Popular Science Monthly/Volume 20/February 1882/The Seven World-Problems
WHEN, eight years ago, I undertook to address a public sitting of the Association of German Naturalists and Physicians, I hesitated for a long time before deciding to choose the "Limits of our Knowledge of Nature" as my subject. The impossibility, on the one hand, of comprehending the existence of matter and force, and, on the other hand, of explaining consciousness, even in its lowest degree, on a mechanical theory, seemed to me a truism. That even the simplest sensation can not be made comprehensible as the result of any arrangement or movement of matter, has long been recognized by eminent thinkers. Although I knew that false ideas on the last point had been widely diffused, I was almost ashamed to offer so stale a draught, and hoped to awaken interest only through the novelty of my arguments. The reception given my exposition showed me that I had mistaken the condition of the case. Treated coolly at first, my essay soon became the object of numerous criticisms, which seemed to come from a diversity of points of view—from cordial approbation to utter rejection and censure—and the word ignorabimus, in which the investigation culminated, became a kind of philosophical shibboleth.
Flattering as it was to me to see my exposition regarded as a Kantian fact, I must decline the honor, for nothing was contained in it of which any one might not have informed himself by a study of the older philosophical writers. But, since philosophy was perverted by Kant, its culture has taken on so esoteric a character; it has, so far, unlearned the language of common sense and intelligent thought, and evaded the questions that move unprejudiced youth most deeply, or treated them from a superior altitude as officious speculations; and has, finally, held so hostile an attitude toward the new world-power, natural science, that it is not surprising that even the recollection of the earlier achievements of philosophy should have been lost. This is, indeed, partly due to the circumstance that the newer philosophy stands in a negative or in no clear relation to positive religion, and avoids expressing itself on certain questions; so that it has happened that the most pregnant problems in metaphysics have not been set forth and discussed by philosophy, at least not in a language acceptable to scientific men, since the middle of the last century. This may be one of the reasons why philosophy is often despised as objectless and useless, and why, when natural science and philosophy touch at so many points, such ignorance and lack of preliminary ideas are shown in connection with actual achievements.
I was reproached, on the other side, because I had assigned impassable boundaries to the human powers of knowledge, by men who could not understand why consciousness could not be made comprehensible in the same way as the development of heat by chemical action, or the excitement of electricity in the galvanic circuit. Cobblers left their lasts and sneered at the humble confession of "Ignorabimus," by which "not-knowledge" was declared in permanency; and I was denounced as belonging to the Black Band by fanatics who should have known better, and who showed anew how nearly together despotism and extreme radicalism dwell. More temperate heads betrayed the weakness of their dialectics in that they could not grasp the difference between the view which I opposed, that consciousness can be explained upon a mechanical basis, and the view which I did not question, but supported with new arguments, that consciousness is bound to material antecedents.
David Friedrich Strauss, who had recently turned from theological studies to natural science, saw more sharply. It did not escape him that I had put myself in regard to mental processes at the point of view of the inductive philosopher, who does not separate the process from the substratum on which he learned to know the process, and who does not without sufficient motive think of the process as disconnected from the substratum.
Even he criticised in a remarkable way my declaration of the incomprehensibility of consciousness on a mechanical basis, saying: "There are confessedly three points in the ascending development of nature to which the appearance of the incomprehensible is especially attached. They are the three questions, How has the living arisen out of the lifeless, how the sensible out of the senseless, how the understanding out of the not-understanding? The author of the 'Limits of our Knowledge of Nature' holds the first of the three problems, A, to be solvable. He facilitates the solution of the third problem, C, that of intelligence and free-will, apparently by including it in the closest connection with the second, that of reason, as the highest degree of the consciousness already given, with sensation. The second problem, B, that of sensation, on the other hand, he holds to be unsolvable. I grant that one might more readily enlighten me, if he should say to me: 'A, that is life, is and must remain inexplainable; but that once given, sensation and thought follow of—themselves that is, by natural development'; or, if it were stated in the inverse sense, 'A and B may indeed be comprehended, but the understanding is strained at C, or self-consciousness.' Either of these views appears to me more acceptable than the one that the middle station only is impassable."
Strauss has not touched the marrow of my observation. I called astronomical knowledge of a material system such knowledge as we might have of the planetary system, if all the observations were accurate and all the difficulties of the theory overcome. If we had astronomical knowledge of what is going on in ever so obscure an organ of the animal or vegetable body, our demand for a causal agency would be as well satisfied, so far as the nature of our intellect permits with reference to that organ, as with reference to the planetary system; but, if we had astronomical knowledge of what occurs within the brain, we would still not be advanced a hair's breadth with reference to the origin of consciousness. In regard to these problems, Laplace and Leibnitz, whose minds were so immeasurably superior, yet similar to ours, were no wiser than we; and if Leibnitz had realized his fiction that he could compose a homunculus, atom by atom, molecule by molecule, he might, perhaps, make his creature think, but not comprehend how it thought.
The primary origin of life in itself has nothing to do with consciousness, but is a question only of the arrangement of atoms and molecules and of the production of certain movements. Consequently, not only is astronomical knowledge thinkable of what we call original production, spontaneous or equivocal generation, or heterogeny, but it would satisfy our demand for a causal agency for the primary origin of life as well as in regard to the motions of the heavenly bodies. This is why, speaking with Strauss, "in the ascending development of nature" the gap in our apprehension does not open at the point A, but at B. I have not maintained that, sensation being given, every higher stage of mental development becomes comprehensible; that problem C is made solvable without further steps. I attached weight to the incomprehensibility of the simplest sensations on mechanical grounds, only because the incomprehensibility of all the higher mental processes follows from it by an a fortiori argument.
The origin of life seems to have become veiled in a deeper obscurity since men have hoped with the aid of the microscope to see the living come from the dead in their laboratories. According to M. Pasteur's researches, heterogeny is underlaid by panspermy, and, where life was believed to originate, it has only been developed from germs that were already present. Yet those who will not adhere to a wholly childish view may be logically compelled to concede a mechanical origin of life. Hardly any one can now be found to advocate the doctrine of periods of creation by which the Almighty was supposed to have repeatedly destroyed his work to do it over again for better or worse, in the face of geological facts and the theory of descent. The believer in a final cause must admit that such a proceeding is little worthy of a creative Almighty. It is most highly becoming to him once by supernatural interference with the world's mechanism to call the simplest germ of life into being, and let further organic creation proceed from that. If this is conceded, it is permissible to ask if it is not still more worthy of the creative Almighty to avoid even that single intervention by means of established laws, and to endow matter from the beginning with the power of originating life under suitable conditions. There is no reason for denying this view, but with its acceptance the possibility of a mechanical origin of life is conceded, and we have only to consider whether the matter which can thus mechanically compose itself into a living condition always existed, or whether, as Leibnitz thought, it was created by God.
I conclude that astronomical knowledge of the brain would not make consciousness more comprehensible on a mechanical basis because it must be indifferent to a number of atoms of carbon, hydrogen, oxygen, nitrogen, etc., how they are situated or how they move, unless they already had individual consciousness; and this would not help to explain consciousness in general, or the aggregated consciousness of the brain.
I hold this conclusion to be fully convincing. Herr Haeckel, however, has advanced as a metaphysical axiom that every atom possesses an inherent quantity of force, and is in this sense "be-souled," and that without the acceptance of an "atom-soul" the commonest and most general phenomena of chemistry are inexplainable. "Pleasure and displeasure," he says, "desire and aversion, attraction and repulsion, must be common to all the atoms, for the movements of atoms that take place in the formation and decomposition of all chemical compounds are susceptible of explanation only if we ascribe feeling and will to them. . . . If the 'will' of man and the higher animals seems to be free in contrast with the ' fixed ' will of the atoms, that is a delusion provoked by the contrast between the extremely complicated voluntary movements of the former and the extremely simple voluntary movements of the latter." Quite in the spirit of the false philosophy from the same source that has been so pernicious to German science, Herr Haeckel goes on with the construction upon "unconscious recollection" of a certain "vivified" atom-complex that he calls "plastidule."
Thus does he disdain the path of inductive research shown us by La Mettrie, and sin against one of the first rules of philosophizing—"Entia non creanda sunt sine necessitate"; for what purpose does consciousness serve, what mechanism? And if the atoms feel, what need of organs of sense? He furthermore overlooks the difficulty that I have fully pointed out, of comprehending how the numerous "atom-souls" can give rise to the aggregated consciousness of the whole brain.
A more accomplished morphologist might he excused for not being able to distinguish the ideas of will and force, for misconceptions similar to this have been shown even by better-schooled men. Philosophers and physicists have attempted to explain the distant action of bodies upon each other through presumably empty space by means of a will dwelling within the atoms. A wonderful will, indeed, that must always belong to two!—that must will whether it wills or not, and that in the direct ratio of the product of the masses, and the inverse ratio of the square of the distance!—a will, the projected subject of which must move in a conic section—a will that reminds us of the faith that can move mountains, but which has never been taken account of in mechanics as a cause of motion.
At all events, the opposition that has been offered to my assertion of the incomprehensibility of consciousness on a mechanical theory, shows how mistaken is the idea of the later philosophy that that incomprehensibility is self-evident. It appears, rather, that all philosophizing upon the mind must begin with the statement of this point, and thus with one of my corresponding arguments; if mechanical consciousness were comprehensible, there would be, in the strict sense, no metaphysics.
A more recent effort to enlarge the barriers of knowledge and throw light upon the nature of matter proceeds from the Scottish mathematico-physical school, from Sir William Thomson and that Mr. Tait whose chauvinism renewed the dispute over Leibnitz's part in the discovery of the infinitesimal calculus, and who went so far as to call Leibnitz a thief, and to whom, therefore, the honor of being named in this hall does not properly belong. Sir William Thomson and Mr. Tait believe that certain important peculiarities that we must ascribe to atoms may be derived from the remarkable properties which Herr Helmholtz has discovered in the vortices of fluids. While it would be rash lightly to reject this theory because it may fall short on some points, it can be safely asserted that it is as little competent as any of the previous theories to reconcile the contradictions which our understanding encounters in its efforts to comprehend matter and force. It, moreover, acknowledges the second of the difficulties that oppose our conception of the world, by granting that the vortex-movement either has existed from eternity or has arisen through a supernatural impulse.
We may count and distinguish seven of these difficulties, of which I call those transcendental which appear insurmountable when we come to meet them in considering the ascending development of nature.
The first difficulty is the existence of matter and force, and is in itself transcendental.
The second difficulty is the origin of motion. We see motion arise and cease; we can conceive matter at rest, and motion appears to be something casual to it. It does not satisfy our demand for a causal agency to think of matter evenly distributed in illimitable space and at rest for endless time. Unless we admit a supernatural impulse, a sufficient occasion for the first motion is lacking. Or, if we imagine matter as in motion from eternity, we give up the elucidation of the point. I regard the difficulty as transcendent.
The third difficulty is the origin of life. As I have often said, I see no ground for considering this difficulty transcendent. When matter has once begun to move, worlds may originate; under suitable conditions, which we can as little imitate as we can those under which a multitude of inorganic processes take place, the peculiar condition of the dynamic balance of matter which we call life may also be produced. If we admit a supernatural act, one such act, creating the animated matter, is enough.
The fourth difficulty is offered by the apparently teleological arrangement of nature. Organic laws of formation can not work adaptively unless matter was created with adaptive purpose in the beginning; and they are inconsistent with the mechanical view of nature. This difficulty is, however, not absolutely transcendent, for Mr. Darwin has pointed out in his doctrine of natural selection a possible way of overcoming it, and of explaining the inner suitableness of organic creation to its purposes and its adaptation to inorganic conditions through a concatenation of circumstances operating by a kind of mechanism in connection with natural necessity.
I have already, on a similar occasion to the present, considered in this place the degree of probability that belongs to the theory of selection. "We might always," I said, "while we hold to this theory, have the feeling of the otherwise helpless sinking man, who is cleaving to a plank that just bears him up even with the surface of the water. In the choice between the plank and destruction, the advantage is decidedly on the side of the plank." The fact that I compared the theory of selection to a plank on which a shipwrecked man seeks deliverance excited so much delight in the camp of the other side that they, in the pleasure of repeating it, made a straw of the plank. There is, however, a great difference between a plank and a straw. The man who is dependent on a straw sinks; a common plank has saved many a man's life. Thus the fourth difficulty is no longer transcendent when it is earnestly, thoughtfully met.
The fifth difficulty is the origin of simple sensations, and is quite transcendent.
Recollecting how I have showed the hyper-mechanical nature of this problem, and consequently its transcendence, it may be profitable to consider how Leibnitz does this. He makes the bare assertion in many places in his writings that consciousness can not arise through any forms and movements, or, as Ave would now say, through any arrangements and movements of matter. In his "Nouveaux Essais sur l'Entendement Humain," he lets his advocate of sensualism, Philalethes, say, almost in the words of Locke, whose views the work otherwise opposes: "It may be proper to lay more stress on the question whether a thinking being can proceed from an unthinking one without sensation and consciousness, like matter. It is tolerably clear that a material particle can never bring about anything by itself, or impart motion of itself to itself. Its motion must either have existed from eternity, or have been imparted to it by a superior being. But, even if it were from eternity, it could not beget consciousness. Divide matter as if in order to animate it, into as small particles as you will; give them whatever figures and motions you will; make them into balls, cubes, or cylinders, whose dimensions shall reach only a thousand-millionth part of a philosophical foot. However small the particle may be, it will produce on other particles of the same order no different influence from that which bodies an inch or a foot in diameter exercise upon each other. We have the same right to expect to produce sensation, thought, consciousness, by the combination of gross particles of matter of the right shape and mode of motion, as by means of the most minute particles. The latter meet, jostle, and resist each other just as the coarser particles do, and they can do no more. But if matter could immediately and without instrumentality, or the help of forms and movements, create of itself out of itself sensation, perception, and consciousness, that would have to be an inseparable attribute of matter in all its parts." Theophilus, representing the Leibnitzian idealism, approves this conclusion as well founded and just, and says that he is of the opinion of its originator, that "there is no combination or modification of the particles of matter, however small they may be, that can beget perception; for, as can be clearly seen, the gross parts can not do it, and all the processes in the small parts are proportional to those in the gross ones." In his "Monadology," Leibnitz says more briefly: "We are constrained to confess that perception and whatever depends upon it are inexplainable upon mechanical principles; that is, by reference to forms and movements. If we could imagine a machine, the operation of which would manufacture thoughts, feelings, and perceptions, and could think of it as enlarged in all its proportions, so that we could go into it as into a mill, even then we would find in it nothing but particles jostling each other, and never anything by which perception could be explained." Thus, Leibnitz has reached the same conclusion as we. Yet we may remark on this point, first, that Locke's demonstration as accepted by Leibnitz has lost its validity through the progress of science; for, according to our present views, we do at least come to a point where matter displays new properties under excessively fine division, as in the cases of diffusions, chemical processes, crystallization, and in organisms. It is remarkable that it never occurred to Leibnitz or Locke that it is by no means all the same whether charcoal, sulphur, and saltpeter lying together are in large lumps or ground down in definite proportions to the fineness of gunpowder. The mechanical performance of similar machines never bears a proportionate relation to their size. If matter thus exhibits different modes of action according to the degree of its division, why may it not even think under a still finer division? It will be best to put away the explanations of these philosophers, and rest upon the simple declaration that consciousness can not be explained as the result of any arrangement or motion of the physical atoms of matter.
I have to say, besides, that we can not at present go further with Leibnitz. He concludes, from the incomprehensibility of consciousness from a mechanical basis, that it is not produced through material causes. We are satisfied with recognizing the incomprehensibility, which we may illustrate by saying that it is of a similar character with the impossibility of understanding why the twitching of the trigeminal nerve provokes infernal pains, while the excitation of certain other nerves is pleasant. While Leibnitz rejected consciousness in the soul-monads imparted to the body, and supposed a series of dream-pictures corresponding with the events of the body to pass along in it under God's direction, we are accumulating the proofs that consciousness is bound to material antecedents.
I name—not with full conviction—as the sixth difficulty, intelligent thought and the origin of language. An immense gap indeed exists between an amoeba and a man—between a new-born child and a man; but it may be filled to a certain extent by transitions. The theory of knowledge apparently requires only memory and the power of generalization to make the way from simple sensation to the higher degrees of mental activity. Great as is the leap still to be taken between the faculties of the highest animal and those of the lowest man, the difference between them, consciousness being once given, is of quite another kind from that which opposes the mechanical explanation of consciousness. The latter problem and the former one are incommensurable. Therefore, to use Strauss's notation again, if problem B is solved, problem C does not seem to me to be transcendent. Problem C, however, is closely connected with another problem, the seventh and last one in our series—the question of the freedom of the will.
It is natural that all the problems enumerated here should have busied mankind as long as it has thought. The constitution of matter, the origin of life and language, have been subjects of disquisition among all civilized peoples at all times. Yet only a few minds have advanced to these questions, and the report of the discussions of them has seldom passed beyond the halls in which they were carried on. It has been different with the question whether man is free in his acts, or is driven by an unavoidable compulsion. This question—touching every one, apparently accessible to every one, intimately connected with the fundamental conditions of society, reaching to the depth of religious convictions—has played a part of immeasurable importance in the history of thought and civilization, and the stages of the development of the human mind are plainly reflected in the discussion of it.
Classical antiquity did not rack its brains very much over this problem. Neither the idea of an inviolably binding law of nature nor that of an absolute control of the universe existing in the general ancient view of the world, no ground was offered for a conflict between free-will and the governing principle of the world. The Stoics believed in a fate, and therefore denied free-will. The Roman moralists, from ethical considerations, set up the doctrine of freedom again on a natural subjective basis. "Sentit animus se moveri," Cicero remarks in the "Tusculans"; "quod quum sentit, illud una sentit se vi sua, non aliena moveri."
It was Christian dogmatism that fell into the darkest self-dug pits over this question. The hopeless, entangling controversy about freewill and predestination has dragged along from the fathers of the Church through all the schools of doctrine and thought to the Reformers, and from them on. God is almighty and all-knowing; nothing comes to pass that he has not willed and foreseen from eternity. Therefore, man is unfree; for, if he had done otherwise than as God had foreordained, then would not God have been almighty and all knowing. Thus it does not lie within man's will whether he do right or sin. How, then, can he be responsible for his acts? How can it agree with God's justice and goodness that he punish or reward men for acts which are fundamentally God's own acts? Such is the form in which the problem presented itself to those minds. The doctrine of original sin, the questions of redemption through merit or through the blood of the Saviour, by faith or by works, and of the different kinds of grace, were complicated in a thousand ways with that dilemma itself, already fruitful in subtilties, and the cloisters of Christendom resounded from the fourth to the seventeenth century with disputations about determinism and indeterminism. Perhaps there is no subject of human thought concerning which more has been written. The contest was not always confined to books, but often culminated in bitter accusations of heresy with all their horrors.
How differently is the problem of free-will regarded in our time! The persistence of energy proves that force ever arises or is extinguished as little as matter. The condition of the whole world, even of a human brain, at each instant, is the absolute mechanical result of the condition in the previous instant and the absolute mechanical cause of the condition in the following instant. That in a given instant one or the other of two things may happen, is unthinkable. The brain molecules can only move in the determined way; and, if one of them should wander from its place or path without an adequate cause, it would be as great a wonder as if Jupiter should break out from its orbit and throw the planetary system into confusion. If, as monism conceives, our conceptions, efforts, and volitions are really incomprehensible, yet necessary and unequivocal companion-manifestations of the movements and environments of our brain-molecules, there is evidently no freedom of the will. To monism the world is a mechanism, in which there is no place for free-will.
Leibnitz was the first to whom the material world was presented in this form. His mechanical view was quite the same as ours. He was acquainted with the persistence of energy, although he was not able to follow it through all the molecular processes, as we are, and stood toward collective molecular processes as we stand toward single ones. Inasmuch as Leibnitz also firmly believed in a spiritual world, brought the ethical nature of man within the circle of his views, and was on the best of terms with positive religion, it is well to inquire what he believed concerning free-will, and how he was able to reconcile it with the mechanical view of the world.
Leibnitz was obliged by his whole teaching to be an absolute determinist. He accepted two substances as created by God, the material world and the world of his monads. One can not act upon the other, but the processes go on in both under an unalterable, Predetermined necessity, quite independent of each other, but keeping an exact, harmonious step; the mathematically calculable oscillations of the world machine, and, in the soul-monads appertaining to each animated individual, the conceptions that correspond with the apparent sensual impressions, volitions, and conceptions of the host of the monad. The very name of pre-established harmony, which Leibnitz gives to his system, excludes freedom. The conceptions of the monads being mere dream-pictures without mechanical cause or connection with the bodily world, it was easy to explain the subjective conviction of freedom by supposing that God has so ordered the flow of the conceptions of the soul-monad that it believes it is free to act.
On another occasion Leibnitz more closely followed the customary line of thought in allowing to man an appearance of freedom behind which a secret compelling impulse is concealed. Considering in his "Theodicy" the famous paradox, attributed to Buridan, concerning
". . . the old gray friend
Which between two bundles of hay"
miserably starved because everything was alike on both sides, and he, as an animal, had no free-will, Leibnitz admitted that, if the case were possible, one would have to decide that he would allow himself to die of hunger; but he held that the case was fundamentally an instance of the impossible, unless God should bring it about designedly; for the whole world could not be so halved by a perpendicular plane bisecting the ass lengthwise that all should be equal on both sides. Neither the parts of the world nor those of the ass could be so laid out. "There would also always be many things within the ass and without him which, although we may not remark them, would eventually determine him to turn to one side or the other. Although man is free, which the ass is not, the case of a perfect balance of the motives for two determinations appears to be impossible in him also; and an angel, or God, would always be able to provide an occasion for the conclusion taken by the man, even though, on account of the far-reaching concatenation of causes, that occasion is often very complicated and incomprehensible to ourselves."
Leibnitz availed himself of his optimism to find a place in determinism for the responsibility of man and the righteousness of God. Carrying out a fiction of Laurentius Valla, he describes in his "Theodicy" how sad it was for Sextus Tarquinius to be obliged to commit offenses for which punishment could not be spared him. Many worlds were possible in which Tarquinius might have played a more or less respectable part, have lived happily, and even have died in honor, full of years and lamented; but God was constrained to create this world, in which Sextus Tarquinius should be a villain, because in his foresight it would be the best, and the good would be in it, on the whole, at the maximum.
Monism can not derive any benefit from this idea, which, though consistent with itself, is decidedly arbitrary and bears the stamp of the unreal, and it must seek for itself its own position with reference to the problem of free-will. When one has resolved to declare the subjective feeling of free-will a delusion, it is as easy to reconcile apparent freedom with necessity on monistic principles as by extreme dualism. The fatalists of all periods have found no difficulty in it; and the feeling that was described by Cicero may be disputed away by one possessing a moderate dialectic versatility. Even in dreams, we feel free, while the phantasms of our sense-substances are still playing with us. We know now, of many acts that are apparently performed deliberately because they seem to have a purpose, that they are the involuntary effects of certain arrangements of our nervous system, of the reflex mechanism, and of the so-called automatic nerve-centers. When we watch the flow of our thoughts, we soon remark how independently of our will fancies come, pictures shine out and are extinguished. Need our supposed willful acts really be much more voluntary? If, moreover, all our sensations, efforts, and conceptions are only the product of certain material processes in our brain, then the molecular movement with which the volition to raise the arm is connected and the material impulse that causes the raising of the arm in a purely mechanical manner correspond, and there is no obscurity about it.
Obscurity conies over the view when the physical sphere is exchanged for the ethical. It is easy, to admit that man is not free, but acts as the tool of hidden causes, so long as his conduct is indifferent. Whether Cæsar in thought put on his right or his left caliga first was all the same; in either case, he went out with his boots on. Whether he crossed the Rubicon or not, on that hung the world's history. So little are we free in some unimportant matters, that one acquainted with human nature can predict with surprising certainty which card out of several laid down under certain conditions we will take up first. But even the most decided monist could hardly adhere to the earnest purposes of practical life in the face of the idea that all of human existence is a fable convenue in which mechanical necessity awards to Caius the part of a traitor, and to Sempronius that of a judge; and therefore Caius is taken to execution, while Sempronius goes to his breakfast. We are not troubled that so many letters in every hundred thousand miscarry because they are not directed; but it stirs our moral feelings to think that, according to Quetelet, so many persons in every hundred thousand are to become thieves, murderers, and incendiaries; for it is painful to have to feel that we are not criminals only because others, instead of ourselves, have drawn the black lots that might have fallen to our share.
Less known than the metaphysical efforts to reconcile free-will and the moral law with the mechanical order of the world are the mathematical essays directed to the same end that have lately been put forth in France. They are related to the unsuccessful attempt of Descartes to explain the working of the soul upon the body, of the spiritual upon the material substance. While Descartes held that the quantity of motion in the world was constant, and did not believe that the soul could produce motion, he nevertheless thought that the soul might determine the direction in which motion should take place. Leibnitz showed that not the sum of motions but the sum of motive forces is constant, and that also the sum of the directive forces, or of the advance in the line of any axis projected in space, continues the same. He, therefore, called the algebraic sum of all those axes parallel components of all mechanical movements. According to the last point, which was overlooked by Descartes, the direction of motion can not be determined or changed without a corresponding expenditure of force. However small we may imagine this expenditure of force to be, it forms a part of the mechanism of nature, and can not be ascribed to the spiritual substance.
The deceased mathematician, Cournot, M. de Sainte-Venant, and Professor Boussinesq, of Lille, have undertaken to break the bands of mechanical determinism by showing that motion can be produced, or the direction of motion can be changed, without the expenditure of force. Cournot and M. de Sainte-Venant have applied the idea of release (Auflösung, Fr. décrochement), which has long been current in the German physiological school. They believe that the force necessary for the release of absolute motion may be not only relatively very small, but even equal to nothing. M. Boussinesq has indicated certain differential equations of motion, the integrals of which permit singular solutions of such a kind that the sense of further motion becomes equivocal or quite indefinite. An example of this kind is the case in which a grave point at the periphery of a perfectly smooth paraboloid, having a perpendicular axis and its apex pointing upward, retains, in ascending in a plane drawn through the axis, the tangential velocity which it had acquired in falling to the same place. It then reaches the apex with a velocity of zero, and remains there till it pleases some directing principle residing there to give it an impulse in a required direction, which, although it is equal to nothing, shall yet be competent to let it glide down the paraboloid again.
Cournot believed that the releasing force, equivalent to zero, M. Boussinesq that the integral, with singular solutions, was needed as a means of explaining, in connection with the directing principle, the diversity and indeterminableness of organic processes. The German physiological school, accustomed to see only simple mechanism in organisms, hesitates to make friends with this conception, fearing, notwithstanding the protestations of its friends, that the vital force that is always, under one form or another, coming to the surface in France might be lurking behind the "directing principle." I may remark here that M. Boussinesq misunderstands me when he makes me say in the "Grenzen des Naturerkennens" that an organism is distinguished from a crystalline form only by its greater complication. On the contrary, I attach importance to having precisely designated the condition in which are grounded all the sensible differences that have caused mankind to recognize, although the same forces rule in both, two distinct kingdoms in living and inanimate nature. This condition is, that, in the inorganic individual, the crystal, matter exists in stable equilibrium, while in the organic individual a more or less complete dynamic equilibrium sways the matter, sometimes with a positive, sometimes with a negative balance. While the stream of matter coursing through the animal promotes the conversion of potential into kinetic energy, it also explains the dependence of life upon external conditions, the integrating stimulus of the older physiology, and the perishability of the organism as opposed to the eternity of the crystal lying inert in itself.
In our opinion, the theory of an unconscious life can subsist without a forking integral and without a directing principle. On the other hand, it is doubtful if anything can be gained in the controversy be between free-will and necessity with these aids or with the theory of release. M. Paul Janet's report to the Académie des Sciences Morales et Politiques admits the possibility of a mechanical indeterminism on the authority of the three mathematicians. But, when the hypothesis that the releasing force may be infinitely small passes to the assertion that it may be really null, it seems to make an unwarrantable use of a process in the infinitesimal calculus which is usual under quite different conditions. The former statement can only mean that the releasing force may be vanishingly small in comparison with the released force. The force of the wing-flapping of a crow which starts an avalanche thus vanishes in the face of the force of the avalanche as it finally plunges through the valley; that is, the former may be neglected in the measurement of the latter, because the influence it exerts can not be indicated by any figures, and because it may fall within the range of errors of observation. But, however insignificant, as regarded from the valley, the wing-flapping above may seem in comparison with the mad force of the avalanche, it is still, there, a blow which corresponds with the raising of a definite weight to a definite height. By the nature of the escapement, the releasing and the released force are independent of each other, connected by no law. Hence it is inaccurate to say that "the ratio of the releasing force to the released force approaches zero," without adding that this depends on an accidental increase, so far as relates to the former, of the latter; as in our example, the wing-stroke being the same, the increase depends on the greater height, steepness, and smoothness of the mountain-slope, on the ever-mightier piling up of snow, etc. So little can the releasing force be in itself really null, it can never, unless we deny the releasing, fall below a certain something (Schwellenwerth) capable of an expansion that is dependent on circumstances. Therefore, to explain by the aid of the principle of escapement how a spiritual substance can effect material changes, is not to be thought of.
As to the solution proposed by M. Boussinesq, the grave point remains at the stationary position simply in unstable equilibrium, and it was not necessary to raise it by integration to calculate the consequences of that situation. The case, in fact, differs only in its abstract form of expression from Buridan's or Dante's paradox, which may be so formulated that the hungry creature—
"Intra duo cibi distanti e moventi
("Between two kinds of food, both equally remote and tempting")—
is in unstable equilibrium. No "directing principle" of immaterial nature is competent to move the grave point at the apex of the paraboloid in the slightest degree; a mechanical force, though it be ever so little, is necessary even upon a wholly frictionless surface. If this could be a force equivalent to nothing, then our second transcendental difficulty, of the origin of motion, would disappear at once; for an impulse equivalent to nothing would never be wanting.
M. Boussinesq also brings up the question of what would be the consequence of the reversal of all the motions of the world. If we could imagine the mechanism of the world to consist only of reversible processes, and that at a given instant the motions of all the particles of matter were reversed as a ball is knocked back, then the history of the material world would play itself over again backward. All that now happens would come to pass again after its time in the inverse order: the hen would become an egg again, the tree would grow backward into a seed, and after an infinite time the cosmos would be resolved again into chaos. What processes would now attend the reverse movements of the brain-molecules? If mental conditions depended only on arrangements of atoms, then with the same arrangements the same conditions would return, leading to surprising results; among them, that, always at the instant before we contemplate anything, the counterpart of it would happen. We may, however, spare ourselves from estimating the possibilities thinkable here. The crank of the world-machinery could not be thus turned backward. The motion of masses, for instance, which has been converted by friction into heat, could not be changed back again into the same amount of similarly adjusted, opposite-faced motion. The reversed world is a bit of impossible mechanical fancy-work, from which nothing can be drawn respecting the origin of consciousness and free-will.
Our seventh difficulty becomes no longer a difficulty, provided we determine to deny free-will, and to declare the subjective feeling of freedom a delusion; but otherwise it must be regarded as transcendent; and it is but a poor consolation to monism that it sees dualism entangled in the same net the more helplessly as it lays more stress on ethics. In this sense I once wrote, in the preface to my "Untersuchungen über thierische Elektricität" ("Researches on Animal Electricity"), the words upon which Strauss now appeals against me: "Analytical mechanics reaches to the problem of personal freedom, the solution of which must remain an affair of the abstractive faculty of each individual." But afterward—and I make no secret of it— the day of Damascus came to me. Repeated reflections on the subject of my public address, "Ueber einige Ergebnisse der neueren Naturforschung" ("On some Results of the Later Natural Philosophy"), led me to the conviction that at least three transcendental problems precede the problem of free-will, viz., besides the problem of the origin of matter and force, which I have previously defined, that of the first motion and that of the first sensation, in the world. That the seven world-problems have been counted out and numbered here as if in a mathematical book of examples, has come to pass in consequence of the scientific divide et impera. We might combine them into a single problem—the world-problem. The mighty thinker whose memory we honor to-day believed that he bad solved this problem. He had arranged the world to his satisfaction. Could Leibnitz, standing on his own shoulders, take part in our reflections to-day, he would surely say with us, "Dubitemus.
- An address delivered in the Academy of Sciences at Berlin, in honor of the birthday of Leibnitz, July 8, 1880.
- See "Popular Science Monthly," vol. v, p. 17 (May, 1874).