But then we hear it exclaimed, “I cannot imagine force without matter; force must have a substratum by which, and an object on which, it acts, and just this is matter; force without matter is a non-thing.”—Let us also consider the à priori side of the speculation, after having perceived that on the empirical side the hypothesis of a substance has no warrant.
In the first place, it may be asserted that man is so organised that he may think everything which is not self-contradictory, i.e., that he may unite all conceptions given in words, provided that the meaning of the conceptions is clearly and precisely given to him, and the required combination contains no contradiction. The above assertion says: “Force cannot be imagined in independent real existence, but only in indissoluble union with matter.” Force is a clear conception, independent real existence likewise; accordingly every sound understanding must be able to unite the two notions, unless this combination contains an inherent contradiction. To prove the latter would doubtless be difficult, consequently the first part of the negative assertion is false. Properly understood, the only question is: Is the combination thinkable? not whether it really exists; otherwise the speculation would be no longer à priori.—The second positive part of the proposition asserts “that force is to be conceived in union with matter.” This part is just as false; one cannot think the union of force and matter, because one cannot think matter, for all conception is wanting to this word. Let us go through the different meanings which might possibly be ascribed to the word. The sensuous meaning is, it is true, quite definite: cause of felt resistance; but it is resolved into repulsive atomic forces, and can thus not be opposed to the notion Force. The notion Mass, which, in a perverse fashion, might be subsumed under the notion matter, has further above been decomposed into atomic force; of it, accordingly, the like holds good; its confusion with matter is, besides, only possible in respect of the crude sensuous meaning of matter by means of the notion of density. The physical notion of impenetrability has likewise been resolved into the infinitely great repulsive power of the ether-atoms at infinitely little distances; and, moreover, only appertains to the repulsive ether-atoms and to bodies, i.e., systems of dynamids, in virtue of the ether-atoms contained therein, but not to the attractive corporeal atoms, since it would not be apparent why, in fact, a perfect interpenetration and blending should not take place between two body-atoms which are not sundered by ether-atoms.
Finally, there still remains the meaning, “substratum of force;” however, I must confess, to my misfortune, that I am just as little able to think anything by substratum as by matter. Schelling says (“System of Transcend. Idealism,” pp. 317, 318; Werke, i. 3, pp. 529, 530): “Whoever says that he cannot imagine action without substratum, just confesses thereby that that putative substratum of thought is itself a mere product of his imagination; thus again is only his own thought, which he in this way is compelled to presuppose as independent ad infinitum. It is a mere illusion of the imagination that after one has taken away from an object the only predicates which it has, still something, one knows not what, remains of it. Thus, e.g., nobody will say impenetrability is implanted in matter, for impenetrability is matter itself” (which certainly is only half the truth). Substratum sometimes means the same thing as subject; one will, however, still not maintain that dead matter is something more subjective than force. Sometimes substratum means “the underlying,” i.e., a causal moment; of which there can be no question here. Usually it signifies prop, plainly in a sensuous meaning of the word; the crude sensuous idea must, however, here be excluded, and so our list ends. In short, we can think here nothing at all by substratum. But even if this were possible, the defenders of matter would always still owe the proof of the validity of their hypothesis of a substratum of force; for I cannot see the need of still supposing something behind force, as I maintain that one can quite well think force to be independently existing. It still remains: Matter is for science an empty word, for one can name no single quality which shall appertain to the notion thereby designated; it is simply an insignificant word, unless we are contented with the notion of a “system of forces,” for which we would rather put “matter.” Accordingly, it is settled that those who assert they cannot think force as independent can assuredly not think it in combination with matter.
Further, it is asserted, “Force must have an object to act upon, otherwise it cannot act.” This is unconditionally allowed; it is only disputed that this object must be matter. “The force of any atom has other atoms for its object;” that is all the physical scientific hypothesis requires; what that is in the atoms which serves as object, about that physical science does not trouble itself at all. We, however, have to show that we as yet know in the atom only force; that nothing stands in the way of regarding force as that in the atom which serves as object to the force of the other atom; that thus for this reason all occasion is wanting for setting up the new hypothesis of matter. In addition to this, there is still the analogy of the mental forces, which likewise have one another for objects, e.g., the idea acting as motive has the will as object, the will again has the idea as object, and so on. The pure reciprocity in the relation of atomic forces to one another should serve as a warning against the assumption of another object than force itself.
But now, let us really assume for one moment that the atoms consisted, beside force, also of matter, and consider what difficulties thereby arise for this idea in the mutual action of two atoms, A and B, and how the one unauthorised and superfluous assumption must always be supported by new and just as arbitrary ones. The force of A is to act upon the matter of B and vice versa, thereby the matter of A and B approach one another, whilst the forces stand out of all relation to one another, the converse of which one indeed would expect, since it is force which acts at a distance, but not matter, since force and force are of homogeneous, force and matter, however, of heterogeneous nature. The matter of A and B then approach in consequence of the momentary attraction of the mutual forces. What follows from this? Manifestly that the force and matter of every atom must be separated, for matter is caused by the foreign force to change its place, but not force. If, now, still the force and matter of every atom remain together, and nevertheless force cannot be necessitated by the force of the foreign atom directly to a change of place, it follows with logical necessity that the force of A must be compelled by the matter of A to change its place. Therewith, however, acting, consequently activity is ascribed to matter, whereas it is in general absolute passivity which must be represented in opposition to the activity of force. The mode and manner of this action is, however, perfectly incomprehensible, for if matter becomes actively acting it becomes indeed again force. Instead, then, of force A, as would be natural, attracting force B, it moves the matter of B, and the matter of B moves the force of B.
How force is to be “bound” to matter, which is the favourite expression of the partisans of matter, I must confess I cannot at all imagine. It would also be difficult for them to answer the following: Is one to imagine force bound to the centre of the material atom, or uniformly distributed over the whole matter of the same? For a material atom must surely have a certain size!
The former assumption certainly evades the difficulties connected with the other, but then force is no longer strictly bound to matter, but to a mathematical point, which yet cannot possibly be material, and which only accidentally coincides with the centre of a material ball. Then the action of matter on the movement of force is not at all comprehensible; rather the material ball is a fifth wheel in the waggon, since only the point, the ideal centre of the same, is in question. On the second assumption the difficulties are, however, far greater, for then indeed from every point of the material atom acts a part of the force, and each of these points has another distance from the atom which is acted upon. There is then the resultant to be taken of all these partial forces, whose point of attack now on action at finite distances by no means falls upon the centre of the material atomic sphere, but becomes
different according to each direction of action. In this speculation, however, one must manifestly imagine the atom decomposed into an infinite number of parts, each of which is burdened with an infinitesimal part of the force. Let one think such an atomic particle as small as one will, it is still always matter, and still no mathematical point; thus the union of the same with force can yet again only be comprehended by imagining the force uniformly distributed within the same. We are thus again constrained to infinite division, and so on, i.e., the material atom must be divided infinitely an infinite number of times, and in spite of it all it can never be comprehended how the force is distributed to matter, since one can absolutely only imagine the manifestation of simple force referred to the mathematical point, and this again is no longer material. (This the most considerable physicists and mathematicians, as Ampère, Cauchy, W. Weber, &c., have recognised, and therefore admitted that the atoms must be conceived as absolutely without extension.)
Let us, on the other hand, consider how the case stands without matter. We have nothing else to do but to retain the idea of atomic force, which the defenders of matter also possess, that it is the final unknown cause of motion, whose paths prolonged backwards cut one another in a mathematical point. Even he who assumes the atomic force to be equally distributed over the whole matter of the atom can, as said, not get rid of this mode of viewing the matter, for he must apprehend the total force of the atom as resultant of an infinite mass of punctual forces within the atom, however contradictory this requirement may be.
Further, the defenders of matter also assume the possibility of a relative change of place of this point, in which the directions of the manifestations of force intersect. We leave, provisionally, the question undiscussed whether force as such, apart from its manifestations, is something to which one may attribute spatiality or a place in space; if it has a place, it is in any case this point of intersection, and we will therefore provisionally call it the seat of force. Further, we assume that the atomic forces mutually serve as objects, i.e., that the mutual attraction of A and B produces local change at the seat of the forces in the sense of the latter approaching one another and separating on repulsion. I do not see where difficulties could be found here. According to the assumption of science, forces act at a distance and are homogeneous; why should they not act upon one another, if one indeed has hitherto granted an action of force on the matter heterogeneous to it and an action of dead matter on the force heterogeneous to it? We only need assumptions which were already there, strip away from these several as superfluous and unauthorised, and arrive notwithstanding not only just as well, but much more simply and more plausibly, at the goal, and avoid all the difficulties which appeared in the train of those useless assumptions. If we reckon, in addition, that those assumptions rest on an empty word without any thought, the gain proceeding from the simplification of the principles cannot be rated lightly.
There is, besides this, the crucial test, that our present rendering of Matter reconciles the two previously distinct parties of atomists and dynamists, since it has arisen from the conversion of Atomism into Dynamism, retains unimpaired all previous advantages of Atomism, which have assured it its exclusive authority in current physical science, purifies it of all the warranted reproaches of the dynamists, and gives birth to the fundamental principle of Dynamism, the denial of matter in a new, and more thorough fashion. We may therefore rightly call this conception Atomistic Dynamism. Dynamism in its previous form, apart from the want of an empirical proof, could never be accepted by physical science, because its formlessness made all calculation impossible. If forces are to act locally, they must determine their effects in space, and thus refer the same to definite starting-points. With this the point is directly given as starting-point of material force, wherefore Dynamism also, as soon as it tried to assume a more definite shape, was necessarily converted into Atomism, for it only then gained for the first time a tangible form, when it referred the play of opposite forces to force-individuals, i.e., atoms. This point of view was advocated by Leibniz in a tolerably pronounced fashion:—“Il n’y a que les points métaphysiques, ou de substance, qui soient exactes et réels.—Il n’y a que les atomes de substance, c’est à dire, les unités réelles et absolument déstituées de parties, qui soient les sources des actions et les premiers principes absolus de la composition de choses, et comme les derniers élémens de l’analyse des substances.” (“Système Nouveau de la Nature,” No. II.)—Leibniz altogether comprehends “substance” only as force, and force is to him the only and genuine substance. Comp. De Primœ Philosophiœ Emendatione et de Notione Substantiœ. That he does this, and with the notion of force implicitly insinuates the notion of the Will into substance, is his main philosophical advance beyond Spinoza. Undoubtedly physical science was then too much behindhand for him to put himself into active alliance with it. Schelling would have succeeded far better, who very decidely confesses to a dynamic Atomism; but on principle deduces his assertions a priori, wherefore also his mode of looking at the matter has not been able to obtain any influence over physical science. He says (Works, i. 3, p. 23):—
“What is indivisible cannot be matter, and, converselv, it must then lie beyond matter; but beyond matter is pure intensity, and this notion of pure intensity is expressed by the conception of action.”—(P. 22): “The original actions, however, are not themselves space, they cannot be regarded as part of matter. Our assertion may accordingly be called principle of Dynamic Atomism. For every original action is for us, just as the Atom for the corpuscular philosophers, truly individual; each is in itself whole and self-enclosed, and represents, as it were, a natural monad.” (P. 24): “In space, however, only its effect is representable; action itself is earlier than space, extensione prior.”—
If thus, on the one hand, Dynamism, even when it attained atomistic individualisation of force, was not able to prove itself to be something empirically authorised, on the other hand, at no time could Atomism defend itself against the reproach of logical contradiction, which was always brought against its material atoms. If, notwithstanding, physical science has inclined to it with ever-increasing confidence, this certainly proves a strong inner compulsion, with which, in spite of the acknowledged contradiction, the force of facts ever and again urged the natural philosophers to the atomistic explanation. Atomistic Dynamism satisfies all requirements by uniting the positive principles of both sides in itself.
If we once more briefly recapitulate these principles, they run thus: There are as many positive as negative, i.e., attractive and repulsive, forces. The directions of action of every force intersect in a mathematical point, which we call the seat of force. This seat of force is movable. Every force acts upon every other in the same way, no matter how it be designated. Positive force is called body-atom; negative, ether-atom. At a certain (molecular) distance the repulsion of an ether-atom and the attraction of a body-atom are equal to one another; but as the law of their change varies with their distance, between ether and corporeal atoms at lesser distances there prevails repulsion, at greater distances attraction. Corporeal atoms with interposed ether-atoms keeping them asunder unite to form the molecules of the chemical elements; these in the same way the molecules of the chemically compound bodies; these the material bodies themselves. Matter is thus a system of atomistic forces in a certain state of equilibrium. From these atomic forces in the most different combinations and reactions arise all the so-called forces of matter, as gravitation, weight, expansion, elasticity, crystallisation, electricity, galvanism, magnetism, chemical affinity, heat, light, &c.; nowhere, as long as we confine ourselves to the inorganic sphere, do we need to call to our aid any other than atomic forces.
We have accordingly seen that of the two materialistic principles, force and matter, the latter dissolves and disappears beneath our hands into the former; and now we know exactly what we have to understand by force, namely, an attracting or repelling, positively or negatively acting point of force. Now the notion of
force is made so precise that we are able directly to consider the same, without in our investigation having any cause to fear that we apprehend it otherwise than physical science and Materialism intends. Let us see what this conception involves.
The attracting atomic force strives to bring every other atom nearer to it; the result of this endeavour is the completion or realisation of the approach. We have thus in Force to distinguish the effort itself as pure act, and that which is aimed at as the goal, content, or object of the endeavour. The endeavour lies before the execution; so far as the execution is already posited, so far is the effort realised, is therefore no more; only the yet to be realised, that is, not yet realised effort is. Consequently, the resulting movement cannot be contained in the effort as reality, since their times are separate. Were this, however, not at all contained in the endeavour, there would be no reason why the latter should produce attraction, and not something else, e.g., repulsion; why it varies according to this and not according to that law with the distance. It would then be empty, purely formal endeavour, without definite goal or content; it must thus remain aimless and without content, and accordingly resultless, which contradicts experience. Experience rather shows that an atom does not accidentally now attract, now repel, but remains perfectly consistent and always equal to itself in the aim of its endeavour. Nothing more is wanting, then, than that the effort of the attractive force contain in itself the approximation and the law of change according to distance, i.e., the whole variable determination of its mode of action; and yet not contain in itself their reality.
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