sensible fact can ever reveal.
Moreover, we know of no sensible phenomenon which has any necessary connection with the continuity of matter. Physicists and chemists, in their scientific explanation of phenomena, have no need of assuming the existence of continuous matter, and acknowledge that there are no facts from which the theory of simple and unextended elements can be refuted. And the reason of this is clear; for the phenomena can be made the ground of experimental proofs only so far as they are perceived by our senses; and since our perception of them is confined within the narrow limits above described, it is impossible to draw from sensible phenomena any distinct conclusion regarding the constitution of molecules. Hence it is plain that no sensible fact exists which directly or indirectly proves the continuity of matter.
Secondly, we may ask, Can the intrinsic extension and continuity of matter be proved from the essence of material substance?
The answer must again be negative. For nothing can in any manner be involved in, or result from, the essence of material substance, unless it be required either by the matter, or by the substantial form, or by the relation and proportion which must exist between the form and the matter. But neither the matter, nor the substantial form, nor their mutual relation requires [pg 274] material continuity or material extension. Therefore the essence of material substance cannot supply us with any valid argument in favor of the extension and continuity of matter.
In this syllogism the major proposition needs no proof, as it is evident that material substance, like all other created things, essentially consists of act and potency; and it is known that its act is called the substantial form, while its potency is called the matter.[74] It is therefore manifest that, if anything has a necessary connection with the essence of material substance, it must be of such a nature as to be needed either by the matter or by the substantial form, or by both together.
The minor proposition can be demonstrated as follows: In the first place, continuous quantity is not needed by the matter, whether actuated or actuable. For, as actuable, the matter is a “mere potency” (pura potentia) which has yet to receive its “first actuality” (primum esse), as philosophers agree; and accordingly it has no actual quantity or continuous extension, nor is it potential with respect to it, as its potency regards only existence (primum esse), and evidently existence is not dimensive quantity. Hence the schoolmen unanimously maintain with Aristotle that the first matter has “no quiddity, no quality, and no quantity” (nec quid, nec quale, nec quantum)—a truth which we hope fully to explain in some future article. As actuated, the matter is nothing else than a substantial term susceptible of local motion; for we know from physics that material substance receives no other determination than to local movement, and for this reason, as we remarked in another place, it has been defined Ens mobile, or a movable thing. Now, a term, to be susceptible of local motion, needs no dimensions, as is evident. And therefore the matter, whether actuated or not, has nothing in its nature which requires continuous extension.
In the second place, material continuity is not required by the nature of the substantial form. This form may, in fact, be considered either as a principle of being or as a principle of operation. As a principle of being, it gives the first existence to its matter; and it is plain that to give the first existence is not to give bulk. Our adversaries teach that what gives bulk to the bodies is quantity; and yet, surely, they will not pretend that quantity is the substantial form. On the other hand, it is evident that to be and to have bulk are not the same thing; and since the substantial form merely causes the matter to be, it would be absurd to infer that it must also cause it to be extended. As a principle of operation, the form needs matter only as a centre from which its exertions are directed. Now, the direction [pg 275] of the exertion, as well as that of the movement, must be taken from a point to a point, not from a bulk to a bulk; and therefore the form, as a principle of operation, needs only one point of matter. Thus it is clear that no material extension is required to suit the wants of the substantial form.
In the third place, material extension is not required to make the matter proportionate to its substantial form. We shall see later that no form which requires a determinate quantity of mass can be a substantial form in the strict sense of the expression; at present it will suffice to keep in mind that the substantial form must give the first being to its matter, and that the matter is therefore perfectly proportioned to its substantial form by merely being in potency to receive its first being. Now, such a potency implies no extension; for if it did, the accident would precede the substance. Besides, the matter before its first actuation is a nonentity, and, as such, is incapable of any positive disposition, as we shall more fully explain in the sequel. But a determinate bulk would be a positive disposition. Hence the matter which receives its first actuation is proportionate to its form independently of material extension. We can therefore safely conclude that the essence of material substance supplies no proof whatever of the continuity of matter.
Thirdly, we ask, Can the continuity of matter be proved from mechanics?
Here also our answer must be negative. For the theorems of mechanics are each and all demonstrated quite independently of the question of material continuity. The old writers of mechanical works (or rather the old metaphysicians, from whom these writers borrowed their notion of matter) admitted the continuity of matter on two grounds: first, because they thought that nature abhorred a vacuum; and, secondly, because they rejected the actio in distans as impossible. But we have already shown that no action of matter upon matter is possible, except on the condition that the matter of the agent be distant from the matter of the patient; which implies that all the material particles, to act on their immediate neighbors, must be separately ubicated, with intervening vacuum. And thus the only reasons by which the ancients could plausibly support the continuity of matter have lost all weight in the light of modern mechanics.
Fourthly: Can the continuity of matter be inferred from geometrical considerations?
We reply that it cannot. For geometric quantity is not a quantity of matter, but a quantity of volume—that is, the quantity of space mensurable within certain limits. Hence it is evident that the continuity of the geometric quantity has nothing to do with the continuity of matter, and is not dependent on it, but wholly depends on the possibility of a continuous movement within the limits of the geometric space. In fact, we have in geometry three dimensions—length, breadth, and depth, which are simple lines. Now, a line is not conceived as made up of material points touching and continuing one another, but as the track of a point moving between certain limits; so that the continuity of the geometric dimensions is not grounded on any extension or continuation of material particles, but on the possibility of continuous movement, on which the continuity of time also depends. [pg 276] We must therefore remain satisfied that no geometrical consideration can lend the least support to the hypothesis of material continuity.
We have thus exhausted all the sources from which any à priori or à posteriori argument in favor of material continuity might have been drawn, if any had been possible; and the result of our investigation authorizes the conclusion that the hypothesis of continuous matter is both scientifically and philosophically gratuitous.
False reasonings in behalf of continuous matter.—But some philosophers, who are afraid that the denial of material continuity may subvert all the scholastic doctrines (to which they most laudably, but perhaps too exclusively, adhere in questions of natural science), contend that the existence of continuous matter can be established by good philosophical reasons. It is therefore our duty, before we proceed further, to acquaint our reader with such reasons, and with our answers to them.
The first reason is the following: Geometry is a real, not a chimerical, science; and therefore it has to deal with real bodies—not indeed inasmuch as they are substances, but inasmuch as they have a quantity which can be considered in the abstract. Hence we must admit that the geometric quantity is a quantity of matter considered in the abstract; and accordingly, if the geometric quantity is continuous and infinitely divisible, as no one doubts, the quantity of matter in the bodies must also be continuous and infinitely divisible.
We reply that bodies have two very different kinds of quantity—the quantity of the mass and the quantity of the volume—and that geometry deals indeed with the latter, but has nothing to do with the former. Hence the geometric quantity is a quantity of volume or bulk, not a quantity of matter; and therefore to argue that, because the geometric quantity is continuous and infinitely divisible, the same must be true of the quantity of matter, is to make an inexcusable confusion of matter with space. The argument might have some value, if the quantity of the volume could be measured by the quantity of the mass; but no one who has studied the first elements of physics can be ignorant that such is not the case. Equal masses are found under unequal volumes, and unequal masses under equal volumes. Volumes preserve the same geometric nature and the same geometric quantity, be they filled with matter or not. A cubic inch of platinum and a cubic inch of water contain different amounts of matter, since the former weighs twenty-one times as much as the latter; and yet they are geometrically equal. Geometry is not concerned with the density of bodies; and therefore geometrical quantities are altogether independent of the quantity of matter, and cannot be altered except by altering the relative position of the extreme terms between which their three dimensions are measured. These dimensions are not made up of matter, but are mere relations in space, with or without interjacent matter, representing, as we have already observed, the quantity of continuous movement which is possible between the correlated terms; and their continuity depends on the continuity of space, not of matter.
The author from whom we have taken this objection pretends also that the geometric quantity possesses no other attributes than those which belong to all quantity, and are [pg 277] essential to it; whence he concludes that whatever is predicated of geometric quantity must also be predicated of the quantity of matter. But the assumption is evidently false; for it is not of the essence of all quantity to be continuous as the geometric quantity, it being manifest that discrete quantity is a true quantity, although it has no continuity. The general notion of quantity extends to everything which admits of more or less; hence there is intensive quantity, extensive quantity, and numeric quantity. The first is measured by arbitrary degrees of intensity; the second is measured by arbitrary intervals of space and time; the third is measured by natural units—that is, by individual realities as they exist in nature. It is therefore absurd to pretend that whatever can be predicated of geometric quantity must be predicated of all kinds of quantity.
The second reason adduced in behalf of material continuity is as follows: To deny the continuity of matter is to destroy all real extension. For how can real extension arise from simple unextended points arranged in a certain manner, and acting upon one another? The notions of simplicity, order, and activity transcend the attributions of matter, and are applicable to all spiritual beings. If, then, extension could arise from simple unextended elements by their arrangement and actions, why could not angels, by meeting in a sufficient number and acting on one another, give rise to extension, and form, say, a watermelon?
This argument has no weight whatever; but, as it appeared not many years ago in a Catholic periodical of great reputation, we have thought it best to give it a place among other arguments of the same sort. Our answer is that to deny the continuity of matter is not to deny real extension, but only to maintain that no real extension is made up of continuous matter. And we are by no means embarrassed to explain “how real extension can arise from simple unextended points.” The thing is very plain. Two points, A and B, being given in space, the interval of space between them is a real interval, really determined by the real points A and B, and really determining the extension of the real movement possible between the same points. Such an interval is therefore a real extension. This is the way in which real extension arises from unextended points.
Nor can it be objected that nothing extended can be made up of unextended points. This is true, of course, but has nothing to do with the question. For we do not pretend that extension is made up by composition of points—which would be a very gross error—but we say that extension results from the simple position of real points in space, and that it results not in them, but between them. It is the mass of the body that is made up of its components; and thus the sum A + B represents a mass, not an extension. The geometric dimensions, on the contrary, consist entirely of relations between distinct points intercepting mensurable space. The distinct points are the terms of the relation, while the extent of the space mensurable between them by continuous movement is the formal reason of their relativity. And since this continuous movement may extend more or less, according as the terms are variously situated, hence the resulting relation has the nature of continuous [pg 278] quantity. This suffices to show that to deny the continuity of matter is not to destroy all real extension.
And now, what shall we say of those angels freely uniting to form a watermelon? It is hardly necessary to say that this bright idea is only a dream. There is no volume without dimensions, no dimension without distance, and no distance without terms distinctly ubicated in space and marking out the point where the distance begins, and the point where it ends. Now, nothing marks out a point in space but matter. Angels, as destitute of matter, mark no points in space, and accordingly cannot terminate distances nor give rise to dimensions. Had they matter, they would, like the simple elements, possess a formal ubication in space, and determine dimensions; but, owing to their spiritual nature, they transcend all local determinations, and have no formal ubication except in the intellectual sphere of their spiritual operation. It is therefore owing to their spirituality, and not to their simplicity, that they cannot form themselves into a volume. Lastly, we must not forget that the “angelic” watermelon should have not only volume, but mass also. Such a mass would, of course, be made up without matter. How a mass can be conceived without matter is a profound secret, which the author of the argument very prudently avoided to reveal. But let us come to another objection.
A third reason adduced in favor of continuous matter is that we cannot, without employing a vicious circle, account for the extension of bodies by the notion either of space, distance, or movement. For these notions already presuppose extension, and cannot be formed without a previous knowledge of what extension is. To think of space is, in fact, to think of extension. So also distance cannot be conceived except by imagining something extended, which lies, or can lie, between the distant terms. Hence, to avoid the vicious circle, it is necessary to trace the origin of our notion of extension to the matter we see in the bodies. And therefore our very notion of extension is a sufficient proof of the existence of continuous matter.
We reply that this reason is even less plausible than the preceding one. To form the abstract notion of extension, we must first directly perceive some extension in the concrete, in the same manner as we must perceive concrete humanity in individual men before we conceive humanity in the abstract. But in all sensible movements we directly perceive extension through space and time. Therefore from sensible movements, without a previous knowledge of extension, we can form the notion of extension in general. Is there any one who can find in this a vicious circle?
This answer might suffice. But we will further remark that the argument may be retorted against its author. For if we cannot conceive movement as extending in space without a previous knowledge of extension, how can we conceive matter as extending in space without a previous knowledge of extension? And how can we conceive matter as continuous without a previous knowledge of continuity, or time as enduring without a previous knowledge of duration? To these questions the author of the argument can give no satisfactory answer without solving his own objection. Space, distance, and [pg 279] movement, says he, involve extension; and therefore they cannot be known “without a previous knowledge of what extension is.” It is evident that this conclusion is illogical; for if space, distance, and movement imply extension, we cannot perceive space, distance, and movement without directly perceiving extension; and, since the direct perception of a thing does not require a previous knowledge of it, the logical conclusion should have been that, to perceive space, distance, and movement, no previous knowledge of extension is needed.
On the other hand, while our senses perceive the extension of continuous movement in space, they are not competent to perceive material continuity in natural bodies. Hence it is from movement, and not from matter, that our notion of continuous extension is derived. In fact, to form a conception of the dimensions of a body, we survey it by a continuous movement of our eyes from one end of it to the other. In this movement the eye glides over innumerable pores, by which the material particles of the body are separated. If our conception of the geometric extension of the body depended on the continuity of its matter, these pores, as not consisting of continuous matter, should all be thrown away in the measurement of the body. Why, then, do we consider them as contributing with their own dimensions to form the total dimensions of the body? Merely because the geometric dimensions are estimated by movement, and not by matter.
Nor is it in the least strange that we should know extension from movement, and not from matter. For no one can perceive extension between two terms, unless he measures by continuous movement the space intercepted between them. The local relation between two terms cannot, in fact, be perceived otherwise than by referring the one term to the other through space; hence no one ever perceives a distance between two given terms otherwise than by drawing, at least mentally, a line from the one to the other—that is, otherwise than by measuring by some movement the extent of the movement which can take place between the two given terms. And this is what the very word extension conveys. For this word is composed of the preposition ex, which connotes the term from which the movement begins, and of the verb tendere, which is a verb of motion. And thus everything shows that it is from motion, and not from continuous matter, that our first notion of extension proceeds.
A sharp opponent, however, might still object that before we can perceive any movement we need to perceive something movable—that is, visible matter. But no matter is visible unless it be extended. Therefore extension must be perceived in matter itself before we can perceive it in local movement.
But we answer, first, that although nothing can be perceived by our senses unless it be extended, nevertheless we can see extended things without perceiving their extension. Thus we see many stars as mere points in space, and yet we can perceive their movement from the east to the west. Hence, although matter is not visible unless it be extended, it does not follow that extension must be first perceived in matter itself.
Secondly, we answer that when we perceive the movable matter as extended, we do not judge of its [pg 280] extension by its movement, but by the movement which we ourselves have to make in going from one of its extremities to the other. This is the only way of perceiving extension in space. For how could we conceive anything as extended, if we could not see that it has parts outside of parts? And how could we pronounce that anything has parts outside of parts, if we did not see that between one part and another there is a possibility of local movement? On the other hand, as soon as we perceive the possibility of local movement between distinct parts, we have sufficient evidence of geometric extension. And thus we have no need of continuous matter in order to perceive the volume of bodies.
Before we dismiss this subject, we must add that the advocates of continuous matter, while fighting against us, shield themselves with two other arguments. If matter is not continuous, they say, bodies will consist of mere mathematical points acting at a distance; but actio in distans is the extreme of absurdity, and therefore bodies cannot consist of mathematical points. They also allege that nature abhors a vacuum, and therefore all space must be filled up with matter; which would be impossible, were not matter continuous. That nature abhors a vacuum was once considered a physical axiom; but, since science has destroyed the physical grounds on which the pretended axiom rested, metaphysics has in its turn been appealed to, that the time-honored dictum may not be consigned to complete oblivion. It has therefore been pretended that space without matter is a mere delusion, and consequently that to make extension dependent on empty intervals of space imagined to intervene between material points is to give a chimerical solution of the question of material extension.
The first of these two arguments we have fully answered in our last article, and we shall not again detain our readers with it. Let us notice, however, that when the elements of matter are called “mathematical” points, the sense is not that they are not physical, but only that those physical points are mathematically, or rigorously, unextended.
The second argument assumes that space void of matter is nothing. As we cannot enter here into a detailed examination of the nature of absolute space, we shall content ourselves with the following answer: 1st. All real relations require a real foundation. Real distances are real relations. Therefore real distances have a real foundation. But their foundation is nothing else than absolute space; and therefore absolute space is a reality. 2d. If empty space is nothing, then bodies were created in nothing, occupy nothing, and all spaces actually occupied are nothing. To say, as so many have said, that empty space is nothing, and that space occupied by matter is a reality, is to say that the absolute is nothing until it becomes relative—a proposition which is the main support of German pantheism, and which every man of sense must reject. 3d. Of two different recipients, the greater has a greater capacity independently of the matter which it may contain; for, whether it be filled with the rarest gas or with the densest metal, its capacity does not vary. It is therefore manifest that its capacity is not determined by the matter it contains, but only by the space intercepted between its [pg 281] limits. In the same manner the smaller recipient has less capacity, irrespective of the matter it may contain, and only in consequence of the space intercepted. If, therefore, space, prescinding from the matter occupying it, is nothing, the greater capacity will be a greater nothing, and the less capacity a less nothing. But greater and less imply quantity, and quantity is something. Therefore nothing will be something.
We hope we shall hereafter have a better opportunity of developing these and other considerations on space; but the little we have said is sufficient, we believe, to show that the assumption of the unreality of space unoccupied by matter is a philosophical absurdity.
We conclude that the existence of continuous matter cannot be proved, and that those philosophers who still admit it cannot account for it by anything like a good argument. They can only shelter themselves behind the prejudices of their infancy, which they have been unable to discard, or behind the venerable authority of the ancients, who, though deserving our admiration in other respects, were led astray by the same popular prejudices, owing to their limited knowledge of natural science. We may be allowed to add that if the ancient philosophers are not to be blamed for admitting continuous matter, the same cannot be said of those among our contemporaries who, in the present state of science, are still satisfied with their authority on the subject.
Mysterious attributes of continuous matter.—Now, let us suppose that bodies, or their molecules, are made up of continuous matter, just as our opponents maintain; and let us see what must necessarily follow from such a gratuitous assumption. In the first place, it follows that a piece of continuous matter cannot be actuated by a single substantial act. This is easily proved.
For a single act gives a single actual being; which is inconsistent with the nature of continuous matter. Matter, to be continuous, must actually contain distinct parts, united indeed, but having distinct ubications in space. Now, with a single substantial act there cannot be distinct actual parts; for all actual distinction, according to the axiom of the schools, implies distinct acts: Actus est qui distinguit. Therefore continuous matter cannot be actuated by a single substantial act.
Again, a piece of continuous matter has dimensions, of which the beginning and the end must be quite distinct, the existence of the one not being the existence of the other. But it is impossible for two things which have a distinct existence to be under the same substantial act; for there cannot be two existences without two formal principles. Hence, if there were any continuous matter, the beginning and the end of its dimensions should be actuated by distinct acts; and the same would be true of any two distinct points throughout the same dimensions. Nor does it matter that the dimensions are supposed to be formed of one unbroken piece; for, before we conceive distinct parts, or terms, as forming the continuation of one another, we must admit the substance of such parts, as their continuation presupposes their being. Hence, however intimately the parts may be united, they always remain substantially distinct; which implies that each one of them must have its own substantial act.
Moreover, continuous extension is divisible. If, then, there is anywhere a piece of continuous matter, it may be divided into two, by God at least. But as division is not a magical operation, and does not give the first existence to the things which are divided, it is plain that the parts which after the division exist separately must have had their own distinct existence before the division; and, evidently, they could not have a distinct existence without being actuated by distinct substantial acts. What we say of these two parts applies to whatever other parts are obtainable by continuing the division. Whence it is manifest that continuous matter needs as many substantial acts as it has divisible parts.
The advocates of continuous matter try to decline this consequence by pretending that matter, so long as it is undivided, is one matter and needs only one form; but this form, according to them, is divisible; hence when the matter is divided, each part of the matter retains its own portion of the substantial form, and thus the same form which gives existence to the whole gives existence to the separate parts. This is, however, a mere subterfuge; for the undivided matter is indeed one accidentally, inasmuch as it has no division of parts; but it is not one substantially, because it has distinction of parts. This distinction exists before the division is made, and we have already seen that no actual distinction is possible without distinct acts. And again, the hypothesis that substantial forms are divisible, is a ridiculous fiction, to say the least. For nothing is divisible which has no multiplicity of parts and consequently a multiplicity of acts. How, then, can a substantial act, which is a single act, be conceived as divisible?
They also argue that as the soul, which is a simple form, actuates the whole matter of the body, so can the material form actuate continuous matter. This comparison may have some weight with those who confound the essential with the substantial forms, and believe that the soul gives the first being to the matter of the body. But the truth is that the substance of the soul is the essential form of the living organism, and not the substantial form giving the first being to matter. The organism and its matter must have their being in nature before being animated by the soul; each part of matter in the body has therefore its own distinct material form and its own distinct existence. The soul is a principle of life, and gives nothing but life.[75] Hence the aforesaid comparison is faulty, and leads to no conclusion.
In the second place it follows that no continuous matter can be styled a single substance.
For within the dimensions of continuous matter there must be as many distinct substantial acts as there are material points distinct from one another; it being clear that distinct points cannot have the same substantial actuation, and accordingly require distinct substantial acts and constitute distinct substances. Against this some will object that a mere point of matter is incapable of supporting the substantial form. But we have already shown that the substantial form is not supported by its matter, as the objection assumes, but only terminated to it, the matter being the substantial term, not the subject, of the substantial form.[76] On the [pg 283] other hand, it is manifest that a form naturally destined to act in a sphere, by actuating a single point of matter, actuates just as much matter as its nature requires. For it is from a single point, not from many, that the action must be directed. Hence nothing more than a point of matter is required to terminate the substantial form and to constitute a perfect substance. Additional proofs of this truth will be found in our next article, where we shall rigorously demonstrate the impossibility of continuous matter. Meanwhile, nothing withstands our conclusion that there must be as many distinct substances in continuous matter as there are distinct points within its dimensions.
In the third place, it follows that this multitude of distinct substances is not merely potential, but actual.
This conclusion is very clear. For every multitude of actual parts is an actual multitude, or, as they say, a multitude in act. But in continuous matter all the parts are actual, although they are not actually separated. Therefore the multitude of such parts is an actual multitude.
The upholders of continuous matter do not admit that this multitude is actual; they contend that it is only potential. For were they to concede that it is actual, they would be compelled to admit either that it is actually finite, or that it is actually infinite. Now, they cannot say that it is actually finite, because this would be against the well-known nature of continuum, which admits of an endless division, and therefore contains a multitude of parts which has no end. On the other hand, they cannot say that it is actually infinite; because, even admitting the absolute possibility of a multitude actually infinite, it would still be absurd to assert that such is the case with a piece of matter having finite dimensions. Indeed, Leibnitz and Descartes did not hesitate to teach this latter absurdity; but they could not make it fashionable, and were soon abandoned even by their own disciples. Thus the difficulty remained; and philosophers, being unable to solve it, tried to decline it by denying that there can be in the continuum an actual multitude of parts. This was, in fact, the view of the old advocates of continuous matter, who uniformly admitted that the parts of an unbroken continuum are merely potential, and form a potential multitude. For, they say, the actual multitude results from actual division, and therefore has no existence in the undivided continuum.
This last view would be very good, if the continuum in question were successive—as is the case with movement and time, which are always in fieri, and exist only by infinitesimals in an infinitesimal present, or if the continuum in question were virtual, as is the case with any mensurable interval of space; for evidently in these continuums no actual multitude is to be found. But the case is quite different with continuous matter. For he who asserts the existence of continuous matter asserts the existence of a thing having parts formally distinct and simultaneous. He therefore affirms the actual existence of a formal multitude of distinct parts, or, in other terms, an actual multitude. To deny the actual multitude of the parts, on the plea that there is no actual division, is to take refuge in a miserable sophism, which consists in denying the substantial distinction of the parts on the ground that [pg 284] they are not divided, and in ignoring their actual being solely because they have not a certain special mode of being.
As to the axiom that “Number results from division,” two things are to be noticed. The first is that the term “division” here means mensuration, not separation. Thus we divide the day into twenty-four hours, without discontinuing time for all that; and in like manner we divide the length of a journey into miles without discontinuing space. This shows that the numbers obtained by the division of the continuum are only artificially or virtually discrete, and that the continuum remains unbroken. The second is that a number is not merely a multitude, but a multitude measured by a certain unit, as S. Thomas aptly defines it: Numerus est multitudo mensurata per unum. Hence, if the unit of measure is arbitrary (as is the case with all continuous quantities), the same quantity can be expressed by different numbers, according as a different unit is employed in measuring it. But so long as the unit is not determined, the quantity cannot be expressed by any definite number. And if the unit employed be less than any given finite quantity, the thing which is measured will contain a multitude of such units greater than any given number. All such units exist in the thing measured prior to its mensuration; and as such units are actual and distinct, there can be no doubt that they constitute an actual multitude.
Some modern advocates of continuous matter have imagined another means of evading the difficulty. Tongiorgi admits extended atoms of continuous matter, but denies that their parts are actually distinct. As, however, he confesses that extension requires parts outside of parts (Cosmol., n. 143), we may ask him: Are not such parts actually distinct? Distinction is a negation of identity; and surely parts existing actually outside of one another are not actually identical. They are therefore actually distinct. Now, to use the very words of the author, “where there are distinct parts there is a plurality of units, that is, a multitude, although the parts which are distinct be united in a common term, as is the case with the parts of continuum”;[77] and therefore it is manifest that the continuous atom involves actual multitude.
Liberatore does not entirely deny the actual distinction of the parts in continuous matter, but maintains that the distinction is incomplete, and accordingly cannot give rise to an actual multitude. The parts of a continuum, says he, are united in a common term; hence they are incompletely distinct, and make no number, but are all one. They are outside of one another, yet in such a manner as to be also inside of one another. They do not subsist in themselves, but in the whole. The whole displays many parts, but it is one, and its parts are so indeterminate that they cannot be measured except by an arbitrary measure.[78]
This view scarcely deserves to be discussed, as the author himself owns that it makes continuous matter seem somewhat contradictory—Contradictoriis quodammodo notis subditur—though he attributes this kind of contradiction to the opposition which exists between the matter [pg 285] and the form—an explanation which we do not admit for reasons which we shall give in our next article. But as to the assertion that the parts of a continuum, on account of their having a common term, are only incompletely distinct, we can show at once that the author is much mistaken. Incomplete distinction is a distinction which does not completely exclude identity. Hence where there is incomplete distinction there is also incomplete identity. Now, not a shadow of identity is to be found between any two parts of continuum. Therefore any two parts of continuum are completely distinct. Thus each of the twenty-four hours into which we divide the day is completely distinct from every other, although the one is united with the other in a common term; for it is evident that the common term, having no extension, is no part of extension, and therefore cannot originate identity between any two parts of extension. To say that there is some identity, and therefore an incomplete distinction, between two extensions, because they have a common term which has no extension, is to pretend that the unextended has some identity with the extended; and this pretension is absurd. We conclude that, in spite of all the efforts of our opponents, it is manifest that continuous matter would be an actual multitude of distinct, though not separated, substances.
Lastly, it follows that actual continuous matter would be an actual infinite multitude of substances.
This conclusion is fully warranted by the infinite divisibility of the continuum. But here again the advocates of material continuity contend that this divisibility is potential, and can never be reduced to act; whence they infer that the multitude of the parts is not actual, but potential. We, however, repeat that if the division is potential, the divisible matter is certainly actual; and therefore the potency of an infinite division presupposes an infinite multitude of distinct terms actually existing in the divisible matter. And as we have already shown that each distinct term must have a distinct substantial act, we must conclude that the least piece of continuous matter would consist of an infinite actual multitude of substances—a consequence whose monstrosity needs no demonstration.
Hence we are not surprised to see that Goudin, one of the great champions of the old physics, considers continuous matter as “a philosophic mystery, about which reason teaches more than it can understand, and objects more than it can answer.”[79] He tries, however, to explain the mystery in some manner, by adding that “when the continuum is said to be infinitely divisible, this must be understood mathematically, not physically—that is, by considering the quantity as it is in itself, not as it is the property of a corporeal form. For in the process of the division we might finally reach a part so small that, if smaller, it would be insufficient to bear any natural form. Nevertheless, mathematically speaking, in that smallest physical part there would still be two halves, and in these halves other halves, and so on without end.”[80]
This explanation is taken from S. Thomas (I Phys., lect. I.), and shows philosophical thought; but, far from solving the difficulty, it rather proves that it is insoluble. For if, mathematically speaking, in the smallest bit of continuous matter there are still halves, and halves of halves, clearly there are in it distinct parts of matter, and therefore distinct forms actuating each of them distinctly, as the being of each part is not the being of any other part. It is therefore false that nothing smaller is sufficient to bear any natural form. And hence the difficulty is not solved. On the other hand, the necessity of resorting to purely mathematical (geometric) quantity clearly shows that it is the space inclosed in the volume of the body (of which alone geometry treats), and not the matter (of which geometry has nothing to say), that is infinitely divisible; and this amounts to a confession that continuous matter has no existence.
While making these remarks, we willingly acknowledge that S. Thomas and all the ancients who considered air, water, fire, and earth as the first elements of all things, were perfectly consistent in teaching that natural forms require a definite amount of matter. For by “natural forms” they meant those forms from which the specific properties of sensible things emanate. Now, all things that are sensible are materially compounded in a greater or less degree, and possess properties which cannot be ascribed to a single material point. So far, then, these ancient philosophers were right. But they should have considered that the required amount of matter ought to consist of distinct parts, having their own distinct being, and therefore their own distinct substantial acts. This would have led them to the conclusion that the natural form of air, water, etc., was not a form giving the first being to the material parts, but a form of natural composition giving the first being to the compound nature. But let us stop here for the present. We have shown that continuous matter cannot be proved to exist, and is, at best, a “philosophic mystery.” In our next article we shall go a step further, and prove that material continuity is a metaphysical impossibility.
To Be Continued.