The proposal to replace Mechanical Physics by Energetics. Whatever it may be worth, this proposal at least puts Mechanical Physics anew upon its trial.

I. What is energy? Professor Tait's definition of Matter as the ‘vehicle or receptacle of Energy’ examined. Relation of Energy to Matter. Helmholtz's exposition of this relation. Relation of Energy to Mass. Is not Mass as much an analytical abstraction as Force?

All change either a transference or a transformation of Energy, and Kinetic Energy only one form of actual energy—this is the new doctrine. Difficulties of the old theory which is bent on resolving all actual energy into kinetic energy. Professor Duhem's protest, and some reflections that it suggests.

Returning to the new theory we note (i.) that quantitative equivalence not qualitative identity is all that is asserted of the several forms of energy; and (ii.) that some of these forms may still remain undiscovered. Some final reflections on the mechanical bias.

II. What is the Conservation of Energy? What it is not; it does not warrant statements about the past or future of the universe. It does not mean that Energy is verily and absolutely the substance of the universe. Its relativity. Its character as a postulate. Implications of this, and new questions opened up.

IN the preface to the Principia, it will be remembered, Newton gave expression to his hope that if the mechanical principles he had laid down should prove inadequate to the explanation of “the other phenomena of nature, they might at least afford some light to a more perfect method of [natural] philosophy.”1 The inquiry which has occupied us for the last two lectures seems to shew that the first alternative is well-nigh, if not quite, hopeless. In place of simplifications of actual phenomena it offers us fictitious mechanisms; or mechanical analogies, in which quasi-rigidity, quasi-elasticity, quasi-mass, and quasi-matter meet us at every turn. One recent writer, the brilliant German physicist, Hertz, did not shrink from assuming that the underlying mechanism, by which he proposed to explain the effects we perceive, consists of hidden masses and motions that exceed by an infinite number the masses and motions to be described.2 And even with all this more than poetic license it has not been found possible to resolve electrical and chemical phenomena into motions, to say nothing of the phenomena of organic life. Yet all these phenomena, it is said, are clearly amenable to the principle of the conservation of energy. In spite of the physicist's complete ignorance as to what the mechanism of electricity, for instance, may be—if indeed it has any mechanism at all—‘electric current’ can be produced, measured, and retailed to consumers like other commodities; and it is so far under control that it can be transformed into its equivalents of heat, light, or motive power. Nay, but for a knowledge of these transformations and their mechanical equivalents, the mechanical treatment of physics could not have advanced as far as it has. Here then is a principle universal in its range, independent of atomic hypotheses and fictitious forces, confirmed by innumerable experiments and contradicted by none, a principle that verily brings all physical phenomena, mechanical as well as the rest, under a single real scheme, surely this, it is said, is the true integral law of the world. And so just forty years ago Rankine sketched “the outlines of the science of energetics.” The project has never been lost sight of, and within the last few years it has been pursued with ardour in many quarters, especially in Germany and in France. The views of the extreme upholders of this new science are still sub judice, so much so that it would ill become me as a complete layman in such questions to venture any opinion. But the doctrine of energy is fully admitted even by those physicists who are not prepared to yield it precedence over the old Newtonian mechanics. At the same time the more progressive doctrines are at least effective as criticisms of the older view. They are a new outgrowth, which, if it does not displace, must at least profoundly modify the older form. For these reasons it has seemed to me best to reserve the discussion of this subject till now, and to do so was easy, as the mechanical ideal contrives to dispense with all forms of actual energy save the old vis viva. And let me remark, by the way, that energy, as I understand, is to be regarded as a physical fact and not as a mathematical conception; in discussing it and the criticisms of the mechanical theory that it suggests, we are not then concerned with abstract mechanics as a branch of mathematics, but only with mechanics applied to physical phenomena.

This becomes evident when we ask: What is energy? It is in the answer to this question that we come upon the new wine that is to try the old bottles of the mechanical theory; for energy is so defined as to threaten the independent existence of that matter which was first of all regarded as its necessary substratum. Thus Professor Tait informs us that “in the physical universe there are but two classes of things, Matter and Energy.” Further, that as “energy is never found except in association with matter … we might define matter as the Vehicle or Receptacle of Energy.”3Vehicle, I presume, we are to take as the appropriate simile where the energy is actual and changes are in process; receptacle, when the energy is only ‘stored,’ and changes are only potential. But either way these figurative expressions distinctly imply that we know by experience each of these two things, just as we know and distinguish the cycle and the rider, the basket and its contents. The appropriateness of such language turns entirely on the question whether or no we have such knowledge. It will not do to say: We must have it, since we know that both matter and energy are conserved. We shall come to that presently; but it is plain our knowledge cannot begin there. To know such laws about the things, we must first have some sensible acquaintance with the things themselves. We get a little nearer to what we want when Professor Tait goes on to say: “Matter is simply passive (inert is the scientific word); energy is perpetually undergoing transformation.” But surely to be perpetually undergoing transformation is no better than the dreariest picture of unmitigated passivity. However, Professor Tait continues: “the one [matter] is, as it were, the body of the physical universe; the other [energy] is its life and activity.”4

Our question, then, can now be more precisely put; it is not, What do we or what does Professor Tait know about this simply passive thing, this inactive unchangeable body, as it were; ‘scientific words’ like inert, conservation, and the like, being used. The question is: What sensible acquaintance have we with the thing itself? Now it is remarkable that, although the book I have been quoting is entitled Properties of Matter—Professor Tait proceeds to say: “From the strictly scientific point of view the greater part of the present work would be said to deal with energy rather than matter;” and he only justifies the title he has used on “the two grounds of custom and convenience.” We are not, however, concerned either with custom or with the convenience of exposition: on the contrary, it is the “strictly scientific” answer we want to the question: How far matter can be known apart from energy? The answer is: It cannot be known at all. I do not give this as the answer of philosophers, it is the answer of the physicists themselves. Every physical quality we distinguish, every physical change we observe, every physical measurement or comparison we can make, relates to energy, to the “life and activity” of the physical universe; not one refers to the supposed vehicle or receptacle, “the body, as it were,” of that activity. In that famous memoir on the subject, which fifty years ago was rejected as nonsense, though it has now become one of the corner-stones of the new edifice, Helmholtz concedes this point, without, however, realizing its consequences. The point is one which, it may perhaps be thought, I have laboured sufficiently already when endeavouring to make clear the extremely abstract nature of the conception of mass. But we are approaching it now from what we might call the opposite side, and I am anxious that at every stage we should keep our authorities well in sight. Let me then quote a few sentences from the philosophical introduction, as he calls it, with which Helmholtz prefaced his essay on The Conservation of Energy. And please note that what primarily concerns us is the answer that his words afford to our question as to the possibility of knowing matter as distinct from energy. His philosophy of the relation of the two conceptions we can examine later. “Science,” he tells us, then, “deals with external objects from two abstract points of view: first, as barely existent, apart from their effects on other objects or on our organs of sense; as such we call them matter, which for us is a thing in itself without motion, without action. Qualitative differences are not to be ascribed to it, for so soon as we speak of different kinds of matter we imply differences of operations, i.e. of energies. Natural objects however are not without action, for we become acquainted with them at all solely through their actions, by which they eventually affect our senses; while from these actions we infer a something acting. In applying the conception of matter, therefore, to actual things, we must restore through a second abstraction what we were previously for leaving aside, the power to produce effects; in other words, we must assign them energy. It is manifest that, when applied to nature, the conceptions of matter and energy are not to be separated. Pure matter would for the rest of nature be a thing of indifference, since it would never determine any change either in this or in our senses. Pure energy would be something that ought to exist and yet again ought not to exist, for the existent we call matter.… Both conceptions are abstractions from the actual formed in the same way; we can in truth perceive matter only through its energies, never in itself.”5 Now here we have the most unequivocal admission that of matter as the simply passive vehicle or receptacle of energy we perceive nothing; that all we perceive of external objects is due wholly and solely to energy and to energy alone. True, Helmholtz proposes to treat both matter and energy as abstractions that are on the same footing; but in so doing, though—like Professor Tait afterwards—he conforms to custom and convenience, he flies straight in the face of the strictly scientific view. No doubt we call matter the existent, attributing energy as a power or property to it, and attributes cannot be separated from their substances. But great as are the forces of custom and the claims of established conventions, all that the facts lead us to infer is a “something acting,” not a something passive, which would be a thing of indifference for everything beside. To the one conception corresponds, in short, all our perceptual experience; to the other the unutterably metaphysical notion of bare existence per se. How then can they be both on the same footing, especially for a scientific view that discards the notion of substance as non-phenomenal and defines matter as “that which can be perceived by the senses?”6 Energy and its transformations are given, and nothing else is given; those who wish may attach the idea of substantiality or actuality to this, but they may not multiply entities needlessly. It would seem, then, that there are not, after all, two classes of things in the physical universe, but one only. Such at least appears to be the logical outcome of the theory of energy.

But what of mass, it will be asked; surely mass is a property of matter, is, in fact, that very passivity which distinguishes matter from energy. To answer this we have only to ask another question: Is mass perceptible by an external sense or is it not? Now, if we turn to our text-book, Professor Tait tells us first of all that “the mass of a body is estimated by its inertia;” next that inertia “may be described as passivity or dogged perseverance” in the motor status quo, “familiar instances of which present themselves in all directions,” as when the “sudden stopping of a train appears to urge the passengers forwards.”7 In other words, we become acquainted with inertia when we experience a change of momentum, and in no other way. But such an experience, whether we regard it as a change or as a perseverance against change, implies time and implies ‘the action of natural objects.’ How are we going to advance from this to mass as pure passivity, which implies neither? To that we can find no answering experience. But we have seen how theoretical mechanics by analysing the dynamical transactions in which momentum is changed has reached the two abstract conceptions of mass and force. That the latter of these terms is nothing but an analytical abstraction Professor Tait has taught us with commendable emphasis and persistence. Is it not then odd that he is so anxious to persuade us that the former is a reality? Surely here at least the two abstractions are on the same footing. Then must we not decline to accept masses as things, in which energy careers like Ariel “on the curl'd clouds”; or between which it is imprisoned, like Ariel “’twixt a cloven pine”?

All change is either a transference or a tranformation of energy—this is the new doctrine. The familiar experiences to which we owe the conception of inertia are transferences of one particular form of energy, viz., motional or kinetic energy. This energy of motion may be mathematically regarded as momentum×velocity/2 or, as Clifford once put it, half the rate at which momentum is carried along.8 It is now, of course, a familiar fact that other forms of energy have their equivalents in kinetic energy and vice versa; it is this fact, indeed, that renders the doctrine of energy physically so important. But it is not a fact that other forms of energy are not only quantitatively commensurable, but qualitatively identical, with energy of motion. This qualitative identity is at best but an assumption; and in the vain endeavour to justify it we have seen the mechanical theory led, “to pass through the very den of the metaphysician strewed with the remains of former explorers, and abhorred by every man of science.”9

It is this instinct of self-preservation that prompts so many physicists just now to abandon as ‘foolhardy’ the adventure of mechanical physics, and to set about the construction of what we might call energetical physics instead. Let me quote one of them, Professor Duhem of Lille. Referring to the mechanical method, and after illustrating its futility in chemical physics, he says:›“We have seen this method at work; we have ascertained to how small an extent experience accords with the results of its deductions. In the face of such rebuffs is it not prudent to renounce the doctrines followed thus far? Why seek by mechanical constructions to set aside bodies and their modifications, instead of taking them as our senses give them, or rather as our abstracting faculty, working on the data of sense, leads us to conceive them? … Why seek to figure changes of state as displacements, juxtapositions of molecules, variations of path, instead of characterising such changes of state by the disturbance introduced into the sensible and measurable properties of the body, such, e.g. as increase or decrease of density, absorption or evolution of heat, etc.? Why wish that the axioms on which every theory must rest should be propositions furnished by statics or dynamics, instead of accepting for principles laws founded on experience and formulated by induction, whatever be the form of such laws and whatever be the nature of the concepts to which they appeal?”10

Such language as a protest against the intellectus mathematicœ permissus sounds like the counterpart to Bacon's against the intellectus sibi permissus, and leads one to wonder whether, after all, one and the same infirmity will not account for both—I mean that hankering after certainty and definiteness by which we are hurried into hasty generalisations. It was this that Bacon exposed as the anticipation of nature, while ironically praising it as so much easier and more satisfying a method than the patient interpretation of nature. It was to this too that Descartes referred when he declared the will and not the intellect to be the source of errors. A mechanism may be very complex, but once get at the working drawings, and then, as Professor Hicks suggests, there are no surprises, no irregularities, no uncertainties; only master the mathematics, and you are intellectually master of the whole. That is one reason why so many “wish that the axioms on which every theory must rest should be furnished by statics or dynamics.” And there is another reason still, and one to which even Descartes, spite of all his rules, completely succumbed—I mean the influence of the imagination. We figure changes of state as being displacements or motions because we can imagine nothing else with equal clearness and distinctness. We cannot be surprised then that the certainty of mathematics, and the freedom from contradiction and obscurity of mechanical imagery, should have led so many able minds to an anticipation of nature that is unwarranted by facts, and even induced them to affirm as Descartes, yes, and Kant too, have done, that a true science of nature extends just as far as mechanics will carry it and no farther. Time's cure for such an error is twofold: first, to leave it to work itself out and so refute itself; and secondly, to confront it with facts to which it will not apply. It was just such a conjuncture that made Bacon's denunciation of scholastic science effective. Perhaps some of you may live to see a second intellectual reformation in which the mechanical ideal of modern science will be proved in its turn to be defective and chimerical. At any rate, we have noted much that is ominous. Rigorously carried out as a theory of the real world, that ideal lands us in nihilism: all changes are motions, for motions are the only changes we can understand, and so what moves, to be understood, must itself be motion. Again, regarded as a descriptive or symbolic scheme, it proves to be only approximate and to become involved in interminable complications in the attempt to be exact. Just when scientific men, who are neither mathematicians nor physicists, Du Bois-Reymond and Huxley, for instance, are preaching “the advancing tide of matter and the tightening grasp of law,” we find professed physicists renouncing their allegiance to this ancient idol. It is remarkable, too, that a change of a precisely opposite kind is going on in the more concrete sciences, which were formerly distinguished, as natural history, from physics, to which was reserved the title of natural science. Boltzmann refers to this: thus, he says: “What were formerly called the descriptive natural sciences triumphed, when Darwin's hypothesis made it possible, not only to describe the various living forms and phenomena, but also to explain them. Strangely enough, physics made almost exactly at the same time a turn in the opposite direction,”11i.e. as I understand, abandoning the attempt to be explanatory and contenting itself with being descriptive.

But returning now to the new theory of Energy. One important point for us to take account of—let me observe once more—is that this doctrine only entitles the physicist to assert the quantitative equivalence of phenomena that are qualitatively diverse: so much energy in the form of heat is equivalent to so much energy in the form of mechanical work; or again, so much thermal or mechanical energy has its equivalent in radiant energy or in energy of electric field. But it is going altogether beyond the facts to assume that all these forms are at bottom the same, i.e. mechanical or kinetic. The endeavour to reduce them to one is of course legitimate and in the interests of simplification. It is, however, pure hypothesis; there is no necessity about it; and, moreover, it is a hypothesis, as we have seen, round which, in spite of all that it has accomplished, difficulties seem steadily to thicken.

There is still another point that we must not overlook,—not only are the several forms of energy qualitatively distinct, but we have, I take it, no means of knowing that all these forms have been ascertained. We have no means of ear-marking a portion of energy; and it is not necessary to know all the transformations and transferences that may intervene in the course of a reversible cycle before it can be said that, whatever changes energy undergoes, it is never destroyed. Indeed it would, I believe, be substantially true to say that it was by assuming the conservation of energy, while still mistaken as to the nature of heat, that Carnot laid the foundation of thermodynamics. A strict quid pro quo is the one thing essential. The Bank of England issues notes equivalent in value to the gold in its cellars, and pays the gold out again to whoever presents the notes, and is so far unconcerned as to all the transactions that have intervened. Whether these transactions were many or few, domestic or foreign, industrial or financial—is of no account. So here: our ignorance of one or many possible transformations does not affect the main doctrine, provided we never find a transformation in which energy appears or disappears, unaccounted for.

But it is obvious that this possibility of unknown forms of energy coupled with the probability that the known forms are not all mechanical, suggests many new vistas, for which it behoves us to keep an open mind. I shall hope to recur to this briefly in dealing with psychophysics. For the present I think we are entitled as spectators of the march of science to say at least this much: Mechanics is no longer, at the end of the nineteenth century, what she was at the beginning, when the author of the Mécanique céleste proposed that “jubilant toast” to her that has served as our text. Absolute supremacy is hers no more; at best she is but prima inter pares, and even this, not because of the paramount value of the real knowledge she can bestow, but solely for her abstract purity of form. Should the science of energetics be destined to grow in importance at her expense, such an event would be by no means without a precedent. Think of the simplicity of the old Ionian and other pre-Socratic philosophies. Without a vestige of that knowledge that looms so large and imposing in the present concrete sciences, they set up their several ἄρχаι or first principles, water, air, fire, and so on; which now, so far from standing out as the obvious Alpha and Omega of all things, are simply lost in the multitude of particulars, quite on a par with them. And so in the history of science, do we see axiomata media, or middle principles, continually dwarfing and overtopping what had appeared as the veritable summits of knowledge in earlier days—such supposed summits constituting, by the way, the philosophy rather than the science of the time. And the remark is relevant, for mechanics, as I have had occasion to say before, has hardly yet ceased to count as natural philosophy, and even carries back its claims to those early times just referred to, when Democritus and Leucippus first broached the atomic theory. Its long supremacy is due largely no doubt to that vividness and mathematical accuracy with which the imagination can follow geometrical constructions. We are familiar with the influence of this fact, direct and indirect, on the minds of Plato, Descartes, Spinoza, and Kant. Had the inadequacy of the old atomism been realised earlier, the sway of the strictly mechanical theory would have been briefer. But it was only as physics and chemistry grew that these defects of the theory of “hard, massy particles” disclosed themselves in the course of attempts to resolve physical and chemical phenomena into mechanical processes between such particles. The result, as we have seen, has been to justify Lagrange's contention that mechanics is essentially a branch of pure mathematics, and as such subservient to, not dominant over, the concrete physical sciences. These meanwhile have a new ground of unity in the doctrine of energy. The only way to a supreme generalisation concerning physical things seems to lie through this; but it is altogether premature to suppose that that generalisation will be found to consist of such a world-formula as Laplace in his enthusiasm ventured to predict.

I have said much of this projected science of energetics, but nothing as yet of its main principle, the so-called Conservation of Energy. What does this mean? Methodologically, in other words, as a formal and regulative principle, it means much; really it means very little. Those who imagine that it furnishes any basis for statements concerning the past, present, or future of the universe, as a whole, are assuredly mistaken. And there are many such. We had an instance, for example, in the passage from Du Bois-Reymond's famous Leipzig address, which I quoted in the second lecture. Referring to Laplace's imaginary intelligence, Du Bois-Reymond represents him as calculating at what moment the universe will lapse into icy chillness, its energy, though conserved, being, in accordance with the second law of thermodynamics, entirely degraded to the unavailable form of heat at one temperature. To say nothing of the impropriety of treating the doctrine of the dissipation of energy as comparable in validity with the principle of the conservation of energy, the gratuitous assumption is here made that the quantity of energy in the universe is finite. If it should be infinite—and why should it not be?—then even Laplace's superhuman intelligence would be effectually nonplussed. But all statements concerning concrete quantity, and energy is such a quantity, imply measurement. There is but that one way of answering the question: How much? It cannot be answered a priori or by mere mathematics. To those who are fond of the ‘high priori road’ I will suggest the following consideration: If the energy of the world is a finite quantity and the second law of thermodynamics valid, how is it that the said degradation and consequent icy stillness are not the fact? On these assumptions that energy can only last a finite time, and the ratio of finite time to infinite duration is strictly infinitesimal. The chances then are infinity to one in favour of the universe being at any given moment ‘played out.’12

But now I will venture to say that not only does the principle of the conservation of energy tell us nothing about the quantity of energy in the universe as a whole, but that it does not even allow us to say that such quantity is an amount eternally fixed. I am quite aware that Mr. Spencer may here interpose with his caveat against “pseudo-thinking,” and remind us of “the experimentally established induction” that energy is indestructible. As to the first—we shall come to the second presently—I am content to make again the reply made when we were discussing the conservation of mass. Reality and substantiality are not identical; if energy be verily and absolutely substantial, it must no doubt be verily and absolutely permanent, neither generated nor liable to decay. But it is obvious that we cannot by observation or measurement show that this is actually the case, nor can we by a priori reasoning prove that it necessarily must be. It would be safe to go further, and to say that if energy were verily and absolutely the substance of things, it could not be measured at all. To what is absolutely substance the notion of unity and totality will apply, but these are not metrical notions. The scientific meaning of the statement, “the energy of the universe is constant,” then, is not what at first blush it seems to be and is often mistaken to be. Apparently an absolute statement, it is really a relative one, and only valid as such. Apparently a statement of fact, it is really only a postulate. As with the conservation of mass, which—as we have seen—it may turn out to include, so with the conservation of energy; there are the same two grounds for making it, but neither will suffice to place it beyond question. First, it is borne out by experience, so far as we know; and secondly, it seems the simplest and best working hypothesis. As to its relativity, this it shares in common with every other empirical statement: all such tell us nothing but the ratio between the quantity measured and the quantity of the unit or standard employed in measuring. If both these quantities were to vary in the same proportion, their ratio, of course, would remain unaffected; hence it can afford no evidence of such variation. We assume, however, that our standard is fixed, or what comes to the same thing for metrical purposes—that, if there is any variation, it is a uniform variation throughout the universe. This is all that constancy means. But a principle that will allow of such an interpretation cannot be one relating to substance.

Regarded as a postulate the conservation of energy appears under a somewhat different aspect, and one of especial interest to us. I greatly regret that there is not time enough left to deal with it more fully.13 It is allowed that as an experimental generalisation the conservation of energy can only claim to be probable; on what ground then is it put forward as a fundamental principle? Helmholtz, also Thomson and Tait, found on “the axiom that the Perpetual Motion is impossible.” Mayer, a genius to whom the world has yet to do justice, and even Joule, are more ‘metaphysical.’ Mayer falls back on the formula, Causa ™quat effectum; and Joule declares it “manifestly absurd to suppose that the powers with which God has endowed matter can be destroyed.”14 It is clear, then, that not only are we not here in the region of experimental proof, but that no direct proof of any kind is offered us. The use of terms such as ‘impossible’ and ‘absurd’ shew plainly that any proof there is, is indirect—a sure sign that, if we are dealing with a truth at all, it is one that is self-evident. And yet it was not till the year 1775 that the French Academy of Sciences, with Lagrange and Laplace at their elbow, were so far convinced that the perpetual motion was impossible, as to decline for the future to receive any pretended demonstration of such a machine. Moreover, as Mach15 has pointed out, the principle of virtual velocities, on which Lagrange's whole Mécanique analytique rests, really presupposes this axiom; yet Lagrange himself was not clearly aware of it, though sensible of the insufficiency of his proof as it stood—an insufficiency that led Poinsot to remark, that Lagrange had only lifted the clouds from the course of mechanics, because he had allowed them to gather at the very origin of that science. But after all the impossibility of perpetual motion only covers half the ground; friction and strain are absent from ideal mechanisms, so that the question what becomes of apparently wasted energy does not arise. It was the study of actual machines, with which Lagrange never troubled himself, that brought this side to the fore; and it is this, the converse of the first axiom, that Joule is attempting vaguely to formulate when he says it is absurd to suppose that material powers can be destroyed. The remark is noteworthy, for it is customary to extol Joule as a sound experimentalist and to depreciate Mayer as a metaphysical dreamer. But there is little doubt that both men first conceived the general truth, and then set about to verify—the one by experiments, the other by computations from ascertained physical constants—what they had thus conceived. Mayer in one of his letters, quoted by Mach, says expressly: “Engaged during a sea voyage almost exclusively with the study of physiology, I discovered the new theory for the sufficient reason that I vividly felt the need of it.”16 But Mayer's statements are the more comprehensive inasmuch as he refers to both the creation and the annihilation of energy as impossible assumptions, summing up both in the one formula, Causa œquat effectum. To be sure this as it stands is too vague and perhaps too general to be impressive. More definite and workable formulations have been devised since. But the point is that, in however imperfect a form, Mayer's statement of the principle embodies all that is axiomatic in the conservation of energy, and that at bottom is none other than the principle of sufficient reason which you will remember Laplace too postulated. More precisely—since in dealing with energy, we are dealing with procession, with changes—the axiom implied is the principle of causality. These two principles of sufficient reason and causality may occupy us at some length later on. But I will anticipate to the extent of mentioning some points that will help us to round off this portion of these lectures, and bring it not merely to an end, but to some sort of conclusion.

Looked at broadly, if you will philosophically, these principles of sufficient reason and causality are part of the postulate that everything shall be intelligible and the whole of things rational. This is the faith of science; on this point all are agreed. Even Hume and Kant are here at one; both allow that such principles do not derive their validity from experience, though they differ widely as to what this validity is worth. The principle of causality is not a logical or a mathematical, but a real principle; in the principle of the conservation of energy we have its aspect as quantitative applied to physical change. So we may see by the way how Lagrange as the representative of abstract mechanics failed to reach it, while Mayer, bent on rendering concrete physical facts intelligible, “vividly felt the need of it.”

But though a real principle, the conservation of energy renders only the quantitative relations of physical processes intelligible. What about the qualitative relations between which it only determines quantitative equivalences? Have we not an equal right to postulate intelligibility here too? It is here that the psychical as distinct from the physical comes in. Action initiated by feeling is now the fundamental fact. True, we still have quantitative distinctions of a sort; that is, we have a scale of values or worth, degrees of pleasure and pain, degrees of beauty and ugliness, degrees of merit and demerit. But qualitative differences not amenable to mathematical treatment underlie them all. Motives, then, are of the nature of causes; and conduct falls within the range of the principle of sufficient reason; although in the last resort conduct carries us back to a sentient being with its pronouncement, Sic volo, sic jubeo, stet pro rationc voluntas. Let me recall your attention to two points in the famous pæan of Laplace: (1) his acceptance of the principle of sufficient reason as fundamental; and (2) his assumption that his imaginary intelligence “shall be acquainted with all the forces [let us say, with all the causes] by which nature is animated.” If pleasures and pains can be sufficient reasons, they too must be reckoned among the causes that animate nature, or at least among the causes that determine events. Laplace, no doubt, was careful to rule out free will; but that is not enough. Quite apart from the difficulties of that venerable problem, motives remain as a class of causes not yet admitting of mathematical treatment, still less of mechanical interpretation. De gustibus non est disputandum here passes from a mere maxim almost into a metaphysical principle. In other words, wherever there is feeling and preference there is something unique. Now, either this uniqueness appears in the physical world or it does not. The admission that it does will make it very difficult to stop short of regarding all the beings that compose the world—so far as ‘being’ implies any sort of unity or individuality—as feeling-agents, monads, or ‘mindstuff.’ Now, though such an admission might still leave room for an omniscient Deity, it would, it seems to me, make an end of the Laplacean physicist. Kant saw this very clearly; unhappily Clifford and other physicists, who have a predilection for ‘mind-stuff,’ do not seem to see it. “Life,” says Kant, “means the capacity to act or change according to an internal principle. But we know of no internal activity whatever but thought, with what depends upon it, feeling of pleasure or pain and desire or will. But matter is lifeless, for on the law of inertia (next to that of the permanence of substance) the possibility of physics proper entirely depends. The opposite of this, and therefore the death of all natural philosophy, would be Hylozoism.”17 By the death of all natural philosophy, however, Kant means only that the mechanical theory would lose its supremacy; and that in 1786 was a thing not to be thought of. Just a century later, in 1886, we have a distinguished organic chemist, Bunge, declaring “So treibt uns der Mechanismus der Gegenwart dem Vitalismus der Zukunft mit Sicherheit entgegen”;18 the mechanical theories of the present are urging us surely onwards to the vitalistic theory of the future. It is mainly the tyranny of imagination that is in the way. Picture the position of Galileo, to whom the mechanical theory is primarily due, and it will be easier to believe in the Galileo that is to be.

Meanwhile, the view holds its ground that the uniqueness of feeling agents does not affect the physical world. To prevent “the death of all natural philosophy,” it is maintained that the psychical never affects the physical sphere, the two being pronounced utterly distinct, disparate, and, so to say, incommensurable. But what if there are not two spheres; and if only one, what if the psychical is that one? However, assuming the dualism now prevalent among scientific men, according to which life and mind are merely impotent concomitants of the physical, epiphenomenal as the latest phrase is—it is difficult to see that the Laplacean physicist will be any better able than before to peer into past or future history. Grant that he knows all the changes of any brain he may select as accurately as he knows the phases of the moon. Yet he only knows them in the same way i.e. as material events. As such, they afford, ex hypothesi, no clue to their mental concomitants; nay, it is of the very essence of the hypothesis that they should afford no clue.

Such dualism, it has been said, means chopping the world in two with a hatchet. It is indeed a murderous stroke, and leaves us with two dead and impotent halves in place of the living whole. Or worse, it gives us two sets of abstractions in place of one reality. This comes out in an odd way when we compare the deliverances of many of our physiological teachers with those of foremost physicists of the Kirchhoff school. Huxley, for example, thus winds up his article on Conscious Automatism: “If these positions are well based, it follows that our mental conditions are simply the symbols in consciousness of the changes which take place automatically in the organism; and that, to take an extreme illustration, the feeling we call volition is not the cause of the voluntary act, but the symbol of the state of the brain which is the immediate cause of that act.” There seems then no escape from the conclusion that the whole world is symbols. Attractions, affinities, undulations, molecules, atoms, ether, are to be regarded primarily as “mere helps or expedients to facilitate our viewing things,” not as the veritable realities: so Kirchhoff or Mach. But on the other hand the ‘perceptual realities,’ which those physicists are content to recognise, are simply shadows and symbols: so the physiologists.

Have we no means of deciding the question at issue: Which is the real and which is the symbolic? If the question is fairly faced, it seems to me the answer is extremely easy. Roundly stated, the real is always concrete, the symbolic is always abstract. The real implies individuality more or less; the symbolic is always a logical universal. Within the range of our experience the real implies always a history, that is, places and dates, converse with a concrete environment. The symbol is the creature of logic. If temporal and spatial relations enter into its definition or description, they are time and space coördinates with no vestige of chronology or topography about them. Now, tried by this standard, it is a glaring absurdity to call Cæsar's resolve to cross the Rubicon or Luther's to enter Worms the symbol of the dance of molecules in their brains. Yet to this pass Huxley brings himself. As I have tried to shew, and as I believe, the very advance of physics is proving the most effectual cure for this ignorant faith in matter and motion as the inmost substance rather than the most abstract symbols of the sum of existence.

And what, it may be asked, do I mean to argue from this? Simply that in our speculation about the universe we should never let go the concrete that we envisage. As long as we keep to that we find no two things absolutely alike, no two events absolutely the same. Intellectually to compass the wealth of particulars we are driven to generalise and symbolise, to employ the instrumentality of identity and uniformity among substances and causes, when the full fact is development and progress. It is far truer to say the universe is a life, than to say it is a mechanism, even such a mechanism as Goethe describes in verses that German men of science are fond of quoting, where the Spirit of the Earth “weaves at the rattling loom of the years the garment of Life which the Godhead wears” We can never get to God through a mere mechanism. I should not like to pin my faith to Leibniz, but of all the dogmatic philosophies his seems to me—in one feature at any rate—by far the best. With him, then, I would argue that absolute passivity or inertness is not a reality, but a limit. I would not say that the atoms of our present physicists are monads, for it is still an open question if they are anything. But to whatever is entitled to be called “one of the beings composing the world,” —Laplace's phrase, you will remember, —I would ascribe enough initiative and individuality to put his famed Intelligence to confusion.

• 1.

  Cf. Lecture 3.

• 2.

  Principien der Mechanik, § 664.

• 3.

  Properties of Matter, pp. 2, 4.

• 4.

  Properties of Matter, p. 5.

• 5.

  Ueber die Erhaltung der Kraft, p. 4, Ostwald's Klassiker der exakten Wissenschaft. ‘Kraft’ translated ‘energy’ throughout.

• 6.

  Thomson and Tait, Natural Philosophy, p. 207.

• 7.

  Properties of Matter, pp. 91 f.

• 8.

  Nature, vol. xxii, p. 123.

• 9.

  Maxwell, Collected Papers, ii, p. 216.

• 10.

  Mécanique chimique, 1893, p. 88.

• 11.

  Methods of Theoretical Physics, Phil. Mag. 1893, vol. xxxvi, p. 40.

• 12.

  Note v.—This entirely ad hominem argument addressed exclusively “to those who are fond of the ‘high priori road’” has been mistaken by some of my reviewers and correspondents as intended indirectly to prove that the energy of the universe is necessarily infinite. The position I had in view is comparable to that of a man who should say: Here is an infinity of balls and only one is white. He is invited to draw, and draws white. That fact, I think, should lead him to reconsider his statement, but it would not justify me in assuming that all the balls are white. It would, however, justify me in supposing the number of white balls to be at least indefinitely great. But I have thought it wiser to disavow such a priori arguments altogether. Of (relative) beginnings and endings, within the universe we have experience enough, but of the (absolute) beginning or ending of the universe we have no experience and no conception. Having experienced filled time, we can form the conception of empty time extending indefinitely into the past and into the future, but we have no warrant for treating this as a reality independent of all reality beside.

• 13.

  Note vi.—On the subject of the Conservation of Energy the reader may with advantage consult a recent work of Professor Poincaré, La Science et l'Hypothèse, 1902. In fact the whole book is to be strongly recommended to all who are interested in the scope and validity of the mechanical theory.

• 14.

  Cf. Mach, Popular Scientific Lectures, p. 246.

• 15.

  Mach, Lectures, pp. 152 f.

• 16.

  Mach, p. 184.

• 17.

  Metaphysische Anfangsgründe der Naturwissenschaft, Hartenstein's edition, vol. iv, p. 439.

• 18.

  Vitalismus und Mechanismus, ein Vortrag., p. 20.