On the Limits of Our Knowledge of Nature and The Seven World-Riddles

Preface to the First Edition (1881)

The lecture "On the Limits of Our Knowledge of Nature," which I gave nine years ago to the German Natural Scientists and Physicians assembled at Leipzig, appears here in its fifth edition, enlarged and corrected in its details. It is followed by the address on "The Seven World-Riddles," with which I opened the Academy of Sciences' Leibniz celebration in July 1880. That address takes up the objections the Leipzig lecture provoked and corrects the misunderstandings it gave rise to; it completes the inquiry into the bounds set to the mechanical view of the world, and together with the earlier lecture it makes up the whole picture of my view of the world. Because the lectures had to keep within their narrow frame, and I had no wish to work them up into a book, some things in them may be said too briefly. Anyone who thinks it worth the trouble will find more in my academic addresses on related subjects: Leibnizische Gedanken in der neueren Naturwissenschaft (Leibnizian Ideas in Modern Science); La Mettrie; and Darwin versus Galiani.

In the objective dissection of the world of appearances that these inquiries undertake, I see a necessary complement to the theory of knowledge, and the true philosophy of nature. They lead inevitably to Pyrrhonism in new dress, a modern form of the old skeptic Pyrrho's suspension of judgment, and that is not to the taste of many. Let them by all means try the only other way out, that of supernaturalism. Only, where supernaturalism begins, science ends.

Berlin, from the Physiological Institute of the University, August 14, 1881.

The Author.

Preface to the Second Edition (1884)

Once again a new edition of "The Limits of Our Knowledge of Nature" has become necessary, the sixth in less than twelve years, and "The Seven World-Riddles" appears here in print for the fourth time in less than four years. The critical zeal of the press of every shade has kept pace with the reading public's interest in my attempt to redraw the boundary. Natural scientists and philosophers have even been joined in attacking my positions by Jesuits: Catholic ones fighting with open visor, Protestant ones with visor closed, though easily recognized. These, admittedly, have turned mostly against the second section of the lecture on the "Limits," which has at last been understood. Other scholars have been kind enough to catch, in my place, some of the missiles aimed at me. Thus Jürgen Bona Meyer recently spoke a calming and clarifying word in the "Ignorabimus controversy."¹

Apart from a few remarks scattered here and there, I must keep silent in that polemic myself, or else this little book will swell into a book, and what readers presumably come to it for, the original text of my lectures, will be swamped in criticism and countercriticism. My critics, besides, have gone on contenting themselves with flat contradiction; against my fundamental conclusion no one has yet raised a single objection. The human mind can never get further than a faint likeness of Laplace's spirit. Since that spirit would face the same limits of knowledge as we do, and the same riddles would remain insoluble for it as for us, the verdict runs, unalterable and inexorable: Ignorabimus.

Berlin, from the Physiological Institute of the University, March 1884.

The Author.

Preface to the Third Edition (1891)

"The Limits of Our Knowledge of Nature" and "The Seven World-Riddles" appear here once more in a separate edition, after having also been printed, since the last such edition of March 1884, in the collection of my Reden (Addresses).²

Among the more recent discussions of the two addresses, one book written expressly about them, by Theodor Weber of Breslau, stands out so far above the rest, in weight as in bulk, that for its sake I must depart from my rule of keeping silent in the polemic that rises around my positions. The book is titled Emil du Bois-Reymond. Eine Kritik seiner Weltansicht (Emil du Bois-Reymond: A Critique of His World-View; Gotha, 1885, 266 pp.).

Weber had already criticized the two lectures once before (in Schaarschmidt's Philosophische Monatshefte, vol. XIX, 1883, pp. 80 ff.), and in the edition of 1884 (pp. 59-60 of that edition) I had answered him with a few remarks, which the book that now bears my name takes up. I must first acknowledge that I am much obliged to Weber: for the friendly way he so often speaks of me, for the importance he attaches to my positions, and for the care with which he has searched all my writings for the passages that characterize my view of the world and gathered them together. That in doing so he has come upon imprecisions of expression here and there, and even apparent contradictions, will, I hope, be forgiven me, given the rather popular character of many of these writings and the long span of years they cover.

Against the picture Weber draws of my view of the world I have little to object, and I let it pass over me calmly when he charges me, in hard words, with unheard-of errors. For given where each of us stands, there can be no question of an understanding between him and me. Against my skeptical resignation, which, he informs me, I wrongly called Pyrrhonism in new dress, he takes the standpoint of a supernaturalist dualism that throws itself without reserve, all the way to the dogma of the Trinity, into the arms of revealed doctrine. That I "include man too in nature, as its last and normal member," he regards "as one of the most monstrous blunders ever committed in the field of science," for "man is not constituted monistically, like the animals, but dualistically; he consists of spirit and nature, soul and body" (pp. 201, 233). Weber demands that we take into our circle of ideas the "idea of Creation in its old, genuinely Christian sense." On the other hand, Weber imagines himself in possession of insights into matter and force of which the likes of us, admittedly, can make nothing at all.

I am glad to hear that he stands at my side in condemning the false philosophy of nature, the speculative system that grew out of Schelling's teaching around 1800. But I must answer yes to his question whether, after his present exposition, I shall still have the courage to assert that his thinking moves in forms like those of the great Schellingian mystification. Weber may build other castles in the air, out of other notions, than that false philosophy of nature built. But take a sentence like this one, which holds the quintessence of his knowledge: "One will have to think that at the moment when the potencies immanent in the natural principle, in its original mode of existence, were called awake into the two actual, living forces of receptivity and reactivity, the principle itself went apart (by a process of diremption) into real parts." This is how "the origin of the atoms from the natural principle, originally not yet atomized but atomizable," is explained (pp. 198, 200). Such a sentence moves (yes, I still have the courage to assert it) in forms of thought quite like those of that lamentable aberration of the German mind.

Berlin, from the Physiological Institute of the University, March 1891.

The Author.

The fourth edition is an unchanged reprint of the third.

On the Limits of Our Knowledge of Nature

In Nature's infinite book of secrecy
A little I can read.

Shakespeare, Antony and Cleopatra

A lecture given at the second general session of the Forty-fifth Assembly of German Natural Scientists and Physicians, at Leipzig, on August 14, 1872.

A world-conqueror of ancient times, resting for a day in the midst of his campaigns, might well want the frontiers of his empire surveyed more exactly: here to find a people not yet paying tribute and make it pay, there to recognize, in a desert of water his horsemen could never cross, a barrier to his power. In the same way it will not be unfitting for the world-conqueror of our own day, natural science, to rest from its labors on a festive occasion and try for once to trace clearly the true limits of its realm. I think the undertaking all the more justified because I believe that two errors about the limits of our knowledge of nature are widely held, and because I think that such reflections, trivial as they may seem, can bring out some new aspects even for those who do not share those errors.

I propose, then, to seek out the limits of our knowledge of nature, and I begin by answering the question of what knowledge of nature is.

Knowledge of nature — more precisely, scientific knowledge, the knowledge of the physical world gained with the help and in the spirit of theoretical natural science — is the reduction of the changes in the physical world to motions of atoms, motions produced by the atoms' central forces, which act along the lines between them and do not vary with time. It is, in short, the resolution of natural processes into the mechanics of atoms. It is a fact of psychological experience that wherever such a resolution succeeds, our need for causal explanation feels satisfied for the time being. The propositions of mechanics can be expressed mathematically, and they carry the same apodictic certainty, the certainty of proof, as the propositions of mathematics. Once the changes in the physical world have been traced back to a constant sum of what we call tensional forces and living forces, or potential and kinetic energy, bound to a constant quantity of matter, nothing remains to be explained in the changes themselves.

Kant asserts, in the preface to his Metaphysische Anfangsgründe der Naturwissenschaft (Metaphysical Foundations of Natural Science), "that in any particular doctrine of nature there can be only as much genuine science as there is mathematics in it." That claim must be sharpened still further: for mathematics, put the mechanics of atoms. Plainly this is what he meant himself when he denied chemistry the name of a science and relegated it to the experimental arts. And it is no small curiosity that in our own day chemistry, forced by the discovery of substitution to give up the electrochemical dualism of Berzelius, has apparently moved further away again from the goal of becoming a science in this sense.³

Imagine every change in the physical world resolved into motions of atoms produced by their constant central forces, and the universe would be known scientifically. The state of the world during one instant, one infinitesimal element of time, would appear as the direct effect of its state during the instant before and the direct cause of its state during the instant after. Law and chance would be nothing but other names for mechanical necessity. Indeed, we can conceive of a stage of knowledge at which the whole course of the world was represented by one mathematical formula, by one immeasurable system of simultaneous differential equations, from which the position, the direction of motion and the speed of every atom in the universe at every moment could be derived. "A spirit," says Laplace, "that knew, for a given instant, all the forces that animate nature and the relative positions of the beings that compose it, and that was moreover vast enough to submit these data to analysis, would embrace in the same formula the motions of the greatest bodies of the universe and those of the lightest atom: nothing would be uncertain for it, and the future, like the past, would be present to its eyes. The human mind, in the perfection it has been able to give to astronomy, offers a faint likeness of such a spirit."⁴

And in fact, just as the astronomer need only give the time in the equations of the moon's motion a certain negative value to find out whether the sun was eclipsed over the Piraeus when Pericles embarked for Epidaurus, so the spirit Laplace imagined could tell us, by a suitable analysis of its world formula, who the Man in the Iron Mask was, or how the steamship President, lost without trace in the Atlantic in 1841, went down. Just as the astronomer predicts the day on which, after many years, a comet will reappear in the vault of heaven out of the depths of space, so that spirit would read in its equations the day on which the Greek cross will flash once more from the mosque of Hagia Sophia, or on which England will burn her last lump of coal. If it set t = −∞ in the world formula, the mysterious original state of things would be revealed to it. It would see matter in infinite space either already in motion, or at rest and unevenly distributed, since had it been evenly distributed its unstable equilibrium would never have been disturbed. If it let t grow without limit in the positive direction, it would learn after how long a time Carnot's principle, the law by which the world's heat runs down, threatens the universe with an icy standstill.⁵ To such a spirit the hairs of our head would be numbered, and not a sparrow would fall to the ground without its knowledge. A prophet facing forward and backward alike, it would find, in the words of d'Alembert, who carried Laplace's thought in germ in his introduction to the Encyclopédie, that "the whole world is only a single fact and one great truth."⁶

Leibniz, too, already had Laplace's thought, and in one respect developed it further than Laplace, since he imagines that spirit endowed with senses and technical powers of matching perfection. Pierre Bayle had objected to the doctrine of pre-established harmony, the doctrine that soul and body never act on each other but were set from the start to keep in step, that for the human body it assumed something like a ship steering itself into harbor by its own power. Leibniz replies that this is not nearly so impossible as Bayle thinks. "There is no doubt," he says, "that a man could make a machine able to walk about a town for some time and to turn precisely at certain street corners. A spirit incomparably more perfect, though still limited, could also foresee and avoid an incomparably greater number of obstacles. So true is this that if, as some believe, this world consisted only of a finite number of atoms moving according to the laws of mechanics, it is certain that a finite spirit could be exalted enough to comprehend and foresee with mathematical certainty everything that must happen in it at a given time; so that this spirit could not only build a ship that would steer itself to a given harbor, once it had been given the proper inner force and direction, but could even form a body that would imitate the actions of a man."⁷

I hardly need say that the human mind will always remain far from this perfect knowledge of nature. One remark is enough to show the distance that separates us even from its first beginnings. Before the differential equations of the world formula could be written down, every natural process would have to be reduced to the motions of a single substrate underlying all that appears to us as matter of different kinds, a substrate with no differences of substance and therefore with no qualities. Every quality, that is, would have to be explained by the arrangement and motion of this substrate, for which I would propose the Greek word for matter, hyle.

That there are in reality no qualities follows from the analysis of our sense perceptions. On our present understanding, in every nerve fiber, whatever effect it finally produces, the same molecular process takes place, spreading in both directions and varying only in intensity. In the sensory nerves this process is set going by the sense organs, each built differently to receive impressions from outside; in the nerves of muscles and glands, of electric organs and of luminous organs, by unknown causes in the ganglion cells of the nerve centers. In principle a piece of optic nerve could be exchanged, fiber for fiber and without harm, for a piece of the nerve of an electric organ, provided due regard were paid to the direction in which each acts physiologically;⁸ once the pieces had healed in, the optic nerve and the electric nerve would conduct correctly. Two sensory nerves could all the more readily stand in for each other. With the optic and auditory nerves cut and healed crosswise, we would, if the experiment were possible, hear the lightning with our eyes as a thunderclap and see the thunder with our ears as a series of flashes.⁹ Sensation as such, then, arises only in the sense substances, as Johannes Müller called the provinces of the brain belonging to the sensory nerves, a part of which Hermann Munk has now marked out in the cerebral cortex as the visual sphere, the auditory sphere, and so on.¹⁰ It is the sense substances that first translate the excitation, which is the same in all nerves, into sensation at all, and that, as the true bearers of Johannes Müller's "specific energies," produce the different qualities each according to its nature; for that is Müller's doctrine, that each sense answers every stimulus with its own kind of sensation and no other. The "And there was light" of Moses is physiologically false. There was light only when the first red eyespot of some infusorian, a single-celled creature of the pond, first told light from dark. Without the sense substances of sight and hearing, this world around us, glowing with color and full of sound, would be dark and silent.

And the world that subjective analysis shows to be silent and dark in itself, that is, without qualities, is no less so for the mechanical view won by objective study. That view knows, in place of sound and light, only vibrations of a primal matter without qualities, which presents itself in the one case as ponderable matter, in the other as seemingly imponderable.

But however well founded these ideas are in general, almost everything is still lacking for carrying them through in detail. The philosophers' stone, which would turn the substances we still cannot decompose into one another and produce them from higher elements, if not from the primal matter itself, would have to be found before we could even begin to guess how matter apparently of many kinds arises from matter in reality without qualities and therefore without differences: how our sixty-eight elements, whose further multiplication tends to excite us as little as that of the minor planets, arise from the hyle. The periodic system of the elements of Lothar Meyer and Mendeleev is certainly a mighty step in this direction, but for the present its chief service is to show us how far we still are from the insight we long for.

The spirit described above — let us call it from now on, for short, Laplace's spirit¹¹ — would possess this insight complete, and so it might seem that there could be no comparison between it and us. Yet the human mind differs from Laplace's spirit only in degree, much as one ordinate of a curve rising from zero to infinity differs from another ordinate of the same curve, exceedingly much greater but still finite. We resemble this spirit, for we comprehend it. It is even a question whether a mind like Newton's differs much more from Laplace's spirit than the mind of an Aboriginal Australian who counts only to three, of a Bushman who counts only to two, or of a Chiquito of Bolivia, who has no number words at all, differs from the mind of Newton.¹² Put another way, the impossibility of setting up the differential equations of the world formula, integrating them and analyzing the result is not grounded in the nature of things. It rests on the impossibility of obtaining the necessary data of fact and, even if that were possible, on their immeasurable, perhaps infinite extent, their variety and their intricacy.¹³

The knowledge of nature that Laplace's spirit possesses is thus the highest conceivable stage of our own, and in inquiring into the limits of that knowledge we may take it as our basis. Whatever Laplace's spirit could not see through will remain all the more hidden from our minds, shut in by so much narrower bounds.

There are, then, two points at which even Laplace's spirit would strive in vain to press further, and at which we, still more, are forced to stop.

First, we must recall that the knowledge of nature I described earlier as satisfying our need for causal explanation for the time being does not in truth satisfy it, and is no knowledge at all. The picture of a world made of smallest parts that have always existed and cannot perish, whose central forces produce all motion, is only a surrogate, as it were, for an explanation. As I said, it traces every change in the physical world back to a constant quantity of matter and the moving force bound to it, and so leaves nothing in the changes themselves to explain, for what has always been there can only be cause, never effect. Given the existence of this constant, we can rest content for a while, glad of the insight we have won; but soon we demand to go deeper and to grasp what the constant itself is. And then, as everyone knows, we find that the atomic picture, though serviceable and at times indispensable for our physical and mathematical reasoning, leads into insoluble contradictions as soon as we ask more of it than it can give and make it a corpuscular philosophy.

A physical atom is a mass imagined as vanishingly small compared with the bodies we handle, but still, despite its name, divisible in idea, to which we ascribe properties or a state of motion that explain the behavior of a mass made of countless such atoms. As such it is a self-consistent fiction, and in some fields, chemistry for instance, or the mechanical theory of gases, an extremely useful one. In mathematical physics, indeed, its use has lately been avoided wherever possible, by going back, instead of to discrete atoms, to volume elements of bodies imagined as continuous.¹⁴

A philosophical atom, on the other hand, a mass of inert, inactive substrate supposedly incapable of further division, from which forces go out to act at a distance across empty space, is on closer inspection an absurdity.

For if the indivisible, inert substrate, inactive in itself, is to have real existence, it must fill some space, however small. And then there is no understanding why it should not be divisible further. Moreover, it can fill space only if it is perfectly hard, that is, only if it resists the entry of anything else material into the same space by a repulsive force that appears at its boundary, acts no further than that, and at once becomes greater than any given force. Quite apart from the other difficulties that spring from this, the substrate is then no longer inactive.

Suppose, conversely, that with the dynamists we take as the substrate only the geometrical center of the central forces. Then the substrate no longer fills space, for a point is the negation of space, pictured in space. Then nothing is left for the central forces to go out from, nothing that could be inert, like matter.

Forces acting at a distance across empty space are in themselves incomprehensible, indeed absurd, and only since Newton's time, through a misunderstanding of his teaching and against his express warning, have they become a familiar idea to scientists.¹⁵ If, with Descartes and Leibniz, we imagine all space filled and all motion produced by transfer from one part to the next in contact with it, then the origin of motion is indeed traced back to a picture familiar to our senses, but other difficulties arise. Among other things, it has so far been impossible on this view to explain the different densities of bodies by different ways of putting together the same primal stuff.¹⁶

The source of these contradictions is easy to uncover. They are rooted in our inability to picture anything but what we have experienced, either with the outer senses or with the inner sense. In trying to analyze the physical world, we start from the divisibility of matter, since the parts are plainly something simpler and more original than the whole. If in thought we go on dividing matter further and further, our imagination stays in the track laid down for it, and we feel no hindrance in our thinking. But we take not a single step toward understanding things, since in fact we are only picturing in the realm of the small and invisible what appears in the realm of the large and visible. In this way we arrive at the concept of the physical atom. But if we now stop dividing at some arbitrary point and halt at supposed philosophical atoms, which are to be indivisible, inactive in themselves, and yet perfectly hard and the bearers of central forces acting at a distance, then we are demanding that a matter we picture after the image of the matter we handle should unfold new, original properties that explain its own nature, and should do so without our introducing any new principle at all. So we commit the error that shows itself in the contradictions laid bare above.¹⁷

No one who has thought about it at all deeply mistakes the transcendent nature of the obstacle that confronts us here. However we try to get around it, in one form or another we run up against it. From whatever side we approach it, under whatever cover, we learn that it cannot be taken. The old Ionian physiologists, the first Greek inquirers into nature, stood before it no more at a loss than we do. All the advances of natural science have availed nothing against it, and all those still to come will avail nothing. We shall never know better than we do today what it is, as Paul Erman used to say, that "haunts space here," where matter is. For even Laplace's spirit, so far exalted above our own, would be no wiser on this point than we are; and by this we recognize, in despair, that here we stand at one of the limits of our wit.

The material world, moreover, would set this spirit one more riddle it could not solve. True, as we saw, its formula would reveal to it the original state of things. But if it found matter, an infinite time ago, at rest in infinite space and unevenly distributed, it would not know where the uneven distribution came from; if it found matter already in motion, it would not know where the motion came from, which would appear to it only as an accidental state of matter. In either case its need for causal explanation would remain unsatisfied. Perhaps, indeed probably, the question of the beginning of motion, which Aristotle had already discussed, is one and the same as the question of what matter and force are. That cannot be proved; nor would it help Laplace's spirit, since the nature of matter and force is precisely what remains closed to it.¹⁸

But let us set all this aside and take matter in motion as given; then the physical world, as I said, is in idea intelligible. For an infinite time, matter that seems to attract itself has been condensing in infinite space. Somewhere in the universe, a vanishing point within it, there also draws together the rotating nebula from which, on Kant's hypothesis as Helmholtz has carried it further with the mechanical theory of heat, our planetary system arises, with its exhaustible dowry of heat that never returns.¹⁹ Already we see our earth roll along its orbit as a drop of fiery liquid, wrapped in an atmosphere of unimaginable composition. We see it, in the course of immeasurable ages, surround itself with a crust of primeval rock as it solidifies; we see sea and dry land separate, the granite, eaten away by hot cloudbursts charged with carbonic acid, furnish the material for potash-bearing strata, and at last conditions arise under which life became possible.

Where on earth and in what form life first appeared, whether as a little lump of protoplasm in the sea, or in the air, with the help of a sun that then sent out still more ultraviolet rays, in an atmosphere still richer in carbonic acid; whether germs of life flew across to us from other heavenly bodies:²⁰ who will ever say? But Laplace's spirit, in possession of the world formula, could say. For when inorganic matter comes together into something living, what is at issue is at first only motion: the arrangement of molecules in more or less fixed positions of equilibrium, and the setting going of a metabolism, partly by motion received from outside, partly by the potential energy of the living being's molecules as they enter into interaction with molecules of the outer world. What distinguishes the living from the dead, the plant, and the animal considered only in its bodily functions, from the crystal, comes in the end to this. In the crystal, matter is in stable equilibrium, while through the living being a stream of matter pours, and the matter in it is in a more or less perfect dynamic equilibrium,²¹ with a balance now positive, now equal to zero, now negative. Hence, without the action of outside masses and forces, the crystal stays forever what it is, while the living being depends for its existence on certain outside conditions, the integrating stimuli or stimuli of life of the older physiology,²² and is subject to a course in time, but also becomes able to turn kinetic energy into potential energy and potential into kinetic as it needs.

Through this fundamental difference between the individuals of dead nature and those of living nature, then, the processes in the living become subject to the law of the conservation of energy. Beside it, the marks that Ernst Heinrich Weber ingeniously devised to tell the two classes of individuals apart, which separate them more superficially, lose their importance, except so far as they come down to this same difference. The other differences vitalism has stressed, the supposedly higher incomprehensibility and inimitability of living beings, their purposiveness, their different way of reacting and their indivisibility, mostly rest on a mistaken view. As to indivisibility in particular, it is true that the so-called divisibility of some organisms depends only on a far-reaching power of regeneration. But in idea living beings are divisible, as crystals are, into the elementary organisms that make them up, so that they hardly deserve to be called individuals at all; machines, on the other hand, are indivisible in the way living beings are, since in both the working of the whole conditions that of the parts and the working of the parts conditions that of the whole. So, without any difference in principle between the forces in the crystal and those in the living being, without a vital force in any form or disguise, we can understand why the two are as incommensurable with each other as a building that can be split into many similar blocks and a machine. And so the inquirer has no reason to accept between the two realms those absolute barriers that plain human sense has seen everywhere and always, and always will, and that a period of science only now ended in our own day raised into a dogma.

It is therefore a misunderstanding to see in the first appearance of living beings on earth, or on any other heavenly body, something supernatural, anything other than an exceedingly difficult mechanical problem. This is one of the two errors I meant to point out, and I do not think it necessary to assume a cosmic panspermia, a seeding of the worlds with germs of life, going on as it were from all eternity.²³ The other limit of our knowledge of nature does not lie here; no more here than in the formation of crystals. If we could produce the conditions under which living beings once arose, as we can for certain crystals, though not for all, then by the principle of actualism,²⁴ the principle that the forces at work in the earth's past are those at work today, living beings would arise now as they did then. And even if we should never succeed in observing spontaneous generation, let alone bringing it about in an experiment, there would still be no absolute obstacle here. If matter and force were intelligible to us, the world would not cease to be comprehensible even if we imagined the earth (to name only the earth) overgrown, from its equatorial belt of emerald to the last lichen-gray cliffs of the poles, with the most luxuriant abundance of plant life, whatever share in shaping the plant kingdom we grant to organic laws of formation and whatever to natural selection. Only the help of the insects, which has been recognized as indispensable for the fertilization of many plants, we must leave out of this reckoning, for reasons that will soon be clear. Otherwise the richest painting of a tropical forest, drawn by Bernardin de Saint-Pierre, Alexander von Humboldt or Poeppig, offers to the eye of theoretical science nothing but matter arranged or moved in particular ways.²⁵

But now, at some point in the development of life on earth, a point we do not know and need not fix here, something new appears, something until then unheard of: something once again incomprehensible, like the nature of matter and force, and like the first motion. The thread of understanding, spun out from a time infinitely far in the past, snaps, and our knowledge of nature comes to a chasm that no bridge spans and no wing can carry us across: we stand at the other limit of our wit.

This new incomprehensible thing is consciousness. I shall now show, in what I believe is a very compelling way, not only that consciousness cannot be explained from its material conditions in the present state of our knowledge, which everyone will probably grant, but that by the very nature of things it will never be explicable from those conditions. The opposite opinion, that we need not give up all hope of understanding consciousness from its material conditions, and that the human mind, having pushed on by then into undreamed-of realms of knowledge, may well succeed in doing so in the course of centuries or millennia: this is the second error I mean to combat in this lecture.

I use the word "consciousness" deliberately, because all that matters here is the fact of a mental process of any kind, even the lowest. We need not picture Newton or Leibniz inventing the infinitesimal calculus, or James Watt setting his parallelogram, the linkage of his parallel motion, working before his inner eye, or Shakespeare, Raphael or Mozart caught up in the most wonderful of their creations, to have an example of a mental process that cannot be explained from its material conditions. In the main, the most sublime activity of the mind is no more incomprehensible from material conditions than consciousness at its first stage, sensation. With the first stirring of comfort or of pain that some simplest of creatures felt at the dawn of animal life on earth, or with the first perception of a quality, that impassable chasm opened, and the world became doubly incomprehensible.

Few subjects have been thought about more persistently, written about more, or fought over more passionately than the union of body and soul in man. Every philosophical school, and the Church Fathers besides, has had its doctrine on it. Modern philosophy troubles itself less with the question, but its beginnings in the seventeenth century were all the richer in theories of how matter and mind interact.

Descartes himself had cut off in advance any possibility of understanding this interaction, by two of his tenets. First, he asserted that body and mind are different substances, united by God's omnipotence, which, since the mind is incorporeal and has no extension, touch each other at only one point, in the so-called pineal gland of the brain.²⁶ Second, he asserted that the quantity of motion present in the universe is constant.²⁷ The more surely it seems to follow from this that the soul cannot produce motion in matter, the more astonished we are when Descartes, to save freedom of the will, simply lets the soul move the pineal gland in the required direction, so that the animal spirits, what we would call the nerve principle, flow to the right muscles. Conversely, the animal spirits stirred up by sense impressions move the pineal gland, and the soul joined to it notices the motion.²⁸

Descartes's immediate successors, Clauberg,²⁹ Malebranche³⁰ and Geulincx,³¹ labored to mend so obvious a blunder. They held fast to the impossibility of any interaction between mind and matter, as two different substances. But to understand how the soul nevertheless moves the body, and is in turn stirred by it, they assumed that the soul's willing prompts God to move the body each time as the soul wishes, and that sense impressions in turn prompt him to change the soul each time to match them. The causa efficiens, the efficient cause, of the changes worked in the body by the soul and in the soul by the body is therefore always God alone; the soul's willing and the sense impressions are only the causae occasionales, the mere occasions, for the endlessly renewed interventions of his omnipotence.

Leibniz, finally, liked to illustrate the problem with an image first applied to it by Geulincx: two clocks that are to keep the same time.³² This can come about, he says, in three ways. First, the two clocks can act on each other through the vibrations they pass to a common mounting, so that they come to keep the same time, as Huygens observed.³³ Second, one clock can be set again and again, to keep it in step with the other. Third, the maker can have been so skillful from the start that he made the two clocks keep the same time, though they are entirely independent of each other. Between body and soul, the first kind of connection is admittedly impossible. The second, which answers to the occasionalist doctrine, is unworthy of God, whom it misuses as a deus ex machina. So only the third remains, and in it we recognize Leibniz's own doctrine of pre-established harmony.³⁴

But in the eyes of modern science these and similar reflections have lost their value, and all their effect on present-day views, because of the dualist foundation on which, true to their half-theological origin, they take their stand from the outset. Their authors start from the assumption of a spiritual substance, the soul, different in every respect from the body, and inquire into its union with the body. They find that a union of the two substances is possible only through a miracle, and that even after this first miracle the two can go on keeping in step only through another miracle, either constantly renewed or working on ever since the Creation. This consequence they then pass off as a new insight, without examining closely enough whether they may not themselves have first shaped the soul in such a way that any interaction between it and the body is unthinkable. In a word, the most successful proof that no interaction of body and soul is possible leaves room to doubt whether its premises are not arbitrary, and whether consciousness might not simply be thought of, and perhaps understood, as an effect of matter. For the natural scientist, then, the proof that mental processes can never be understood from their material conditions must be carried through independently of any assumption about the ultimate ground of those processes.

By astronomical knowledge of a material system I mean such knowledge of all its parts, of their positions relative to one another and of their motion, that their position and motion at any past or future time can be calculated with the same certainty as the position and motion of the heavenly bodies, assuming perfectly exact observations and a perfected theory. This requires knowing, first, the laws by which the forces acting between the parts of the system vary with distance; and second, the positions of the parts of the system at two moments separated by an instant, or, what comes to the same thing, the positions of the parts and their velocities, resolved along three axes, at a given time.³⁵

Astronomical knowledge of a material system is, given our inability to comprehend matter and force, the most perfect knowledge of the system we can attain. It is the knowledge at which our need for causal explanation is used to coming to rest, and the knowledge of the system that Laplace's spirit itself would possess if it made proper use of its world formula.

Suppose, now, that we had attained astronomical knowledge of a muscle, of a gland, of an electric or a luminous organ together with the stimulated nerves belonging to it, of a ciliated cell, of a plant, of an egg in contact with the sperm or at any stage of its development. We would then possess the most perfect knowledge of these material systems possible to us, and our need for causal explanation would be satisfied so far that all we would still ask is to comprehend the nature of matter and force themselves. The contraction of the muscle, secretion in the gland, the shock of the electric organ and the glow of the luminous one, the beating of the cilia, the growth and chemistry of the cells in the plant, the fertilization and development of the egg: all these processes, still almost hopelessly dark today, would be as transparent to us as the motions of the planets.

If, on the other hand, we make the same assumption of astronomical knowledge for the human brain, or even only for the organ of the mind of the lowest animal, whose mental activity may be confined to feeling pleasure and pain or perceiving a quality, then with regard to all the material processes that take place in it our knowledge will indeed be just as perfect, and our need for causal explanation will feel just as satisfied, as with regard to twitch or secretion once we have astronomical knowledge of muscle and gland. The involuntary actions of the nerve centers, those not necessarily bound up with sensation, the reflexes, associated movements, movements of breathing, muscle tone, the metabolism of brain and spinal cord and the like, would be known exhaustively. The material processes that always coincide in time with mental processes, and so presumably coincide with them of necessity, would be seen through just as completely. And it would of course be a high triumph if we could say that during a particular mental process a particular motion of particular atoms takes place in particular ganglion cells and nerve fibers. It would be boundlessly interesting if we could look into ourselves with the mind's eye and watch the brain mechanics that belong to a sum in arithmetic play themselves out like the mechanics of a calculating machine; or even if we only knew what dance of carbon, hydrogen, nitrogen, oxygen, phosphorus and other atoms answers to the bliss of musical feeling, what whirl of such atoms to the height of sensual pleasure, what molecular storm to the raging pain when the trigeminal nerve, the great sensory nerve of the face, is mistreated. The kind of intellectual pleasure we take in the beginnings of psychophysics that Fechner created, or in Donders's measurements of how long the simpler acts of the mind take, lets us guess how such unveiled insight into the material conditions of mental processes would edify us. As things stand, we do not even know whether only the gray matter of the brain thinks or the white matter as well, or whether a particular state of mind answers to a particular position or to a particular motion of the brain's atoms or molecules.³⁶

As for the mental processes themselves, however, we find that with astronomical knowledge of the organ of the mind they would be just as incomprehensible to us as they are now. In possession of that knowledge we would stand before them as we do today, before something wholly unmediated. Astronomical knowledge of the brain, the highest we can attain, reveals in it nothing but matter in motion. And no arrangement or motion of material particles that anyone could devise will throw a bridge into the realm of consciousness.

Motion can only produce motion, or turn back into potential energy. Potential energy can only produce motion, maintain static equilibrium, exert pressure or pull. The sum of energy always stays the same. More than this law determines cannot happen in the physical world, and no less; the mechanical cause is used up wholly in the mechanical effect. The mental processes that go on alongside the material processes in the brain therefore lack, for our understanding, a sufficient reason. They stand outside the law of causality, and for that reason alone they cannot be understood, any more than a mobile perpetuum, a perpetual-motion machine, could be. But they are incomprehensible on other grounds as well.

On a superficial view, it is true, it might seem that knowing the material processes in the brain could make certain mental processes and dispositions intelligible to us. Among these I count memory, the flow and association of ideas, the effects of practice, special talents and the like. The least reflection shows that this is an illusion. We would be informed only about certain inner conditions of mental life, roughly equivalent to the outer conditions set by sense impressions, and not about how mental life comes about through those conditions.

What conceivable connection is there between particular motions of particular atoms in my brain on the one hand, and on the other the facts, primary for me, that cannot be defined further and cannot be denied: "I feel pain, feel pleasure, feel warm, feel cold; I taste sweetness, smell the scent of roses, hear the note of an organ, see red," and the certainty that flows just as directly from them, "Therefore I am"?³⁷ It is quite simply and forever incomprehensible that it should not be a matter of indifference to a number of carbon, hydrogen, nitrogen, oxygen and other atoms how they lie and move, how they lay and moved, how they will lie and move. There is no way of seeing how consciousness could arise from their working together.³⁸ If the way they are placed and move were not indifferent to them, we would have to think of them, after the manner of monads, as each endowed with consciousness already. That would neither explain consciousness in general nor gain the least toward explaining the unified consciousness of the individual.

It is therefore impossible in principle to explain by any mechanical combination why a chord on König's tuning forks pleases me,³⁹ and why touching red-hot iron hurts me. No mathematically reasoning understanding could determine a priori, from astronomical knowledge of the material events in the two cases, which is the pleasant process and which the painful one. That it is wholly impossible, and will always remain so, to understand higher mental processes from the mechanics of the brain's atoms, supposed known, needs no demonstration. But, as I have already said, there is no need at all to reach for higher forms of mental activity to give our argument more weight. It gains in force precisely from the contrast between the complete ignorance in which astronomical knowledge of the brain would leave us about how even the lowest mental processes come about, and the equally complete unriddling of the highest problems of the physical world that such knowledge would grant.

A brain that is unconscious for whatever reason, one sleeping without dreams, for instance, would hold no further secret once it had been seen through astronomically; and with astronomical knowledge of the rest of the body as well, the whole human machine, with its breathing, its heartbeat, its metabolism, its warmth and so on, would be completely deciphered, all but the nature of matter and force. The dreamless sleeper is as comprehensible as the world was before there was consciousness. But just as the world became doubly incomprehensible with the first stirring of consciousness, so does the sleeper again with the first dream image that dawns on him.

The insoluble contradiction in which the mechanical view of the world stands to freedom of the will, and through it directly to ethics, is certainly of great importance. The acuteness of thinkers of every age has exhausted itself on it, and will go on exercising itself there. But apart from the fact that freedom can be denied and pain and pleasure cannot, desire, which gives the impulse to act and so first gives occasion to do or to refrain, is necessarily preceded by sensation. It is therefore the problem of sensation, and not, as I once said, that of freedom of the will, to which analytical mechanics reaches.⁴⁰

With this the other limit of our knowledge of nature is marked out. No less than the first, it is absolute. In deriving mental processes from material conditions, humanity has made no more essential progress in two thousand years, for all the discoveries of natural science, than in understanding force and matter. It never will. Even Laplace's spirit, with its world formula, would be like an aeronaut straining toward the moon in its efforts to lift itself over this barrier. In its world, built up of matter in motion, the molecules of the brain do stir, as in a dumb show. It surveys their hosts, it sees through their interlacings, and experience teaches it to read each of their gestures as answering to this or that mental process; but why the gesture answers to it, the spirit does not know. Between a particular position and motion of certain atoms of matter without qualities in the sense substance of sight, and seeing, there is as little relation as between a similar event in the sense substance of hearing and hearing, or a third in the sense substance of smell and smelling, and so on; and that is why, as we saw a while ago, the objective world of Laplace's spirit remains without qualities.⁴¹

In Laplace's spirit we have the measure of our own capacity, or rather of our impotence. Our knowledge of nature, then, is shut in between the two limits set for it forever by our inability, on the one hand, to understand matter and force, and on the other, to derive mental processes from material conditions. Within these limits the natural scientist is lord and master; he takes apart and he builds up, and no one knows where the bound of his knowledge and his power lies. Beyond these limits he cannot go, and he never will be able to.

But the more unreservedly the natural scientist acknowledges the limits set for him, and the more humbly he submits to his ignorance, the more deeply he feels his right to form his own opinion on the relation between mind and matter by way of induction, in full freedom, undeterred by myths, dogmas and philosophemes proud of their age.⁴²

He sees material conditions influence mental life in a thousand cases. To his unprejudiced eye there is no reason to doubt that sense impressions really do communicate themselves to the so-called soul. He sees the human mind grow, as it were, with the brain, and, on the empiricist theory, even acquire the essential forms of its thinking only through outward perceptions. In sleep and dream; in fainting, intoxication and narcosis; in epilepsy, insanity and dementia, cretinism and microcephaly; in starvation, fever, delirium, inflammation of the brain and its membranes; in short, in countless states, some still within the range of health, others diseased, mental activity shows itself to the natural scientist as dependent on the lasting or passing condition of the organ of the mind. No theological prejudice prevents him, as it prevented Descartes, from seeing in the souls of animals members of one and the same series of development, akin to the human soul and less perfect by degrees. On the contrary: among the vertebrates, the parts of the brain to which physiological experiment and pathological experience also assign the seat of the higher mental activities keep pace in their development with the rise of that activity. Where, from the anthropoid apes to man, mental capacity makes the leap marked by the possession of language, there is a corresponding leap in the mass of the brain. But the different arrangement of the same elementary parts, ganglion cells and nerve fibers, in vertebrates and invertebrates teaches the natural scientist that here, as with other organs, what matters is less the architecture than the structural elements. With reverent astonishment he contemplates the microscopic speck of nerve substance that is the seat of the ant's soul, so industrious, so eager to build, so fond of order, so faithful to duty, so brave.⁴³ Finally, the theory of descent, together with the doctrine of natural selection, forces on him the conjecture that the soul arose as the gradual result of certain material combinations, and perhaps, like other heritable gifts useful to the individual in the struggle for existence, has grown and perfected itself through a countless line of generations.⁴⁴

Now if the old thinkers recognized every interaction between body and soul, as they conceived the soul, to be unintelligible and impossible, and if the riddle of how the two substances nonetheless keep in step can be solved only by pre-established harmony, then the idea of the soul they formed, caught as they were in the concepts of the schools, was probably false. Being driven to a conclusion so plainly contrary to reality is, as it were, an apagogic proof, a reduction to absurdity, against the premise that leads to it. To stay with the clock simile: should not the simplest solution of the problem be the fourth possibility, which Leibniz rejected in advance,⁴⁵ that the two clocks whose keeping together is to be explained are at bottom only one? Whether we shall ever understand mental processes from material conditions is a question quite different from whether these processes are the product of material conditions. The first question can be answered no without anything being settled about the second, let alone its being answered no as well.

In the passage quoted earlier, Leibniz says that the spirit incomparably superior to the human mind but finite, to which he ascribes senses and technical powers of matching perfection, could form a body that would imitate the actions of a man. He plainly does not say that it could form a man, because in his view the automaton of flesh and bone, which he imagines as soulless, as Descartes imagined the animals, would still lack the soul-monad, which no mechanics can grasp, to make it a man. But our idea of the relation between matter and mind becomes especially clear if we carry this fiction of Leibniz's a little further. Imagine all the atoms of which Caesar consisted at a given moment, at the Rubicon, say, each brought to its place by mechanical art at a single stroke and given its velocity in the right direction. On our view, Caesar would then be restored, in mind as in body. The artificial Caesar would have in the first moment the same sensations, strivings and ideas as his original at the Rubicon, and would share his memories, his inherited and acquired abilities, and so on. Imagine the same feat performed once, twice, several times, at the same time or at different times, with an equal number of other carbon, hydrogen and other atoms. How else would the new Caesar and his doubles differ in the first moment, except in the place where they had been put together? And yet the spirit Leibniz imagined, which had formed the new Caesar and his several Sosias, doubles like the slave in Plautus whose very likeness Mercury puts on, would still not understand how the atoms it had itself arranged correctly, and sent flying in the right direction at the right speed, bring about their mental activity.

Everyone will remember Carl Vogt's bold assertion, which in the 1850s set off a kind of tournament over the soul: "that all those capacities we comprehend under the name of activities of the soul are only functions of the brain, or, to put it somewhat crudely, that thoughts stand in roughly the same relation to the brain as bile to the liver or urine to the kidneys."⁴⁶ Laymen took offense at this comparison, which in essentials is already found in Cabanis,⁴⁷ because putting thoughts beside the secretion of the kidneys seemed degrading to them. Physiology, however, knows no such aesthetic differences of rank. To physiology the secretion of the kidneys is a scientific subject of exactly the same dignity as the study of the eye or the heart or any other of the organs commonly called nobler. Nor is the "secretion simile" much to be blamed for presenting the activity of the soul as the product of the material conditions in the brain. Where it goes wrong is in suggesting that the activity of the soul is, by its nature, as comprehensible from the structure of the brain as secretion would be from the structure of the gland, once our knowledge had advanced far enough.

Where the material conditions for mental activity in the form of a nervous system are lacking, as in plants, the natural scientist cannot admit a life of the soul, and on this he seldom meets contradiction. But what answer could be given him if, before agreeing to assume a world-soul, he demanded to be shown somewhere in the world a mass of ganglion cells and nerve fibers, matching in extent the mental powers of such a soul, bedded in neuroglia, the supporting tissue of the nerve centers, fed with warm arterial blood at the right pressure, and furnished with suitable sensory nerves and organs?

Finally the question arises whether the two limits of our knowledge of nature may not perhaps be one and the same: whether, that is, if we comprehended the nature of matter and force, we would not also understand how the substance underlying them can, under certain conditions, feel, desire and think. This idea is certainly the simplest, and by well-known principles of inquiry it is to be preferred, until it is refuted, to the one by which, as I said a little while ago, the world appears doubly incomprehensible. But it lies in the nature of things that on this point, too, we cannot reach clarity, and all further talk about it remains idle.

Faced with the riddles of the physical world, the natural scientist has long been used to pronouncing his Ignoramus,⁴⁸ "we do not know," with manly resignation. Looking back over the victorious road he has traveled, he is borne up by the quiet consciousness that where he does not know now, he could at least under certain circumstances know, and perhaps one day will. But faced with the riddle of what matter and force are, and how they are able to think, he must bring himself once and for all to the far harder verdict, that we shall never know:

Ignorabimus.

The Seven World-Riddles

Today I ratify this confession all the more readily because,
having since read far more and thought far more, and being
better informed, I am in a better position to affirm that I
know nothing.

Voltaire, Dictionnaire philosophique

Yet I dare say that I have deserved
Neither this excess of honor nor this indignity.

Racine, Britannicus

A lecture given at the public session of the Royal Academy of Sciences in Berlin in celebration of Leibniz Day, on July 8, 1880.

Eight years ago, when I had undertaken to give a lecture at a public session of the Assembly of German Natural Scientists and Physicians, I hesitated a long time before I resolved to take the limits of our knowledge of nature as my subject. The impossibility of grasping, on the one hand, what matter and force are, and on the other of explaining consciousness mechanically, even at its lowest level, seemed to me really a trivial truth. That atomism, dynamism and the continuous filling of space all come to grief alike is an old experience, which no discovery of natural science has been able to change. That no arrangement and motion of matter can make even the simplest sensation intelligible, excellent thinkers saw long ago. I knew well enough that false ideas on this last point were widespread; but I was almost ashamed to pour out so stale a draught for the German natural scientists, and I hoped to arouse interest only through the novelty of my proof.

The reception my argument met showed me that I had misjudged the state of things. The lecture, coolly received at first, soon had the honor of becoming the subject of numerous reviews, in which a great variety of standpoints made themselves known. The critics struck every note from joyful assent and praise to the most contemptuous censure, and the word Ignorabimus, in which my inquiry culminated, became a regular shibboleth of the philosophy of nature, the password by which one camp told itself from the other.

The excitement my lecture caused in the German world does not show the philosophical education of the nation, on which we are used to priding ourselves a little, in a favorable light. Flattering as it was to see my argument praised as a deed worthy of Kant, I must decline the glory. As I have said, my propositions contained nothing that could not have been known to anyone who cared about such things and had read a little in the older philosophical writers. But since Kant transformed philosophy, the discipline has taken on so esoteric a character; it has so unlearned the language of common sense and plain reflection; it has so far evaded the questions that move the unprejudiced student most deeply, or treated them so much from on high as impertinent demands; and finally it set itself for so long in such hostility against the new world power growing up beside it, natural science, that it is no wonder if, among natural scientists above all, even the memory of results quite solidly won in philosophy's earlier days has been lost.

Part of the blame lies, I think, in the fact that modern philosophy has mostly stood in a negative relation to positive religion, or at least in no clear one, and that it has avoided, consciously or not, speaking out plainly on certain questions, as Leibniz, for instance, could, who would have had nothing to hide before any church tribunal. Philosophy is to be neither praised nor blamed for this here; but the result is that from the middle of the last century on, the most gripping problems of metaphysics are not set out and discussed openly by the philosophers, or at least not in a language that suits the inductive natural scientist. This may also be one of the reasons why philosophy is so often pushed aside as empty of any object and unprofitable, and why now, when natural science has itself arrived at philosophizing on many points, such a want of the preliminary notions and such ignorance of what has really been achieved so often show themselves.

For while on the one side my merit was greatly overrated, on the other they cried anathema on me because I had drawn insurmountable limits to the human power of knowing. People could not understand why consciousness should not be intelligible in the same way as the heat given off in a chemical combination, or the electricity excited in a galvanic battery. Cobblers left their lasts and turned up their noses at "the confession of the Ignorabimus, which tastes almost of a consistorial councillor's humility, and by which ignorance is declared in permanent session." Fanatics of this persuasion, who could have known better, denounced me as one of the black band, the party of the clerics, and showed once again how close together despotism and the most extreme radicalism live.⁴⁹ More moderate heads, for their part, betrayed on this occasion that their dialectic was in poor shape. They believed they were saying something different from me when they set against my Ignorabimus a "We shall know," on condition that "we, as the finite human beings we are, content ourselves with human insight." Or they could not grasp the difference between the assertion I had refuted, that consciousness can be explained mechanically, and the assertion I had not doubted, and had indeed supported with many reasons, that consciousness is bound to material processes.⁵⁰

David Friedrich Strauss saw more sharply. Late in life the great critic of the Gospels had made the change, from the study of theology to natural science, that certain natures used often to run through quickly in their youth. The natural scientist by profession may think little of the second-hand expositions in which the author of The Old Faith and the New perhaps takes a little too much pleasure. The moralist, the jurist, the teacher, the physician may find something troubling in the rather forcible consistency with which Strauss tries to carry his view of the world into life. Though I myself once turned against him in that sense from this very place,⁵¹ I admire no less the power of mind and strength of character that carried this master of thought, so gifted an artist besides, into the midst of the old world-riddles, which he too does not solve, to be sure, but which he calls by their names without any earthly fear.

Strauss did not miss that, in facing mental processes, I had taken my stand entirely on the ground of the inductive natural scientist, who does not separate a process from the substrate on which he came to know it, and who does not believe, without sufficient reason, in the existence of a process set free from its substrate. Somewhat more practiced in tangled paths of thought, and used to more abstract ways of speaking, he naturally understood the difference between those two assertions. Strauss and Lange, the author of the Geschichte des Materialismus (History of Materialism), snatched from science too soon,⁵² spared me the trouble of putting down, with the saying "And whoever cannot understand me, let him learn to read better," the jubilation of those who fancied that in me a champion of dualism had arisen.

But Strauss too, remarkably enough, found fault with my proposition that consciousness cannot be understood from mechanical causes. He says: "There are, as is well known, three points in the ascending development of nature to which the appearance of the incomprehensible chiefly clings. They are the three questions: how did the living come from the lifeless, the sentient from the insentient, the rational from the irrational? The author of 'The Limits of Our Knowledge of Nature' holds the first of the three problems, A, the coming forth of life, to be soluble. He prepares the way for solving the third problem, C, that of intelligence and freedom of the will, so it seems, by taking it in the closest connection with the second, and conceiving reason only as the highest stage of the consciousness already given with sensation. The second problem, B, that of sensation, he holds on the other hand to be insoluble. I confess it would sooner make sense to me if someone said: A, namely life, is and remains inexplicable; but once that is given, B and C, namely sensation and thought, follow of themselves, that is, by natural development. Or, for all I care, the other way round: A and B can still be understood, but at C, at self-consciousness, our understanding breaks off. Either of these, as I say, would seem to me more acceptable than that the middle station alone should be the impassable one."⁵³

So much for Strauss. I regret having to say it, but he did not grasp the nerve of my argument. By astronomical knowledge of a material system I meant such knowledge as we would have of the planetary system, assuming perfectly exact observations and a perfected theory. If we had astronomical knowledge of what goes on inside an organ of an animal or plant body, however mysterious, our need for causal explanation would be satisfied with regard to that organ as it is with regard to the planetary system: that is, as far as the nature of our intellect allows, which founders from the outset on grasping matter and force. If, on the other hand, we had astronomical knowledge of what goes on inside the brain, we would not have come one hair's breadth nearer to understanding how consciousness arises. Even in possession of the world formula, Laplace's spirit, so immeasurably superior to our own mind and yet like it, would be no wiser here than we are. Indeed, equipped, as in Leibniz's fiction, with such technical skill that it could put together a homunculus atom by atom and molecule by molecule, it would make it think, to be sure, but it would not understand how it thought.⁵⁴

The first origin of life in itself has nothing to do with consciousness. It is only a matter of arranging atoms and molecules and setting certain motions going. Consequently, not only is astronomical knowledge conceivable of what is called spontaneous generation, generatio spontanea seu aequivoca, and lately abiogenesis or heterogeny; such astronomical knowledge would also satisfy our need for causal explanation with regard to the first origin of life just as it does with regard to the motions of the heavenly bodies.

That is why, to speak with Strauss, "in the ascending development of nature" the gap in our understanding does not yet come at point A, but only at point B. For the rest, I by no means asserted that once sensation is given every higher stage of mental development is intelligible, and problem C soluble without more ado. I laid such great weight on the mechanical incomprehensibility of even the simplest sensation only because the incomprehensibility of all higher mental processes follows from it all the more, by an argumentum a fortiori, an argument from the stronger case.

It is true that the first origin of life now seems wrapped in still deeper darkness than when one could still hope to see the living come forth from the dead in the laboratory, under the microscope. In Pasteur's experiments heterogeny has probably lost to panspermia for a long time, if not forever: where people believed life was arising, germs of life already present were developing. And yet things have taken such a turn that anyone who does not cling to an altogether childish standpoint can be compelled by logic to admit that life arose mechanically. Against geological actualism and the theory of descent, hardly a serious defender is still to be found of the doctrine of periods of creation, according to which creative omnipotence was forever destroying its work anew, only to begin it again from the start, like a bungling artist, better on one point, perhaps worse on another. Even someone who believes in final causes will admit that such proceedings seem little worthy of creative omnipotence. The most that befits it is to call the simplest germs of life into being by a single supernatural intervention in the mechanics of the world, but endowed so that today's organic creation would come out of them without further help. If this is granted, the further question is permitted whether it would not again be worthier of creative omnipotence to refrain even from that single intervention in laws it had itself laid down, and to endow matter from the very beginning with such forces that, under suitable circumstances, on earth or on other heavenly bodies, germs of life were bound to arise without further help. There is no reason to say no. But that is to grant that life could arise in a purely mechanical way; and then the only remaining question will be whether the matter that can join itself together into something living in a purely mechanical way was always there, or whether, as Leibniz thought, it was first created by God.

That astronomical knowledge of the brain would make consciousness no more intelligible from mechanical causes than it is today, I concluded from this: it must be a matter of indifference to a number of carbon, hydrogen, nitrogen, oxygen and other atoms how they lie and move, unless they already had consciousness one by one; and that would explain neither consciousness in general nor the unified consciousness of the whole brain.

I held this conclusion to be entirely convincing. David Friedrich Strauss thinks that in the end only time could decide whether this is really the last word on the matter. Well, it has certainly not remained the last word, inasmuch as Haeckel has taken the assumption I made for the sake of a reductio ad absurdum, that the atoms each have consciousness, and set it up the other way round as a metaphysical axiom. "Every atom," he says, "possesses an inherent sum of force, and is in this sense 'ensouled.' Without the assumption of an 'atom-soul' the commonest and most general phenomena of chemistry are inexplicable. Pleasure and pain, desire and aversion, attraction and repulsion must be common to all atoms of mass; for the motions of the atoms that must take place in the formation and dissolution of every chemical compound can be explained only if we ascribe to them sensation and will. . . . If the 'will' of man and the higher animals seems free in contrast to the 'fixed' will of the atoms, that is an illusion, produced by the highly complicated movement of will in the former in contrast to the highly simple movement of will in the latter." And quite in the spirit of the false philosophy of nature that once, from the very same place, Jena, did German science such harm, Haeckel goes on to constructions about the "unconscious memory" of certain "animate" complexes of atoms, which he calls "plastidules."⁵⁵

So he scorns the road La Mettrie showed us, of inquiring inductively under what conditions consciousness arises.⁵⁶ He sins against one of the first rules of philosophizing, "Entia non sunt creanda sine necessitate," entities are not to be created without necessity: for why consciousness where mechanics is enough? And if atoms feel, why sense organs as well? Haeckel passes over the difficulty, which I stressed sufficiently, of understanding how the unified consciousness of the whole brain springs from the countless "atom-souls." For the rest, I mention his proposition only to attach to it a question. Why does he think it Jesuitical to deny that consciousness can be explained from the arrangement and motion of atoms, when he himself does not dream of explaining it in that way, but postulates it as an attribute of the atoms that cannot be analyzed further?

A morphologist more practiced in looking at forms may be forgiven if he cannot keep apart concepts like will and force.⁵⁷ But similar blunders have been committed by better-schooled minds too. Reviving the anthropomorphic daydreams of the childhood of science, philosophers and physicists have explained the action of body on body at a distance, across empty space, by a will dwelling in the atoms. A strange will indeed, which always takes two! A will that, like Adelheid's in Goethe's Götz, is to will whether it wills or not, and that in direct proportion to the product of the masses and in inverse proportion to the square of the distances! A will that must move the hurled subject in a conic section! A will, in truth, that recalls the faith that moves mountains, but which has not yet been put to use in mechanics as a cause of motion. Such absurdity is what one comes to if, instead of humbly accepting one's bounds, one nails the flag to the mast and tries, with noisy phrases, to keep oneself and others in the intoxicated belief that one has succeeded where Newton despaired. In what contrast to such a venture stands the wise restraint of the master who sets analytical mechanics the task of describing the motions of bodies.⁵⁸

In any case, the fierce and widespread opposition to my claim that consciousness cannot be understood from mechanical causes shows how wrong modern philosophy is to take this incomprehensibility for granted. Rather, all philosophizing about the mind seems bound to begin by establishing this point, that is, with some argument corresponding to mine. If consciousness could be grasped mechanically, there would be no metaphysics; for the unconscious alone we would need no other philosophy than mechanics.

If I add here an attempt of recent times to push back the other barrier of our knowledge of nature and to throw light on the nature of matter, only to call it unsatisfying too, I do not mean to rank it as low as the ensouling of the atoms. The attempt came from the Scottish school of mathematical physics, from Sir William Thomson and that Professor Tait whose chauvinism rekindled the quarrel over Leibniz's share in the invention of the infinitesimal calculus, and who does not shrink from calling Leibniz a thief,⁵⁹ so that the honor of being named today in this hall does not properly belong to him. Sir William Thomson and Professor Tait believe that several important properties we must ascribe to the atoms can be derived from the remarkable properties that Helmholtz discovered in the vortex rings of fluids. We might think of the atoms, they say, as exceedingly small vortex rings, knotted in various ways and spinning on and on from all eternity.⁶⁰ Nothing could be more unjust than to pass off this theory, as was done in Germany, as a revival of the Cartesian vortices. In the vortex rings, it is true, ponderable matter does not circulate parallel to the axis bent into a ring, as electricity does in the little currents Ampère supposed to surround the particles of iron, but around that axis; still, Ampère's theory disposes one favorably toward Thomson's. But rash as it would be to dismiss Sir William Thomson's ingenious speculation lightly because it falls short in many respects, one thing can be asserted with certainty already: that it does no more than any earlier idea to resolve the contradictions our intellect runs into in its effort to grasp matter and force. For even if, on the assumption of a continuous filling of space on which it rests, it managed to derive the different densities of matter, it would still have to let the vortex motion either exist from all eternity or arise from a supernatural push; and so it would at once stand helpless again before the second difficulty that resists our understanding of the world, the problem of the origin of motion.

In all, seven of these difficulties can be distinguished. Among them I call transcendent those that seem to me insurmountable even when I imagine solved all those that come before them in the ascending development of nature.

The first difficulty is the nature of matter and force. As one of my two limits of our knowledge of nature, it is transcendent in itself.

The second difficulty is precisely the origin of motion. We see motion arise and pass away; we can imagine matter at rest; motion appears to us as something accidental to matter, something for which the sufficient reason must be given in each single case. If, then, we try to think of an original state in which no cause has yet acted on matter, so that our need for causal explanation has no further question left to ask about motion, we come to imagine matter, an infinite time ago, at rest and evenly distributed in infinite space. Since a supernatural push does not fit into our world of concepts, there is then no sufficient reason for the first motion. Or else we imagine matter as having been in motion from all eternity; and then we give up understanding on this point from the start. This difficulty seems to me transcendent.

The third difficulty is the first origin of life. I have said often, and only just now again, that against the received opinion I see no reason to hold this difficulty transcendent. Once matter has begun to move, worlds can arise; and under suitable conditions, which we can imitate no better than those under which a host of inorganic processes take place, the peculiar state of dynamic equilibrium of matter that we call life may also have come about. I repeat it and insist on it: if we were to allow a supernatural act, a single such act creating matter in motion would be enough. In any case we would need only one day of creation.

The fourth difficulty is presented by the apparently purposeful design of nature. Organic laws of formation cannot act purposively unless matter was created purposively at the beginning; laws acting in that way are therefore incompatible with the mechanical view of nature. But this difficulty too is not unconditionally transcendent. In natural selection Darwin showed a possible way around it, a way of explaining both the inner purposiveness of organic creation and its adaptation to inorganic conditions by a chain of circumstances working with natural necessity, after the fashion of a mechanism. What degree of probability the theory of selection may claim I weighed once before, on a like occasion, in this place. "In holding to this doctrine," I said, "we may well have the feeling of a man otherwise sinking past saving, who clings to a plank that just keeps him above water. But in the choice between the plank and going under, the advantage is decidedly with the plank."⁶¹ That I compared the theory of selection to a plank on which a shipwrecked man seeks rescue gave such satisfaction in the opposing camp, the camp of the world beyond, that in the pleasure of retelling it they turned the plank into a straw. But between a plank and a straw there is a great difference. The man who has only a straw to cling to sinks; a sound plank has saved many a human life. And so the fourth difficulty too is not transcendent for the present, however often serious and conscientious reflection comes to a halt before it, faltering.

Only the fifth is transcendent again, and wholly so: my other limit of our knowledge of nature, the origin of simple sensation.

I recalled just now how I proved the hypermechanical nature of this problem, and so its transcendence. It is not without use to see how Leibniz does it. In several places in his unsystematic writings we find the bare assertion that consciousness cannot arise from any figures and motions, or, in our language today, from any arrangement and motion of matter.⁶² In the Nouveaux Essais sur l'Entendement humain, which is otherwise directed against the Essay on Human Understanding, Leibniz has Philalethes, the advocate of sensualism, say, almost in Locke's own words:⁶³ "It will perhaps be fitting to lay some stress on the question whether a thinking being can come from an unthinking being without sensation or consciousness, such as matter. It is fairly clear that a particle of matter is not even able to produce anything by itself or to give itself motion. Its motion must therefore either be from eternity, or have been impressed on it by a more powerful being. But even if it were from eternity, it could not produce consciousness. Divide matter into parts as small as you please, as if to spiritualize it; give it whatever figures and motions you like; make of it a sphere, a cube, a prism, a cylinder and so on, whose dimensions are only one thousand-millionth of a philosophical foot, that is, of a third of the length of a pendulum beating seconds at latitude 45 degrees. However small this particle may be, it will act on particles of the same order no differently from the way bodies an inch or a foot across act on one another. And one could hope with as much right to produce sensation, thought and consciousness by putting together coarse parts of matter of a certain figure and motion as by means of the smallest particles in the world. These knock, push and resist one another just as the coarse ones do, and that is all they can do. But if matter could draw sensation, perception and consciousness out of itself directly, without a machine, or without the help of figures and motions, then these would have to be an inseparable attribute of matter and of all its parts." To this Theophilus, the spokesman of Leibniz's idealism, replies: "I find this reasoning as firmly grounded as it could be, and not only exactly right but also deep, and worthy of its author. I am entirely of his opinion that there is no combination or modification of the particles of matter, however small they may be, that could produce perception; since, as one clearly sees, the coarse parts could not do it, and in the small parts everything that happens is proportional to what happens in the large."⁶⁴

In the Monadologie, written later for Prince Eugene, Leibniz says it more briefly and with a characteristic turn of his own: "We are forced to admit that perception, and what depends on it, cannot be explained on mechanical grounds, that is, by figures and motions. If we imagine a machine whose structure made it think, feel and perceive, we can think of it enlarged in the same proportions, so that we could go into it as into a mill. And this granted, we shall find inside it nothing but parts pushing one another, and never anything from which a perception could be explained."⁶⁵

So Leibniz arrives at the same result as we do; but two things must be said about it. First, Locke's argument, which Leibniz adopted, has lost some of its force through the progress of natural science. For from today's standpoint one could object that as matter is divided ever more finely, a point does come at which it unfolds new properties. It is even very striking that neither Locke nor Leibniz considered how far from indifferent it is whether lumps of charcoal, sulfur and saltpeter a foot across lie beside and on top of one another, or whether these substances are ground together in a fixed proportion into a powder and corned into grains of a certain fineness. Not even the mechanical performance of similar machines is proportional to their size. If matter, then, according to the degree of its division, shows effect after effect that can be understood mechanically, why should it not, divided still more finely, also think, without this new effect ceasing to be mechanically intelligible? So as not even to give occasion for this question, which is only apparently justified but might mislead some people, it is better to leave out of play Locke's progressive grinding of matter and Leibniz's thought-mill, and to prove directly, of matter broken down into atoms, that no arrangement and motion of atoms will ever explain consciousness.

The second remark is that we go with Leibniz this far, but for the present no further. From the incomprehensibility of consciousness from mechanical causes he concludes that it is not produced by material processes. We content ourselves with acknowledging that incomprehensibility, to which I like to give the drastic form that it is just as impossible to understand why a pinch of the trigeminal nerve causes the pain of hell, as why the excitation of certain other nerves gives pleasure.⁶⁶ Leibniz places consciousness in the soul-monad assigned to the body, and has God's omnipotence run off in it a series of dream images corresponding to what the body goes through. We, on the contrary, pile up reasons for holding that consciousness is bound to material processes.

Moreover, not a word has been brought from any side against my proof that consciousness cannot be grasped mechanically; people have contented themselves with flat contradiction. According to Haeckel, my Leipzig lecture was "in essence a grandiose denial of evolutionary history," since I did not take into account that mankind will in time reach an organization standing as high above the present one as this stands above that of our progenitors in some earlier geological period.⁶⁷ Meanwhile our species seems to have been fairly stable since about the time of Homer; since Epicurus, who already knew that matter and force are constant, the nature of the physical world has become no more intelligible, nor, since Plato and Aristotle, the nature of mind; and before Haeckel's prophecy is fulfilled the earth may well have become uninhabitable. But if anyone here has sinned against evolutionary history, it is the prophet of Jena. However quickly or slowly the human brain advances, it must stay within the given type, whose highest product would be the unattainable ideal of Laplace's spirit. Now since my limits of our knowledge of nature hold for that spirit too, mankind will never rise above them by evolution either; and if Haeckel has nothing to set against my argument but the possibility of paratypical development, development beyond the type, I think I shall be proved right.

Not with full conviction do I set up as the sixth difficulty rational thought, and the origin of language, which is closely bound up with it. Between the amoeba and man, between the newborn child and the adult, there is certainly an enormous gulf; but it can be filled up to a certain degree with transitions. The development of the mental faculties along the series of animals does this objectively as far as the anthropoid apes; and to get from simple sensation to the higher stages of mental activity in the single individual, the theory of knowledge probably needs nothing but memory and the faculty of generalization.⁶⁸ However great the leap that remains between the highest animals and the lowest human beings, and however hard the problems to be solved here, once consciousness is given their difficulty is of a wholly different kind from the one that stands in the way of explaining consciousness mechanically at all: the two are incommensurable. Hence, once problem B is solved, to use Strauss's notation again, problem C does not seem to me transcendent. But as Strauss rightly remarks, problem C is closely connected with another, which comes seventh and last in our series. This is the question of the freedom of the will.

It lies in the nature of things, of course, that all the problems listed here have occupied mankind as long as it has thought. People have brooded at all times, among all civilized peoples, over the constitution of matter, the origin of life and the origin of language. Yet it was always only a few choice minds who pressed on as far as these questions, and if scholastic wrangling now and then arose over them, the quarrel hardly reached beyond academic halls. It is otherwise with the question whether man is free in his actions or bound by inescapable compulsion. Touching everyone, seemingly open to everyone, intimately woven into the basic conditions of human society, reaching into religious convictions at their deepest, this question has played a part of immeasurable importance in the history of the mind and of civilization, and the stages of development of the human mind are clearly mirrored in the way it has been treated.

Classical antiquity did not rack its brains much over the problem of free will. Since the ancient view of the world had, in general, neither the idea of natural laws that bind without exception nor that of an absolute government of the world,⁶⁹ there was no ground for a conflict between free will and the ruling principle of the world. The Stoa believed in a fate, and accordingly denied freedom of the will; but the Roman moralists, out of an ethical need, restored it on a naively subjective foundation. "The mind feels that it moves," we read in the Tusculan Disputations,⁷⁰ "and when it feels this, it feels at the same time that it moves by its own power and not by another's." Stoic fatalism was mocked with anecdotes like the one about the slave of Zeno of Citium who excused a theft he had committed by pleading fate, and was told: Very well, then it was also your fate to be flogged. It is a story that could still be played out today on the Bosporus, where the Turkish kismet has taken the place of the Stoic heimarmene, the fate that is allotted.

It was Christian dogmatism (no matter how many Semitic and how many Hellenistic elements fused in it) that the question of free will led astray into the darkest of mazes, mazes it had dug for itself. From the Church Fathers and the schismatics, from Augustine and Pelagius, through the scholastics John Scotus Eriugena and Anselm of Canterbury, down to the Reformers Luther and Calvin and beyond, there runs the hopelessly tangled quarrel over free will and predestination. God is almighty and all-knowing; nothing happens that he did not will and foresee from eternity. Therefore man is not free; for if he acted otherwise than God had foreordained, God would not have been almighty and all-knowing. Therefore it does not lie in man's will whether he does good or sins. How, then, can he be responsible for his deeds? How is it consistent with God's justice and goodness that he punishes or rewards man for actions that are at bottom God's own?

That is the form in which the problem of free will presented itself to the human mind, darkened by holy madness. The doctrine of original sin, the questions of redemption by one's own merit or by the blood of the Savior, by faith or by works, of the various kinds of grace, grew together in a thousand ways with that dilemma, already fertile enough in subtleties; and from the fourth century to the seventeenth, monasteries and schools all through Christendom echoed with disputations over determinism and indeterminism. There is perhaps no subject of human reflection on which longer rows of folios, never opened again, molder in the dust of libraries. But it did not always stay a war of books. Furious charges of heresy, with all the horrors that the ruling religious party was free to inflict on those who thought otherwise, attached themselves to these abstruse controversies all the more readily the less they had to do with reason and an honest search for truth.

How differently our own age conceives the problem of free will. The conservation of energy states that force, no more than matter, ever comes into being or passes away. The state of the whole world, and so of a human brain, at every moment is the unconditional mechanical effect of its state in the moment before, and the unconditional mechanical cause of its state in the moment after. That under given circumstances either one of two things could happen is unthinkable. The molecules of the brain can only ever fall in one determinate way, as surely as dice once they have left the cup. If a molecule swerved from its position or its path without sufficient reason, that would be a miracle as great as if Jupiter broke out of his ellipse and threw the planetary system into turmoil. Now if, as monism conceives it, our ideas and strivings, and therefore our acts of will too, are incomprehensible but necessary and unambiguous accompaniments of the motions and rearrangements of the molecules of our brain, then it is clear that there is no freedom of the will. For monism the world is a mechanism, and in a mechanism there is no room for free will.

The first to whom the material world appeared in this shape was Leibniz. As I have often pointed out in this place, his mechanical view of the world was entirely the same as ours. Though he could not yet follow the conservation of energy, as we can, through the various molecular processes, he was convinced of that conservation. He stood toward all molecular processes where we still stand toward some of them. Now, since Leibniz believed just as firmly in a world of spirits, took the ethical nature of man within the circle of his reflections, and indeed came to excellent terms with positive religion, it is worth asking what he thought of free will, and above all how he managed to join it to the mechanical view of the world.

Leibniz was an unconditional determinist, and the whole of his teaching obliged him to be one.⁷¹ He assumed two substances created by God, the material world and the world of his monads. The one cannot act on the other. In each, processes run their course in harmony with those of the other, with an unalterable, predetermined necessity, perfectly independent of each other yet keeping exact step: in the one, the works of the world machine, which can be calculated mathematically forward and backward; in the other, in the soul-monads that belong to each animate being, the ideas that correspond to the apparent sense impressions, acts of will and ideas of the monad's host. The mere name Leibniz gives his system, pre-established harmony, rules freedom out. And since the ideas of the monads are only dream images, without mechanical cause and without connection with the bodily world, Leibniz has an easy time explaining our subjective conviction that our actions are free. God has simply so regulated the flow of the soul-monad's ideas that it believes it acts freely.⁷²

On other occasions Leibniz falls in more with the ordinary way of thinking, leaving man an appearance of freedom behind which secret compelling impulses hide. With the article "Buridan" in his Dictionnaire historique et critique,⁷³ Pierre Bayle had once again drawn attention to the much-discussed sophism, wrongly ascribed to that scholastic and found already in Dante,⁷⁴ indeed in Aristotle, of⁷⁵

starves miserably to death, because everything is equal on both sides and he, being a beast, lacks the franc arbitre, the free choice of the will. "It is true," says Leibniz in the Theodicy, "that if the case were possible, one would have to judge that he would let himself die of hunger; but at bottom the question is of something impossible, unless God brought the thing about on purpose. For the universe could not be halved by a vertical plane halving the ass lengthwise so that everything would be equal on both sides, as an ellipse is halved, or any other of the plane figures I call amphidextrous, which are halved by every straight line drawn through their center. For neither the parts of the universe nor the entrails of the animal are alike, and alike placed, on the two sides of that vertical plane. There would therefore always be many things in the ass and outside the ass which, though we do not notice them, would determine him to turn to one side rather than the other. And although man is free, which the ass is not, yet in man too the case of a perfect equilibrium between the grounds for two decisions appears impossible; and an angel, or at least God, could always give a reason for the decision man has taken, even if, because of the far-reaching chain of causes, that reason were often very complex and incomprehensible to ourselves."⁷⁶

Leibniz gets past the question of what becomes, under determinism, of man's responsibility and of God's justice and goodness, with the help of his optimism. At the end of the Theodicy, a large part of which is given over to this subject, he spins out a fiction of Lorenzo Valla's⁷⁷ to show how it was hard, to be sure, on Sextus Tarquinius to be obliged to commit crimes for which he could not be spared the punishment. Countless worlds were possible in which Tarquinius would have played a more or less respectable part and lived more or less happily, among them even worlds in which he would have died at a great age, a virtuous old man, honored and mourned by his fellow citizens. But God had to prefer to create this world, in which Sextus Tarquinius became a villain, because he foresaw that it was the best, the one in which the ratio of good to unavoidable evil was a maximum.⁷⁸

It need hardly be said that monism can be served by none of these ideas, consistent in themselves but, to say the least, highly arbitrary and stamped with unreality; and so it must seek its own position toward the problem of free will. As soon as one decides to declare the subjective feeling of freedom an illusion, it is as easy on monist ground as on Leibniz's extreme dualism to reconcile apparent freedom with necessity. The fatalists of every age, whatever their conviction was rooted in, Zeno, Augustine and the Thomists, Calvin, Leibniz, Laplace⁷⁹ — not forgetting Diderot's Jacques the Fatalist and his captain, for whom everything here below was written up above — found no difficulty in it. With moderate dialectical skill one can be argued out of the feeling Cicero describes. In dreams, too, we feel free, though there the phantasms of our sense substances are playing with us. Of many actions that seem to be carried out with conscious intention, because they serve a purpose, we now know that they are involuntary effects of certain arrangements of our nervous system, the reflex mechanisms and the so-called automatic nerve centers. If we attend to the flow of our thoughts, we soon notice how independently of our willing ideas come to us, images light up and go out. Should our supposed acts of will really be so much more voluntary? Besides, if all our sensations, strivings and ideas are only the product of certain material processes in our brain, then the molecular motion bound up with the sensation of willing to raise the arm may at once be matched by the material impulse that raises the arm purely mechanically, and at first sight no obscurity is left at all.

But for most natures the obscurity appears as soon as one exchanges the physical sphere for the ethical. For we readily admit that we act not freely but as the instrument of hidden causes, so long as the action is indifferent. Whether Caesar, lost in thought, puts on his right or his left caliga, his soldier's boot, first makes no difference; either way he steps out of the tent booted. Whether or not he crosses the Rubicon, on that hangs the course of the world's history. So little are we free in certain small decisions that a connoisseur of human nature can foretell with surprising certainty which of several cards laid out under particular conditions we will pick up. But even the most resolute monist, faced with the graver demands of practical life, finds it hard to hold on to the idea that the whole of human existence is nothing but a fable convenue, a fable agreed upon, in which mechanical necessity handed Caius the part of the criminal and Sempronius the part of the judge, the two stock names of the Roman law books, so that Caius is led to the place of execution while Sempronius goes off to breakfast. When Heinrich von Stephan, the head of our postal service, tells us that year in, year out, of every hundred thousand letters so and so many are dropped into the box without an address,⁸⁰ we think nothing in particular of it. But that, according to Quetelet, year in, year out, of every hundred thousand inhabitants of a city so and so many are, by natural necessity, thieves, murderers and arsonists,⁸¹ outrages our moral feeling. For it is painful to have to think that we did not become criminals only because others drew for us the black lots that might also have fallen to our share.

Whoever walks through life as if sleepwalking, whether in his dream he rules the world or chops wood; whoever, as historian, jurist or poet, in one-sided contemplation, deals mostly with human statutes and passions, or whoever, studying and mastering nature with an equally narrow gaze, deals only with natural laws: he forgets that dilemma on whose horns our understanding languishes, impaled like the prey of the shrike, the butcher-bird, on its thorn; just as we forget the double images of our two eyes, which would otherwise pursue us everywhere and make us dizzy. The small band of those who, with the rabbi of Amsterdam, Spinoza, look on the All sub specie aeternitatis, under the aspect of eternity, wear themselves out in all the more desperate efforts to wrest free of this torment, unless, like Leibniz, they calmly deny themselves self-determination. The writings of the metaphysicians offer a long series of attempts to reconcile free will and the moral law with the mechanical order of the world. Had one of them, Kant perhaps, really succeeded in this squaring of the circle, the series would probably have come to an end. Only invincible problems are so immortal.⁸²

Less well known than these metaphysical efforts are the mathematical ones, aimed at the same goal, that have lately appeared in France. They take up Descartes's unlucky attempt to explain the interaction between soul and body, the spiritual and the material substance he assumed. For although Descartes held the quantity of motion in the world to be constant, and although he did not believe that the soul could produce motion, he thought all the same that the soul determined the direction of motion.⁸³ Leibniz showed that what is constant is not the sum of the motions but the sum of the moving forces, and that the sum of the directive forces, or of the progress along any axis drawn in space, present in the world also stays the same; by this he means the algebraic sum of the components, parallel to that axis, of all the mechanical momenta. By this last theorem, which Descartes had overlooked, so Leibniz argued, the direction of motions, too, cannot be determined or changed without a corresponding expenditure of force. However small one imagines that expenditure, it forms part of the mechanism of nature and cannot be ascribed to the spiritual substance.⁸⁴ It is an insight for which the apparatus Leibniz brought to bear was hardly needed, since a reference to Galileo's laws of motion is enough.

The late mathematician Cournot of Dijon,⁸⁵ Boussinesq, professor at Lille,⁸⁶ and the Paris academician de Saint-Venant, honorably known for his work on elasticity,⁸⁷ have one after another set themselves the task of breaking the bonds of mechanical determinism by proving that, contrary to Leibniz's claim, motion can be produced, or the direction of motion changed, without any expenditure of force. To this end Cournot and de Saint-Venant bring in the concept, long⁸⁸ familiar to the German physiological school, of triggering (décrochement): the release of a large store of energy by a small force, as the pull on a trigger fires a gun. They believe that the force needed to trigger a voluntary movement may be not merely very small in proportion but zero. Boussinesq, for his part, points to certain differential equations of motion whose integrals admit singular solutions, of such a kind that the sense in which the motion continues becomes ambiguous or wholly undetermined. Poisson had already drawn attention to these solutions as a sort of mechanical paradox.⁸⁹

Such a case is, for example, this. Take a frictionless cone with its axis vertical and its apex pointing upward, and a heavy point on its surface. Give the point, in the direction of the apex, exactly the speed it would gain by falling freely from the apex down to its own horizontal plane. It then arrives at the apex with a speed of zero and stays there at rest, until, on Boussinesq's assumption, a principe directeur, a directing principle dwelling there, is pleased to give it, in whatever direction it likes, a push that robs it of its support: a push that, though mechanically equal to zero, is supposed to be able to send it sliding down the surface of the cone again. A point of a curve or surface where something of this kind can happen Boussinesq calls a point d'arrêt, a stopping point; a point where the path forks, a point de bifurcation; and he holds that such points are where, in the organism, an immaterial principle can produce mechanical effects.⁹⁰

Cournot believes he needs the triggering force equal to zero, and Boussinesq the integrals with singular solutions, even to explain by them, together with the "directing principle," the variety and indeterminacy of organic processes. The German physiological school, long used to seeing in organisms nothing but mechanisms of a peculiar kind, will hardly make friends with this conception. In spite of assurances to the contrary, and in spite of the authority of Claude Bernard,⁹¹ to which Boussinesq appeals, it will fear behind the "directing principle" the vital force that in France keeps surfacing again, in one shape and under one name or another. Cournot's vitalist cast of mind lies in plain view.

I may remark here that Boussinesq misunderstands me when he has me say, in "On the Limits of Our Knowledge of Nature," that an organism differs from a crystalline growth, say the frost flowers on a windowpane or the Tree of Diana, the silver crystals chemists grow in a solution, only by its greater complexity. On the contrary, I set store by having named precisely the one circumstance from which, as I see it, spring all the palpable differences that have driven mankind always and everywhere to see two different realms in living and dead nature, although, on our present conviction, the same forces rule in both. That circumstance is this: in the inorganic individuals, the crystals, matter is in stable equilibrium, while in the organic individuals, living beings, a more or less perfect dynamic equilibrium of matter prevails, with a balance now positive, now negative. The stream of matter that rushes through the animal serves to turn potential energy into kinetic; and at the same time it explains the dependence of life on outside conditions, the integrating stimuli or stimuli of life of the older physiology, and the transience of the organism, set against the eternity of the crystal, resting in itself and needing nothing.⁹²

In our judgment the theory of unconscious life can do without integrals that fork or become undetermined, and without a "directing principle." On the other hand, it is to be doubted that anything can be achieved with them, or with triggering, in the dispute between free will and necessity. Paul Janet's favorable report to the Académie des Sciences morales et politiques,⁹³ the Academy of Moral and Political Sciences, whose luminous beauty I greatly admire, accepts, on the responsibility of the three mathematicians, the possibility of a mechanical indeterminism. But when this doctrine passes from the claim that the triggering force may be infinitely small to the claim that it may actually be zero, it seems to make an illegitimate use of a procedure that is customary in the infinitesimal calculus under quite different conditions. The first claim means only that the triggering force can be vanishingly small compared with the force it releases. In this sense the force of the wingbeat of a crow that sets off an avalanche vanishes beside the force of the masses of snow that end by plunging into the valley; that is, we may neglect a force equal to the wingbeat when we measure the avalanche, because it has no noticeable influence on any numerical reckoning and falls well within the limits of the errors of observation. But however tiny the wingbeat high above may look from the valley, beside the raging violence of the avalanche, close up it remains a wingbeat, equivalent to a definite weight lifted to a definite height. It lies in the nature of triggering that the triggering force and the force released are independent of each other and joined by no law; in Julius Robert Mayer's apt phrase, triggering is no longer a subject for mathematics at all.⁹⁴ It is therefore inexact at the least to say that "the ratio of the triggering force to the force released tends toward the limit zero"⁹⁵ without adding that this rests only on a growth of the released force that is accidental from the standpoint of the triggering force: in our example, with the wingbeat staying the same, on an ever greater height, steepness and smoothness of the mountainside, an ever mightier heaping up of snow, and so on. The triggering force is so far from being really zero in itself that, if the triggering is not to fail, it may not even fall below a certain threshold value, which depends on the circumstances. There is no thought, then, of explaining with the help of triggering how a spiritual substance could bring about material changes.

As for the solution Boussinesq proposes, the heavy point at the point d'arrêt has simply come to lie in unstable equilibrium, and to weigh the consequences of its lying there it was not necessary first to bring it up by integration. Indeed the case differs only in its abstract mode of expression and its mathematical dress from that of Dante or of Buridan, which can also be put by saying that the hungry creature, set

	"Between two foods, equally far off and equally
	Enticing . . .,"

is in unstable equilibrium. No "directing principle" of immaterial nature can shift the heavy point on the apex of the cone by the smallest amount; that always takes a mechanical force, however small. If a force equal to zero could do it, our second transcendent difficulty would vanish at the same time, the origin of motion when matter is evenly distributed in infinite space; for a push equal to zero is lacking nowhere.⁹⁶

Boussinesq also raises the well-known question of what would follow if all the motions in the world were reversed. Imagine the mechanism of the world made up only of reversible processes, and at a given instant the motions of all the parts of matter, great and small, reversed, at the same speed and along the same line, like those of a ball thrown back: then the history of the material world would have to play itself out again backward. Everything that ever happened would come to pass again in reverse order after its measured interval; the hen would turn back into the egg, the tree would grow backward into the seed, and after an infinite time the cosmos would have dissolved again into chaos.⁹⁷ What sensations, strivings and ideas, then, would accompany the reversed motions of the molecules of the brain? If mental states were bound only to positions of atoms, the same states would return with the same positions, which leads to strange conclusions: for example, that immediately before every act of will the reverse of what was willed would happen. But we may spare ourselves weighing the possibilities that can be imagined here. Not only because of the integrals that fork or become undetermined, as Boussinesq argues, but for other reasons too, the assumption is false that the crank of the world machine could be set in this way to "reverse." Among other things, the motion of masses that friction has turned into heat would not be turned back into the same amount of motion of masses, all in one direction, with its sign changed. The world turned backward remains an impossible mechanical fantasy, from which nothing can be inferred about how consciousness comes about or about free will.

With our seventh difficulty, then, the case stands thus: it is none at all, if one decides to deny free will and to declare the subjective feeling of freedom an illusion; but otherwise it must count as transcendent. And it is poor comfort to monism that it sees dualism caught in the same net, and the more helplessly the more weight dualism lays on the ethical. It was in this sense that I once wrote, in the preface to my Untersuchungen über thierische Elektricität (Researches on Animal Electricity), the words that Strauss has now invoked against me:⁹⁸ "Analytical mechanics reaches as far as the problem of personal freedom, whose settlement must remain a matter for each individual's power of abstraction."⁹⁹ But later, I make no secret of it, my own day of Damascus came. Repeated reflection for my public lectures "On Some Results of Recent Natural Science" brought me to the conviction that at least three transcendent problems come before the problem of free will: besides the one I had recognized earlier, what matter and force are, there are the problem of the first motion and that of the first sensation in the world.

That the seven world-riddles have been counted off and numbered here as in a book of mathematical exercises was done for the sake of the scientific divide et impera, divide and rule. One can also gather them into a single problem, the world problem.¹⁰⁰

The mighty thinker whose memory we celebrate today believed he had solved this problem: he had arranged the world to his own satisfaction. Could Leibniz, standing on his own shoulders, share our reflections today, he would surely say with us: Dubitemus, let us doubt.