Prof. Paul du Bois-Reymond is not only as powerful and at the same time as subtle a thinker as his more famous brother Emil du Bois-Reymond, but he also agrees with the latter's philosophical attitude. Both are agnostics and both represent an unusually profound and scientifically elaborate agnosticism. They have become agnostics because they have arrived at results which, to their mind, present an insolvable problem. Prof. Paul du Bois-Reymond does not despair of a final solution of the problem of life, which according to Emil du Bois-Reymond decidedly belongs to "the seven world-riddles," but he considers gravitation as incomprehensible. The purpose of all our attempts to explain phenomena is to limit the incomprehensible to the smallest space possible and to reduce it to the simplest expression (p. 13). Comprehension, according to Paul du Bois-Reymond, can be attained by three methods, (1) the empirical, (2) the mechanical, and (3) the meta-mechanical. The empirical is inductive, the mechanical is deductive, and the meta-mechanical attacks those problems which are at the bottom of all our fundamental conceptions. The meta-mechanical tendency of science is not satisfied with the results of the empirical and mechanical investigations; it attempts to conquer all the difficulties or at least to arrive at the limits of human comprehension. "Its province is to comprehend matter, how matter can have effect on other matter, how actio in distans can produce pressure or motion; it tries to understand the great concepts of time and space and whatever profound problems may now or during the further progress of science be proposed."
Having explained these preliminary views concerning the methods of comprehension, the author discusses the following topics: Is the Space-filling Substance Continuous or Atomistic? (Chap. iii).—Actio in Distans (Fernkraft) (Chap. iv).—Several Syntheses (Chap. v).—The Idealistic and the Empiristic World Conception (Chap. vi).—Atomism and Actio in Distans with Reference to the Absolute (Chap. vii).—Concerning World-Conceptions (Chap. viii). In the first of these chapters (viz. in Chap. iii. of the book) the author presents the difficulties which beset the theory of a continuous substance. At first sight it appears most plausible to conceive of that which fills space as something constant and uninterrupted, but continuity of substance, our author declares, excludes a possible change of volume; compressibility and expansibility, properties which we predicate of any kind of substance, stand in a patent contradiction to a continuous filling of space. Substance therefore cannot be continuous, it must consist of a material which can be shifted, which is compressible, can be mixed, is liable to chemical changes, and allows imponderabilia to pass freely through; it is porous, or in other words it is permeated by space free from substance. Prof. Paul du Bois-Reymond conceives of substance as dust-like, viz. it consists of spatially distinct corpuscles, and he thinks that there must be supposed to be different kinds of dust. These dust-particles are in his synthesis the vehicles of any actio in distans, their properties are energy and inertia. Actio in distans, we are informed in the next chapter, cannot be explained by constructing a world-synthesis either out of absolutely rigid elements or out of absolutely elastic elements. Since we cannot derive a construction of actio in distans from mechanical concepts, we are led to the conclusion that we have reached here the limit of cognition. Indeed, the incomprehensible in all forces is and remains the actio in distans. All the hypotheses which try to explain the problem, will only defer it by introducing some medium which is to be the vehicle of the actio in distans, and the simplest method is after all to consider the atom as this vehicle. "The far-effective atom, conceived as a centre of activity, endowed with inertia, freely movable, is the simplest mechanism that can be used as the basis of our synthesis, and we call it briefly the far-effective (fernwirkende) atom" (p. 52).
It seems to us that Professor du Bois-Reymond has disposed of the idea of a continuous substance too easily, and that he is at the same time too easily satisfied with the shortcomings of his atomistic theory of a dust-like substance. We grant most willingly that the idea of an actio in distans is inconceivable, for an action can be effective only where it takes place, it can have no effect in other and more distant places. But action is never confined to a limited point: it always stretches over a field of some size. Suppose an action a takes place along the line b c, can we speak of b as being effective in c; or is it not rather a, i. e. the whole process, which takes place in b and in c. The sun's mass exercises an effect upon the earth; and yet they are about 80,000,000 miles distant. But let us use an instance which can become a more direct object of our observation. We have a pair of scales and put a weight on one of them. At once, simultaneously with the sinking of the weighted scale, the other scale rises. Is this not just as much an actio in distans as any other instance of gravity? In fact our astronomers compare the gravitating celestial bodies quite frequently to the action of a balance. It may be objected to this comparison that we see the beam of the scales, while there is no beam between the sun and the earth. If there is no beam, there must be a connection of some kind. If the earth and the sun are two disconnected bodies, we see no possibility for an explanation that the effects of the sun's mass are felt upon the earth. Is not after all the hypothesis of a continuous world-substance the easiest explanation of gravity? It seems to me that it is the only possible way of explaining what is commonly and perhaps awkwardly called actio in distans. The atomistic philosophers are bound to have the world a composition of innumerable particles of dust; they wish to construct the universe mechanically and this view of things appears for certain purposes very well adapted. Yet they cannot construct the world of isolated world-dust particles, they must have some glue or cement to fasten their atoms into a single whole that sticks together. Professor Du Bois-Reymond is consistent enough to see the impossibility of this construction. The cement of which the mortar of atomism consists is the inconceivable, unthinkable idea of an actio in distans.
Let us try to look at things from the other side. Our world-conception consists of the sum of all the divers things we are acquainted with; but daily experience teaches, that the world is not a composition of things or of atoms, the world is one inseparable whole, and the least change in one part affects the whole universe. Some one said, if I raise my finger the entire cosmos is shaken; and this we know is true, although the vibrations are too insignificant to be noticed by our dull senses. We speak of the earth and we speak of the sun, but in reality there is neither an isolated sun on the one side nor an isolated earth on the other, there is a whole and continuous world, one part of it is called sun and another part is called earth. Every action of every part of the world has its effects on all the other parts, and there is no action taking place in the world which in this sense is not an actio in distans. If we call the part played by the sun alone his action, then there is certainly actio in distans, and actio in distans would be the basis of the existence of the world as a cosmic whole. Yet we should remember that the sun does not perform any action alone for itself. The actions that take place in reality are relations among the inseparable parts of the universe. The sphere of every action extends, closely considered, over the whole world.
This view of things is not a construction of the world, it has not been invented for making a philosophical synthesis, it is a description of the world as we know it by experience. The description is imperfect and it presents many difficulties which will have to be formulated in problems. But we are confident that this descriptive method is the only procedure that promises success and will produce results in the future.
Attempts to reconstruct a world-system from its analysed elements have been made and, although we have not as yet reached a general consensus, we must consider these attempts as being at least in part successful. Suppose we call the simplest and most original state of substance ether and consider matter as ether-whirls of a certain kind. The ether must have a peculiar aggregate state of its own which in some respect is like a fluid, for its parts are continuous as well as interchangeable. An ether whirl, or an atom, being a condensation of ether, would naturally produce a tension which stands in some proportion to the condensed mass.
Let an india-rubber plate in a frame such as the designers use for altering the size of a picture represent the normal relation among the different parts of pure ether. Now put the finger-tips of both hands upon the india-rubber and contract them so as to condense in both places the india-rubber inside your finger-tips. Would not the tension between both condensations be increased? and suppose the two condensed spots were swimming freely in the india-rubber, they would in that case attract each other in a similar way as masses of matter gravitate toward each other.
This comparison is of course rude, but it may serve here as an illustration of how we can conceive of actio in distans without committing ourselves to the assumption that an action has its effects in a place where it does not operate. We should not venture to speak of the absolute rigidity or absolute elasticity of the world-substance until the phenomena which urge us to form our views about ether have been better classified and understood.
In the chapter on "Several Syntheses" the author discusses problems without coming to any conclusion. The synthesis of organised life may lead us to something which is quite as incomprehensible as actio in distans and cannot be reduced to it (p. 70). The riddles grow before our eyes, "above the fog of that which lies near us rises the imposing problem of the soul and towering above all other things appears the awful question of the consciousness of the ego." Prof. Du Bois-Reymond does not attempt any solution and proposes no reconciliation between the empirical and idealistic world-conceptions (which are contrasted in Chapter vi). This lack of arriving at a definite solution leads our author into mysticism, in which he indulges in the last chapters to a greater extent than we are inclined to allow a man of science. He speaks of a treble world in which we are shut up as if in a treble cage, (1) the world of immediate apprehensions, (2) the world of conceptions, and (3) the world of reality. The third world is "extra-phenomenal," it is the physical beyond our ego included. But "we are lacking the organ of reality" (p. 120) and "in the physical beyond nothing is impossible" (p. 122). It is strange that Prof. Du Bois-Reymond mentions Professor Kirchhoff's famous preface to his mechanics, in which he replaces the word "explain" by "describe" (p. 13). He also mentions Professor Helmholtz's term that phenomena (i. e. sensations) are symbols or signs of reality, Zeichen der Wirklichkeit (p. 121). But he overlooks entirely that the world-conception derived from these ideas can be developed in a positive world-conception that can satisfactorily reconcile idealism with empiricism. As soon as we know that cognition means description, we can dispense with meta-mechanics and need not join in the disheartening cry of the agnostic ignorabimus. The inscrutableness of reality, says our author, is almost a matter of course. Happily we forget it constantly, for the idea is one of the dreariest and the most weird (trostlosest and unheimlichst).
The whole result is negative, for we can predicate of reality nothing save that it is contained in a space and that there is motion taking place in it. But of what kind this space and the time depending on the motion are, and in what relation they stand to our conceptions of time and space we can say nothing.