"Experience never gives us an example of an isolated system; on the contrary, every system is a part of higher systems. The inner relations of its stability are not conditioned by its own parts only, but also, more or less, by those of other systems, so that the destruction of one part-system is always only in the direction towards the stability of a higher, ultimately of the highest, system; that is, of the system of the universe."

"Thus the teleological principle coincides with the principle of the Tendency to Stability, and at the same time the latter constitutes the link between the former and the law of Causality. Though, in truth, this manner of looking at the matter signifies a generalization of the concept of 'end,' since it defines all stable conditions as ends. The view is justified, however, by the fact that the greatest possible physical satisfaction—for us, the criterion of teleology—is always bound up with the longest possible preservation or slow change of a stable organic condition. The physical Tendency to Stability 'bears with it a psychical tendency to the attainment and conservation of just those conditions' towards which the physical tendency is directed."

Of the fact that Lange "feels the lack of the proof of this 'Tendency to Stability,'" Dr. Petzoldt says: "But how is there a need of proof here? To prove is to refer back to known facts. But what is there in Fechner's remarks that stands in need of such a reference? They simply draw our attention to the result of evolution as a state which bears, in itself, the guarantee of some continuance. Can any one contest this? Is there anything further to prove? It is said that Gauss once remarked that Lagrange's equations of motion are not proved, but only historically stated. The case is exactly the same here. The fact is attested, merely, that evolution ends in a stable condition; and herein lies the pith and the great merit of the theory of the Tendency to Stability."

Dr. Petzoldt criticises, among other things, especially Fechner's concept of approximate stability, in that no distinction is made by the author between three different cases. The first case comprises forms of motion in which periodicity is only approximate, but in which, nevertheless, no retrogression in stability takes place; this case is illustrated by our solar system. The second case comprises forms of motion in which the stability increases up to a certain point, but beyond this, despite relative constancy in outer conditions, decreases again until complete destruction of the system supervenes; an illustration of this form of motion is found in all organisms. The third case comprises forms of motion which we cannot concede to be stable. "For, if we ascribe periodic motion to pendula and musical strings which vibrate in a resisting medium, this is nevertheless a periodicity, which continually changes in the same sense, and we certainly cannot say that pendula and strings approach, in a resisting medium, a condition of absolute, through a condition of approximate, stability. We recognize in these vibrations, decreasing in amplitude, merely unstable changes which tend toward a final stable condition,—namely that of rest."

The author finds a further ground of criticism in Fechner's assertion that organisms are entirely dependent upon the periodicity of their functions. Only a part of such functions are periodic. Periodicity is not conceivable without stability, but stability is conceivable without periodicity.

In the process of evolution towards a stable form of movement, Dr. Petzoldt recognizes briefly two factors, "Tendency and Competition."[102] Tendency is defined, in general, as the direction, actual or potential, of material parts or of mental or physical function; competition, as the conflict of tendencies, from which a tendency of a higher order results. "The concept of Competition is, like that of Tendency, to be taken in a general significance. A number of forces which act upon a single point compete. Different mental images, observations, concepts, laws, come into competition, from which result concepts and laws of lower and higher orders. The struggle for existence is only a special case of competition. Though this often ends with the immediate or gradual destruction of systems entering upon it, nevertheless only a middle worth between all the competing tendencies can be ascribed to the resultant. Even the conqueror is, after the struggle, other than what he was before it; a part of the tendency destroyed by him lives on in him, has combined with his original tendency to a resultant. Tendencies can as little disappear without compensation as can forces, whether the compensation consists in a strengthening or in a weakening of others, and the conservation of competing tendencies might be regarded as a further qualitative addition to the law of the conservation of force. Hence, in the examination of the effects of the struggle for existence, the like claim of all tendencies taking part in it is not to be left out of consideration. Each makes its full force felt. But not all attain to competition; of the numerous tendencies bound up in one organism, only a few unite, in the single case, to a resultant, which has a direction towards a definite issue." The less the opposition of competing tendencies of concepts or laws, the less the deviation of the resultant from its components, and the less the change these have to undergo. The higher concepts and laws are, the less are the number of distinguishing marks which they take from all single conceptions; for they are the resultants of very strongly opposed components.[103]

Fechner's views are related to, and, to some extent, dependent upon, certain ones of Zöllner adduced in connection with a consideration of sun-spots.[104] Du Prel, who also acknowledges special indebtedness to Zöllner, attempted in his "Struggle for Existence in the Heavens" ("Der Kampf ums Dasein am Himmel") to demonstrate the fact of a struggle and selection among the heavenly bodies analogous to that claimed for life upon the earth. The title of the book was afterwards changed to "The History of the Evolution of the Universe,"[105] its scope having "grown far beyond the limit of the former title." Du Prel finds one of the chief advantages of an application of Darwinian ideas to astronomy in the fact that, unlike our earth, the heavens in their immensity afford us existing, or to our eye existing, examples of the various stages of their evolution, in nebular mist, comets, suns, fixed stars, planets, rings, and moons,—all subject to processes of development, which we may to some extent observe. In the first chapter of this book, Du Prel says: "The existing condition of the Cosmos with respect to all forms of the Purposeful[106]—whether we regard the realm of the organic or the inorganic—can be looked upon only as an attained, moving equilibrium of forces. Immanent in Nature lies the capacity to develop from chaotic conditions to teleologic forms; for, in the ceaseless play of forces, all other than such combinations are by their nature given over to destruction, while it lies, on the contrary, in the essence of all purposeful combinations to be preserved. In every system of mechanical forces an adjustment of the same must finally be arrived at through the removal of all immanent oppositions." "It is impossible for nature to remain in chaotic conditions." "Every system of forces tends to a state of equilibrium. This is as true of the conflict of images in a human brain, from whose mutual accommodation the resultant of a unified theory of the universe arises, as of oppositions in the social organism, of the conditions of power and civilization of neighboring peoples, of the meteorologic states of the earth, of the mechanical forces of a solar system, or the atoms of a cosmic mist. Every war of the elements ends with an adjustment of ideal justice, for every 'moment' of force has influence proportioned to its power and the duration of its activity."[107]

There is one portion of Fechner's theory as above stated (its metaphysical phases being beyond the scope of the present chapter have not been touched upon) that raises a question which may perhaps appear to have in itself no special significance, but which nevertheless opens up, by its implications, new fields of inquiry, and may possibly lead to further theory. The condition of stability which evolution in the universe as a whole gradually approaches but can never attain to in finite time is declared, namely, to be one not of rest, but of motion. A question might be raised, here, as to the definition of the "infinite time" asserted to be necessary to the attainment of such full stability,—whether the phrase be used in the mathematical or the philosophic sense; and the question would be found, I believe, to involve the unanswerable problem of the finite or infinite character of the universe in space. Of a universe conceived under the philosophic concept of spatial infinitude, obviously no final state as the result of evolution can be predicated, the evolution supposing a progress which, as involving infinite matter, cannot be accomplished in finite time. If we, however, conceive the universe as occupying finite space and undergoing continual evolution as a whole in the direction of equilibrium, it is a question whether the end must not be attained in finite time. For a universe conceived as finite, however immense, there must be a finite number, however great, representing the changes necessary to the attainment of final equilibrium; and if progress in the direction of such equilibrium is of necessity continual, the final equilibrium must be attainable in finite time. The question of the nature of such a state of final, universal stability is bound up with the problem of motion through a perfect void, and of the possibility of the formation of such a void through the concentration of matter. Leaving out of consideration the problem in its metaphysical form, which concerns the possibility of conceiving inter-material space, it may be said that it is not now supposed that the heavenly bodies move through an absolute void; and the existence of any medium opposing resistance, however slight, is a condition rendering impossible the attainment of absolute stability of motion or a full stability which suffers no diminution and is, therefore, in effect, an absolute stability. It may be questioned whether the very nature of motion is not coincident with change, and this with action and reaction, or competition. Such a view would reduce evolution to a single ultimate principle, in place of Darwin's Variation and Selection through struggle, or Petzoldt's Tendency and Competition. We should have left, instead of these, only the final principle involved in moving matter considered in its ultimate parts. The metaphysical problem of the infinite divisibility of matter need not here concern us; the ultimate parts of an organism could not be, however, its organs as Lewes defined them, but rather, from a positive standpoint, the ultimate units recognized by science in cell and cell-parts. We may, indeed, since we know no beginning of motion, legitimately regard all tendency as itself resultant. Just as we cannot separate matter and motion, except by abstraction from reality, so, too, we cannot conceive of motion except as having definite direction; and thus we arrive, by a final analysis, at the ultimate philosophic principles of matter and its motion. I use these terms in no metaphysical sense, but merely as generic terms including under one head specific forms of material combination and the specific forms of motion of their wholes or parts.

The question of the character of a conceived state of final equilibrium may be approached from a somewhat different side, though the emphasis falls, as before, on the solidarity of the universe and the nature of motion as change. We may, for instance, regard the earth as an isolated system whose isolation makes possible the continual progress of the evolution taking place on its surface. But this whole evolution is, on the other hand, dependent upon the light and heat of the sun. Again, the sun is undergoing an evolution whose continuous progress may be regarded as in a certain sense dependent upon isolation; but we see, on reflection, that this very process is the result of the cooling nature of the sun's surroundings, and that it is sending its motion in every direction through space. The moon, which has passed through both the evolution that the sun is undergoing and that which is in progress upon the earth, is now passing through another stage which the earth must reach in time by diffusion of its atmosphere, in case its destruction is not accomplished by some catastrophic event before the arrival of that distant period. Suns and planets, all the heavenly bodies, are sending their influence in every direction through the unfathomable depths of space; and just as the capacity of the earth to be warmed by the influence of the sun involves its reciprocal capacity to act as a cooling medium for that body, so the conditions throughout the universe must be regarded as everywhere interdependent and mutually implying one another. Thus we again arrive finally at a universal action and reaction among the parts of the universe, all motion implying change of the direction of motion. Or, since we may and are, in fact, obliged to regard every direction or form of motion as a resultant,—for of motion as of matter we know no absolute beginning,—even this simple assumption may supply us with the conclusion which we have reached in a more roundabout way. We may regard motion in any direction as counterbalanced by a resistance in every other direction sufficient to produce it in this one; in other words, motion takes place at every instant, in the direction of least resistance, even though this direction may represent, in the next instant, through the action of new "moments" of force, the greatest resistance. Any direction as well as any change of direction implies, then, resistance; resistance is equivalent to the interference of force, or, in other words, to competition; and competition may, at any moment, become catastrophe. The difference between competition and catastrophe is one merely of degree, or rather it is a subjective difference depending upon the point of view of the observer. In other words, all that we can testify to is a certain periodicity of motion, all motion meeting with resistance, the accumulation of which finally induces motion in another sense. Larger periodicities are made up of smaller periodicities, and, according to the point of view taken, any period of such motion may be regarded as an evolution, that which Fechner terms "full" stability being only the maximum towards which motion during that period tends. Absolute stability can be conceived only as perfect rest, whether we conceive it as merely an abstraction, its realization as rendered impossible by the conservation of energy, or whether we conceive it as possible in a universe regarded as finite; an absolute stability of motion is a self-contradiction, and a full stability which knows no retrogression is equally a self-contradiction. Periodicity is, then, all into which the Tendency to Stability resolves itself for nature as we know it.

We perceive, in the actual universe, the fact of a certain imperfect periodicity. This wave form of movement in great and little plays, as Spencer has shown far more elaborately than Fechner, a large part in the universe.