Volume 20 — A Bit Of Modern Thought On Matter.

We have now accomplished the first portion of our task, by establishing on good philosophical and physical grounds the fundamental truths regarding the essence and the properties of material substance as such. We might, therefore, take up the second part of our treatise, and begin our investigation about the nature of the metaphysical constituents of matter and their necessary relations, in order to ascertain how far the principles of the scholastic doctrine on matter can nowadays be maintained consistently with the principles of natural science. But we think it necessary, before we enter into the study of such a difficult subject, to caution our readers against some productions of modern thinkers, whose speculations on the nature of material things confound all philosophy, and tend by their sophistry to popularize the most pernicious errors. The number of such productions is daily increasing, owing to the efforts of powerful societies, and the philosophical imbecility of the scientific press and of its patrons. The heap of intellectual rubbish thus accumulated, both in Europe and in America, is quite prodigious; to sweep it all away would be like purging the Augean stable—a task which some new Hercules may yet undertake. We shall confine ourselves to a small portion of that task, by scattering to the winds some plausible quibbles we have lately met with in an American scientific magazine.

J. B. Stallo is the author of a series of articles published in the Popular Science Monthly under the title “The Primary Concepts of Modern Physical Science.” He is a clever writer; but his conclusions, owing to a lack of sound philosophy, are not always correct. Some of them are altogether unfounded, others demonstrably false; and many of them, while attempting to revolutionize science, tend to foster downright scepticism. We shall single out a few of those propositions which clash with the common doctrines of modern physics no less than with the common principles of metaphysics; and we hope to show, by their refutation, the incomparable superiority of our old over his new philosophy.

Indestructibility of matter.—“The indestructibility of matter,” says the writer,181 “is an unquestionable truth. But in what sense, and upon what grounds, is this indestructibility predicated of matter? The unanimous answer of the atomists is: Experience teaches that all the changes to which matter is subject are but variations of form, and that amid these variations there is an unvarying constant—the mass or quantity of matter. The constancy of the mass is attested by the balance, which shows that neither fusion nor sublimation, neither generation nor corruption, can add to, or detract from, the weight of a body subjected to experiment. When a pound of carbon is burned, the balance demonstrates the continuous existence of this pound in the carbonic acid, which is the product of combustion, and from which the original weight of carbon may be recovered. [pg 787] The quantity of matter is measured by its weight, and this weight is unchangeable.”

So far all is right; but he continues: “Such is the fact familiar to every one, and its interpretation equally familiar. To test the correctness of this interpretation we may be permitted slightly to vary the method of verifying it. Instead of burning the pound of carbon, let us simply carry it to the summit of a mountain, or remove it to a lower latitude; is its weight still the same? Relatively it is; it will still balance the original counterpoise. But the absolute weight is no longer the same.... It is thus evident that the constancy, upon the observation of which the assertion of the indestructibility of matter is based, is simply the constancy of a relation, and that the ordinary statement of the fact is crude and inadequate. Indeed, while it is true that the weight of a body is a measure of its mass, this is but a single case of the more general fact that the masses of bodies are inversely as the velocities imparted to them by the action of the same force, or, more generally still, inversely as the accelerations produced in them by the same force. In the case of gravity, the forces of attraction are directly proportional to the masses, so that the action of the forces (weight) is the simplest measure of the relation between any two masses as such; but in any inquiry relating to the validity of the atomic theory, it is necessary to bear in mind that this weight is not the equivalent, or rather the presentation, of an absolute substantive entity in one of the bodies (the body weighed), but the mere expression of a relation between two bodies mutually attracting each other. And it is further necessary to remember that this weight may be indefinitely reduced, without any diminution in the mass of the body weighed, by a mere change of its position in reference to the body between which and the body weighed the relation subsists.”

The aim of the author is, as we shall see, to prove that “there are and can be no absolute constants of mass”; hence he endeavors at the very outset to shake our opposite conviction by showing that there is no absolute measure of masses. Such is the drift of the passage we have transcribed.

But we beg to remark that absolute quantities may be known to be absolute independently of any absolute measurement. Three kinds of quantity are conceivable: intensive quantity, which is measured by degrees; dimensive quantity, which is measured by distances; and numerical quantity, which is measured by discrete units. Of course dimensive quantity is altogether relative, inasmuch as it entirely consists of relations, and cannot be measured but by relative and arbitrary measures; but intensive quantity, though measured by arbitrary degrees, is altogether absolute, because it consists of a reality whose value is independent of correlative terms. And in the same manner numerical quantity is altogether absolute, because it consists of absolute units, by which it can be measured, absolutely speaking, though we may fail to reach such units, and are then obliged to measure it by some other standard. Now, the mass, or the quantity of matter in a body, is a numerical quantity; for it consists of a number of primitive units, independent of one another for their essence and for their existence, and therefore absolute in regard to their substantial being. Consequently, every mass of matter has an absolute value corresponding to the number of absolute [pg 788] units it contains; and thus every mass of matter is “an absolute constant of mass.” It is true that we have no means of ascertaining the absolute number of primitive units contained in a given mass; hence we are constrained to measure the quantity of matter by a relative measure—that is, by comparing it with an equal volume of another substance, whose density and weight we assume as the measure of other densities and weights. But does our ignorance of the absolute number of primitive units contained in a given mass interfere with their real existence? or, can our method of measuring change the nature of the thing measured?

We are told that “the weight of a body may be indefinitely reduced without any diminution in the mass of the body weighed.” Would not this show that, contrary to the author's opinion, the body weighed possesses “an absolute constant of mass”? We are told at the same time that “the weight of a body is a measure of its mass.” This cannot be true, unless, while the mass remains unchanged, the weight also remains unchanged. Hence the author's idea of carrying the pound of carbon to the summit of a mountain in order to diminish its weight, is inconsistent with the law of measurement, which forbids the employment of two weights and measures for measuring one and the same quantity.

The atomists measure the quantity of matter by its weight, because they know that every particle of matter is subject to gravitation, and therefore that the weights, all other things being equal, are proportionate to the number of primitive particles contained in the bodies. Thus, if a body contains a number, m, of primitive particles, and each of these particles is subject to the gravitation, g, while another body contains a number, m´, of primitive particles subject to the same gravitation, the ratio of the weights of the two bodies will be the same as the ratio of the two masses; for

mg : m´g : : m : m´;

and if the two bodies were carried to the summit of a mountain, where the gravitation is reduced to g´, the weights would indeed be changed, but their ratio would remain unaltered, and we would still have

mg´ : m´g´ : : m : m´.

Hence, whether we weigh two bodies in the valley or at the summit of the mountain, so long as we keep the same unit of gravitation for both, the ratio of their masses remains the same. This shows that the quantity of matter existing in those bodies implies “a constant of mass” independent of the intensity of gravitation, and that the ratio of the two masses is the ratio of two “absolute” quantities—that is, of two numbers of primitive material units.

It is not true, therefore, that the weight is not “the presentation of an absolute substantive entity,” as the author pretends. Weight implies mass and gravitation, and presents the one as subject to the other. Now, the mass is an “absolute substantive entity,” as we have shown. Nor is it true that weight is “the mere expression of a relation between two bodies mutually attracting each other,” as the author imagines. The pound of carbon is a pound not because of an attraction exercised by the carbon upon the earth, but merely because of the attraction exercised by the earth on the mass of the carbon. Were it otherwise, the mathematical expression of weight should contain, besides the mass of the body weighed and the action of gravity upon it, a third quantity representing the action [pg 789] of the body upon the earth, and the gravitation of the earth towards the body.

The writer proceeds: “Masses find their true and only measure in the action of forces, and the quantitative persistence of the effect of this action is the simple and accurate expression of the fact which is ordinarily described as the indestructibility of matter. It is obvious that this persistence is in no sense explained or accounted for by the atomic theory” (p. 708).

We admit that, owing to our inability to determine the absolute number of primitive elements in a body, we resort to the persistence of the weight in order to ascertain the persistence of a certain quantity of matter in the body. But this does not show that the action of forces is the “only measure” of masses. A mass is a number of material units; its true measure is one of such units, and it is only in order to determine the relative number of such units in different bodies that we have recourse to their weights. It is not the quantity of matter that follows the weight of the body, but it is the weight of the body that follows the quantity of matter; and therefore, although we determine the relative quantities of matter by the relation of their weights, it is not the weight that measures the quantity of matter, but it is the quantity of matter that measures the weight. In other terms, the persistence of the mass is merely known through the persistence of the weight, but the persistence of the weight is itself a consequence of the persistence of the mass. Hence the persistence of the mass is perfectly accounted for by the atomic theory, notwithstanding Mr. Stallo's contrary assertion.

He says: “The hypothesis of ultimate indestructible atoms is not a necessary implication of the persistence of weight, and can at best account for the indestructibility of matter if it can be shown that there is an absolute limit to the compressibility of matter—in other words, that there is an absolutely least volume for every determinate mass” (p. 708). Both parts of this proposition are false. The first is false, because the weight of a body is the result of the gravitation of all its particles; and, therefore, it cannot persist without the persistence of the gravitating particles. The second part also is false, because the persistence of the weight implies the persistence of the mass independently of all considerations concerning a limit of compressibility or an absolute minimum of volume. Hence, whatever the author may say to the contrary, it is quite certain of scientific certainty that there can be, and there is, in all bodies, “an absolute constant of mass.”

Atomic theory.—The writer objects to the atomic theory on the ground that it does not explain impenetrability, and that it misconceives the nature of reality. He begins by remarking that “the proposition, according to which a space occupied by one body cannot be occupied by another, implies the assumption that space is an absolute, self-measuring entity, and the further assumption that there is a least space which a given body will absolutely fill so as to exclude any other body” (p. 709). We think that the proposition implies nothing of the kind. The space occupied by one body cannot naturally be occupied by another, because all bodies are made up of molecules which at very small distances repel one another with actions of greater and greater intensities, thus preventing compenetration, while successfully struggling for the preservation of their own individuality. This the molecules can [pg 790] do, whether space can be filled or not, and whether space is a self-measuring entity or not. Hence the remark of the author has no foundation.

But he continues: “The atomic theory has become next to valueless as an explanation of the impenetrability of matter, since it has been pressed into the service of the undulatory theory of light, heat, etc., and assumed the form in which it is now held by the majority of physicists. According to this form of the theory, the atoms are either mere points, wholly without extension, or their dimensions are infinitely small as compared with the distances between them, whatever be the state of aggregation of the substances into which they enter. In this view, the resistance which a body, i.e., a system of atoms, offers to the intrusion of another body is due not to the rigidity or unchangeability of volume of the individual atoms, but to the relation between the attractive and repulsive forces with which they are supposed to be endowed. There are physicists holding this view, who are of opinion that the atomic constitution of matter is consistent with its compenetrability—among them M. Cauchy, who in his Sept Leçons de physique générale (ed. Moigno, Paris, 1868, p. 38), after defining atoms as material points without extension, uses this language: ‘Thus, this property of matter, which we call impenetrability, is explained when we consider the atoms as material points exerting on each other attractions and repulsions which vary with the distances that separate them.... From this it follows that, if it pleased the Author of nature simply to modify the laws according to which the atoms attract or repel each other, we might instantly see the hardest bodies penetrate each other, the smallest particles of matter occupy immense spaces, or the largest masses reduce themselves to the smallest volumes, the entire universe concentrating itself, as it were, in a single point’ ” (p. 710).

We think that the author's notion of the form in which the atomic theory is now held by physicists is not quite correct. The chemical atoms are now considered as dynamical systems of material points, so that the atomic theory is now scarcely distinguishable from the molecular theory. That such a theory “has become next to valueless as an explanation of the impenetrability of matter” is not true. Of course two primitive elements of matter, if attractive, would, according to the theory, as we understand it, pass through one another; as nothing can oppose their progress except repulsion, which is not to be thought of in the case of attractive elements. But the case is different with molecules; for every molecule of any special substance contains a number of repulsive elements, and possesses a repulsive envelope182 which resists most effectually all attempt at compenetration on the part of other molecules. Hence the impenetrability of bodies (not of matter, as the author says) is a simple result of the molecular constitution of bodies, as explained in the atomic theory of the modern chemists.

That the resistance which a body offers to the intrusion of another body is due “not to the rigidity or unchangeability of volume of individual atoms, but to the relation between the attractive and repulsive forces with which they are supposed to be endowed,” is an obvious truth. We do not see by what kind of reasoning the author can infer from it [pg 791] that “the atomic theory has become next to valueless as an explanation of impenetrability.” We rather maintain that the theory is correct, and that no other theory has yet been found which explains impenetrability without assuming much that philosophy condemns. As to M. Cauchy's views, we remark that, when he defines atoms as “material points without extension,” he does not speak of the chemical atoms, or equivalents, but of the primitive elements of which such atoms or equivalents are composed.

The author says: “The assumption of atoms of different specific gravities proves to be not only futile, but absurd. Its manifest theoretical ineptitude is found to mask the most fatal inconsistencies. According to the mechanical conception which underlies the whole atomic hypothesis, differences of weight are differences of density; and differences of density are differences of distance between the particles contained in a given space. Now, in the atom there is no multiplicity of particles and no void space; hence differences of density or weight are impossible in the case of atoms” (p. 715).

This conclusion would be quite inevitable, if it were true that the atom of the chemists contains no multiplicity of particles and no void space; but the truth is that chemical atoms are nothing but equivalents, or molecules—that is, dynamical systems of material points intercepting void space. Hence the author's argument has no foundation. The very fact that men of science unanimously agree in attributing to different atoms a different weight, should have warned Mr. Stallo that the word “atom” could not be considered by them as a simple material point.

The author in his second article (November, 1873) argues against the actio in distans. We have given his words in one of our own articles, where we undertook to show that actio in distans cannot be impugned with any good argument.183 The author, however, we are glad to see, honestly acknowledges that “the transfer of motion from one body to another by impact is no less incomprehensible than the actio in distans” (p. 96); which shows that, after having rejected the action at a distance, he is at a loss how to account for any communication or propagation of movement. A little later he quotes a passage of Faraday, which we have given in another place, and in which the English professor considers the atoms as consisting of a mere sphere of power, with a central point having no dimensions. Then he gives his own view of the subject in the following words:

“The true root of all these errors is a total misconception of the nature of reality. All the reality we know is not only spatially finite, but limited in all its aspects; its whole existence lies in relation and contrast, as I shall show more at length in the next article. We know nothing of force, except by its contrast with mass, or (what is the same thing) inertia; and conversely, as I have already pointed out in my first article, we know nothing of mass except by its relation to force. Mass, inertia (or, as it is sometimes, though inaccurately, called, matter per se), is indistinguishable from absolute nothingness; for matter reveals its presence, or evinces its reality, only by its action, its force, its tension, or motion. But, on the other hand, mere force is equally nothing; for, if we reduce the mass upon which a given force, however small, acts, until it vanishes—or, mathematically [pg 792] expressed, until it becomes infinitely small—the consequence is that the velocity of the resulting motion is infinitely great, and that the ‘thing’ (if under these circumstances a thing can still be spoken of) is at any given moment neither here nor there, but everywhere—that is, there is no real presence. It is impossible, therefore, to construct matter by a mere synthesis of forces.... The true formula of matter is mass × force, or inertia × force” (p. 103).

The author is greatly mistaken in assuming that those who consider the atoms (primitive elements) as centres of force totally misconceive the nature of reality. That Faraday, notwithstanding his saying that “the substance consists of the powers,” admits with the power the matter also, is evident from his very mention of the centre of the powers; for such a centre is nothing else than the matter, as we have proved above. He says, indeed, that the nucleus of the atom “vanishes”; but by “nucleus” he means the bulk or the continuous material extension of the atom. This bulk, says he, must vanish, inasmuch as the centre of the powers must be a mere unextended point. He therefore denies, not the matter, but only its intrinsic extension.

Mr. Stallo volunteers to show us “the true root” of all our errors. According to him, we totally misconceive the nature of reality. “All the reality we know,” he says, “is not only spatially finite, but limited in all its aspects.” About this we will not quarrel, for we admit that all created substances are limited; yet we would ask the author whether he thinks that the range of universal attraction has any known limit in space; and, if so, we would further ask where it is; for we admit our full ignorance of its existence. “We know nothing of force,” he continues, “except by its contrast with mass, or, what is the same thing, inertia.” Our readers know that mass and inertia are not the same thing; the mass is a quantity of matter, while inertia is the incapability of self-motion. A writer who can confound the two as identical is not competent to correct our errors and to teach us the nature of reality. As to the contrast of force with mass, we have no objection; yet, while speaking of the nature of things, we would prefer to contrast matter with form rather than force with mass. The term force applies to the production of phenomena, and is usually confounded with action and with movement, neither of which is a constituent of substance; whilst the term mass expresses any quantity of matter from a single element up to a mountain; and thus it does not exhibit with precision the matter due to the primitive material substance.

“Mass, or matter per se, is indistinguishable from absolute nothingness.” Of course, matter per se—that is, without form—cannot exist. In the same manner “mere force is equally nothing”—that is, the material form, which is the principle of action, has no separate existence without its matter. This every one admits, though not on the grounds suggested by Mr. Stallo. “If we reduce,” says he, “the mass upon which a given force, however small, acts, until it vanishes—or, mathematically expressed, until it becomes infinitely small—the consequence is that the velocity of the resulting motion is infinitely great.” We deny this consequence, as well as the supposition from which it is inferred. Masses are numbers of material elements, or units. When such units are reached, the division is at an [pg 793] end, because those primitive units are without dimensions. Hence the extreme limit of the reduction of masses is not an infinitesimal quantity of mass, as the author imagines, but an absolute finite unit; for this unit, when repeated a finite number of times, gives us a finite quantity of mass. But, even supposing that the hypothesis of the author might be entertained (and it must be entertained by all those who consider matter as materially continuous), his consequence would still be false. For, let there be a continuous atom having finite dimensions. If such an atom is acted on, say by gravity, it will acquire a finite velocity. Now, it is evident that, when the atom has a finite velocity, every infinitesimal portion of it will have a finite velocity. Therefore the action which produces a finite velocity in the finite mass of the atom, produces a finite velocity in the infinitesimal masses of which the atom is assumed to consist. The error of the author arises from his confounding quantity of movement with action. A quantity of movement is a product of a mass into its velocity; and evidently the product cannot remain constant, unless the velocity increases in the same ratio as the mass decreases. The action, on the contrary, is directly proportional to the mass; and therefore, in the author's hypothesis, the consequence should have been the very opposite of that which he enounces; that is, the velocity acquired by an infinitesimal mass would still be finite instead of infinitely great. But, as we have said, the hypothesis itself is inadmissible, because only continuous quantity can be reduced to infinitesimals, whilst masses are not continuous but discrete quantities.

That it is impossible “to construct matter by a mere synthesis of forces” is undeniable; but there was no need of arguing a point which no one contests. The author should rather have given us his ground for asserting that “the true formula of matter is mass multiplied by force.” This assertion can by no means be made good. All physicists know that mass multiplied by force represents nothing but a quantity of movement; and the author will not pretend, we presume, that matter is a quantity of movement. The true formula of matter is its essential definition; and it is not a mathematical but a metaphysical product, or rather a metaphysical ratio, as we have shown in another place. Material substance is matter actuated by its substantial form, and nothing else.

The author continues thus: “We now have before us in full view one of the fundamental fallacies of the atomic theory. This fallacy consists in the delusion that the conceptual constituents of matter can be grasped as separate and real entities. The corpuscular atomists take the element of inertia, and treat it as real by itself: while Boscovich, Faraday, and all those who define atoms as centres of force, seek to realize the corresponding element, force, as an entity by itself. In both cases elements of reality are mistaken for kinds of reality” (p. 103).

It is rather singular that a man who is so little at home in questions about matter should undertake to point out the fallacies and delusions of the best informed. Is it true that Boscovich, Faraday, and others of the same school, consider force as an entity by itself? And is it true that the corpuscular atomists treat the element of inertia as real by itself? There is much to be said against corpuscular atomists for other reasons, but they cannot surely be accused [pg 794] of maintaining that the element of inertia—that is, the mass of the atom—can exist separately without any inherent power, as they uniformly teach that their atoms are endowed with resisting powers. The accusation brought against Boscovich, Faraday, and others, is still more glaringly unjust. They do not seek to realize force “as an entity by itself”; on the contrary, when they define the atoms as centres of force, they manifestly teach that both the force and its centre are indispensable for the constitution of a primitive atom. And, since by the word force they mean the principle of activity (the form), and in the centre they recognize the principle of passivity (the matter), we cannot but conclude that the accusation has no ground, and that the fallacy and the delusion is on the side of Mr. Stallo himself.

Moreover, is it true that mass and force, or, to speak more accurately, the matter and the form, are nothing more than “the conceptual constituents” of material substance? This the author assumes as the base of his argumentation; yet it is plain that, if the constituents of a thing are only conceptual, the thing they constitute cannot be anything else than a conceptual being—that is, a being of reason. We must therefore either deny the reality of matter or concede that its constituents are more than conceptual. Could not the author perceive that, if mass is a mere concept, and force another mere concept, their alliance gives nothing but two concepts, and that the reality of the external world becomes a dream?

We live in times when men of a certain class presume to discuss metaphysical subjects without previous study and without a sufficient acquaintance with the first notions of metaphysics. One of these first notions is that all real being has real constituents. Such constituents, when known to us, are the object of our conceptions, and consequently they may become conceptual; but they do not cease to be real outside of our mind. Were we to conceive matter as separated from its form, or form as deprived of its matter, nothing real would correspond to our conception; for nowhere can real matter be found without a form, or a real form without its matter. Hence form without matter and matter without form are at best beings of reason. But when we conceive the matter as it is under its form, or the form as it is terminated to its matter, we evidently conceive the real constituents of material substance as they are in nature—that is, as metaphysical realities contained in the physical being. Does it follow that “elements of reality,” as the author objects, “are mistaken for kinds of reality”? By no means. The constituents of physical reality are themselves metaphysical realities, but they are not exactly two kinds of reality, because they belong both to the same essence which cannot be of two kinds. Hence the matter and the substantial form, or, in general, act and potency, notwithstanding their real metaphysical opposition and distinction, are one essence, one kind, and one being. But let us go back to our author.

In his third article (December, 1873) he says: “The ordinary mechanical explanation of the molecular states of matter, or states of aggregation, on the basis of the atomic theory, proceeds on the assumption that the molecular states are produced by the conflict of antagonistic central forces—molecular attraction and repulsion—the preponderance of the one or the other of which gives rise to the solid and gaseous forms, while their balance or equilibrium results in the [pg 795] liquid state. The utter futility of this explanation is apparent at a glance. Even waiving the considerations presented by Herbert Spencer (First Principles, p. 60 et seq.), that, in view of the necessary variation of the attractive and repulsive forces in the inverse ratio of the squares of the distances, the constituent atoms of a body, if they are in equilibrio at any particular distance, must be equally in equilibrio at all other distances, and that their density or state, therefore, must be invariable; and admitting that the increase or diminution of the repulsive force, heat, may render the preponderance of either force, and thus the change of density or state of aggregation, possible, what becomes of the liquid state as corresponding to the exact balance of these two forces in the absence of external coercion? The exact balance of the two opposing forces is a mere mathematical limit, which must be passed with the slightest preponderance of either force over the other. All bodies being subject to continual changes of temperature, the equilibrium can at best be but momentary; it must of necessity be of the most labile kind” (p. 223).

This argument against the atomic theory would be very good, if its premises were not deceptive. Mr. Stallo, unfortunately, relies too much on the terminology of physical writers, which is not always correct. Thus, it is not true that the solid form is the result of an actual preponderance of attraction between the molecules. If attraction prevailed, the molecules would not remain in their relative position, but would move in the direction of the attraction. The truth is that molecules, whether in the solid or in the liquid form, are in equilibrium of position; accordingly, neither attraction nor repulsion actually prevails between them.

Their position of equilibrium is determined by their own constitution, and may change; for the molecules admit of accidental changes in their constitution. Hence the distance of relative equilibrium is not necessarily constant, but changes with the change of state of each molecule. This shows that bodies, whether solid or liquid, can retain their solid or liquid form while subjected to considerable molecular changes, and that therefore neither the solid nor the liquid form is necessarily impaired by “the changes of temperature” or other molecular movements. The molecules of bodies attract each other when their distance is great, and repel each other when their distance has become very small; whence we immediately infer that there is for every kind of molecules a distance which marks the limit of their mutual attraction and repulsion, and that at such a distance the molecules must find their position of equilibrium. A body will be solid when, its molecules being in the position of relative equilibrium, from a small increase of their distance an attraction arises, which does not allow of the molecules being easily separated or arranged in a different order around one another. A body will be liquid when, its molecules being in the position of relative equilibrium, from a small increase of their distance a weak attraction arises, which allows of the molecules being easily separated or easily arranged, without separation, in a different manner around one another. A body will be expansive and fluid when its free molecules are at a distance sensibly less than that of relative equilibrium, and therefore repel each other, and are in need of exterior pressure to be kept at such a distance. But we must not forget that the distance of relative equilibrium varies with the [pg 796] intrinsic dynamical variation of the molecules, and that therefore “the exact balance of the two opposing forces is not a mere mathematical limit,” but is comprised between two mathematical limits determined by the amount of the variations of which each species of molecules is susceptible before settling into a different form.

Having thus disposed of the main argument by which the author wished to show “the utter futility” of the ordinary mechanical explanation of the molecular states of matter on the basis of the atomic theory, we may add a few words concerning Herbert Spencer's argument alluded to by the author. The law of actions inversely proportional to the squares of the distances is true for each primitive element of matter, but it is not applicable to molecules acting at molecular distances, as we have proved in another place.184 Hence Spencer's argument, which assumes the contrary, is entirely worthless. On the other hand, were the argument admissible, we do not see how the proposition, “The constituent atoms of a body, if they are in equilibrio at any particular distance, must be equally in equilibrio at all other distances,” can justify the conclusion that “their density or state must be invariable.” It seems to us that a change of molecular distances must entail a change of density; but, of course, we are behind our age.

Relativity of material realities.—“It has been a favorite tenet, not only of metaphysicians, but of physicists as well, that reality is cognizable only as absolute, permanent, and invariable, or, as the metaphysicians of the XVIth and XVIIth centuries expressed it, sub specie æterni et abroluti. This proposition,” Mr. Stallo continues, “like so many others which have served as pillars of imposing metaphysical structures, is the precise opposite of the truth” (p. 223). Do you understand, reader? Metaphysicians and physicists of all centuries count for nothing; they were blind, every one of them; but a great luminary has appeared at last, a Mr. J. B. Stallo, whose superior wisdom, if not philosophical infallibility, opens a new era of thought, and dispels the darkness which has been thickening around us up to the present day. Yet even the sun has spots; and Mr. Stallo will permit us to remark that his statement of the metaphysical doctrine of the ancients is not altogether correct. They did not teach “that reality is cognizable only as absolute, permanent, and invariable”; they well knew and taught that there were realities cognizable, both relative and changeable. Substance, of course, was considered by them, and it is still considered by us, as an absolute reality; but they never imagined that the essence of such a reality was cognizable except through its constituent principles as related to one another, and therefore through an intelligible relation. This relation, as intelligible, was considered necessary and invariable, but, as an actual reality in nature, was considered contingent and changeable; the intelligible essence of things was known sub specie æterni, but their existence was known sub specie contingentis. Now, on what ground does Mr. Stallo impugn this doctrine? How does he prove that it is “the precise opposite of truth”? Alas! we should be exceedingly simple were we to expect proofs. Progress consists nowadays of stout assertions on the part of the writer, and of a silly credulity on that of most readers. [pg 797] Hence our author, instead of proving what he had rashly asserted, gives us a strain of other assertions equally rash and ridiculously absurd.

He says: “All material reality is, in its nature, not absolute, but essentially relative. All material reality depends upon determination; and determination is essentially limitation, as even Spinoza well knew. A thing ‘in and by itself’ is an impossibility” (ibid.) Spinoza! a great authority indeed! But we should like to know how the proposition, “Determination is essentially limitation,” can lead to the conclusion that “a thing in itself and by itself is an impossibility.” To make a logical connection between the two propositions, it would be necessary to assume that “nothing finite can be in itself and by itself.” But the assumption is so foolish that even Spinoza, who based on it his revolting system of Pantheism, could never support it except by a false definition of substance, and by giving to the phrases “in itself” and “by itself” an extravagant interpretation, which proved, if not his malice and bad faith, at least his profound philosophical ignorance. Let Mr. Stallo consult any good philosophical treatise on this subject, and he will see how stolid a man must be to fall a victim to the gross sophistry of the Jewish dogmatizer.

What shall we say of the other assertion, “All material reality is, in its nature, not absolute, but essentially relative”? Can anything be relative without at the same time being absolute? Can relation exist without two absolute terms? Relativity connects one absolute thing with another; the things thus connected acquire a relative mode of being, but they do not for that lose their absolute being. Thus Mr. Stallo may be an American citizen without ceasing to be a man, though he cannot be a citizen without being endued with a relation not involved in his nature as roan. So, also, husband and wife are essentially relative; yet we hope the author will not say that the relative Husband annihilates the absolute Man, or that the relative Wife excludes the absolute Woman.

These remarks apply to all relations, whether merely accidental or founded in the essence of things. Pantheists imagine that creatures cannot have any absolute being, because their being is essentially dependent, and therefore relative. They should consider that a creature is a created being—that is, a being related to its Creator. Such a creature, inasmuch as it is a being, is; and inasmuch as it is related, connotes its Maker. Now, to be and to connote are not identical. The first means existence, the second dependence; the first is perfectly complete in the creature itself, the second is incomplete without a correlative term; and therefore the creature is in possession of absolute being, while it is endued with an essential relativity. Take away the absolute being; nothing will remain of which any relativity may be predicated.

Perhaps the author, when pronouncing that “all material reality is in its nature essentially relative,” alludes to the essential constitution of material realities, and to the essential relation of matter and form. If such is his meaning, the utmost he can claim is that the reality of the form is essentially connected with the matter, and the reality of the matter essentially connected with the form. This every one will concede; but no one will infer that therefore the reality which results from the conspiration of matter and form is not an absolute reality. For as the matter and the form are the principles of one essence, and as their mutual relativity [pg 798] connotes nothing extrinsic to the same essence, but finds in it its adequate consummation, it is evident that the resulting reality is intrinsically complete, and subsistent in its individuality. Hence this resulting reality is an absolute reality; and only as such can it become the subject of relativity, and acquire the denomination of relative.

Our author, entirely taken up by Spinoza's views, proceeds in the following strain: “All quality is relation; all action is reaction; all force is antagonism; all measure is a ratio between terms neither of which is absolute; every objectively real thing is a term in numberless series of mutual implications, and its reality outside of these series is utterly inconceivable. A material entity, absolute in any of its aspects, would be nothing less than a finite infinitude. There is no absolute material quality, no absolute material substance, no absolute physical unit, no absolutely simple physical entity, no absolute constant, no absolute standard either of quantity or quality, no absolute motion, no absolute rest, no absolute time, no absolute space.... There is and can be no physical real thing which is absolutely simple” (p. 225).

This string of blunders needs no refutation, as no reader who has a modicum of common sense can be deceived by what is evidently false. Yet, as to the assertion that “there is and can be no physical real thing which is absolutely simple,” it must be observed that there are two kinds of simplicity, as there are two kinds of composition. A being is physically simple when it is free from physical composition; whilst it is metaphysically simple, if it has no metaphysical components. Now, God alone is free from metaphysical as well as physical composition; and therefore God alone is absolutely simple. Hence, created beings, though physically simple, are always metaphysically compound.

What follows is a curious specimen of Mr. Stallo's philosophical resources. He says: “Leibnitz places at the head of his Monadology the principle that there must be simple substances, because there are compound substances. Necesse est, he says, dari substantias simplices, quia dantur compositæ. This enthymeme, though it has been long since exploded in metaphysics, is still regarded by many physicists as proof of the real existence of absolutely simple constituents of matter. Nevertheless, it is obvious that it is nothing but a vicious paralogism—a fallacy of the class known in logic as fallacies of the suppressed relative. The existence of a compound substance certainly proves the existence of component parts, which, relatively to this substance, are simple. But it proves nothing whatever as to the simplicity of these parts in themselves” (p. 226).

Our reader will ask when and how Leibnitz' enthymeme has been “exploded.” We shall inform him that it has not been exploded, though the attempt has often been made; because in the whole arsenal of metaphysics no powder could be found that would produce the explosion. The enthymeme, therefore, is as good and unanswerable now as it was in Leibnitz' time; and it will be as good and unanswerable hereafter, notwithstanding Mr. Stallo's efforts against it. He says that “it is nothing but a vicious paralogism”; but he himself, while endeavoring to prove this latter assertion, resorts to a paralogism (vicious, of course) which we may call “fallacy of the suppressed absolute.” The existence of a compound proves the existence of its component parts, as the author [pg 799] admits. These parts are either compound or simple. If simple, then there are simple substances. If compound, then they have components; and these parts are again either compound or simple. We must therefore either admit simple substances, or continue our analysis by further subdivisions of the compound substance without any chance of ever coming to an end. But if the analysis cannot come to an end, the compound has no first components; and thus it will be false that “the existence of a compound substance proves the existence of the component parts.” The fallacy of the author consists in stopping his analysis of the compound before he has reached the first components. If the parts he has reached are still compound substances, why does he not examine their composition and point out their components? For no other reason, we presume, than that he did not wish to meet with an absolute substantial unit, which he was sure to find at the end of the process. His argument is therefore nothing but a despicable fraud.

In his fourth article (January, 1874) Mr. Stallo remarks that “the recent doctrine of the correlation and mutual convertibility of the physical forces, as a part of the theory of the conservation of energy, has shaken, if not destroyed, the conception of a multiplicity of independent original forces” (p. 350). Of course, there are men whose convictions can be shaken, or even destroyed, by the sophistic generalizations of the modern school; but there are men also whose convictions rest on too solid a ground to be destroyed or shaken; and these latter have ere now challenged the abettors of the “recent doctrine” to clear up their case with something like logical precision—a thing which modern thinkers must have found impossible, since they have constantly ignored the challenge. We have proved elsewhere185 that “the mutual convertibility of physical forces,” as understood by the champions of the theory, confounds movement with action and the effects with their causes. The facts on which the theory is based are true; but the theory itself is false, for it attributes to the powers by which the phenomena are produced what exclusively belongs to “the phenomena”, besides deforming the nature of the phenomena themselves by denying the production and extinction of movement. It is plain that such a theory can have no weight in philosophy; and it is no less plain that no philosopher will, for the sake of the new theory, renounce his firm conviction concerning “the multiplicity of independent original forces.”

“I have endeavored,” says the author, “to show that there are no absolute constants of mass; that both the hypothesis of corpuscular atoms and that of centres of forces are growths of a confusion of the intellect, which mistakes conceptual elements of matter for real elements; that these elements—force and mass, or force and inertia—are not only inseparable, as is conceded by the more thoughtful among modern physicists, but that neither of these elements has any reality as such, each of them being simply the conceptual correlate of the other, and thus the condition both of its realization in thought and of its objectivation to sense” (p. 350).

As we have already discussed all the points which the author vainly endeavored to establish, we shall only remind the reader that the matter and the form have no separate existence; and therefore have no reality in nature, unless they are together. The [pg 800] author, therefore, is right when affirming that neither of them has any reality as such; but he is wrong in inferring that they have no reality as united. As action has no reality without passion, nor passion without action, so also matter has no reality without form, nor form without matter; but as action producing passion is real, so also is a form actuating matter; and as passion is no less real than the action whence it proceeds, so matter also is no less real than the form by which it is actuated. Both are, of course, only metaphysical realities.

The author says: “The mathematical treatment of mechanical problems, from the nature of the methods, necessitates the fiction that force and mass are separate and distinct terms” (p. 351). By no means. It is not the nature of the methods, but the nature of the things that compels the distinction of the two terms. Their distinction, therefore, is not a “fiction.” But the author's remark has no bearing on the question of the constitution of matter; for mechanical forces are not substantial forms.

He adds: “A material object is in every one of its aspects but one term of a relation; its whole being is a presupposition of correlates without.... Every change of a body, therefore, presupposes a corresponding change in its correlates. If the state of any material object could be changed without a corresponding change of state in other objects without, this object would, to that extent, become absolute. But this is utterly unthinkable, and therefore utterly impossible, as we have already seen.... Mechanically speaking, all force, properly so-called—i.e., all potential energy—is energy of position.... Whatever energy is spent in actual motion is gained in position; ... thus we are led to the principle of the conservation of energy” (p. 351).

This is a heap of absurdities. If a material object is the term of a relation, it is absolute in itself, as we have shown. Again, the change of a body presupposes only the exertion of active power, and not the change of another body, as the author imagines. That the absolute is unthinkable he has failed to prove. Lastly, mechanical force, properly so-called, is the product of a mass into its velocity, whilst “energy of position” is a myth.186

But the author says: “Force is a mere inference from the motion itself under the universal conditions of reality, and its measure, therefore, is simply the effect for which it is postulated as a cause; it has no other existence. The only reality of force and of its action is the correspondence between the physical phenomena in conformity to the principle of the essential relativity of all material existence. That force has no independent reality is so plain and obvious that it has been proposed by some thinkers to abolish the term force, like the term cause, altogether. However desirable this might be in some respects, it is impossible, for the reason that the concept force, when properly interpreted in terms of experience, is valid; and, if its name were abolished, it would instantly reappear under another name.... The reality of force is purely conceptual; ... it is not a distinct and individual tangible or intangible entity” (p. 354).

Here the author treats us to a luxury of contradictions. Force is “a mere inference from motion,” yet it causes motion; for it is active. Hence the causality is a mere inference of its effect. It is therefore the effect [pg 801] that gives existence to its cause, and the cause “has no other existence” than that which may be imbibed in the effect for which it is postulated. What, then, becomes of the “force, properly so-called”—that is, of the potential energy, or of the energy of position, which has no actual effect? Again, “the reality of force, is purely conceptual.” This means that the reality of force is unreal; which would just amount to saying that Mr. Stallo's intellect is unintelligent or that his writings are unwritten. Again, the “reality of force and of its action is the correspondence between the physical phenomena”; but, if the reality of force is merely conceptual, the correspondence between the physical phenomena must be merely conceptual; which would prove that the concept “force,” when properly interpreted in terms of experience, is not valid, though the author maintains the contrary. Moreover, what can the author mean by “the action of force”? Is this action real or unreal? If unreal, it is no action at all; and if real, it implies a real active power. We defy Mr. Stallo to conceive a real action of an unreal force. We are informed that “some thinkers” wish to abolish the term “force,” like the term “cause,” and we are told that this proves how plain and obvious it is that force has no independent reality. This, however, proves only that some so-called “thinkers” are either lunatics or knaves. After all, if force is purely conceptual, as the author pretends, its reality must be denied without any restriction. Why, then, does he deny merely that force has an “independent” reality? Has it any “dependent” reality if it is “purely conceptual”?

But we must come to an end. Mr. Stallo's conclusion is that “the very conception of force depends upon the relation between two terms at least,” and that therefore “a constant central force, as belonging to an individual atom in and by itself, is an impossibility” (p. 355). In this argument the term “force” is used equivocally. It stands for active power in the consequence, while it stands for action or for movement in the antecedent. Hence the conclusion is worthless. “I have shown,” says he, “that there are and can be no absolute constants of mass. And it is evident now that there are similarly no constant central forces belonging to, or inherent in, constants of mass as such” (p. 356). We say in our turn: No, Mr. Stallo, you have not shown what you imagine; and, if anything is evident, it is not that there are no constant central forces, but that philosophical questions cannot be solved without good logic and a clear knowledge of metaphysical principles.

[pg 802]