The World as Will and Idea (Vol. 2 of 3)

(1) To No. 4 of Matter.

The essence of matter is acting, it is acting itself, in the abstract, thus acting in general apart from all difference of the kind of action: it is through and through causality. On this account it is itself, as regards its existence, not subject to the law of causality, and thus has neither come into being nor passes away, for otherwise the law of causality would be applied to itself. Since now causality is known to us a priori, the conception of matter, as the indestructible basis of all that exists, can so far take its place in the knowledge we possess a priori, inasmuch as it is only the realisation of an a priori form of our knowledge. For as soon as we see anything that acts or is causally efficient it presents itself eo ipso as material, and conversely anything material presents itself as necessarily active or causally efficient. They are in fact interchangeable conceptions. Therefore the word “actual” is used as synonymous with “material;” and also the Greek κατ᾽ ενεργειαν, in opposition to κατα δυναμιν, reveals the same source, for ενεργεια signifies action in general; so also with actu in opposition to potentia, and the English “actually” for “wirklich.” What is called space-occupation, or impenetrability, and regarded as the essential predicate of body (i.e. of what is material), is merely that kind of action which belongs to all bodies without exception, the mechanical. It is this universality alone, by virtue of which it belongs to the conception of body, and follows a priori from this conception, and therefore cannot be thought away from it without doing away with the conception itself—it is this, I say, that distinguishes it from any other kind of action, such as that of electricity or chemistry, or light or heat. Kant has very accurately analysed this space-occupation of the mechanical mode of activity into repulsive and attractive force, just as a given mechanical force is analysed into two others by means of the parallelogram of forces. But this is really only the thoughtful analysis of the phenomenon into its two constituent parts. The two forces in conjunction exhibit the body within its own limits, that is, in a definite volume, while the one alone would diffuse it into infinity, and the other alone would contract it to a point. Notwithstanding this reciprocal balancing or neutralisation, the body still acts upon other bodies which contest its space with the first force, repelling them, and with the other force, in gravitation, attracting all bodies in general. So that the two forces are not extinguished in their product, as, for instance, two equal forces acting in different directions, or +E and -E, or oxygen and hydrogen in water. That impenetrability and gravity really exactly coincide is shown by their empirical inseparableness, in that the one never appears without the other, although we can separate them in thought.

I must not, however, omit to mention that the doctrine of Kant referred to, which forms the fundamental thought of the second part of his “Metaphysical First Principles of Natural Science,” thus of the Dynamics, was distinctly and fully expounded before Kant by Priestley, in his excellent “Disquisitions on Matter and Spirit,” § 1 and 2, a book which appeared [pg 225] in 1777, and the second edition in 1782, while Kant's work was published in 1786. Unconscious recollection may certainly be assumed in the case of subsidiary thoughts, flashes of wit, comparisons, &c., but not in the case of the principal and fundamental thought. Shall we then believe that Kant silently appropriated such important thoughts of another man? and this from a book which at that time was new? Or that this book was unknown to him, and that the same thoughts sprang up in two minds within a short time? The explanation, also, which Kant gives, in the “Metaphysical First Principles of Natural Science” (first edition, p. 88; Rosenkranz's edition, p. 384), of the real difference between fluids and solids, is in substance already to be found in Kaspar Freidr. Wolff's “Theory of Generation,” Berlin 1764, p. 132. But what are we to say if we find Kant's most important and brilliant doctrine, that of the ideality of space and the merely phenomenal existence of the corporeal world, already expressed by Maupertuis thirty years earlier? This will be found more fully referred to in Frauenstädt's letters on my philosophy, Letter 14. Maupertuis expresses this paradoxical doctrine so decidedly, and yet without adducing any proof of it, that one must suppose that he also took it from somewhere else. It is very desirable that the matter should be further investigated, and as this would demand tiresome and extensive researches, some German Academy might very well make the question the subject of a prize essay. Now in the same relation as that in which Kant here stands to Priestley, and perhaps also to Kaspar Wolff, and Maupertuis or his predecessor, Laplace stands to Kant. For the principal and fundamental thought of Laplace's admirable and certainly correct theory of the origin of the planetary system, which is set forth in his “Exposition du Système du Monde,” liv. v. c. 2, was expressed by Kant nearly fifty years before, in 1755, in his “Naturgeschichte und Theorie des Himmels,” and more fully in 1763 in his “Einzig möglichen Beweisgrund des Daseyns Gottes,” ch. 7. Moreover, in the later work he gives us to understand that Lambert in his “Kosmologischen Briefen,” 1761, tacitly adopted that doctrine from him, and these letters at the same time also appeared in French (Lettres Cosmologiques sur la Constitution de l'Univers). We are therefore obliged to assume that Laplace knew that Kantian doctrine. Certainly he expounds the matter more thoroughly, strikingly, and fully, and at the same time more simply than Kant, as is natural from his more profound astronomical knowledge; yet in the main it is to be found clearly expressed in Kant, and on account of the importance of the matter, would alone have been sufficient to make his name immortal. It cannot but disturb us very much if we find minds of the first order under suspicion of dishonesty, which would be a scandal to those of the lowest order. For we feel that theft is even more inexcusable in a rich man than in a poor one. We dare not, however, be silent; for here we are posterity, and must be just, as we hope that posterity will some day be just to us. Therefore, as a third example, I will add to these cases, that the fundamental thoughts of the “Metamorphosis of Plants,” by Goethe, were already expressed by Kaspar Wolff in 1764 in his “Theory of Generation,” p. 148, 229, 243, &c. Indeed, is it otherwise with the system of gravitation? the discovery of which is on the Continent of Europe always ascribed to Newton, while in England the learned at least know very well that it belongs to Robert Hooke, who in the year 1666, in a “Communication to the Royal Society,” expounds it quite distinctly, although only as an hypothesis and without proof. The [pg 226] principal passage of this communication is quoted in Dugald Stewart's “Philosophy of the Human Mind,” and is probably taken from Robert Hooke's Posthumous Works. The history of the matter, and how Newton got into difficulty by it, is also to be found in the “Biographie Universelle,” article Newton. Hooke's priority is treated as an established fact in a short history of astronomy, Quarterly Review, August 1828. Further details on this subject are to be found in my “Parerga,” vol. ii., § 86 (second edition, § 88). The story of the fall of an apple is a fable as groundless as it is popular, and is quite without authority.

The quantity of a given matter can only be estimated in general according to its force, and its force can only be known in its expression. Now when we are considering matter only as regards its quantity, not its quality, this expression can only be mechanical, i.e., it can only consist in motion which it imparts to other matter. For only in motion does the force of matter become, so to speak, alive; hence the expression vis viva for the manifestation of force of matter in motion. Accordingly the only measure of the quantity of a given matter is the quantity of its motion, or its momentum. In this, however, if it is given, the quantity of matter still appears in conjunction [pg 227] and amalgamated with its other factor, velocity. Therefore if we want to know the quantity of matter (the mass) this other factor must be eliminated. Now the velocity is known directly; for it is S/T. But the other factor, which remains when this is eliminated, can always be known only relatively in comparison with other masses, which again can only be known themselves by means of the quantity of their motion, or their momentum, thus in their combination with velocity. We must therefore compare one quantity of motion with the other, and then subtract the velocity from both, in order to see how much each of them owed to its mass. This is done by weighing the masses against each other, in which that quantity of motion is compared which, in each of the two masses, calls forth the attractive power of the earth that acts upon both only in proportion to their quantity. Therefore there are two kinds of weighing. Either we impart to the two masses to be compared equal velocity, in order to find out which of the two now communicates motion to the other, thus itself has a greater quantity of motion, which, since the velocity is the same on both sides, is to be ascribed to the other factor of the quantity of motion or the momentum, thus to the mass (common balance). Or we weigh, by investigating how much more velocity the one mass must receive than the other has, in order to be equal to the latter in quantity of motion or momentum, and therefore allow no more motion to be communicated to itself by the other; for then in proportion as its velocity must exceed that of the other, its mass, i.e., the quantity of its matter, is less than that of the other (steelyard). This estimation of masses by weighing depends upon the favourable circumstance that the moving force, in itself, acts upon both quite equally, and each of the two is in a position to communicate to the other directly its surplus quantity of motion or momentum, so that it becomes visible.