if. LIBRARY OF THK UNIVERSITY OR- CALIFORNIA Received. Accessions No. .'t s/u if JVo... ;-S',v-., ' ;: ^'":;.:':l THE WORLD-ENERGY AND ITS SELF-CONSERVATION. BY WILLIAM M. BRYANT. "In each there is something of all." Anaxagoraa. CHICAGO: S. C. GRIGGS AND COMPANY, 1890. 'B7T COPYRIGHT 1890, BY S. C. GRIGGS & COMPANY. PRESS OF KNIGHT & LEONARD CO. CHICAGO. PKEFACE. present volume owes its origin to studies that -*- began more than twenty years ago. The studies themselves were prompted by a desire which soon became imperative. And that desire was to find a satisfactory answer to the question: What is " Man's Place in Nature ?" Many things highly interesting and suggestive were said from time to time -by the naturalists upon this theme. And yet, as I came at length to notice, the question itself seemed to be ambiguous. For, whatever answer might be given it, all must depend at last upon the answer to this further question, namely : What is that reality which we call "Nature?" Allowing that man is a product of "Nature/' there still seemed no other way to learn the real nature and destiny of man than through a successful inquiry as to the essence, the inmost nature of "Nature" itself. If this term "Nature" should prove to have a wider, and even so much wider as to be a radically different, significance from that which it is usually assumed to represent, then our estimate of "man's place in Nature" must be correspondingly modified. And this might very likely iii IV PBEFACE. mean nothing more nor less than that man's " nature " is far more complex than could be inferred from any- thing we are able to learn through what is commonly understood by the descriptive phrase "Natural Science." At the same time, the results in this particular field of inquiry show a vitality in the method of inquiry through which the results are obtained, that could not be lightly esteemed. Indeed, the more I learned of the "speculative" method of inquiry on the one hand, and of the method of inquiry in Natural Science on the other, the more did it appear to me that so far as men really think, the method of their thinking not only must prove, but actually does prove, to be one and the same. The method may be consciously pursued, and thus may, or rather must, itself become the object of investiga- tion in which case it shows itself as explicitly " specu- lative;" or, on the other hand, it may be unconsciously pursued and applied (for example) in the investigation of physical phenomena; in which case it is still "specu- lative," though it is so only implicitly its form here being that of "hypothesis." It appeared, then, that in the scientific movement of the present time we have the conspicuous external counterpart, or rather complement, of the speculative movement, which first assumed an explicit scientific character with the Greek schools of thought, and which again developed into special vigor and effectiveness in Germany during the closing years of last century and the first quarter of the present. PEEFACE. V In short, the famous Hegelian dialectic is in truth nothing less or else than the speculative aspect of the doctrine of the Conservation of Energy, which consti- tutes the vital element of all that is known as " Modern Science." The former presents the principle of Evolu- tion in its most abstract, but also in its most rigidly consistent form. The latter unfolds the "dialectic" under the form of the necessary relations or laws that "govern," or rather constitute, natural (in the sense of physical) phenomena. Thus, instead of being contradictory the one of the other, these two great movements are in reality but complementary and increasingly adequate phases of the ceaseless struggle on the part of the human mind to bring itself into harmony with the actual world in its essential, and therefore ultimate, significance. It is true that on his part Hegel treated slightingly the work of the empirical school, which had already developed admirable results in his time. And the members of this school have ample revenge when they point to the astounding absurdities to be found in Hegel's " Naturphilosopliie;" a work which, it cannot be reasonably denied, consists in great part of a series of perverse assumptions defying all observed facts. But, on the other hand, empiricists who scoff at that method which they (wrongly) assume to be fairly illustrated in this work, have on their part only too often attempted to interpret "Nature" without the guidance of any clearly defined speculative principle; and precisely for VI PREFACE. that reason they have been now and then betrayed into speculations that would grace the most arbitrary pages of Hegel's " Naturpliilosophie." What Hegel needed was a better appreciation of the empirical aspects of inquiry. What the empirical scien- tist needs is a better appreciation of the speculative aspects of inquiry. And clear indications are not wanting that the true relation between the empirical and the speculative is coming to be better understood by many in both these special schools of thought. If this be true, we may infer that the scientist of the future will not be content, nor even feel secure, without a " speculative" training; while the specialist in speculative studies will not dare, even if he should desire, to remain in ignorance of the special methods and results of the so-called empirical sciences. Indeed, as was just intimated, these sciences are already far from wanting in sufficiently daring specula- tions. And it is to be added that the culmination of these speculations, in their most elaborate and most consistent presentation, we owe to Herbert Spencer. It is for this reason that I have never been able to separate the work of Mr. Spencer from that of Hegel, widely as these two are contrasted in many respects. Evolution, and fixity of order in Evolution that is the key-note of both systems. The one develops this con- ception in the form of the necessary process of Thought itself. The other traces the evidences verifying this conception throughout the realm of " Nature " consid- PREFACE. Vll ered as the physical universe. The system of Hegel has been named: Absolute Idealism. Mr. Spencer calls his own system: Transfigured Realism. The latter begins with the external and simpler forms of Reality and traces them through their relations to their ulti- mate source to which indeed he would evidently find satisfaction in applying the term : Absolute Being, though he refrains from using any more definitely de- scriptive name than : Persistent Force. Hegel begins with the simplest, most abstract concept which it is possible to form, and names that concept "Being." And this name, it is all-important to notice, is the name of a concept only; that is, the name of a concept cor- responding to which there is no reality other than the concept itself. But to become aware of the fact that there is no outer reality corresponding to the inner real concept of mere pure being, that is to form in the mind another concept with reference to this outer no-reality. And it is a fact sufficiently familiar to all that to this other concept the term Nothing is applied. It turns out, then, that the term nothing, equally with the term being, represents a real concept, while yet in each case there is equally no objective reality to which the concept or its corresponding category can apply. Hence the often repeated and seldom understood expression of Hegel that " Being and nothing are the same." But in these barren concepts it is impossible for thought to rest. On the contrary, it is driven onward by its own nature to more and more concrete concepts Vlll PEEFACE. until there is reached the concept expressed in the category of Totality with all that this implies; in short, until there is reached the concept of Cause in the sense of a totality that is eternally complete in its own self-activity. And this,, as it seems to me, is just the Persistent Force to which Mr. Spencer's system leads up only with far more adequate and consistent definition than Mr. Spencer gives it. Mr. Spencer traces out an "established order" in the world of Things. Hegel traces out the necessary or "established" order in the world of Thought. Thus far these two systems seem on first view to be merely antithetical. And yet, as I have attempted to show in the argument of the present volume, the established order of the world of Things is what it is precisely because it is the outer expression, and nothing else than the outer expression, of the ' ' established " that is, the necessary or logical order of Thought. In other words, Thought and Things are but the necessary complementary aspects of the one Totality of Existence. In short, what I have attempted to do is: To trace out, and thus to render explicit, the speculative thread that is already present implicitly as the vital principle of the modern scientific movement. It will thus be manifest that my purpose has not been "critical" so much as interpretative. I have not been concerned to discover the momentary weaknesses of that movement so much as to find its central, permanent elements of power. PKEFACE. IX Feeling the need of help in my efforts to solve for myself the problem that involves the whole significance of life, I have not hesitated to seek for help wherever there seemed promise of finding help being no less grateful for a clue in the realm of empirical science than for one in the realm of speculative science. Thus, at length, it became clear to me that Nature is not something apart from Mind. On the contrary, it became manifest that Nature is nothing else than the outer mode of, and hence has its only truth in, Mind. And this conviction seemed to already present, at least in germ, that solution for which I had been seeking. For now the relation of man to "Nature" was seen to be in truth his relation to the Mind which manifests itself in Nature a conclusion which gives to the question as to man's Nature and destiny an immeasurably more hope- ful aspect than Natural Science in the usual acceptation of the term would seem to warrant. And not only so, but there appears to be here pre- sented a basis for the complete reconciliation of what have only too commonly been regarded as contradictory views of the world. As already indicated, the empirical and the speculative aspects of thought are by no means necessarily antagonistic. On the contrary, when rightly estimated, they are but the complementary phases of all true inquiry. Nor is this all, for in the given view (justified, as I hope, in the following pages) we have a secure basis for the complete reconciliation of all science, whether predominantly speculative or predominantly X PREFACE. empirical, with any Religion that is worthy the name. For according to this view the whole course of Science, whatever aspect may for the hour be predominant, really tends to prove beyond all reasonable doubt that the one all-inclusive Substance is in its very nature a conscious Energy; or, in other words, that it is the one absolute Person. On such view, it is evident that the "conflict between Science and Religion" is rather imaginary than real; even though an occasional dogmatic scientist should still persist in announcing, as by authority, the overthrow of Religion as nothing more than an old wives' fable; and though here and there a skeptical theologian should more or less scoffingly declare that Science is only a collection of idle fancies, having their origin in the unregenerate pride of man. In short, just as the empirical and the speculative aspects of science cannot be separated from each other without destroying science; so Religion approaches only so much the nearer to gross superstition the less it is per- vaded by the scientific spirit. To bring one's thought into unison with the established order of the World itself a world of Reason that is the religion of the intellect. To deliberately bring one's conduct into har- mony with that order that is the religion of the will. To harmonize one's feeling, the entire range of his sentiment, with that order, so that he delights in doing whatever is consistent with the rational World-order that is the religion of the emotions. And yet these PREFACE. XI three are but the essential and complementary aspects of Eeligion in its genuine, practical, concrete signifi- cance. To decry science is to commit oneself to the per- petuation of superstition. To decry religion is to threaten the existence of the ultimate motive leading to any and every effort in the field of science. Equally true is it, whether in the realm of science or in the realm of religion, that nothing can survive save that which is adapted to its environment. And in the out- come the one. real environment of human thought, as of human faith, is the abiding Truth of the World. While, then, it may be true that "man is what he eats (Mann ist was er isst,") it is equally true that man is what he thinks and what he does in pursuance of his thinking. So that " man's place in Nature" is essentially his relation as a thinking (and therefore indestructible) agent to -the ultimate Reason, which con- stitutes all that is of the reality we call "Nature." Such are the convictions at which I have myself arrived. Whether the following discussion will justify these convictions to the reader must, of course, be deter- mined by the reader himself. I have only to add that for the carefully prepared index accompanying this volume, I am indebted to the kindness of my young friend, Mr. Charles L. Deyo. ST. Louis, March, 1890. CONTENTS. CHAPTER I. PAGE INTRODUCTION. ELEMENTS AND CONDITIONS OF KNOWLEDGE, . 1 CHAPTER II. MATTER AND ITS PROPERTIES, ... 40 CHAPTER III. PHENOMENON AND NOUMENON. THE ATOM AS FIGURED IN IMAG- INATION, .... 53 CHAPTER IV. TRUTH OF THE ATOM. PENETRABILITY OF MATTER, . . 65 CHAPTER V. TRANSITION TO THE QUANTITATIVE ASPECTS OF MATTER THROUGH INCREASE IN QUALITATIVE CHARACTERISTICS, . .71 CHAPTER VI. DEFINITE QUANTITATIVE RELATIONS IN MATTER, . . 80 CHAPTER VII. As TO CONTINUITY AND DISCRETENESS OF QUANTITY IN MATTER, 83 xiii XIV CONTENTS. CHAPTER VIII. EXTENSIVE AND INTENSIVE PHASES OF QUANTITY IN MATTER, 86 CHAPTER IX. MEASURE AND THE MEASURELESS, 97 CHAPTER X. OF THE POSSIBILITY OF MOTION IN GENERAL, . . . 109 CHAPTER X OF THE NATURE OF MOTION, . . . . . .122 CHAPTER XII. THE LAWS OF MOTION, . 131 CHAPTER XIII. ENERGY AS ADEQUATE CAUSE OF MOTION, . . . .143 CHAPTER XIV. THE LAW OF UNIVERSAL GRAVITATION, . . 150 CHAPTER XV. MOMENTUM, 157 CHAPTER XVI. LAWS OF PALLING BODIES, 163 CHAPTER XVII. CURVILINEAR MOTION, . . 170 CONTENTS. XV CHAPTER XVIII. MOLECULAR MOTION, . . . . . . . 178 CHAPTER XIX. CORRELATION OF FORCES AND CONSERVATION OF ENERGY, . 196 CHAPTER XX. DOCTRINE OF CAUSE, 207 CHAPTER XXI. CREATOR AND CREATION, . .... 215 CHAPTER XXII. THE WORLD-ENERGY AS SPIRIT, ... .218 CHAPTER XXIII. FUNDAMENTAL MODES OF MANIFESTATION OF THE WORLD-ENERGY AS SPIRIT, . 242 CHAPTER XXIV. EVOLUTION OF LIFE-FORMS, 255 CHAPTER XXV. FURTHER CONSIDERATIONS AS TO THE EVOLUTION OF LIFE-FORMS, 265 CHAPTER XXVI. CULMINATION OF THE LIFE-PROCESS IN A LIVING UNIT WHICH IS CHARACTERIZED BY REFLECTIVE CONSCIOUSNESS, . . 286 THE WOKIJWB^ffRGY Al^D ITS SELF-CONSERVATION. CHAPTER I. INTRODUCTION. ELEMENTS AND CONDITIONS OF KNOWL- EDGE. a. FACT AND THEORY. POPULAR convictions have ever tended toward com- pact embodiment in the form of maxims. Nor in truth is this anything else than the inevitable outcome of the inherent demand of the mind for definition, clear formulation. There is nothing really surprising, there- fore, in the fact that examples of this tendency present themselves in the scientific world no less than in the world of every-day affairs. There is one maxim, indeed, that has found special favor among men of science. No other has, in fact, been received more widely or with less question. This favorite maxim commonly runs thus: " Facts rather than theories." In other words, in all investigations, whether in the physical world or in the world of mind, one ought always to put his trust in facts rather than in theories. The latter are always to be distrusted. The former alone can safely be relied upon. i 2 THE WOKLD-ENEKGY From the confidence with which this rule has com- monly been urged, it would seem that there could be no question as to the precision and adequacy of its sig- nificance. And yet it can require no very prolonged or very profound reflection to discover that if a fact is to be truly a fact for us, it must first be subjected to interpretation by us. We can never know a fact until we have given it some sort of interpretation. And our knowledge of the fact will depend, for its completeness,, precisely upon the adequacy of our interpretation. But "interpretation" is substantially the construction of a "theory." For theory is primarily just a look- ing-at or contemplation, which in turn unfolds into a conviction of the mind requiring nothing but conscious formulation to render it clearly recognizable as a "theory," in the ordinary sense of the term. Hence a fact becomes real and trustworthy as a fact to us, only in so far as we have formed a theory concerning it. It appears then, that, in our experience, "facts," without theories, are just as empty and worthless as are theories without facts. Or rather, it would agree with the truth still more precisely to say that, so far as the experience of any thinking being is concerned, it is impossible that there should be any such thing, either as a fact without a theory or a theory without a fact. The fact may be misapprehended that is, misinter- preted but it does not become a fact at all for the indi- vidual otherwise than through his giving it his interpre- tation, however distorted the interpretation may be. Thus it can become a fact in its truth for him only in so far as he gives it a true interpretation, only in so far as he forms a rational theory concerning it. And AND ITS SELF-CONSERVATION. 3 now, recurring to what was said at the beginning, it may be added that a maxim is nothing else than an abridged statement of a theory. Following which it would perhaps not be wholly amiss to inquire whether the "scientific" maxim we have just been considering is wholly exempt from the untrustworthiness so confi- dently assumed to inhere in all other theories. In truth it is extremely likely to be just that theory which has been least scrutinized, least subjected to criticism,, which turns out to be the most untrustworthy. b. FUNCTION OF CONSCIOUSNESS. It is impossible then that a "fact" should come into the consciousness of an individual otherwise ' than as in part the actual creation of that consciousness. A sup- posed passive impressibility of the mind is, in truth, but a contradiction in terms. In order that the mind may be impressed as mind, it must be no less active than passive. It must receive that is, actively take up into itself the element or force tending to produce an eifect upon the mind from without. But this active reception is also a transformation. It adds to the outward element an inner element namely, that of the mind's own activity and the two are now fused into a single, indivisible fact of con- sciousness. The spontaneous activity of the mind itself is a necessary phase of every fact of consciousness, with- out which phase, therefore, it would be impossible that any such fact of consciousness should ever arise. The first "facts," then, for which the mind must account* are the facts of its own consciousness. Nay, rather the only facts with which the mind can ever THE WORLD-ENERGY deal the only facts that can exist for it are the facts of its own consciousness. The only world for me is the world I know. At the same time, this statement is far from being equivalent to saying that at any given moment the individual, empirical consciousness already possesses all the facts that can ever exist for it. This would indeed be manifestly absurd, for the reason that the indi- vidual consciousness has even thus far been unfolded into reality only through the reciprocal activity that has taken place from time to time between the " inner " mind and the " outer " world. On the contrary, it is to be understood as meaning that no new fact can be added to the world of the individual save through the activity of the individual in his character of a conscious unit. And this is as much as to say that each new "fact," as it comes into the consciousness of the indi- vidual, passes through a transforming, creative pro- cess, the primary element of which process, so far as the individual is immediately concerned, is the spon- taneous activity of the individual's own mind, consist- ing in the seizure and fusion with itself of the given outer element. It is only thus that any "fact" what- ever can become known to the individual at all. Whence, let us repeat, it is impossible that the indi- vidual should ever really know any fact whatever, other- wise than in so far as it has already come to be a fact of his own consciousness. So that the function of con- sciousness appears to be primarily this: To seize upon the elements offered it in the outer world of nature and to interpret those elements into the inner world of thought. AND ITS SELF-CONSERYATION. 5 C. RANGE OF CONSCIOUSNESS. We have next to observe that these facts of the indi- vidual consciousness necessarily have relation to a world lying beyond the range of the individual's immediate experience. They had a beginning as such facts of con- sciousness, and with whatever powers we may regard the mind of any individual man as endowed, we cannot in- clude as among those powers the ability to create, out of pure nothing, the facts which go to make up its own world of growing consciousness. If, in a certain sense, the individual consciousness possesses creative powers, those powers can still be regarded as creative only in the sense of being powers of transformation, or rather of transfiguration. It reaches out to a world "beyond itself," and in that world finds material which it seizes upon and appropriates to its own uses. At the same time, this " reaching out " is but a self -expansion of the individual consciousness so as to include in, and assimi- late to, its own inner world more and more of what previously belonged to a world that was external and apparently alien to such consciousness. And yet this gradual appropriation by the individual consciousness of the world which, at the outset, lies beyond such consciousness, could not take place at all, if that world were wholly an alien world. Rather, it demonstrates that the world lying beyond the immediate range of the individual consciousness is still in vital relation to the actual present facts of such consciousness. The limit of the possible experience of the individual then is to be found only where the "outer world" ceases to be in relation to the world of consciousness at all. 6 THE WORLD-EKERGY It is only because the unknown is fundamentally related to that is, possesses the same nature as the known, that it can ever be transformed into the known. Just that and only that which is wholly unlike the known, and hence wholly incapable of ever being brought into relation with the known, is, with the utmost ease and certainty, already known as being absolutely "unknow- able." It is opposed to intelligence in its very nature, and hence may be at once " recognized " by the intelli- gence as unknowable, simply because of its sheer vacuity, because of its being absolutely void of any characteristic through which it can or could ever be an object to the intelligence. The only world, then, which can possibly be known, or even conceived as existing, is a world essentially related to, and hence possessing, in truth, the same fundamental nature as the knowing self. Such would seem, at this point, to be the natural inference. There is suggested here also this further inference : That the only intelligence I can ever know is of the same fundamental nature as my own intelligence. For I could only know it by taking up its modes of activity into my own consciousness. And that must mean that thus far the modes of my own consciousness are the same as the modes of that intelligence assumed to be essentially differ- ent from my own. It is only by an act of my own reason that I could conceive of a reason as different from my own. But in the very act of conceiving it as different from my own I must pronounce such " reason " to be unreason. In other words, such conception utterly con- tradicts itself and thus annuls itself in the very process of its formation. AND ITS SELF-CONSERVATION. 7 There is then a universal ideal or type of intelligence to which every particular intelligence, so far as it truly is intelligence, must conform. Whence the limit of possible development for each individual intelligence is nothing, less or else than the total round of facts and relations capable of being justified to such intelligence as an abso- lutely rational world. And further, since the universal ideal of intelligence as such is the true ideal of every individual intelligence realized as a person, it would seem that if the individual can ever trace out the fundamental characteristics of this universal ideal or typical nature common to all intelli- gences, he will, at the same time, trace out the funda- mental nature of all that can ever appeal to reason of all, therefore, that can be conceived as pertaining in any way to a rational world. In other words, he will trace out the fundamental system of the only knowable that is, the only possible world. It appears, then, that all looking implies a looking within ; all investigation, an investigation of self ; all judging, a judging of that which pronounces judgment. All seeing is double. Every act of the mind is two-fold. It seizes upon a world beyond itself, and yet, in so doing, identifies that world with itself ; or rather, in so doing, it discovers an essential identity as already existing between that world and itself. The ultimate range of consciousness is thus seen to be commensurate with the total round of the rational world. d. SENSATION THE PRIMAKY PHASE OF CONSCIOUSNESS. In any inquiry into the nature and limits of the exter- nal world, then, it is essential, first of all, to consider the 8 THE WORLD-ENERGY mode in which such external world comes within the range of the individual consciousness. And it is to be remarked that the simplest phase of the mind's activity is precisely that through which the mind comes into relation with this external world. That the experience of every individual necessarily begins with and in sensation, is a philosophic truism. It is, then, of the first importance to ascertain the conditions under which sensation can and must take place. It is evident, first of all, that there are two phases of these conditions. The one phase is subjective the phase in which the mind itself is specially considered. The other phase is objective the phase in which "objects/' in the sense of things of the external world, are specially attended to. Every sensation necessarily implies an act of an individual mind and also an object other than such individual mind, which yet the individual mind seizes upon. Sensation is a concrete relation between subject and object, and its primary condition is the direct " con- tact " between the two factors concerned. Of this concrete relation between subject and object there are many degrees. It is that degree of such con- crete relation in which the subject seizes upon the object so as to result in a definite and more or less abiding "impression" or "image" in the mind that is appropri- ately termed perception. But this perception, this seizure and appropriation of the object by the mind, through the sensory organs, implies that the object perceived is specially characterized by externality. It is made up of parts which are outside one another. Whence it is evident that the object of sensation is necessarily in space. AND ITS SELF-CONSERVATION. 9 On the other hand, the act of sensation is either after or before other such acts. That is, the act of sensation is necessarily in time. It is evident, therefore, that both space and time are necessary conditions of sensation. Without these condi- tions not a single act of sensation would be possible. We have accordingly to consider the precise measure in which these conditions determine all our sense-per- ceptions. 1. Space as a condition of sensation. The object of sensation, as being extended, is necessarily in space. It cannot be perceived save as occupying space. On the other hand, it is perfectly easy to withdraw atten- tion from all actual objects in space and thus think of space as itself mere blank extension. Thus we come to recognize that objectively space is at once a necessary condition of the existence of bodies and a relation of body to body. That is its "reality." Otherwise it is mere boundless nothing. Remove bodies, and you remove the one positive characteristic of space. But space is not merely a necessary condition of all possible objects of sensation. This fact itself is dis- covered only through, as being necessarily involved in, the further fact that in every possible sensation, space is necessarily presupposed as a fundamental condition of the very act of sensation itself. For sensation is ever a practical, concrete relation between a sensitive subject and a space-bounded and space-occupying object. And this concrete relation completed, shows us the object with its space-characteristics as taken up into the conscious- ness in the form of an "image," which image is, in truth, just a mode of the mind, of which the outer 10 THE WORLD-ENERGY " object" has been merely the occasion. But the image can no more be dissociated from space. than can the object of which it is the image. In any sensation there is an interfusion of a given subject or mind, with a given object or definite quality of matter, and the product of this interfusion is an "image." So that while the image is a subjective fact, it has also an objective origin. It is a creation of the mind and in the mind, but is neverthe- less subject to the limitations characterizing the material out of which it is created. Act-of-sensation and object- of-sensation are the necessary complementary factors of every possible sensation. Whence, in every sensation, as well as in every product of sensation, both subjective characteristics and objective characteristics necessarily inhere. Thus space is seen to be a necessary condition of both object and act of sensation. In so far, therefore, as it is a necessary condition of the object of sensation, space is objective; while in so far as it is a necessary condition of the purely mental act of sensation, space is subjective. It is neither exclusively the one nor exclusively the other, for the reason that it is both the one and the other. The objective and the subjective, let us repeat, are but complementary aspects of every knowable that is, of every possible fact. It is to be noted, however, that, considered objectively, space is a purely negative factor. It has no positive characteristics or properties. It is pure void, and as such can be known only as relation of externality between object and object, or between part and part of a given object ; though this latter case can, of course, be resolved into the former, since the moment one's attention is AKD ITS SELF-COKSEKVATIO^. 11 explicitly directed to the parts of an object, those parts become, in turn, mutually exclusive objects of attention. Now, as pure void, space can have no limits. For any possible boundary of space could only be the limit between the given space and another space on the other side of the boundary. Any possible limited space must have geometrical form. But every geometrical form is neces- sarily bounded by surfaces. Nay, a surface is ever to be regarded as a boundary in a two-fold sense, if we are to accept the guidance of mathematicians by whom in gen- eral, and by Professor Clifford in particular, a surface is denned as ' ' the boundary between two adjacent portions of space. "* But a real boundary that is, a surface constituting a transition between two volumes distinguishable in quality can have no reality for space as such, since space, merely as space, possesses and can therefore present no positive difference in quality by which one space or portion of space can be distinguished from another. It is evident, therefore, that any supposed limit of space could only be a limit in space, the limit having objective reality only through the existence of some object occupy- ing space. So that all talk of a possible "curvature of space" is at once chargeable with confounding extension, as the universal and purely negative possibility of all physical modes of existence, with a particular, positive, material, extended object that might (and must) exist in space, but could never coalesce with space. The distinction here indicated was long ago pointed out and emphasized by Kant in his " Metaphysical Foundations of Natural Science," where he speaks repeat- * "Common Sense of the Exact Sciences " (N. Y. Ed.), P 50. 12 THE WORLD-ENERGY edly of "empirical space/' "relative space/' and "mova- ble space."* Applying such terms to " the sum total of all experi- ence" for the sensuous consciousness, he, at the same time, emphasizes the absurdity of confounding such " empirical, relative space " (by which he evidently means extended objects in general) with "pure, non-empirical and absolute space/' which is necessarily presupposed as the universal and indispensable negative condition of that is, total absence of resistance to all movement whatever. In defining space as such, then, we can, it would seem, use no other than negative forms of expression. In space, pure and simple, all definite dimension is annulled. It is true that space presents the possibility of all dimension. Space is formless, and hence wholly indif- ferent to form. But just for that reason, space is in a negative sense again the possibility of all form. That is, it has no characteristics offering any opposition to the development of form. Objects are said to be " in space." At the same time, every definite that is, arbitrarily selected portion of space, however large or however small, is still an " outside " to every other portion. It is further evident that space has no twternality at all ; for that would imply positive or real characteristics by which one portion of space could, on its own account, be distinguished from another portion. On the contrary, it is only through our sensations of objects in space that we can distinguish between space and space, or ever know anything at all about the purely negative, empty infinitude *See Kant's "Prolegomena," etc. Translated by Belfort Bax (Bonn's Library), p. 151, and elsewhere. AND ITS SELF-CONSEKVATION. 13 which we call space. For we can only know space as the negative of body.* It is not even true that space has extension, for space just is extension, pure and sim- ple. That is its one positive characteristic* In its object- ive character, it is nothing else than indistinguishable, immovable, boundless externality. It is the pure blank form of perfect continuity. No power can quarry out a block of space and carry it away. Subjectively considered, on the other hand, space is, as we have seen, the pure form or mode of all possible per- ceptions of external objects. So that, on the one hand, space proves to be a universal and necessary condition of the existence of all possible objects of sensation; while, on the other hand, it is seen to be a universal and necessary form or mode of the subjective fact or act of sensation itself. 2. Time as a condition of sensation. But besides perceptions of external objects, there are perceptions of changes in those objects, and not only so ; there are also perceptions of internal states of consciousness and of transition from one to another of these states. These transitions, however, involve, or rather are themselves forms of, succession. But it is precisely the relation of succession that constitutes time. Thus, just as no object can be perceived except as in space, so no change in a perception, implying change in a perceived object, can take place otherwise than as in time. Time * Strictly speaking, a point is the true negation of space. But it is such merely as the simplest phase of limit ; and limit can be realized only in and through body. So that the point, which is the abstract negation of space, may be regarded as the initial phase of body which is the concrete negation, that is, the realization, of space. In other words, the point is the transition from pure to empirical space. 14 THE WORLD-ENERGY is thus the universal form of all succession,, as space is the universal form of all physical co-existence. Transition, in short, is change a going over from one state to anothe*. But this takes place both in the inner consciousness and also in the outer sensuous object of consciousness. Thus it becomes evident that time, as the universal form of all change,, both inner and outer, is also both subjective and objective. Like space, too, time is, merely as time, an abstraction pure and simple. Just as we could never become con- scious of space, save through the perception of objects in co-existence, so we could never become conscious of time, save through the perception of events occurring in suc- cession. And just as space would be meaningless save as a relation of object to object, so time would be devoid of meaning save as a relation of event to event. Both are purely negative factors, and yet, with their utter lack of all positive characteristics^ they are precisely the factors in our perceptions of objects and changes in those objects which we find it absolutely impossible to eliminate from our perceptions. Neither space nor time can be perceived by the senses, and yet it is alone through our perceptions that we become aware of space and time. They are not objects of special perception, and this they could not be, for they are the universal forms of all possible perceptions. It is this fact that lifts the conceptions of space and time com- pletely out of the domain of merely empirical knowledge. The proposition, " Every force is a form of electricity," is an empirical proposition which has been more or less definitely affirmed at different times within the present century, in spite of the somewhat arbitrary and exclusive AND ITS SELF-CONSERVATION. 15 way in which it reduces energy, a universal mode of exist- ence, to one of its particular phases. 'But the proposi- tion, " Every event must take place in time," is seen upon reflection to be necessarily implied in every single instance of the perception of an event. For it would contradict reason itself to say that an event can take place apart from the conditions of time. It may be noted finally, that, while internal or subject- ive transitions as such may occur within the limitations of time alone, no external or physical change can take place otherwise than as conditioned by both time and space. 6. SENSE-PERCEPTION FURTHER IMPLIES CONCEPTION. We have seen that space and time are the universal and necessary modes of all perception. And yet, on fur- ther examination, perception is found to involve as one of its essential factors a mode of mind extending beyond the limits of perception, as such. It has already been inti- mated that every phase of mental activity necessarily pre- supposes a two-fold character. We have now to note more explicitly that even the simplest perception is still a highly complex fact. For the sensuous consciousness of an object arises not merely from a fixing of attention upon a given object; it is also a singling out or selection of that object from among an indefinite number of objects all presenting themselves to notice. And still further, it is a direct reference of the perceived object to the self as perceiving. It is true that in these acts of selecting objects and referring them to himself as a conscious unit, the individ- ual is not necessarily aware of the fact that he is making 16 THE WORLD-ENERGY such selection and reference. Rather,, in common experi- ence, the process goes on without the individuaFs noticing the details of the process. At the same time, however, reflection shows that in every such act the selection itself is necessary in order that the perception may be distinct, and the reference of the object to the self is necessary in order that the perception may exist at all. And thus again the receptivity of the mind in perception is seen to be quite as definitely active as passive; or rather, it is evident that passivity is but receptivity, or reaction. But now this reference, whether of object to object, or of an object to the self (both of which must take place in every act of perception), implies a seizure of a relation; and this seizure of relations does not belong to perception as such, though necessarily involved in every act of per- ception. The office of perception as such is to seize par- ticular objects. The relation of object to object can come into the consciousness in no other way than through a seizing together of the objects related. And this seizing together of objects is again a primary, original act of the mind an act which has appropriately come to be called, in English, conception. Individual sensuous objects are perceived. Relations can only be conceived. But now let us note that this relation seized through conception is a relation at once of identity and of differ- ence. A number of objects different from one another are yet found to possess some characteristic through which they are all similar to one another. The several objects could not be seized as several as separate otherwise than through the seizure of their difference. But this seizure of the difference separating object from AND ITS SELF-CONSERVATION. 17 object is itself a reference of those objects to one another. Their severalty, or state of severance., can not be compre- hended in thought save through a corresponding recog- nition of their unification or identity. In other words, the recognition of them in their par- ticularity necessarily implies the recognition of them in their universality. These, indeed, are but complementary phases of every possible stage of knowing. The recogni- tion of difference between objects is the negative reference of those objects to each other that is, the recognition of their dependence upon one another in that, to a greater or less degree, the one has what the other lacks and lacks what the other has. On the other hand, the recognition of their similarity is the positive reference of them to each other that is, the recognition of their tendency to coa- lesce into one continuous, independent whole. The negative reference of object to object is the basis of the recognition of multiplicity. The positive reference of object to object is the basis of the recognition of unity. Whence it is evident that the "one "and the "many" are but complementary aspects of one and the same total. But, let us repeat, both the negative and the positive reference of object to object is the seizure of a relation; and while the seizure remains implicit in every act of per- ception it becomes explicit as an act of ^owception. Thus perception necessarily implies conception. The single object cannot be seized in isolation. The seizure of it as a single object is already implicitly a seizure of it in its relations. On the other hand, the seizure of a relation between objects necessarily implies that the objects them- selves are already, in that very fact, perceived. Whence it is evident that these two phases of the mind's activity 18 THE WOELD-ENEEGY perception and conception mutually and necessarily imply one another. However far the one may predomi- nate in any given instance, the other is always involved in the same act. Or, as somewhat picturesquely expressed in a phrase attributed to Kant * (whom we are here sub- stantially following), (i Conceptions without perceptions are empty. Perceptions without conceptions are blind/'' f Nevertheless, perception is of a distinctly lower rank than conception in the scale of the mind's modes of activ- ity. As we have seen, the former is the distinctive mode by which particular objects are taken up into conscious- ness; while the latter is the mode by which the more wide-reaching result is obtained of bringing into clear definition in the individual consciousness the comple- mentary relations of identity and difference necessarily involved in the objects which appeal directly to the senses. So that mere sense perception, so long as it pre- dominates as such in the activity of any given mind and thus includes conception only in its implicit phase, is necessarily a very inadequate, superficial stage of mental activity. And the development of conception into its explicit phase as the dominating mode of mental activity is essential to anything approaching adequate knowledge, even of the simplest fact. Any " fact," indeed, can be truly known in no other way than through its relations ; and it is,, let us repeat, * I have to acknowledge my indebtedness in the study of Kant to the expositions of Dr. W. T. Harris, and also to Professor E. Caird's admirably clear " Critical Account of the Philosophy of Kant" t Kant's own expression is: Gedanken ohne Inhalt sind leer, Anschau- ungen ohne Begriffe sind blind. (Kritik, der reinen Vernunft. Ed. Harteu- stein. S. 82.) But the context shows that the form given above the form used by Professor Caird, and which also exactly translates the words used in SchwegleVs exposition (Geschichte der Philosophic, i2te Auflage, S. 191), is a perfectly accurate rendering of Kant's meaning. AND ITS SELF-CONSERVATION. 19 only through the power of conception that the fact can be seized in its relations and thus thoroughly compre- hended. This remarkable power of the mind, then, which we call conception, is found in its most elementary character to be a subordinate phase of perception. And yet, through its own expansion into its complete, explicit significance and vigor, it transcends perception, includes and subordinates it, and proves to be the mode of activity by which the outer world of objects and relations is brought together or comprehended as a harmonized, uni- fied whole, completely within the grasp of the mind.* /. PRIMARY UNITY OF SELF-CONSCIOUSNESS. It will now be desirable to bring into more explicit statement the significant fact already more than once referred to : That in every act of knowing, whether that act be predominantly perceptive or predominantly con- ceptive, there is necessarily involved not merely a refer- ence, implicit or explicit, of object to object ; but also a reference of every object to a self as perceiving and as conceiving. Thus every possible act of knowing necessa- rily implies a self-reference as the fundamental character- istic of the individual consciousness. Knowing is, first of all, ^//"-knowing a knowing- together, as the word consciousness itself implies. And this collectedness and vital unification of knowing in selfhood has been further emphasized among English- speaking people in the term se^-consciousness. It is, *It will be noticed that the term conception is here used in a sense so wide as to include thought an extension of meaning not without prece- dent, and not without psychological justification. For just as conception is implicit in every act of perception, so thought, properly speaking, is implicit in every act of conception. Hence the frequent use of the expression "to conceive," meaning " to think." 20 THE WORLD-ENERGY indeed, precisely in self-consciousness that every possible phase of knowing must, in the first place, take its rise, and in the outcome find its culmination. Nay, the self is in truth the fundamental, vital unity actually constitut- ing the whole manifold series of perceptions and concep- tions that take shape in the individual consciousness. It is, therefore, nothing more than a truism to say that, apart from this unity, the series could never be known, either as a whole or in its parts ; for without the unity the series could have no existence. The unity oi self is the universal which, at first abstract, brings itself into concrete realization, through its own activity dis- played in the development of the manifold particular phases of perception and conception. Underlying all knowledge, then nay, rather consti- tuting the very core of all knowledge is the primary, or rather primordial, unity of self -consciousness. At the same time it is easy to see that this unity is far from being a simple, abstract, empty unity. On the con- trary, it is dual and triple, nay, infinitely manifold. First, as that which knows, it is subject; secondly, as that which is known, it is object; and thirdly, as that which in its very nature is self-known, it is subject-object, which also necessarily implies infinite complexity. This indeed is substantially the standpoint of all mod- ern philosophy. Descartes, the founder of modern philoso- phy, finds the ultimate ground of certitude in self-refer- ence. "I think, therefore I am." I, who think, first of all know myself as thinking; and so long as this conscious self-reference continues, I am absolutely assured in that very fact of my own existence. I can indeed conceive of an object as having existence, and yet as being destitute AND ITS SELF-CONSERVATION. 21 of consciousness. But I find it absolutely impossible to conceive of a consciousness that yet has no existence. It may indeed prove, in the sequel, that every phase of existence implies intelligence or consciousness; but it is manifest without further demonstration that every phase of consciousness explicitly and of necessity involves exist- ence. Thus it appears that consciousness is the wider, richer term, and involves existence. And it may be that perfect consciousness is precisely the highest term of exist- ence, that it is just another name for self -existence. So that existence not otherwise defined, is vastly the poorer, more abstract, and hence subordinate term. Self-consciousness, then, appears to be the root from which every branch of knowledge springs. If I turn " experimentalist," and apply myself to the acquisition of knowledge of external things, here too, as I have seen, every step imperatively demands, absolutely cannot be taken without, the reference of all to self. Every fact, however simple or however complex, must inexorably be tested by reference to laws which I find in my own con- sciousness laws which I find it impossible to think of as undergoing change. For change itself is meaningless, save in so far as it is referred to the permanent, to the changeless, as the standard of judgment. Nor will it avail here any better than elsewhere to take refuge in the mists of " relativity." For the " relatively permanent " must in the outcome ever prove to be some- thing undergoing change. Such standard is therefore in its very nature self-contradictory, since a changing stand- ard can be in truth no standard at all. This truth is verified that is, empirically " proven" in the ordinary affairs of life. In so far as standards of 22 THE WORLD-ENEKGY value fluctuate, they cease to have reality as standards. It is rightly assumed that the value of the changing can be estimated only in comparison with that which is abso- lutely unchanging, with that which is permanent, in the ultimate and legitimate sense of the term. Even stand- ards of weights and measures are assumed to be unchang- ing. Not a single transaction in commerce, nor an exper- iment in science ever occurs that does not involve this assumption. Otherwise, indeed, no sane people, and therefore no people at all, would exist to pursue .either commercial or scientific or any other interests. To this it need only be added here that any change in consciousness that is not subordinated to the unity and therefore permanent identity of consciousness could be nothing else than a complete break in, and hence the utter annihilation of consciousness. And this is as much as to say that consciousness, in its universal character, in its ideal nature or type, can never undergo any change. Underlying the unity of the self, and constituting its fundamental characteristic, is the law of self-consistency, which may be stated in the following form : Perfect con- sistency in consciousness is the ultimate and absolute ground of all certitude. By this standard every " fact " must be accepted or rejected, every " theory " approved or condemned. Here is the ultimatum of " experimental," as of all science. It is upon the results of the supreme, inner experiment which thought performs upon thought that all knowledge must ultimately rest. Thus while all really systematic, scientific research begins with the outer or physical, it culminates and must ever culminate in the inner or spiritual. And while AND ITS SELF-CONSERVATION. 23 these two phases or fields of investigation may appear to be mutually exclusive, they in reality merge into one another; so that the physical may be rightly described as the initial phase of the spiritual, the spiritual as the maturity, the fulfilment of what is only vaguely inti- mated in the physical. On one side our knowledge depends upon sensuous experience ; on another side it transcends that phase of experience ; while finally it coincides with experience in the widest, richest meaning which the term experience can have. Knowledge is, in truth, the very core of experience, and experience is but the unfolding or outer realization of knowledge. Experience is practical knowl- edge ; knowledge, theoretical or reasoned experience. Evidently, then, sensuous experience is neither all nor the best experience. Bather, the best experience is that which realizes with the most perfect consistency the greatest extent and degree of truth. That, doubtless, is the most "practical" way of life which serves best to symmetrically unfold the spirit into the concrete reali- zation of all its powers. Once more, then, the sensuous is seen to be the poor- est, least adequate phase of experience, for the reason that it is but the simplest, most rudimentary phase thereof ; while "experience," in its truth and completeness, is just the total process of the development of man in the entire compass of his nature. All genuine knowledge is, in truth, experimental. There can be no other. If experimental science has its initial point in the discovery of physical relations, it has its culmination in the discovery of the higher relations unfolded in the world of thought. 24 THE WORLD-ENERGY g. THE LAWS OF THOUGHT. The " necessary laws of thought" are nothing else than the technical presentation in three abstract proposi- tions, expressing successively, with greater explicitness, the conviction above set forth, namely: That perfect consistency in consciousness is the ultimate and only absolute ground of certitude. The law of identity declares that "whatever is, is." Regarded formally, this is pure, empty tautology. But the statement also contains implicitly the deepest signifi- cance. It declares in effect that existence is absolute and uniform. Already in the fifth century before the Chris- tian era, this truth was felt, and Parmenides sought to give it utterance in his dictum that "Being alone is and non-being is not." Aristotle also reaffirmed it in his representation of the " Unmoved mover of the world," while in the modern world it reappears in the affirmation that the total quantity of matter or of energy can never be either increased or diminished. Thus the first law of thought is, in germ, the doctrine of the conservation of energy. It implies that existence can never be changed into non-existence, nor the latter into the former. So far as existence itself is concerned, there is neither past nor future, but only a ceaseless, changeless present. This law is, then, the law of consistency under the form of absolute continuity. The truly existent, how- ever great its complexity, however much of mutual oppo- sition there may possibly be between its various multi- form phases, can still never contradict itself. The law, as stated, says nothing whatever as to whether multiplicity AND ITS SELF-CONSERVATION. 25 is or is not necessarily involved in existence. It simply affirms existence as changelessly one with itself. Nevertheless, this is but vaguely intimated in the law of identity, which thus proves to be sufficiently ambigu- ous. And yet, as already shown, the formula may be fairly interpreted as meaning that whatever is cannot cease to be, and still more, that whatever is cannot, at the same time, not be. Thus the first law of thought, when unfolded into the negative form, is found to involve also the second law, or the law of contradiction, which, in truth, only empha- sizes and aids in rendering explicit the law of identity. The law of contradiction declares that " anything can- not both be and not be." And this is simply an advanced form of the law of consistency. Nor does this advanced form of the law of consistency exclude the dialectic of change inhering in all things finite. This is sufficiently evident even in the form just quoted, and which is the form in which the law of contradiction is more commonly stated. But still less does this law exclude change when stated in the form given it by Aristotle, namely: To Y&P " /* onapxeiv xal fjiij U7!:dp%iV) dduvarov rw aoroj xard TO auro. f{ It IS impossible that precisely the same phase of reality should both begin and not begin at the same time and in the same sense." * Thus stated, Aristotle declares the law of contradic- tion to be the "most firmly established of all first princi- ples." And as he makes this statement immediately following the declaration that the philosopher must come provided with a first principle that is "independent of * "Metaphysics," Lib. III. (IV.), cap. III. 26 THE WORLD-ENERGY hypothesis," it is evident that he regarded this as the primal law of the reason, and as such necessarily self-evi- dent in its truth. With such assurance from such a thinker, then, one may well be encouraged to inquire with care and diligence whether there may not be something more in this law, even in the form ordinarily given it, than the shallow, contradictory abstraction which, as simply the negative power of the law of identity, it has been represented by Hegel as being. * When it is declared that A can not be both A and not A, it is implied in the very form of the statement that A may be either A or not A, according as it is siibjected to this or that set of conditions. It is sim- ply declared that the two affirmations, " A begins " and " A does not begin," could not possibly both be true at the same time and in the same sense. But if A possesses any definiteness, that is, any reality, then so far as the characteristics of A are determined by any given set of conditions undergoing change, A must necessarily change as the conditions change, and in so doing must thus far necessarily become not A. For example, with sufficient increase of temperature, a given portion of carbon now constituting a diamond may be vaporized and combined with oxygen; the resulting car- bon-dioxide may be decomposed through absorption into a vegetable organism, the carbon that was diamond now becoming woody fiber, to undergo still further trans- formation, perhaps into coal, etc., etc. Thus the same group of carbon particles may be both diamond and not diamond. But if by this declaration it is meant that both these mutually exclusive states can be *." Werke" (ate Auflage), VI., 230. AND ITS SELF-CONSERVATIOK. 27 assumed at the same time, by the same group of particles, it can be true only in a special sense. If true in the same sense it can be only in different times. At the moment when the particles constitute diamond in reality, they can at that moment be said to constitute not-diamond (woody fiber, coal, etc.) only in the sense of potentiality. Or, in general terms, any given quantity of matter can be in one and only one state at one and the same time; so that, whatever the number of states possible for such given quantity of matter, those states can be realized by and for it only serially, or through successive periods of time. Thus the law of contradiction might also be called the law of consistency as exhibited in the actual world the law of precision in the modes of existence. It would seem then that the true significance of the law of contradiction is rather this: First, that whatever the forms successively assumed by any portion of substance, that portion of substance, through whatever transforma- tions it may pass, still exists absolutely, and is wholly excluded from non-existence in the sense of mere nothing- ness; secondly, throughout its transformations a given portion of substance can as a unit assume at any given moment but one consistent grouping of its parts, from which it follows that no two contrary descriptions could be true of it at the same time. It is perfectly consistent with our conception of the existent that it should assume all possible forms of existence; but it is wholly inconsist- ent with that conception to suppose that the existent in any of its possible aspects should ever become utterly null or non-existent. It is to be noted, too, that while the law of identity would seem on first view to exclude change, and while it 28 THE WORLD-ENERGY does exclude change from existence as a whole, yet the law of contradiction, which is but a more explicit form of stating the same truth as that contained in the first, dis- tinctly assumes change to be perpetual for every finite form of existence. Any given thing is perpetually in pro- cess, and can <( begin/' at any given moment, in this or that particular phase of the process only. The first law declares the permanence and continuity of existence as a whole. The second law declares that the particular aspects of existence are in a ceaseless process. Again let us regard A as a symbol of the totality of all that exists. Then it becomes evident that while all change is involved in A, there can never by any possibility be any change of A. We find ourselves thus contemplating that absolute Identity which includes all possible difference within itself. Here the seemingly negative law of contradiction is found to negate the non-existent absolutely, and thus to be the positively developed form of the law of identity in that it is the absolute affirmation of all reality. The "law of excluded middle" finally, announces that the existent and the non-existent exhaust the possibilities of thought. " A thing must either be or not be; " there is no third or " middle " possibility. Whatever is, not only must T>e, but must be in a state of perfect definiteness. The first law of thought affirms positively that what exists is self -consistent; the second affirms the same thing negatively in declaring that the existent cannot contradict itself, either by being at the same time non-existent, or by presenting the same portions of itself at the same time under mutually exclusive forms; while the third law reaffirms absolutely the self-consistency of the existent as being necessary. ITS SELF-CONSERVATIOK. 29 Rightly understood, then, these laws are valid and vital as the laws of thought. They affirm under a pro- gressive series of forms the primordial law of perfect con- sistency in consciousness as the absolute test of certitude.* They are " necessary laws," not in the sense in which Professor Jevons seems to think that expression must be understood, namely, in the sense that they are "laws which cannot but be obeyed;"! but rather in the sense that one's thinking must inevitably be self -contradictory in just so far as it fails to be in conformity with those laws. They are the laws in accordance with which one must think if he is to think truly. The order of the only world we can ever really know is the order of reason, of self -consistency. And this is a " necessary " order, in the sense that it can never change without destroying itself. Whence no thinking can really be true thinking that is, self-consistent thinking -unless it follow this law of the inner necessity of reason itself. Doubtless it is in this sense that one ought to under- stand the remark of Hegel that, " True thinking is the thinking of necessity." J A. THE LAWS OF THOUGHT ARE THE LAWS OF THJNGS. It is certainly not without significance that while these laws are named the laws of thought, they are neverthe- less formulated as the laws of things. At first view this seems a radical inconsistency. And yet it is not neces- sarily so. They are rightly named "laws of thought," because, as has just been pointed out, they are the three *This appears to me to summarize the aspects of truth involved in the three laws of thought; though Prof. Jevons expresses doubt as to the possi- bility of such summary statement. "Principles of Science," (3d ed.) p. 6. t Ibid, p. 7. t " Logic of the Encyclopedia," 119. 30 THE WOELD-ENEEGY essential forms positive,, negative and infinite (or abso- lute) under which the primary law of the necessary unity and self-consistency of thought may be presented. But they are equally the laws of things, since the only "things" with which thought can really deal, and hence the only things concerning which affirmations possessing any real significance can be made, are the facts of the world such as they present themselves in consciousness ; that is, in thought. But thus presented in conscious- ness, these facts, so far as they are really facts for the individual, are just the perceptions and conceptions which the individual has formed in his own mind. No doubt any given perception has taken place in any given mind only in consequence of certain stimuli which such mind has received from outer "things." But to say this, is only to describe another conception which the individual has formed concerning the conditions under which perceptions and conceptions in general can arise in his mind. That is, while such statement emphasizes the fact, that in one sense, we can never get beyond our own perceptions and conceptions, and that thus all our knowledge seems purely subjective ; yet the very con- sciousness of these subjective states necessarily involves a reference of them to some external exciting cause and thus proves that knowledge is no less objective than sub- jective in its nature. It is especially worthy of note in this connection, too, that even in the ordinary use of language it is the sub- jective phase of mental activity that is called thought, while the objective aspects of that activity are denomi- nated "things." And again, this implicit rationality of the ordinary consciousness is developed into more explicit AND ITS SELF-CONSERVATION. 31 form by the psychologist, who points out the fact that the only " objects" which we can ever know are in reality our own perceptions of what seems to us to be objects lying beyond and independent of us and of our perceptions. The complementary relation between thought and things thus indicated, is made still more evident if we fol- low out the clue and consider i. THE VARIOUS ASPECTS OF IDEALISM. The first aspect of idealism is that in which the ideal- ist presents himself in his subjective, most elementary stage of development. In this stage he puts his own interpretation upon the fact to which the psychologist has drawn attention. "Yes," he declares, "the only ' things ' I can ever know are, indeed, just my own states of consciousness. That is the only real world for me, and hence for me the only true world. What I really think, that is true for me and the only truth. Allowing the existence of an ' objective' world, I can never know any- thing of its real nature and can not even find any valid proof of its existence. So, also, allowing the existence of other minds, their convictions, however valid for them, can have no significance for me, to whom there can be no truth apart from my own mental states." Such is the standpoint of what may be called sub- jective idealism, pure and simple ; or, as it has commonly been known since the time of the later Greek thinkers, it is the standpoint of sophistry. It has appeared again and again with more or less elaborateness and subtlety of form and presenting a greater or less degree of substan- tial truth. THE WOELD-E^EKGY But such one-sided view could not but be confronted by its opposite that is, by objective idealism* Naturally, too, the latter is marked by distrust of the ' ' human intel- lect " and its powers. "Speculation" is regarded as idle and mischievous. If one is ever to put himself in posses- sion of the truth, he must abandon the absurd effort to find it in the empty depths of his own consciousness, and must turn his attention to the real objective world. It is in the world of nature alone that one can hope to find continuity, consistency, truth. Here the "ideal" is that of an outside, solid, material world. It is of a world already given, but given one knows not how. Doubtless the investigator in this field would prefer to be known as a realist; and indeed the "speculations" that inevitably force themselves into formulation here as elsewhere do lead up to a very lofty phase of idealism which has been named (by Herbert Spencer) "trans- figured realism.'' And yet this transfigured realism is itself a speculative or ideal representation of the object- ive world, as that world is conceived to be in its essence. Finally, there comes a third idealist and appeals in turn to each of the other two. To the subjective ideal- ist he says: "You have abandoned reason and in its place have substituted caprice. You are right in declar- ing that thought is all one can know; but radically wrong *The reader familiar with the history of philosophy will notice the difference between the use here made of these terms and that given them in Germany in the early part of the present century. At the same time I cannot but think that the crude form of subjective idealism specially referred to in the text is in reality nothing more nor less than the initial aspect of what in its subtler form develops into such theories as that of Berkeley; or even, in another direction, into theories like that of Fichte. It is scarcely necessary to add that the " objective idealism " here referred to is that (apparently for the most part unconscious) aspect of idealism involved in the current move- ment in natural science. AND ITS SELF-CONSERVATION. 33 in your assumption that the mere private, and very likely wholly undisciplined, thinking of the individual is the only attainable form of thought, or that it is necessarily true thought at all. If the thinking of each individual is the truth for him, then there can be no truth at all, since the untrained mind makes no effort to avoid contradictory thought, nor does it even recognize the fact that contra- dictions are constantly arising in its own thinking. And yet thought can only be true, as thought, in so far as it is consistent with itself. The contradiction of thought by thought must be the utter negation of thought ; that is, must prove that what was taken for thought is in reality not thought at all. " If, therefore, you are sincere in your search for truth, you must recognize that your standpoint is one-sided and superficial, and therefore requires to be supplemented and deepened through fusion with another element. That element is the objective phase of thought. Thought, as such, is universal and necessary in its nature. It is abso- lutely consistent and unchanging. That is the funda- mental characteristic of thought ; and because no sub- jective caprice which you or I may entertain can ever, in the least, affect this fundamental nature of thought, as such, the latter may very properly be called objective or true thought, in contrast with our own subjective, often self-contradictory, and in such case necessarily untrue thought. "I readily admit, and with you emphatically declare, that it is only by our own individual thinking that we, as individuals, can reach any conclusion at all. But I also declare, with no less confidence, that we must ever and inevitably be led to the conclusion I have just been 34 THE WOKLD-EISTEBGY stating, if we carefully put our individual thinking to the crucial test of self-criticism. For self-criticism must ever culminate in the clear recognition of the fundamental law of perfect consistency in consciousness as the absolute, unchanging, and hence objective test of certitude as to the truth in any given case of inquiry. It is only when the thinking of the individual unfolds into this objective character that it becomes genuine, true thinking/' So, again, this third idealist will appeal to the idealist of the second type, and say to him: tf Admirable as are your work and the results of your work, there is, never- theless, a phase of your method that remains as yet almost wholly implicit ; and this fact proves at times to be the occasion of serious error. You say rightly that truth is to be attained only through a searching examination of the objective, real world. But you seem to have not suf- ficiently regarded the fact that the only way by which a real knowledge of the ' objective ' or outer world can be attained is through the exertion of your own subjective or inner powers. You are thus led to look upon the object- ive world as something independent of your own mind, or even as independent of mind in any and every sense. So that when you discover necessary laws in ( nature' you not only regard the necessity of those laws as a ' natural ' necessity, but also make the unwarrantable assumption that f natural' is synonymous with ' physical/ And yet, as a matter of fact, you can scarcely fail to admit, upon reflection, that ' natural' means the same as t rational/ if it means anything. For whatever contra- dicts reason, the reason cannot but regard as unnatural; and it is only through reason that we can pronounce upon this, or, indeed, upon any question whatever. AND ITS SELF-COKSERVATION. 35 " Do but remember that the ' nature ' in the study of which you find such delight, and whose orderliness and symmetry you have so superbly demonstrated, is by no means all there in space is by no means objective merely in the sense of being outer and foreign to mind ; but rather that it is ' objective ' in the sense of being the embodiment of consistency, of necessary truth,, and hence as involving mind or reason as its very essence. Indeed, with every advance in your investigation of nature, you develop more and more conclusive proofs that nature is an embodiment of ' laws ' that justify themselves to the trained reason as possessing universal and necessary validity. " Thus there is constantly increasing ground for confi- dence in the justice of the maxim which virtually under- lies all your work. And we may well go to nature and trust to the guidance of its "facts" if we would find the truth. At the same time, it is of the utmost importance that we should know, as precisely as possible, both the character and the extent of the significance which the maxim contains. "And, on careful examination, this appears evident enough. Thus the maxim implies that truth is in Nature, and that the truth thus embodied is not beyond the reach of thought. For it is, indeed, only through thought that we can go to nature, or ' go ' anywhere in search of truth. "If, indeed, nature were something wholly distinct from thought, then the proposal to go to nature in order to find the truth would imply that thought must abso- lutely go beyond itself to find the truth. In which case thought must itself appear to be something untrue. At 36 THE WORLD-E^EKGY the same time, taken in the absolute sense of the term, the demand that thought should 'go beyond itself ' is wholly self -contradictory, and therefore destitute of mean- ing. It is only when taken in a special, limited sense that the expression is found to be consistent and to possess real significance. Thus, the ' thought ' of the individual human mind, considered in the sense of the actual state of consciousness of a given person at any given moment, may indeed, be developed or ' expanded ' into greater com- plexity and consistency. But it can do this only because it already contains implicitly in itself, as its own funda- mental nature, objective universality and truth. "In so far, then, as the individual consciousness devel- ops or ' expands" itself, it is only harmonizing or iden- tifying its real self with its ideal or true self. That is, in 'going beyond itself it is merely going beyond its present immature, untrue self, and in so doing is coming to its substantial, universal, true self. ' ' But now, you who insist upon the truth that the total quantity of energy forever remains unchanged, must admit that the individual human mind has no power to produce out of pure nothing any phase of reality what- ever, least of all the richest of all phases of reality realized reason itself. The human mind doubtless has the power to discover and transform, but not the power to create, in the sense of producing something which abso- lutely had no existence before. So that every step by which the individual mind 'goes beyond itself as an imperfect embodiment or realization of reason, implies of necessity, that both the phases of reason already reached, and also all the phases possible to le reached, by such mind must already possess perfected and permanent realization AND ITS SELF-CONSERVATION. 37 in the universe as a whole. Otherwise the growth of the individual as a power-to-think, must ultimately involve a change in (and of) the total quantity of energy. "But thus, again, it becomes evident that wherever the individual as a power-to-think can 'go/ there thought is of necessity already present in realized form. The ' where ' of thought proves to be just the total round of the possible modes of thought itself ; which modes, to be possible at all, must be already realized in the universe as a whole. Whence it appears that the thought of the individual can ' go ' to nature on this one condition alone: that thought, in its universal character, is already there present and realized in nature. " You would separate nature from thought as if nature were something objective and thought a merely subjective process. And this is right as far as it goes. But it remains only a half-truth until supplemented by the recognition of the fact that in the strict sense of the term the only possible objects of thought are pre- cisely thought itself, and the modes of thought in their manifestations. "And, in truth, your maxim really conforms to this view. For our examination of it has already shown sub- stantially that the thought of the individual can go to nature only on the condition that thought in at least some of its essential modes is already there in nature. But thought can only be 'in' nature by being fused with nature. "I submit, therefore, that this is the real truth of the case: Nature is the external and thought the internal; internal, that is, in the sense that thought is the inner, vital principle, which manifests, unfolds, utters or outers 38 THE WORLD-ENERGY in nature. So that, nature is ' object ' not in the sense of being external to thought, but rather in the sense that it is the externalization of thought. It is, in short, as a mode of thought, and only as a mode of thought, that nature is accessible to intelligence in any degree whatever. "Thus, it appears that the separation between nature as object, and mind as subject, is valid only in so far as concerns the experience of this or that individual mind. To the untrained mind nature, and still more, all the more complex modes of thought, are quite foreign or external. On the other hand, as the untrained mind ' goes to nature ' and expands its own powers into fuller realization, it approaches more and more nearly to the apprehension of that great truth that, in the final outcome, subject and object are but the necessary com- plementary phases, not merely of each individual human mind's experience, but also that they are the necessary complementary phases of the one only world or universe. ' ' On this view it is perfectly ' natural ' (i. c. rational) that on the one hand the. individual mind in its investi- gations of nature should discover .everywhere in nature the most beautiful manifestations of the law of consist- ency, harmony, continuity, rational system; and that on the other hand the testing and verifying this dis- covery should lead at length to the recognition of the fact that this law is, in truth, one and the same with the law of consistency, harmony, continuity, rational method underlying the very nature of thought itself. (( Thus the laws of thought and the laws of the only things that can ever be known by thought prove to be identical. And the truth is to be attained, not by an AND ITS SELF-CONSERVATION. 39 exclusively ' subjective ' method, as if one could exhaust the possibilities of thought by a mere examination of his own inner consciousness; nor by an exclusively ' objective' method, as if one could possess himself of the whole or even the highest phase of truth by a mere examination of that outer world of appearances occupying space, and which is commonly called ' nature.' On the contrary, the truth, in its vital reality, is to be attained only through a complete blending of these two methods; that is, through a constant recognition of the true relation between the outer and the inner, between the objective and the subjective, as the mutually complementary modes of existence in its ultimate reality and perennial vigor as the ever-living truth/' Such would be the appeal of our third idealist, who, as insisting upon this: that the absolute fusion of the sub- jective and the objective is the truth alike of things and of the method of inquiry concerning things, proves to be the representative of absolute idealism. And because this mode of viewing the world appears to bring us to, or at least to point us toward, the ultimate equilibrium of thought, it is the mode of view which we would hope to maintain in all our further investigations. What follows in the present volume is an attempt to develop dialectically the fundamental characteristics of nature. This logical process of thought in the investiga- tion of nature leads up to a conclusion in which there is found to be represented the logical presupposition of nature. Our final discovery is the primal Fact. CHAPTER II. "MATTER" AND ITS PROPERTIES. T~N the introductory chapter, it has been shown that -7 every object of sense-perception must necessarily occupy space. It must, in other words, be extended. We come, then, to ask, in the next place : What is the necessary significance of this characteristic inhering in the matter of sense-perception ? a. RESISTANCE OR REPULSION. To answer this question, we have but to reflect that our impression of an object as extended is due primarily to the resistance which the object offers to our activity. Without such resistance we could never even know that the object exists. But the resistance which an object presents to our activity necessarily implies that the parts of which the object, as a whole, is composed, must themselves be mutu- ally resistant. I attempt to compress a given object. I feel the object as resisting. That is, the object presents itself to my consciousness as resistance. Thus the object, as object of perception, is not only, by that fact, necessarily extended, and hence made up of mutually exclusive parts ; but this very mutual exclusion is found to be realized under the form of mutual resist- ance. The entire body resists my efforts to compress it, because the parts of which the body is composed resist AND ITS SELF-CONSEKVATION. 41 any effort, either to bring them into mutual mclusion, or to alter their positions relatively to one another. In other words, while the mutual resistance of the component parts of a body would seem, on first view, to be a merely positive characteristic, consisting of the sim- ple action of a force from the center outward, it really proves, on further examination, to be quite as much neg- ative as positive. It is not merely that the body holds together in a given positive form, but also that each com- ponent part excludes every other part. And in this respect the parts or particles are negative, as toward one another, and thus give to matter the negative, or at least negatively named, characteristic, of impenetrabil- ity. That is, so far as we regard matter merely under the aspect of resistance, it is evident that we can have no doubt of the impossibility of any two bodies ever occupy- ing the same space at the same time. Apparently, then, the truth of anything I can know as a body is found in the characteristic of resistance, or, otherwise named, repulsion. And yet I have but just noticed that the resistance which any given body offers to any effort I may make to change its form consists in part of the resistance which the parts composing the body pre- sent to any change in their positions relatively to' one another. But this can only mean that the parts are positively connected with one another, that they hold fast upon one another so as to hinder my efforts to bring them into a relatively different position. That is, they attract, as well as repel, one another. Besides, were the negative characteristic of repulsion the sole truth of bodies, we must be driven to a conclu- sion wholly at variance with the very idea of body. For 42 THE WOKLD-ENERGY unrestrained repulsion, as between all portions of matter between the smallest, no less than between the largest absolute continuity of repulsion must have the effect to infinitely diffuse each body through space. Whence, not only must every particular body lose all outline or boun- dary, and thus contradict the conception of body as something both extended and also limited ; but every particular body must thus penetrate every other body completely, and hence occupy the same space at the same time. In other words, there would be but one uniformly diffused mass, which, by the very fact of its infinite pene- trability, must forever remain wholly unknown to us. It appears, then, that a " matter " which should consist solely of resistance must, by that very fact, be infinitely diffused, and hence infinitely penetrable, or absolutely non-resistant. And this is the same as to say that the conception of matter as consisting solely of resist- ance is a self -contradictory conception a conception wholly at variance with the law of consistency, the central law of all thought and of all reality that can ever be known by thought. Our conclusion is, then, that though mere resistance may be the truth of matter as extended, it is far from being the whole truth of matter. We have, then, to make this further inquiry : What is the real truth involved in the conception of resistance ? We have certain impressions, to the objective phase of which we give the name "body," or "matter." And for us body or matter consists of a resistance which we name repulsion. We cannot account for these impressions in any other way. And yet, thus accounting for them, we AND ITS SELF-CONSERVATION. 43 find ourselves involved in contradiction. From this con- tradiction we are to seek a way of escape. In doing so, let us assume any series of particles, as : (1) (2) (3) (4) (5) If repulsion is an essential characteristic of matter, then each of these particles must repel every other in the series. Hence (3) repels (2) and (1) on one side, and (4) and (5) on the other side. But each of these repels (3) in turn. That is, repulsion is a relation of reciprocal action. One particle cannot repel the other without being in turn repelled by it. Indeed, there can be no exertion of force in any direction except in so far as there is opposition or resistance from that direction. There can be no push without something to push against no action without a corresponding reaction. And the degree of force actually exerted in either direction will depend upon the degree of force actually exerted in the opposite direction. So that, no matter what possibility of force there may be in (3), it can actually repel (2) only in so far as it is repelled by (2). And the same is true of whatever pair we may consider. But (3) repels (2) not merely by its own isolated power of repulsion (setting aside for the moment the ques- tion of the possibility of such isolated power), but also with the added impetus which it receives from the repulsion exerted upon it by (4) and (5). It is evident, then, that not only do (1) and (2) mutually repel each other, but also that (2) is actually driven toward (1) by the cumulative repulsions between itself and (3), (4) and (5). It is true that while (4) and (5) repel (2) through (3), they also repel (1) through both (3) and (2); so 44 THE WOKLD-EKEBGY that it would seem as if (1) must be driven from (2) still more powerfully than (2) is driven toward (1). At the same time, however, it must be remembered that (1) is the limiting particle of the series on one side. As such its repulsion for (2) and for the remaining particles in the series must be less than that of (2) for those remaining particles. For the repulsion of (2) for (3), (4) and (5) is intensified by the repulsion between (1) and (2), which thrusts (2) back upon (3), but only to be the more pow- erfully urged toward (1) again. Thus the tendency of the repulsion between (2) and the particles of the series beyond (2) is to cause an actual approach of (2) toward (1). And it is to be also noted, at the same time, that the repulsion between (1) and (2) counteracts in a measure the tendency toward separation between (2) and (3) ; and so throughout the series. But, again, it has already been incidentally observed that each intermediate particle in the series exerts its repulsion in two precisely opposite directions. In the case of (3), indeed, these repulsions in opposite directions must balance each other. Hence, (3) is the point of equilibrium in the series. And it is to be noticed especially that the repulsion of this middle particle for those on either side presents this peculiar aspect : that in thus exerting its power of repulsion in opposite directions, it necessarily concentrates upon itself. And this brings to explicit utter- ance the truth that no particle, under any conditions whatever, can push outward in any direction from itself save by pressing in upon itself in the same act. Repulsion, then, even in so inadequate an example as the one assumed, proves to be something more than a mere tendency toward indefinite diffusion. Instead of being AND ITS SELF-CONSERVATION. 45 merely a more explicit phase of externality, of matter as the extended, it proves to be a tendency toward concen- tration as well, and hence to involve internality no less than externality. And this will become only the more apparent the more concretely it is viewed. Imagine the particles in such series as that above repre- sented to be retained in the same relative positions, and the whole revolved about the central one in such way that the several other particles shall describe concentric circles in the same plane. It is evident that every possible diameter of the circles thus described has been repre- sented in succession by the line joining the series of par- ticles, and that the same relations would be true in every position assumed by the series. If, now, the distances of (1) and (2) from (3) in the original series be assumed to be different from the distances separating (4) and (5) from (3), then we should have four circles, each with a material circumference about a com- mon material center. In such case it is evident that the complexity of relations must be vastly multiplied, since the repulsions will be exerted not merely between the members of each series in any given diameter, but also between each member of each series, and every member of each and all the other series as well. But, again, let us imagine each diameter to be rendered material throughout its whole length through the further multiplication of particles. We should then have a con- tinuous disc, involving still further complication of repul- sions and counter-repulsions the lines of relation running out from each particle to every other particle in the whole disc, and thus forming a most minutely complicated web of relations. 46 THE WORLD-ENERGY And yet, once more, suppose the disc itself to be revolved about one of its diameters., so as to describe a sphere. The described sphere would be a material one, such that every section through a great circle of the sphere would present a- set of relations identical with that of the revolved disc. We should then have not merely an indefinite repetition of the web of relations existing in the disc, but also a wholly new and immeasur- ably more complicated network of relations, consisting of lines of repulsion between each particle and every other particle throughout the entire sphere. Each particle would be repelled by every other particle; that is, every particle within the sphere would be repelled in all directions. Hence it would be driven toward as well as from every other particle. And, still further, each particle, as exerting repulsion in all directions, is driven in upon itself from all sides; so that the more intense and complicated the repulsion exerted by it, with only so much the greater energy must it concentrate upon itself. Finally, let the sphere since there is no necessary limit to its volume be regarded as co-extensive with space ; that is, let it be regarded as infinite. The repulsion of part for part would then necessarily react in such way that the tendency to concentration would, in the total quantity of matter, exactly balance the tendency toward expansion. In other words, the " repulsion" must prove in its very development as repulsion to constantly unfold into its own opposite, and to be in its very nature attraction no less than repulsion. For "attraction" is the name we give to the inherent tendency of matter toward aggregation or con- centration upon itself. AND ITS SELF-CONSERVATION. 47 And here it is to be remarked, that not only is there no necessary limit to the ultimate " sphere/' or total volume of matter in the universe; in reality it would seem that no such limit is possible. For, on the assumption that such limit existed, the particles of matter at the surface would then be bounded on one side by pure space. That is, in all directions from the center there would be repul- sion outward, which would, indeed, on first view, seem to develop itself into attraction about the center of the sphere. But, on the other hand, at the surface there would be complete absence of reaction; that is, there would be absolutely no resistance to the thrust outward from the center. Hence the sphere must go on expand- ing indefinitely through space, and result at length in the complete dissipation of whatever energy may be allowed to have been accumulated, by whatever incom- prehensible means, upon the supposed center in past time. Thus I find that in reality it is impossible for me to conceive that any definite portion of " matter" should be so aggregated as to present a definite surface and an appreciable resistance (through which alone I could ever become conscious of its existence) otherwise than upon the condition that the total volume of matter is co-exten- sive with s]face; that is, upon the condition that the total quantity of matter is infinite. It appears, then, that every portion of matter exists, not merely on its own account, but also and necessarily that is, in its very nature for every other portion of matter. It has just been seen that resistance the primary characteristic of the objects of sense-perception proves this to be true. And the conviction that such is the 48 THE WORLD-ENEKGY case a conviction arrived at, apparently, by no very explicit dialectic lias long since become general under the form of the " impenetrability " of matter, which term is defined as meaning that " no two portions of ' matter' can occupy the same space at the same time." It is especially important to notice, too, that though presented in the negative form, the definition is expressed as having universal and absolute validity. If no two portions of matter can occupy the same space at the same time, then we but alter the mode of statement in saying that every portion of matter is necessarily related as repel- lant to every other portion of matter that every portion of matter exists not merely by itself, or in isolation, but also for all other portions of matter ; that is, in essential relation to them. Nor is the mutual repulsion of all portions of matter for one another a merely negative rela- tion. It is also, as we have seen, a positive relation or connection, which we can only name attraction. If again, we still further consider the nature of repul- sion, it is evident that this universal characteristic or property of matter is essentially a strain of separation. And yet a strain in one direction, let us repeat, necessarily implies a strain in the opposite direction. Already, in the very conception of repulsion between two bodies, there is necessarily implied that the bodies ai^ related to each other positively as well as negatively. For the fact that the action of a force is required to separate them, or to widen the already existing separation between them, necessarily presupposes that there is already in action a force drawing them toward each other. Repulsion would therefore be absolutely meaningless were there not con- stantly presupposed in it its own correlative phase of AND ITS SELF-CONSERVATION. 49 force, that is, attraction. And in tracing the dialectic of repulsion we have seen how, in its own activity as repul- sion, it necessarily develops into its own opposite, that is, into attraction. Thus it would seem that either of these two modes of force is wholly unthinkable apart from the other. They appear to be but different aspects of one and the same force or energy. And this becomes only the more evident as we trace out the dialectic of attraction from the assumption that it is an independent mode of force. 1. ATTRACTION. Throughout the scientific world attraction is con- stantly referred to as if it were regarded as pre-emi- nently the one universal mode of force. And in some of its phases it does seem to act quite independently. It will be well, then, to examine it in its seeming independence. Objects of sense-perception present definite boundaries, and we have seen that they offer resistance to any force tending to compress them. But they also offer resistance to efforts made to change their shape, or to divide them. Evidently then the particles hold fast upon one another attract each other. Thus at once it comes to light that the resistance which a body offers to pressure is due, not merely to the repul- sion of its particles for one another, but also quite as much to the relation of attraction between them holding them in fixed relative positions. So that the impenetrability of bodies proves to be a repulsion, which in large measure has its truth in attraction. If I press a piece of moist clay between my fingers it yields, not because of the lack of repulsion between the particles in the immediate line 50 THE WORLD-ENERGY of resistance, but rather because of the feeble attraction between particles in other directions. But let us trace out the nature of attraction in the same way as that in which we examined into the nature of repulsion. Assume the same series of particles, and regard them now under the aspect of attraction. Remem- ber also that attraction, to be attraction at all, must be mutual. No relation can be wholly one-sided. Each particle in the series, then, attracts and is in turn attracted by every other. Applying this in detail, (3) evidently stands in the relation of mutual attraction with (1) and (2) on one side, and with (4) and (5) on the other. But in this double relation it is drawn at the same time in contrary directions. And since the drawing is partly its own, it draws itself in contrary directions. But this drawing in contrary directions thus proves to be an opposition of the particle against itself, tending to separate it from itself. So that the middle point of the central particle as the " center of gravity" of the whole series is precisely the point where gravity cancels itself and becomes null ; or rather it is the point where gravity, or attraction, undergoes transformation into its own oppo- site, that is, into repulsion. And this must be true in greater or less degree of every intermediate particle in any series, since such intermediate particle must, in the very fact of its being intermediate, be drawn, and hence must draw itself, in opposite directions at the same time. Thus attraction proves to involve not merely the approach of particles toward each 'other, but also their separation from each other nay, it involves with each and every particle a tendency toward separation from itself. For every particle situated between two other AND ITS SELF-COKSEEVATION. 51 particles is, we have seen, necessarily drawn, and even nec- essarily draws itself, in opposite directions ; and thus the particle inevitably tends toward its own infinite division. On the other hand, as we have already seen, the repulsion which a particle exerts in opposite directions must have the effect to concentrate such particle upon itself. In further consideration of attraction we need hardly do more than mention briefly that, as before, our single series of particles may be conceived a^revolved about the middle one, so as to form a series of concentric circles in the same plane, while these circles may be conceived as having their perimeters made up of actual particles, thus forming circular bands, through which every diameter will present the same conditions as the series we have just considered. Thus at the same time we should have the additional attractions between each particle in each series, and every particle in every other series, with the same results of counteraction and transformation of at- traction into repulsion throughout. And this complica- tion must go on increasing with the increased complexity of grouping of particles, as the circular bands are con- ceived to coalesce into a solid disc, and the disc, by revo- lution on its own diameter, to unfold into a sphere. At the same time there should be borne in mind the vastly complex network of attractions and counter-at- tractions, involving the connection of every particle with every other particle throughout the sphere, and the consequent tendency, not, merely toward infinite concen- tration of the total mass upon its own center, but also toward the obverse phase of its expansion, and even of the disruption, not only of the sphere itself, but also of every particle of matter in the entire sphere. 52 THE WORLD-ENERGY Lastly, conceive the sphere to be the total quantity of matter in the universe, in which case it is evident that we should again have the total of attractions so reacting upon itself as to unfold into an exactly balancing total of repulsions. For in the physical universe as a whole (that is, the only extended universe we can ever know) the sum of reactions in attraction, just as the sum of reactions in repulsion, must be equal to the sum of the actions. And the more fully to satisfy ourselves that this is the case, we have only to repeat that the action of a force in any given direction necessarily implies that there is resist- ance to overcome. In other words, there can only be action in so far as there is reaction. In the sum-total of the physical world it could not, in the nature of things, be otherwise than that " action and reaction are equal, and in opposite directions." Thus, once more, attraction and repulsion prove to be but the complementary modes of an all-pervading force or energy, which constitutes the fundamental characteristic, the inmost essence, of "matter" of whatever is real and at the same time extended. They are thus the truly essential " properties of matter." CHAPTER III. PHENOMENON AND NOUMENON. THE ATOM AS FIGURED IN IMAGINATION. TT is now to be further noted that, as implied in our -I- investigation of particles in their relation to one another in any series, there are present in inseparable union throughout the minutest possible portion of matter both attraction and repulsion, as the necessary comple- mentary phases of that force which constitutes the sub- stance of matter. Neither of these phases can exist anywhere, in however limited a sphere, except through the co-existence of the other phase throughout the same sphere. There is latent here, indeed, the long-vexed question of the relation between phenomenon and noumenon, be- tween appearance or manifestation, and reality. Plato would have it that there is a world of ideas or archetypal forms constituting the real, the eternal and unchanging world; while the world of man's experience is the world of appearance, of change, and hence a vanishing world. So, again in modern times, Kant urged that we can only know phenomena, while the noumenon, or thing-in-itself (Ding-an-sicJi) is forever beyond our ken. And again, in quite recent times, it is confidently affirmed that while appearance may be regarded as fairly within the grasp of the finite mind, the reality must forever remain to such mind something wholly unapproachable, absolutely unknowable. 53 54 THE WORLD-ENERGY It would seem worth while to note, however, that the phenomenon, otherwise called appearance or manifesta- tion, must at least be allowed " reality " as appearance, and that thus it cannot be absolutely separated from reality. Similarly also, the reality can only be known as reality through its manifestation. And, since it is the only " reality/' the manifestation so far from being some- thing apart from reality, is simply the reality manifesting itself. Indeed, Mr. Spencer himself declares that by no mental effort is it possible to suppress the idea of absolute being, that the unknowable, as absolute being, manifests itself, and that this self -manifestation is in accordance with an " established order." * And from this standpoint it would seem that one ought to recognize the truth that all reality exhibits or manifests just its own essential being precisely in unfolding itself in phenomena. In other words, mani- festation is not " something " apart from reality. It is nothing unless the manifestation of reality. Whence it would seem that the ultimate Reality or Absolute Being can be rightly called the Unknowable only in a relative sense; that is, in the sense that we can only progressively learn all there is to know about it, that we can never absolutely know it in the sense of having attained an absolutely complete, exhaustive knowledge of it in all its infinitely manifold details. The term noumenon has indeed already faded away into what might very properly be styled a mere phenomenon. It simply marked a confused phase of thought, which must therefore prove a vanishing phase. *" First Principles' (N. Y. Ed.), pp. 117, 122, and elsewhere. AND ITS SELF-CONSERVATION. 55 It is to be further noted that physical science has long used forms of expression clearly implying the insepara- bility of reality and manifestation. Certain of the ' ' prop- erties of matter" have been classed as essential an expression which can mean nothing else than that these properties are the very essence of matter; that matter exists in and through these properties, and could have no existence without or apart from them. This, indeed, we have seen to be the case in our tracing of the simplest relations necessarily involved in the objects of sense-per- ception, which are, in general, the sum of things extended or characterized by externality. And yet physical science has not been able to prevent the re-appearance of the shadowy nqumenon within its own domain. For, from the unquestionably just opinion that there can be no action save as there is something to act upon, the conclusion has been leaped to that force can act only upon matter as a something apart from force. Of course physicists have not failed to note the contra- diction involved in this conception. Thus Thomson and Tait, in their "Elements of Natural Philosophy" ( 173), after remarking that they "cannot, of course, give a definition of matter which will satisfy the metaphysician," proceed to say that " the naturalist may be content to know matter as that which can be perceived by the senses,, or as that which can be acted upon by, or can exert, force." To which they immediately add that "The latter, and indeed the former also, of these definitions involves the idea of 'Force, which, in point of fact, is a direct object of sense; probably of all our senses, and certainly of the ( mus- cular sense.' " 56 THE WORLD-ENERGY This remarkable paragraph, in which the identity between matter and force is fairly asserted, concludes with the statement that " To our chapter on the ' Properties of Matter ' we must refer for further discussion of the ques- tion, What is matter 9 " The part of the joint work of these two physicists con- taining the promised chapter on the properties of matter does not seem to have appeared. But a volume under that title has been published by Professor Tait, while Pro- fessor Thomson has also separately developed his own theory upon the subject ; from which it may be guessed that the two could not entirely agree as to what should be said upon this particular theme. Indeed, after certain introductory remarks, Professor Tait declares (p. 11) that these "have been brought in with the view of warning the reader that we are dealing with a subject so imperfectly known, that at almost any part of it one may pass by a single step, as it were, from what is acquired certainty to what is still subject for mere conjecture." To which he adds that : "An exact or adequate conception of matter itself, could we obtain it, would almost certainly be something extremely unlike any conception of it which our senses and our reason will ever enable us to form." A little further on (p. 14) this declaration of nescience on the part of the scientific man concerning matter is even more emphatically set forth. He has been indicating the various theories concerning the constitution of matter, and, referring especially to W. Thomson's theory of vortex atoms, declares that this "has the curious peculiarity of making matter, as we can perceive it, depend upon the existence of a particular kind of motion of a medium which, under AND ITS SELF-COKSERVATION. 57 many of the definitions above, would be entitled to claim the name of matter, even when it is not set in rotation." After thus indicating that the theory which his former associate had developed, with a view to explaining the constitution of matter, has the " curious peculiarity " of assuming the thing it was proposed to prove, Professor Tait adds : " But as we do not know, and are probably incapable of discovering, what matter is, what we want at present is merely a definition which, while not at least obviously incorrect, shall for the time serve as a working hypothesis." He therefore chooses to "define, for the moment, as follows : ''Matter is whatever can occupy space;" and this for the following reason : "Experience has proved that it is from this side that the average student can most easily approach the sub- ject." * * * The point of view from which we have set out in the present essay, then, is not one that the strictly scientific mind would call an " obviously incorrect " one. And it is reassuring to have such confirmation from one who has gained the right to speak as one having authority, and not as the scribes, or "paper scientists." Amid such uncertainties, too, it would seem to be not wholly unwarrantable for even the "mere meta- physician" to throw in his conjecture also, though, from the expressions Professor Tait uses, it can hardly be expected that such conjectures will be estimated above the merest infinitesimals by the mere ( ?) mathe- matician. 58 THE WORLD-ENERGY Even the infinitesimal has its value, however, and so we proceed upon the line of our argument, not without some glimmer of hope. The course of the argument thus far has tended toward the conclusion that the essence or truth of matter is force or energy. And we have seen that such eminent physicists as Thomson andTait define matter to be "that which can be acted upon by, or can exert, force/' We have also seen that Professor Tait accepts as a tentative definition of matter, "whatever can occupy space." In either case matter cannot be a something apart from force, but, rather, must be identical with force, so far as we can ever know anything about it. For, as already noticed, it is only through a counter force opposing the force we ourselves exert that we can know anything about " whatever occupies space," or about space either, seeing that we become aware of extension only through the extended. But that which is extended, or "can occupy space," is in that very fact divisible, at least theoretically, without limit ; and it is divisible, experimentally, far beyond our powers of observation. Whence all bodies within our ex- perience must be aggregations of infinitesimal bodies beyond our experience at least beyond our sensuous experience. Nor is there any necessary contradiction between the " metaphysical " conception of the infinite divisibility of matter, and its practically limited division, as will perhaps become more evident with the further progress of the argument. The Democritean conception of the atom, or ultimate division of matter, has, of course, long been given up. Instead of the minute, absolutely hard, and therefore AND ITS SELF-CONSEKVATION. 59 inelastic and eternal, body named "atom" in the ancient doctrine, physical science has first cautiously defined the atom as the smallest division of matter arising in chemical reactions, and has lately come to look with favor upon the conception of the perfectly elastic and plastic vortex atom as somehow existing in, as parts of, a, perfectly elastic fluid pervading all space. That the atomic theory has been an instrument of wondrous efficiency in the furtherance of physical science there can be no question. And this can only be because there is an essential truth involved in that theory. At the same time, as leading scientists themselves clearly recog- nize and explicitly affirm, this does not necessitate the conclusion that the atom, as a necessarily permanent, unalterable unit, is anything more than a mere product of the "scientific imagination" something, indeed, not so very far removed from things " metaphysical." So long as modern science held fast to the conception of rigid atoms, it was under the necessity of also assuming the "void," in so far as " pores" were indispensable to the elasticity of a body. But this again led to another assumption. As "action at a distance" is unthinkable, according to Newton, and also according to anyone else who has done any genuine thinking, and as atoms, never- theless, act upon one another, though separated from each other by the void "pores," it was assumed by Clausius and others that each atom was surrounded by a sphere of force which was elastic, but which also prevented the enclosed atom from ever coming into contact with any other atom. With the impact theory, on the other hand, the force- sphere seemed no longer indispensable. Each atom, having 60 THE WORLD-ENERGY an irrepressible and more or less irresistible way of beat- ing about among its neighbors as if it were a "little demon/' preserves its own eminent domain inviolable. The impetus given in such impacts would produce the phenomena of repulsion, while the rebound', allowing the atoms to be elastic, would give rise to like phenomena in opposite directions, and the approach of atom to atom in either way would likewise give rise to the phe- nomena of attraction. At the same time, the tf ^void" appears here in its primitive simplicity. Indeed, this theory approaches nearest to that of Democritus, the difference, in one respect at least, being that the cause of motion in the atoms is left as something unknown, if not inexplicable, while, in the other, the atom is assumed to have an inherent eternal motion a kind of self-activity. From such crude "science" as that of Democritus, indeed, one could hardly expect the mythical element to be wholly excluded. Accordingly, with him the atom seems to have been a sort of uncon- scious symbolical eternizing of the beautiful, self-complete divinities of the Greek popular faith. Thus, with the father of the atomic theory, matter, or substance, was absolutely discrete, and "bodies" such as those appealing to our senses could only result from the accidental and temporary aggregation of the ever-self-sufficient and, in some sense, divine, atoms. It is also to be noted that, however superior the modern methods of science, the impact theory still leaves us no alternative. From this theory we must also accept the absolute discreteness of matter, and thus find ourselves forced into irreconcilable contradiction with the conception of the continuity of matter. And this is as much as to AND ITS SELF-CONSERVATION. 61 say -that it is irreconcilable with the theory of the all- pervading,, perfectly elastic fluid, which fluid would seem to be in its very nature perfectly continuous in spite of its seeming discreteness as developed in the vortex atom. To this it may be added that,, on the supposition that matter consists solely of atoms, and that it is therefore absolutely discrete, then the essential properties of matter must really be the essential properties of the atom. Thus, in the first place, the atom must be pervaded throughout by attraction at least, since, being of a definite volume, it must be drawn together by an infinite force in order that it may be able to maintain its integrity as against all forces tending toward its disintegration. And yet, as we have already seen, the attraction thus demanded for the assured existence of the atom must appear, in however limited a compass, as the complement of repulsion. Nay, the incompressibility of the atom is itself once more a manifestation of repulsion, which is at the same time equally the infinitely vigorous truth of its attraction. In other words, here, as everywhere, the existence of attraction at any point necessarily implies repulsion at the same point, and equally the contrary. It may be added, too, that, on the supposition of rigid atoms, in order that the atom may retain its rigidity in form and volume, it would be necessary that the relations between the attractions and repulsions within it should never be disturbed. And this again would require that the . external relations of the atom should forever remain unchanged. In other words, the atom could only be and remain absolutely rigid upon condition that the whole universe should likewise remain absolutely rigid, and hence wholly destitute of motion in any and every sense. 62 THE WORLD-ENERGY On the other hand, should the external conditions change, then the relations between the attractions and repulsions within the atom must change, following upon which or, rather, necessarily accompanying which the volume and the form would undergo change. That is, the "atom" must then prove to be itself an aggregate of an indefinite number of parts, each of which must in the same way prove to be changeable in volume, and hence also to be made up of parts, and so on until the atom slips completely from our grasp, and the irritating, if not terri- fying, "metaphysical" conception of the infinite divisi- bility of matter once more stares us in the face. In fact, there is here presented to us an intimation that there is some other relation between the discreteness and the continuity of matter than that of their mutual exclu- sion. And, it may as well be added, this is the one valid excuse for introducing the foregoing discussion of the rigid atom. What that other and truer relation really is will, it is hoped, appear in the further course of the argument. In resuming, it may be remarked that the tendency of the argument thus far is to show that while, of course, force cannot act save as there is something for it to act upon, the " something" required is not a "matter" as apart from force, but rather it is force itself. Force can in truth act upon nothing else than force. It can, let us repeat, prove itself to be force no otherwise than in the opposition of contrasted phases. Force is exerted only in opposing force, and force not exerted is no force at all. In the common acceptation of the term "matter," there is implied just the passive phase of the physical world, while " force" is the active phase. Or, to use AND ITS SELF-CONSERVATION. 63 G. H. Lewes's form of expression, te Matter is the passive aspect of existence/'* But we have already seen that force is,, in its very nature, at once active and passive. So that the conception of a matter apart from force only darkens the stream of thought with a sediment having no corre- sponding reality in nature. The theory of Clausius, already referred to, has a germ of suggestiveness which may be put to use along with the theory of Boscovich. In the theory of the former, the material atom is surrounded by a sphere of force. In the theory of the latter, the atom or ultimate element of mat- ter is a mathematical point, from which radiate out to a greater or less distance, both attraction and repulsion. In either case the force-sphere, as limited, must still present the difficulty of "action at a distance. " It is also evident that in the theory of Clausius the atom itself plays absolutely no part whatever. All that is done is done by the force-sphere surrounding the atoms. What- ever action is directed toward an atom is already received and reacted upon by the sphere of force in which the neither active nor passive atom is imprisoned in blissful unconsciousness, it may be presumed to all eternity. It seems evident, then, that any supposed matter as apart from force, is the veriest fiction; that, in short, the " atom," as generally figured, is simply an unscientific creation of the insufficiently restrained phantasy; that is, of the -wwscientific imagination. In other words, it is simply the re-appearance, under a changed and scarcely improved form, of the mysterious, unapproachable, met- aphysical noumenon of the Middle Age modes of thought, from which it might reasonably be supposed that the * " Problems of Life and Mind" (Boston Ed.), II., 302. 64 THE WORLD-ENERGY progressive science of the nineteenth century should long ago have freed itself. And mainly, indeed, this has actually been accom- plished. The word " atom" is used more and more in a symbolic sense, and now really involves no contradiction with the conception that matter, as that which is ex- tended, or which can occupy space, simply consist of its properties manifested in various degrees, under various conditions. And let us recall that, thus far in the present essay, two opposite and complementary forces, or modes of force, have appeared as constituting the very basis or essence of matter as that which is extended. From whatever side we view the subject, then, force appears to be the sole reality of matter; while the " atom," as a something existing apart from force, proves to be nothing else than a phantasmal product of that "bad metaphysics," which is, perhaps, indulged in most of all by those who know least of, and therefore Have least patience with, metaphysics, properly speaking. CHAPTER IV. TRUTH OF THE ATOM. PENETRABILITY OF MATTER. ^TEVEKTHELESS, as already stated, the conception -*--^ of the atom has served an excellent purpose in the progress of physical science. And we have next to in- quire what the truth of this conception is. We have seen that the really essential elements of mat- ter in its most rudimentary state must be the two comple- mentary modes of force, attraction and repulsion, and thus have grounds for the assurance that matter consists of, and is nothing apart from, force. It has also become evident that neither of these modes of force can exist in reality, save as in completely blended unity with the other. Indeed, when either is assumed as real, the other necessarily proves to be already contained in it. Or, more strictly speaking, each is not itself merely, but is itself and the other. It cannot be too strongly emphasized, then, that in every minutest possible portion of whatever is real, and at the same time characterized by externality, attraction and repulsion must be present in completely blended unity. Or, it may just as well be said, each must be present, both as itself, and the other. And this is but to say that everywhere where " matter" exists there must be at every point a center whence force radiates in every direction, and with an intensity diminishing uniformly with in- crease of distance from that center. 65 66 THE WOKLD-ENEKGY Thus far, indeed, it would seem that matter would necessarily be distributed uniformly through space, and that therefore " body" would have no meaning. To this objection an answer will develop in the further course of the argument. What we have now to note is that the force radiating from the centers everywhere appearing in whatever occupies space, would not, according to the conception of the constitution of matter thus far developed, ever reach any absolute limit. And this would seem to be the same conception as that which would result from the fusion of the two theories before mentioned. The " atom " of Clausius vanishes into the non-extended point of Bosco- vich, and from such focus a sphere of force extends indef- initely, though with gradually diminishing intensity. That is, the points of force in the one case and the atoms in the other are seen to be each in reality just a focus of force. That, it would seem, is the truth of the "atom." But, this once recognized, a number of important in- ferences are seen to logically follow. In the first place, if the atom is in truth nothing else or less than a focus of force, it is evident that it has no absolutely fixed boundary. Its nucleus must indeed possess a maximum of tension, but as it radiates outward in all directions, its extent or volume must be indefinitely great. Hence, secondly, we would express the truth more precisely if, instead of using the formula, " every par- ticle of matter attracts every other particle of matter," we were to say: Every focus of force, through its unlim- ited expansion, takes hold upon every other focus of force. And thus, thirdly, instead of the atoms, or foci of force, being merely side by side in space, and AND ITS SELF-CONSERVATION. 67 therefore characterized in their absolute isolation by exter- nality solely, it is evident that each in its unlimited expansion includes all at the same time that it is included in all. In other words, each "atom," in its relation to every other " atom/' includes the whole physical universe. It therefore has in some sense internality as well as exter- nality ; that is, the greater its extent, the greater also would seem to be its intent or content. NorJn saying this is there any latent purpose to trifle with the reader's time. We are attempting to examine the "atom" in its nature and essence. That is, we are endeavoring to trace out its fundamental characteristics and relations. And in so far as this is really accom- plished, there lies open before us the fact that this so-called ultimate, simple division of matter is in truth a highly complex phase of the physical universe. It exists not merely by itself, or in isolation that is, within abso- lutely fixed boundaries but rather it exists for all else- that is extended just as all else that is extended exists reciprocally for it. That is, the total sum of the extended can only be con- ceived as an indivisible unit, which is at the same time an immeasurably complex manifold ; though in our present investigation only the relatively simplest phases of this manifoldness have as yet received explicit statement. The next thing, indeed, that lies on the surface after what has already been developed is the solution of the con- tradiction between impenetrability and compressibility as properties of the extended. Even in the diffusion of gases "matter" shows itself to be practically in greater or less degree penetrable. And while this is usually explained on the theory of the <( porosity" of matter, yet in every 68 THE WORLD-ENERGY chemical combination there is evidently a genuine inter- penetration on the part of the elements, so that at no minutest point is there to be found any particle of either element untransformed. "Atoms " combine, become inter- fused, mutually penetrate, whenever a chemical reaction takes place. Thus, even empirically, the porosity theory, in expla- nation of so-called impenetrability, is found to be unneces- sary, at least in such cases, seeing that in such cases " matter " is really penetrable. And on the theory which we have seen reasons to adopt namely, that the atom is just the nucleus of an indefinitely extended force- sphere porosity appears to be in its ultimate character simply a fiction, having its only claim to reality in the complementary fiction of the absolutely rigid "atom." Nor can we too strongly emphasize the proposition that this force-sphere constituting the truth of the "atom" (and, hence, constituting the truth of " matter") is a reality. And because every "atom" is indefinitely or, rather, infinitely extended, then there can be no part of space where there is no force, no physical reality. Doubt- less this plenum presents various and varying degrees of tension, but everywhere it would appear that there must be some degree of tension, some degree of reality. Thus, what are called "pores," or inter-atomic spaces, are to be regarded as relative degrees of density in the matter that fills all space. So that when the atoms or molecules of two gases mutually occupy the "pores" of one another, it would seem that the gases really penetrate one another, according to the law that motion takes place in the direction of greatest traction or of least resistance. Least resistance, not no resistance. ITS SELF-CONSERVATIOK. 69 But, still further, and leaving aside such concrete example, which at the present stage of our argument must be considered an anticipation, it is evident that the rela- tions of force running out from every minutest center, and connecting it essentially, really, with every other center, must penetrate each other to an unlimited extent. It is, once more, the mutual inclusion of each in all and all in each. It appears, then, that impenetrability, as already hinted, is but the negative aspect of resistance or repulsion, which, as we have seen, also necessarily involves attraction the opposite but also the necessary complement of repulsion. Whence we may conclude that a body is " impenetrable " in this sense, and this sense only: That in so far as it is real it is simply a nucleus of force; or, if one prefers, it is a compacted cluster of such nuclei. It cannot, there- fore, be infinitely compressed that is, reduced in volume to a point, or to no-volume because, if that is to be accomplished, whatever force is brought to bear upon it must be applied on all sides. That is, the applied force simply unites its own volume with, by completely sur- rounding, the body to be compressed, and then presses in upon that body on all sides. In other words, since what is to be compressed is enfolded in and now constitutes the central portion of that by which it is to be compressed, the whole now constitutes in reality one continuous system, which to all intents and purposes can compress nothing but itself. It is a proposed self-crusher. But the greater the strain applied toward the center the greater the strain developed from the center. As the hollow golden sphere forces its way into the enclosed water, the water at the same time forces its way out 70 THE WORLD-ENERGY through the enclosing sphere. It is an initial metamor- phosis, in which the outer shows its readiness to become inner, and the inner an equal readiness to become outer. But as to crushing anything out of existence that can never be done; not even were the whole universe to join in the attempt. For it would still be the universe strain- ing at self-annihilation, and all the while in such effort, nay, as the very consequence of such effort, only suc- ceeding in bringing into fullest manifestation or realiza- tion whatever could possibly lie within it as hidden or potential. " Matter " is impenetrable, then, in this sense, and in this sense only: That action and reaction are, in the long run, absolutely equal and in opposite directions, and that therefore force or energy is forever indestructible. At the same time, as previously noticed, so far as there may be local changes of relation between attraction and repulsion, bodies will inevitably alter in volume. The bringing external pressure to bear is itself a change of conditions; and a change of such character as, within certain limits, to diminish the volume of that is, to compress the given body. Limited portions of matter (bodies) are measurably compressible, but not indefinitely so. Compressibility is, in fact, just a relation between attraction and repulsion, the two elementary factors of matter. CHAPTER V. TRANSITION TO THE QUANTITATIVE ASPECTS OF MATTER THROUGH INCREASE IN QUALITATIVE CHARACTERIS- TICS. ~| FERE, we may now observe, there is already presented -* *- to us the ground of the varying states of "matter," or the extended. Attraction tends toward concentration, repulsion toward diffusion, of matter. According, then, as the former or the latter predominates at any given moment in any given portion of matter, the tension will be increased and the volume diminished, or the contrary. With the predominance of attraction, the given portion of matter will be in the solid state. With the approach toward a balance of the two complementary modes of force, the solid will become viscid. With further increase of the relative degree of repulsion, the liquid state will be reached ; and the continuance of increase in this tendency must result at length in the matter assuming the gaseous state. Similarly, on the contrary, relative increase of attrac- tion over repulsion must result in a given gaseous mass becoming condensed into a liquid, and again in the liquid passing into the solid state. Of this, indeed, something more remains to be said at a later stage of our inquiry. What has just been said concerning the relation between attraction and repulsion brings us to note this further point: That there is doubtless more in the distinction 71 72 THE WORLD-EKERGY between ponderable and imponderable matter than modern scientists are for the most part disposed to admit. " Pon- derable " matter is matter that has weight. But weight is, properly speaking, an accident of matter, not a necessary property. It is wholly erroneous to regard it as identical with attraction. It is, as Professor Tait points out, a rela- tion between bodies ; or, as we should here prefer to say, weight is simply the excess of attraction or centripetal force over repulsion or centrifugal force. Even in the ordinary text-books on physics, indeed, it is pointed out that the " weight " of a given body is less at the equator than at any point distant from the equator, and that the greater " weight " always corresponds with greater distance from the equator. Of course this difference in the weight of a body, corresponding with difference in latitude, is due chiefly to centrifugal force that is, to the mass of the body itself combined with, or "multiplied into," the "tangential velocity." And one need only recall the frequently repeated calculation that, were the equatorial velocity increased to seventeen times its present rate, the weight of bodies at the equator would be just nil. That is, even solid bodies would become thus far "imponderable." But in another way matter may become imponderable. Weight, as we have seen, is the measure of the excess of attraction over repulsion, or centrifugal force. We have also seen that in respect of the states of matter, the excess of attraction over repulsion is the condition essential to the solid state (the production or retention of matter in the solid state through pressure, being but a special phase of attraction). Thus what we know as "ponderable matter " is directly associated with a large mass of solid AND ITS SELF-COtfSERVATIOH. 73 matter the earth. On the other hand, it would seem that imponderable matter is in this sense just that phase of matter in which repulsion is so highly developed that within a given volume (of any finite extent), the tendency toward separation is vastly greater than the tendency toward concentration, and that therefore in such volume even gravity is masked, while weight would have no existence at all. Thus, as all matter consists primarily of the interaction of attraction and repulsion, and as there is no absolute limit to the degree in which this interaction may vary locally, so there is no absolute limit to the possible diffuse- ness of matter in any given portion of space. It would seem, then, that throughout the spaces far removed from large, dense masses of matter, there is dif- fused what may properly be called imponderable matter. And there seems no good reason why we should not adopt for this imponderable matter the name, ether. It is the " unseen universe "; nay, in some sense the unseeable uni- verse, since it is that part of physical reality which, as such, must forever elude all efforts to bring it to the test of the chemist's balance. It seems in some sense to especially court inquiries of the metaphysical kind, and more or less to refuse answer to questions put in any other form. Doubtless the reader has already observed that the proof of the possibility of any change whatever in matter, considered as constituted of absolutely balanced modes of force, is not as yet by any means forthcoming in the present essay. It is well, at least, to have this explicitly called to mind, in order that the demand for such proof may not be forgotten or in any degree slurred over. Nor 74 THE WORLD-ENERGY shall we omit to look carefully for such proof as we proceed. For the present, however, we must leave the question in abeyance. Change unquestionably does take place in the extended world which constitutes the object or sum of objects of our perceptions, however these changes may be ultimately accounted for. What has thus far been proven is that the truth of the extended world is force, which in turn is a complex of mutually inclusive, everywhere inter- penetrating, attractions and repulsions. What is proven is, that the world is so constituted. What remains to be shown in this connection is, how such balance of forces can result in an active universe. What follows will, it is believed, be seen to join on naturally to the already completed portion of proof, and furnish an important stage in the movement leading up to the more adequate developments of the argument. It has already been shown that increase in the number of atoms or radiant centers, within a given compass, must increase the complexity of lines of relation between those centers. From this it is to be inferred that with the advancing concentration of matter in any given locality from any cause, there could not fail to be increased intricacy of interpenetration of the indefinitely extended dynamical spheres. But increased complexity of dynamical relations can only be manifested as increased complexity of material characteristics. On the contrary, the more widely sep- arated the radiant centers are, the less intricate and less tense must be the dynamical relations, and hence also the less must be the complexity of material char- acteristics. AND ITS SELF-CONSERVATION. 75 While, then, attraction is a strain toward simple unity, in that it tends to concentrate all into a single totality, it proves also to be a strain toward the heterogeneous, in that it tends to develop a multiplicity of qualitative differences within that total. And so, also, on the other hand, while repulsion is a strain toward infinite multiplicity, in that it is a continuous outputting or development of yet other ones from the total one, it proves also to be none the less a strain toward the homogeneous, since it is, after all, a development of " ones," each qualitatively indistinguish- able from the others; the result being a cancellation or annulment of qualitative differences. Condensation means increased tension, and increased tension means increased complexity of matter; just as, on the con- trary, rarefaction means decreased tension, and de- creased tension means decreased complexity of matter. Such is the logical conclusion to which the argument thus far leads. And this conclusion is distinctly in agree- ment with the results of the most searching investigations in physical science, and especially with the brilliant results achieved by means of the spectroscope, in connection with the nebular hypothesis. * It is well known that, previous to the invention of this remarkable instrument, there was no means of answering the question whether certain cloud-like patches in the heavens consisted of diffuse incandescent matter, or of star-clusters so distant that, to the eye of an observer from the earth, their light blended together. With the invention of the spectroscope, however, scientists found themselves in possession of an instrument that revealed * See the special works on "Spectrum Analysis,' 1 '' by Schellen and by Lockyer, the latter in the "International Science Series." 76 THE WORLD-ENERGY instantly whether or not the light received into it was from a body in the gaseous state. Not only so, but in addition to this it also revealed the remarkable fact that each of the so-called elements has its own peculiar and exclusive spectrum. With this instrument the vexed question as to the reality of true nebulae was at once set at rest. The spectrum of nebula after nebula was found to present unmistakable characteristics-, showing that these were actual masses of matter in extremely attenuated gaseous form. But what is especially to our present purpose is the fact that of these nebulae some were found to consist of but few elements, mainly hydrogen and nitrogen; while in the spectra of others there are lines indicating a greater number of elements, and so on, until the continuous spectrum indicating the presence of all the known elements is developed from the sun and other incandescent bodies in the solid or in the liquid state. From these grounds alone, the logical or natural that is, rational inference is that increase in multiplicity of elements, which is the same as increase in complexity of matter, goes hand in hand with, and is a consequence of, the increased complexity of those force-relations consti- tuting matter which must inevitably result from the con- densation of nebulous masses in space. Thus it seems that the more diffuse the nebula, the more simple the spectrum; that is, the more simple the constitution of the "matter" composing the nebula; while the more advanced toward solidification, the more complex must be the spectrum; in other words, the more complex the con- stitution of the " matter'" composing the nebula. AND ITS SELF-CONSERVATION. 77 What shall we say, then, of the claim that all matter is permanently divided into seventy or more elements, all differing essentially from one another ? It is true that chemists themselves are beginning to doubt the finality of their analyses ; and while the tendency still is in the main to look to a further increase in the number of elements, there is already arising here and there a guarded query as to whether, after all, the elements may not prove to be only specialized conditions of a <( matter" that, theoretically at least, is primarily homogeneous.* I say "theoretically," because it is evident that there can be no actual case of concrete matter which can be strictly homogeneous. This we have already seen in the attempt to form a conception of matter as consisting solely of repulsion. It was found that such conception cannot be formed, because no sooner has the representa- tion of such assumption been made than it becomes evi- dent that any real repulsion must develop attraction as a necessary aspect of such real repulsion; just as any real attraction must include, as a necessary phase of itself, repulsion also. In this connection the following significant paragraph from Lockyer (" Spectrum Analysis," N. Y. Ed., p. 190) may be cited. "It is," he says, "abundantly clear that if the so-called elements, or, more properly speaking, their finest atoms those that give us line spectra are * It was not until after the foregoing was written that I read Mr. Spen cer's " Principles of Psychology" and found therein (N. Y. Ed., Vol. I., p. 155) the following statement: "Moreover, there- is reason to suspect that the so-called simple substances are themselves compound, and that there is but one ultimate form of matter, out of which the successively more complex forms of matter are built up." Other suggestions of a similar nature had been previously made as that hydrogen is the ultimate form of matter; though this has the obvious fault of regarding one of the various differen- tiated phases of matter as itself the primal undifferentiated aspect of matter. 78 THE WORLD-ENERGY really compounds, the compounds must have been formed at a very high temperature. It is easy to imagine that there may be no superior limit to temperature, and there- fore no superior limit beyond which such combinations are impossible. Because the atoms which have the power of combining together at these transcendental stages of heat do not exist as such, or rather, they exist combined with other similar atoms, at lower temperatures. Hence association will be a combination of more complex molecules as temperature is reduced, and of dissociation, therefore, with increased temperature there may be no end." To this conclusion, indeed, the facts brought to light by means of the spectroscope clearly point, and thus, as already remarked, offer a strong confirmation of the argu- ment we have presented above in abstract form, showing that increased complexity of " matter" must necessarily result from increase of condensation, involving, as that necessarily does, increased complexity of concrete relations in the mass; while, on the other hand, this complexity must grow less and less with the diffusion of matter into wider space. We can but conclude, then, that matter is not only constituted by and of force, and that it is thus ultimately (at least in a relative sense) homogeneous, but also that the seeming complexity of matter that is, the multi- plicity of " elements " is in reality but the increasingly complex grouping of and multiplied tension between the indefinitely extended dynamical spheres which constitute the initial phase of the development or manifestation of force the added complexity of grouping and increased intensity of relation being due to the steadily accumulating AND ITS SELF-CCWSERVATION. 79 strain incident to the condensation of nebulous masses into stars and suns and their attendant spheres. It is a notable fact, too, that even by artificial means a gas may be subjected to so great a pressure as to cause it to give off a continuous spectrum. It is as if, out of a single element, the increased complexity of grouping of centers of force together with the intensified strain between those centers corresponding to increase in the number of ele- ments by the analogous process exhibited on the grand scale in nature could thus temporarily be reproduced at will in the laboratory. CHAPTEK VI. DEFINITE QUANTITATIVE RELATIONS IN MATTER. WE have seen that as the qualitative relations of matter develop into increased definiteness they necessarily involve quantitative aspects also, though this has appeared thus far only in the form of indefinite mul- tiplicity. We have now to trace this quantitative aspect into its more precise forms. The elements of which we have just traced the origin constitute in large measure the subject-matter of what is known as modern chemistry. It was largely in the inter- ests of chemistry that the atomic theory was revived in modern times; and it is directly in the field of chemis- try that the more elaborate part of the theory in its spe- cially modern character, and particularly in its quantita- tive aspects, has been developed. The " atomic weights " of the several elements have been ascertained with at least the appearance of great precision. Nor is there any sufficient reason to call in question the substantial accuracy of these results, so far as they are understood merely as the expression of the quantitative relations necessarily involved in matter. And, as we have already mentioned, the more advanced chemists themselves regard the "atom" as hypothetical, and even look to an entire change of view respecting the so-called "elements. " 80 AND ITS SELF-CONSERVATION. 81 What has thus far been said, then, far from conflicting with the assured results of science, proves rather to be quite in harmony with those results. The only conflict developed is with what scientists themselves have already begun to call in question, and which they are definitely prepared to set aside as forming no necessary part of any of the various phases of truth which science has brought to light and verified beyond all reasonable question. It will be quite in the direct line of our inquiry to trace some of the more characteristic of the confirma- tions which science presents to our theory, and to develop such consequences as the theory thus confirmed may be found to involve. We may recall that the development of the interrela- tions of attraction and repulsion necessarily involve on the one hand the unifying of matter in that at every point there is a center of attraction fundamentally related to the whole of the material universe. This, as has been shown, is involved in the received statement that every particle of matter attracts every other particle of matter, an expression which, developed so as to explicitly con- form to the conception that matter has its substance in force, would take the form: Every nucleus of force radi- ates outward to the farthest points of space and takes hold on every other nucleus of force. Thus, it may be remarked by the way, the physical uni- verse, regarded as commensurate with space, is a verita- ble sphere whose center is everywhere and whose circum- ference is nowhere. It is also manifest that there is no possible object in space that can be in absolute isolation, since even the simplest force-center still radiates outward into the whole of immensity. 82 THE WORLD-ENERGY The smallest thing in the universe, then, is still, in its truth, commensurate with the universe itself. The small is not merely included within the great; the great is also included within the small. Each presupposes the other and could not exist without the other. Force regarded as attraction, let us repeat, then, unifies the extended world absolutely, gathers the physical universe into an absolutely indivisible One. On the other hand, however, we have also seen that the complementary mode of force, namely, repulsion, puts restraint upon this unifying tendency and gives rise to an infinitude of independent centers within the all-embracing one. And yet this one itself is but the totality of rela- tions between attraction and repulsion. Thus the One, as this totality of relations, itself gives rise to an infini- tude of ones within itself, each of which in turn is essen- tially related to the whole, and thus also to all the other ones. Thus the phase of unity finds its necessary comple- ment in an infinite multiplicity which, however, still proves to be but a mode of the unity itself. The appear- ance of multiplicity is but the unfolding of the unity. The qualitative distinctions as they emerge into view prove to already necessarily involve quantitative distinc- tions also. Each center of force is already something definitely opposed to, as well as connected with, every other center of force. And each in comparison with every other is seen to be necessarily a greater, or a less, or an equal, as regards that other. CHAPTER VII. AS TO CONTINUITY AND DISCRETENESS OF QUANTITY IN MATTER. AT this point we come upon the question as to the relation between continuous and discrete quantity in matter. And in our search for the answer to this question we have but to revert to what has already pre- ceded. We have seen that matter, as constituted of force, is simply a manifestation of the relations between the complementary modes or phases of force attraction and repulsion. But the interaction of these phases of force cannot but result in the focusing at every point in space of a greater or less intensity of strain between those phases. And yet each of these foci of force necessarily ex- tends outward so as to act upon, and in turn to be reacted upon by, every other focus of force. Thus constituted, then, matter is necessarily continuous. At the same time, however, the very focusing of force through the interac- tion of its two complementary modes is a setting up of distinctions which necessarily mark off or limit one por- tion of matter as thus far separate, at least quantitatively, from every other portion. Whence it is to be concluded that matter is not merely continuous, but is also at the same time, and not less truly, discrete. That is, the same totality presents itself under the two different but also complementary aspects of discreteness and continuity. 84 THE WOKLD-ENERGY Thus in a concrete sense the continuity of matter necessarily implies the absolute fluidity of matter; just as, on the other hand, the discreteness of matter no less necessarily implies its perfect rigidity. But it is precisely in this concrete sense, as we have already seen, that matter (that is, force) in its very character of the con- tinuous develops within itself infinite discreteness. The infinite fluidity of the extended is nothing more nor less than the varying relation between the complementary aspects of force, known as attraction and repulsion, whereby any and every given quantity of "matter" is constantly undergoing expansion or contraction, and whereby, at any given moment, therefore, the complete disruption of the given quantity of matter may begin; following which, or even accompanying which, such given quantity may become completely fused with other quan- tities and thus undergo entire re-constitution. And it may be that the conception here presented is not so very far removed from that of the perfectly elastic fluid which, in the vortex-atom theory, is assumed to fill all space. Here, then, the puzzle of the infinite divisibility of matter finds its solution. Considered as continuous merely, matter is, like space, infinitely divisible ; for as simply continuous matter must be as absolutely indifferent to division as is space itself. But, on the other hand, matter considered as merely discrete and such the atomic theory makes it cannot possibly be thought as undergoing infinite division, since it has already undergone final division, and hence consists of ultimate, unalterable particles. It would seem, then, that the reconciliation of these two apparently irreconcilable views is found in the fore- AND ITS SELF-CONSERVATION. 85 going conception of matter as force which necessarily so unfolds itself as to present everywhere two primary and complementary aspects rendering matter fluid through- out its whole extent, and at the same time specializing it into more or less complex and distinct, but still more or less unstable, concrete masses. As is well known, the densest mass still retains the character of fluidity. And this must be true of the minutest (i atom" no less than of directly perceptible masses. CHAPTER VIII. EXTENSIVE AND INTENSIVE PHASES OF QUANTITY IN MATTER. TT is to be noted that, in so far as matter is considered -* as merely continuous, its qualitative characteristics do not appear. On the other hand, its discrete character arises from distinctively qualitative phases of the relation between attraction and repulsion. It is precisely through qualitatively developed differences that discrete quantity is perceivable in matter. But the more and less of strain, as between the con- centrative and the expansive tendencies, within any given sphere involves still another quantitative contrast. With diminished strain there is a canceling of qualitative differ- ences and an increase in mere space-occupancy. As the tension diminishes the extension increases. That is, the intensive quantity proves to be inversely as the extensive quantity. Here, indeed, then, comes to light the deeper meaning involved in the contrast between extensive and intensive quantity, as set forth in the ordinary formal logic. There the term having the greatest extent of meaning is ordina- rily understood to be merely the most abstract term, since, in order to increase the number of objects included within it, the term must be restricted to fewer and fewer distin- guishing characteristics. That is, with increase of extent there must necessarily be decrease of intent or content. AND ITS SELF-CONSERVATION. 87 So that, formally, the intensive phase of quantity must be completely set aside in precisely the same measure that the extensive phase is brought into prominence. But "set aside" may also mean, "held in abeyance," rendered latent or potential. It is evident, for example, that the matter of a nebula is, in the first place, quantita- tively extensive ; and yet the quantity will not be dimin- ished by its development of the intensive phase through condensation into a planetary system, with the resultant unfolding of chemical elements, followed by the appear- ance of the whole vast order of compounds in vegetal and animal organisms. Doubtless through this development (which is also an envelopment) there will be a differentiation of tendency toward the merely extensive phase of quantity in the sub- stance through the radiation of the most diffusible phases of the substance into space as the concentrative process goes on. But also in this concentrative process the ten- dency toward diffusion, toward mere extensive quantity, still remains as a necessary factor in every stage of the condensation. For while the latter is the process in which the intensive phase of quantity is realized, there is also necessarily involved in this the development of the ten- dency toward expansion, toward diffusion, toward the extensive aspect of quantity. Or, in the more concrete terms of physical science, pressure toward a common center must inevitably develop its complement, heat, which is pressure away from the common center. * * Professor Helmholz's calculation showing that the continued high tem- perature of the sun is fully accounted for by its continued concentration upon its own center will doubtless occur to the reader as verifying what is said in the text. 88 THE WORLD-ENERGY In the same way, also, the extensive term in logic im- plies, though it does not explicitly include, all the charac- teristics of all the special objects included under it. The term "rock" formally excludes all the special characteris- tics, which distinguish granite from sandstone, and either from marble. But since the term "rock" includes all these, there is implicit in it all that belongs to whatever objects it may be applied to. The quantity of steam used in propelling a ship in safety from New York to Liverpool would, if developed instanta- neously in its boilers, inevitably shatter the ship to atoms. The quantity might be precisely the same in either case; but in the former it would be predominantly extensive, while in the latter it would be predominantly intensive. In either case the qualitative result depends upon the relation between the extensive and the intensive aspect of the quantity of force in exercise. With continued preponderance of attraction, as we have already seen, there is also corresponding increase in the development of qualitative characteristics, from the diffuse, almost qualitiless nebula, to the solid earth, with its intense strain of forces and endless wealth of quali- tative developments. At the beginning of this process of concentration the quantity of matter is indeed mainly extensive, and hence only in the simplest degree special- ized in point of quality. At the very outset, indeed, this extremely diffuse matter is already found to qualitatively distinguish itself into the two opposite but complementary phases of attraction and repulsion. Now, extension is itself a universal form of all physical magnitude, while magnitude, as a phase of extended real- ity, is a given quantity of matter, which must necessarily AND ITS SELF-CONSERVATION. 89 be both extensive and intensive, these phases appear- ing always as reciprocals. So that attraction and re- pulsion are, in the first place, the initial and funda- mental qualitative differences, constituting the reality of matter, or the extended. And the varying relations between these complementary phases of the extended must involve the whole series of relations between exten- sive and intensive quantity. At the same time, the transition in matter from the state in which its quantity is predominantly extensive to that in which the quantity is predominantly intensive proves to be a process of qualitative evolution. That is, the increase in the degree of strain between attraction and repulsion within any given quantity of matter results necessarily in the increased complexity of qualitative manifestations within the matter. Attraction and repulsion, then, appear in the first place as if merely qualitative; but as the complementary phases of the extended they prove also to be quantitative, while their varying quantitative relations under the re- ciprocal forms of extensive and intensive quantity again give rise to an infinitude of qualitative determinations. So that quality and quantity prove to be but different aspects of the same sum of facts in the physical universe. And science has for its special mission to unfold into explicit form the orderly representation of this entire sphere of relations. A few illustrations, selected mainly from chemistry, may serve to make clearer the truth of what we have just been saying. It has already been more than once remarked in the present inquiry that the condensation of a nebulous mass 90 THE WORLD-ENERGY into solid spheres must, through an increasing strain between attraction and repulsion, develop as a phase of that strain a correspondingly increasing tension in and between the local centers of force constituting the sub- stance of the sphere, and that increase of such local ten- sion is the real secret of the development of the so-called chemical elements. It is now to be added to this that the farther this process of condensation has advanced in any given portion of the developing system the greater will be not only the actual number of these elements, but also of the actual number and complexity of the combina- tions of these elements. All chemical compounds appear as manifestations of the special phase of attraction known as <( affinity." At the same time chemical decomposition also appears as a negative aspect of chemical combination; for the separation or dissolution of a compound may be due to the approach of an element between which and one of the elements of the compound there is a still stronger attraction or "affinity" than exists between the elements already in combination, That is, the breaking up of an existing compound may be involved in the very process of the formation of a new compound. One degree of attraction is annulled in its qualitative result by the interposition of a greater degree of attraction, bringing about a different result. On the other hand, the phase of repulsion, as such, must tend toward the complete disintegration of all com- pounds. As the separative phase of force it still further tends to dissolve all solids and to dissipate all liquids into vapor, and again to still further attenuate the vapor until it ceases to belong to the type of ponderable matter at all, and thus comes to exist in the state of imponderable AND ITS SELF-CONSEBVATION. 91 space-filling substance, where, as we have previously intimated, it is the true ether. Such would seem to be the legitimate inference. And in any case it is evident that where the separative tendency as yet greatly over- balances the tendency toward concentration, the number and complexity of chemical compounds must be corre- spondingly limited. So that in the sun, for example, with its enormously high temperature that is, with the still existing relatively intense repulsion or strain toward sep- aration the number of chemical compounds must be exceedingly few and those compounds must be of the simplest character. More explicitly, it is impossible that oxygen and hydrogen should there realize their combi- native tendency in the actual formation of water, even in the vaporous state, while not a single one of the whole series of known carbon compounds can possibly exist otherwise than in the purely potential state. It is to be noted further that the whole of modern chemistry is built up from the precise quantitative rela- tions existing between the " elements. " So that on this side chemistry is simply one form of applied mathematics. As M. Berthelot declares in closing his remarkable work, " Essai de Mecanique CMmique," chemistry "approaches more and more nearly to that ideal conception, followed out for so many years by the efforts of scholars and of philosophers, in which all speculations and all discoveries tend to establish (concourent vers) the unity of the uni- versal law of natural movements and forces." That is, chemistry is coming more and more to be regarded as simply a branch of mechanics in the general sense of the term in proportion as chemical phenomena are found to be capable of mathematical treatment. At the same time 92 THE WORLD-ENERGY this in no way obscures the fact that each new compound developed through change in quantitative relations ex- hibits new qualitative characteristics. Take, for exam- ple, the simplest cases those of allotropic substances. Oxygen combines with itself, the result being what is called ozone. The quantitative change is simply one from extensive to intensive quantity. Externally the only change is a reduction of one-third in volume. So, too, carbon presents the three strikingly different states of graphite, coal, and diamond, by mere variety in the com- bination of carbon particles with carbon particles. The same remarkable development of qualitative dif- ference through mere change in quantitative relation is seen again in all those cases where one element combines with another in more than one ratio. A conspicuous example is found in the various oxides of nitrogen, where a con- stant quantity (28 parts by weight) of nitrogen combines successively with five different quantities (16, 32, 48, 64 and 80 parts by weight) of oxygen, producing as many qualitatively different results. It is noticeable that each succeeding quantity of oxygen in the series is a simple multiple of the first. And chemists have often called attention to the fact that no combinations take place be- tween these elements in other proportions than those given. It was precisely such facts as these that led Dalton to enter upon those investigations which resulted in his revival of the atomic theory under a genuinely scientific form. The core of Dalton's discovery is that this combination in definite proportions is the universal characteristic of all chemical activity that chemical compounds are, without exception, dependent upon precisely fixed quantitative relations. Nor is it without significance that in Dalton's AND ITS SELF-CONSERVATION. 93 theory the numbers representing the proportions in which the elements combine have direct reference to the weights of the combining atoms. For weight, as we have seen, is simply the excess of attraction over centrifugal force in the neighborhood of a gravitating body like the earth. So that the relative weights of the atoms of different ele- ments really means the relative excess of attraction over centrifugal force as between the earth on one side, and the atoms or force-centers in the elements taken severally. Now, the weight of an atom of hydrogen being taken as 1, the weight of an atom of nitrogen is 14, and that of an atom of oxygen is 16. But the simplest compound of nitrogen and oxygen known to take place consists of two parts of the former and one of the latter. Hence the combining numbers for these two "elements" expressed in their atomic weights are: 28 for nitrogen and 16 for oxygen. And since the " atoms " can only combine as wholes, the next more complex compound, supposing the quantity of nitrogen to remain fixed, would be that in which the quantity of oxygen would be doubled, and so on. Allowing, then, that the atom is real, not as an infin- itely hard, absolutely fixed particle of something existing independently of force, but rather as itself simply a focus of force which constitutes a relation that must remain fixed so long as the surrounding conditions remain ap- proximately the same ; allowing this, we can see that the law of multiple proportions only becomes the more sig- nificant, without losing in any degree its simplicity. This law, indeed, but expresses the fixed relation be- tween the general mass of the earth in its present rela- tively matured stage of condensation and the various classes of force-centers constituting, through their varied 94 THE WORLD-ENERGY intensive quantities, the qualitatively different phases of force-substance known as the elements, and in any given case arbitrarily assumed not to be of the earth's mass. In reality, the mass of the earth holds these force-centers in definite relation to itself/ and in definite relations to one another. Thus many compounds take place " naturally" (the mass and temperature being what they are) which would be impossible as "natural" compounds on the sur- face of a sphere of very much less mass, or of very much greater temperature. In short, all chemical compounds must arise as the realization of inherent relations of attraction and repulsion between definitely determined force-centers, which, doubtless, there is 110 harm in call- ing atoms. And should there be more than one compound possible between any two elements, as in the example of oxygen and nitrogen cited above, it is evident that the several compounds formed must show in the successive groups of atoms that the combining numbers of one or the other element stand to each other in such relation that all after the first are exact multiples of the first. The law of multiple proportions, however, presents the external conditions of chemical combinations; or, more precisely, the qualitative relations here presented are figured rather as the relations of extensive quantity. On the other hand, the phase of intensive quantity is shown in affinity, properly speaking in the energy of attraction between the particles themselves. At the same time there is, as must ever be the case, a variation of the intensive quantity presented in the compound, through a variation in the extensive quantity of combination. And this variation of the intensive quantity is precisely what determines the qualitative differences of the several AND ITS SELF-CONSEKVATIOJtf. 95 compounds. Thus, the several oxides of nitrogen already referred to present each its own group of distinguishing qualitative characteristics. The whole of chemistry is, indeed, but an extended illus- tration of this, so that we need here do no more than call special attention to the immense number of exceedingly complex compounds which carbon forms with one or more of the three other elements, oxygen, hydrogen and nitro- gen the great number of the compounds being rendered possible, as the chemists assure us, by a "fundamental and distinctive property of carbon itself." That property is the power, possessed by no other element in so high a degree, of combining with itself, and forming a variable basis for multitudes of complicated compounds involving one or more of the other elements just named. The point we have here specially to emphasize is, that the mere variation of the quantitative relations in the combinations of these four elements gives rise to the entire series of qualitative differences which lend such immense variety to the products, both of the vegetal and of the animal world. To what has been said respecting the relation between extensive and intensive quantity as illustrated in chem- istry, there may be added the following, from what is known of electricity. Statical electricity is said to be characterized by intensity, while dynamical electricity is distinguished by its quantity. And yet these two modes of electricity do not differ in kind, but rather in the mode of their development, which fact becomes explicit in the alternative names: frictional and chemical electricity. Not only so, but a Leyden jar may as well 96 THE WORLD-ENERGY be charged from a Voltaic battery, as from an electrical machine. The real truth of the relation between statical and dynamical electricity comes out in the estimate of Fara- day,* that a current of dynamical electricity which would decompose a single grain of water by acting upon it during three and three-fourths minutes would, if its whole force were expended instantaneously, be equal in intensity to a powerful flash of lightning. Here the quantity of force is evidently the same. Acting through a longer time, it is extensive quantity; while the instantaneous expenditure of its whole energy presents the same quantity of force under the character of intensive quantity. Statical electricity, then, is a phase of force, whose quantity is characteristically intensive, while dynamical electricity is a phase of force whose quantity is characteris- tically extensive. And, as is well known, all that is neces- sary in order to concentrate the extensive quantity of the latter, so that its manifestation shall be specifically inten- sive, is to introduce into its circuit an induction coil. It is evident, then, that the "intensity" of statical electricity is simply intensive quantity, while the " quan- tity " of dynamical electricity is quantity manifested under the specific character of extensive quantity. And when it is said that quantity and intensity are inversely the one as the other in electricity, it is evident that this is but a loose way of saying that in any given quantity of elec- tricity as of any other phase of force : the extensive and the intensive aspects are reciprocals. *See his "Experimental Researches in Electricity," (3d Ed.) L, 250. OHAPTEE IX. MEASUEE AND THE MEASUEELESS. WE have thus seen that the extended world is first known to us through the qualitative differences of attraction and repulsion; that these in turn, through their necessary interactions, develop, or rather are seen to involve, an unlimited complex of quantitative relations; and again, that these quantitative relations reciprocally serve to render completely explicit a whole world of qual- itative characteristics. It is also evident that these mutually inclusive qualitative and quantitative relations constitute the reality of the extended world. Let us noAV inquire further of this extended world and obtain, as far as we may, a more adequate knowledge of its fundamental character and modes of existence. In the first place, it is evident that whatever knowledge we possess of the quantitative relations of this extended world must involve comparison of one phase with another. But these comparisons also imply a fixed standard. And comparison with a fixed standard constitutes measure. At the same time, we must soon become aware that all standards of measurement in the extended world must be arbitrary, and hence the measure must be purely relative. Hence, it may be remarked by the way, there can be no absolute distinction between extensive and intensive quan- tity. On the contrary, a given quantity may be regarded as either extensive or intensive, according to the standard A^ /"! Trt-TT * 98 THE WORLD-ENERGY of comparison. The rending force of gunpowder would be regarded as intensive compared with that of freezing water, while on the other hand, it would rather bear the character of extensive quantity, when compared with dynamite. In other words, any given quantity of energy is not merely extensive or intensive; it is both extensive and intensive. The distinction between these phases can never be suppressed, while, at the same time, their unity is inseparable. And yet all measure proves to be relative, even abso- lutely relative. So that, as it seems to turn out, we know absolutely that all our knowledge, especially our exact knowledge, is relative. It is a hopeful-discouraging out- come. Assuredly, if we are anywhere to obtain knowledge that may be called absolute, it must be in the realm of measure, which is pre-eminently the realm of the exact sciences. There is, at least, one science universally ac- knowledged to be exact the science of pure quantity, or mathematics. And yet, even here, there have been skep- tical murmurings, not to say loud protests. The very axioms of mathematics have been called in question.* And not only so, but here and there, especially in the applications of mathematics, there is full confession of the necessity of approximation, as will be seen more fully when we come to consider the subject of motion. So that a momentary shadow of suspicion arises lest the very sci- ence in which men have so long confided with absolute serenity may prove to be, after all, only the exact science of approximation. And so much the more as those sciences which have come to be called " exact/" through the * See, for example, Helmholz's criticism cm The Axioms of Mathematics, in his Popular Scientific Lectures (Second Series). AND ITS SELF- CONSERVATION. 99 application of mathematics to them, must keep within the limits of measure, seeing that they have constantly to do with the quantitative phases of the extended world, and must, therefore, bear the mark of "relativity" inherent in all things within the realm of measure. In sober truth, that the application of mathematics to the actual extended world may be brought within the range of finite powers of thinking, it is necessary to con- fine the calculations to a simple set of relations more or less arbitrarily chosen, and to regard this set of relations as if completely isolated from the rest of the universe. For example, Thomson and Tait, in their " Treatise on Natural Philosophy," call special attention to the fact that even in so simple a case as that of the investigation of the lever it is necessary to assume that a lever is a bar, perfectly rigid, inflexible, and without weight an assumption which, of course, can never be realized. In short, the assumption made in every single instance in the application of mathematics to the concrete sciences is more or less in direct contradiction to the actual facts. Or, if not exactly this, at least all except certain more or less arbitrarily chosen aspects of those facts are of neces- sity ignored in each and every problem proposed. It is true that the very purpose of the mathematical phase of the sciences is to discover the exact measure of things. And yet the really exact is not the approximately exact. The former is, no doubt, that which is desired, though the latter is the utmost that is ever actually attained. The " exact sciences" propose an ideal which they can never hope to realize ; and this is inevitable from the very nature of the case. The so-called exact sciences are necessarily restricted to the realm of measure that is, 100 THE WORLD-ENERGY to the realm of infinite. For in every such case measure consists in the comparison of any given object with an arbitrarily chosen, and therefore finite, standard. Every- thing measured is by that fact limited. Hence it is that the realm of mathematics is the realm of finite thought. At the same time, we have seen that the sum-total of the extended world is necessarily a unit a whole of which the infinitely varied phases constitute the specific objects of all sense-perception. That is, these objects are but the precisely defined forms resulting from the activity of the total World-Energy. But measure is the comparison of these various forms, one with another, or with some purely conventional stand- ard. That is, these forms present the only realm of the actually measurable ; so that the world, as a whole, thus proves to be measureless. And yet these forms, we have just seen, are not only the specific objects of sense-perception, but they are also the direct product of the activity of the World-Energy. They are modes of its manifestation. In other words, the measurable proves to be just a phase of the measureless. Or, again, the measurable is found to constitute the modes in which the measureless manifests itself. Nay, Mr. Spencer himself, as we remember, allows that even the "Unknowable" has an established order of self- manifestation. Thus the measurable is found to be the finite, while the measureless is the infinite ; so that the finite is not something contrasted with the infinite, but is in truth a mode or phase of the infinite. Otherwise the infinite would have to maintain itself in contrast with, or in opposition to, the finite. It would then be in external AND ITS SELF-CONSERVATION. 101 relation to the finite that is, it would be limited ~by 'the finite, in which case it would itself prove to be something finite, and not the true infinite. Thus the infinite and the finite prove to be but the more adequate aspects of what were previously called continuous and discrete quantity. Bjit here something further suggests itself. It is this: As the true infinite must include the finite within itself as phases of itself,, then the infinite must be the compre- hensive total of all reality. And as such it must be abso- lutely equal with itself. It can be compared with noth- ing else than itself, for it is itself the only reality. It is, then, absolutely immeasurable by any finite standard, and yet at the same time it is the eternally self-measured. Thus the finite is seen to constitute nothing else than the endlessly varied modes of the self-measurement of the true infinite. The world as a whole is, therefore, a mighty process in which all that is finite or measur- able is dissolved and absolutely fused in the infinite or measureless. In this connection a significant hint is found to be latent in the most elementary phase of mathematics. The beginner learns that "once one is one." At a later stage he learns something of the "powers "of numbers. He learns that 2 multiplied by itself produces 4, while 1 multiplied by itself is still 1. Unity, he is assured, is peculiar to itself in the fact that it remains unchanged, however persistently it may be multiplied by itself. Surely that is a wonderful property wonderful, in- deed, if true! Let one attempt its verification in prac- tice and see what the result will be. If 1 is a line, then 1 x 1 is a surface still 1, it is true, but 1 having a quite 102 THE WORLD-EKEKGY new value. So again 1 x 1 x 1, is a solid. It is still 1, but 1 with added wealth of meaning. And what do the higher "powers" of numbers signify but varying degrees of "solidity"? And what are these varying degrees of solidity but varying degrees of tension within a given mass, resulting in qualities that is, in enriched modes of existence? That plaything of modern mathematics the "fourth dimension in space" is in truth a symbol representing the transition from extensive to intensive quantity. And the higher "powers" of numbers in general are nothing else than abstract ex- pressions hinting obscurely at the concrete fact that the more intensive a given quantity of energy becomes, the richer does it become in quality. In other words, what is commonly called quality as distinguished from quantity is in reality, let us repeat, nothing else than intensive quantity, which is the recip- rocal of quantity in its aspect of extent. But again, the abstract formula, 1x1 = 1, not only seems unquestionable. It is unquestionable from two points of view. The first is that point of view (the usual one) from which the formula is taken in its purely ab- stract sense. In pure or formal mathematics the express- ion: Ixl=l 2 =l is faultless. On the other hand, the second point of view is that in which unity is taken in its richest, most concrete significance. From this point of view it is equally unquestionable that the absolutely per- fect unit, the total, self-sufficing Energy, maintains its eternal self-equality by the faultless continuity of its fusion, its combination, its multiplication of itself with itself. And here indeed the formula is no longer 1x1 = l a =l;but 1x1 = 1 a =1. AND ITS SELF-COKSEKVATION. 103 Again, zero is commonly defined as a symbol which, when standing alone, expresses no value. That seems simple enough. And yet on further examination the symbol represents, even in its very lowest term, a product of very abstract thinking. It really represents the negation in thought of all reality. That is, its subjective meaning may be said to be greatest when its objective meaning is least. Or if, as is sometimes done, we take the term "objective" to mean valid, true, then we would have to change the mode of our expression, and say that the objective significance of the term zero in its ultimate abstraction consists pre- cisely in its subjective character. For in its ultimate abstraction the term zero represents a perfectly valid concept to which there is no corresponding reality other than the concept itself. It represents just that nega- tive concept which consists in the recognition that beyond reality there is absolutely no limitation, for limitation is itself a mode of reality, or, if the technical reader prefers, a mode of actuality. But still further, in concrete science zero represents a multitude of values on occasion. In the higher geometry a right line is represented by an equation, of which one member is 0. Again, in physics zero of temperature (Cen- tigrade) represents that balancing of the molecular attrac- tions and repulsions in water, the slightest disturbance of which one way or the other will (under given conditions of pressure) cause the water to assume the solid state or assure its remaining liquid. But this is by no means all. The theoretical "absolute zero" (273 below Centi- grade) gives a scale in which Centigrade is found to represent an "absolute" positive temperature of 273. 104 THE WORLD-ENERGY It seems worth remarking, too, that the "absolute zero " logically represents the complete absence of molec- ular repulsions, and therefore also the complete absence of molecular attractions. But this can only mean the complete absence of matter that is, complete vacuum (such vacuum itself being in great danger of collapse, one might suppose). But not to extend illustrations further, we may say in general that in concrete science zero represents a positive value; and that value is always of precisely one character. It is invariably a point of indifference, or equilibrium. And this is the clew to the ultimate, most concrete sig- nificance of zero. For, as representing the equilibrium of concrete modes of energy in general, it becomes evident at once that the ultimate, most concrete significance of the symbol, is that of the equilibrium, the perfect self- poise of the total Energy; just as 1, in its richest meaning, represents the absolute wholeness of the total Energy. Finally, the formula ^ = oc is meaningless if stands for pure nothing. Or, if it represents any positive quan- tity, the formula is absurd if 1 stands for any finite quantity. It can have genuine concrete significance only when 1 represents the absolute totality of existence, and the absolute equilibrium of that totality, in the sense of the absolutely perfect method of the totality, as self- consistent energy. In the first of the supposed cases it is a formula of division, representing no-division. In the last case it represents, not the division of one quantity by another, but rather, the absolute self-division of the total Energy; and such self -division is nothing else than the self-specialization, the self-differentiation, that is, the self-realization of the total World-Energy. AND ITS SELF-CONSERVATION. 105 Thus, there comes into something like distinct view the one central conception which has been gradually focusing into definite utterance throughout the whole of our inquiry, thus far. Before proceeding with the further stages of the argu- ment, it seems worth while to notice that the result here reached is altogether in agreement with the doctrine re- garding the relation between substance and its attributes, as defined by Spinoza. That is, to use his phrase, " attri- butes are what we may know of substance." So, also, the same results may be reached through a consideration of the interdependence of the categories of Aristotle. It has been claimed that Aristotle gathered his cate- gories together in more or less arbitrary fashion, from the current speech of his time. But it is also to be borne in mind that his writings have reached us in exceedingly fragmentary form, and that our judgment regarding the arbitrariness of his mode of procedure ought to be guarded accordingly. In any case, the categories as they stand in the list handed down to us as the one he proposed, are open for interpretation. And it seems but reasonable and just to allow that the most adequate and consistent interpretation which can be given them is the one which Aristotle himself put upon them, in more or less explicit fashion. Or if not so much as this, at least it ought to be allowed that such interpretation is not inconsistent with the general estimate he gave them. Let us see, then, what interpretation will be borne by these categories as presented in the Organon. They are as follows: Substance (ob