CHAPTER VI. The Logical Character of Descriptive

THE LOGICAL CHARACTER OF DESCRIPTIVE SCIENCE

§ 1. Scientific description may be contrasted with philosophical or teleological interpretation, but the contrast is not absolute. § 2. The primary end of all scientific description is intercommunication with a view to active co-operation. Hence all such description is necessarily restricted to objects capable of being experienced in the same way by a plurality of individuals. § 3. A second end of scientific description is the economising of intellectual labour by the creation of general rules for dealing with typical situations in the environment. In the course of evolution this object becomes partially independent of the former. § 4. From the interest in formulating general rules arise the three fundamental postulates of physical science, the postulates of Uniformity, Mechanical Law, and Causal Determination. § 5. The mechanical view of physical Nature determined by these three postulates is systematically carried out only in the abstract science of Mechanics; hence the logical completion of the descriptive process would mean the reduction of all descriptive science to Mechanics. That the chemical, biological, and psychological sciences contain elements which cannot be reduced to mechanical terms, is due to the fact that their descriptions are inspired by æsthetic and historical as well as by primarily “scientific” interests. § 6. The analysis of such leading concepts of mechanical Physics as the Conservation of Mass and of Energy shows them to have only relative validity.

§ 1. In its general outlines our interpretation of the significance of the physical order is now complete. We have seen reason to hold that in that order we have the appearance to our human senses of a great system or complex of systems composed of purposive sentient beings, whose interests are for the most part so widely removed from our own as to preclude all direct intercourse, but who are nevertheless historically connected with ourselves by that unceasing process of the development of new forms of individual interest which we know empirically as the evolution of life and intelligence on our planet. As we have tried throughout the four preceding chapters to show in detail, there is no real inconsistency between this general interpretation of the meaning of the physical order and the working assumptions of our various empirical sciences. At the same time it is obvious that in executing the task of the detailed description and calculation of the phenomenal course of events, the empirical sciences, while not rejecting such a metaphysical interpretation, ignore it; and the more conscientiously they exclude from their programme all amateur excursions into extraneous metaphysical speculation, the more thoroughly is the work of description and mathematical formulation done. It seems advisable, therefore, to conclude our brief sketch of the principles of Cosmology with a short discussion of the nature of the limitations imposed on empirical science, by the special character of the objects it sets before it, and of the way in which the existence of these limitations is revealed by analysis of the most general concepts of the empirical sciences themselves.

It is important, in the first place, to be quite clear as to the sense in which we speak of description as the work of the empirical sciences, and as to the meaning of the contrast between such description and a philosophical interpretation of existence. In this connection there are two points which seem to call for special and repeated emphasis. (1) The contrast between interpretation and description is not an absolute one. Complete description would of itself be something more than mere description, and would pass into philosophical interpretation. Thus a significant purposive movement is not adequately described when, e.g., its direction, velocity, momentum, and duration have been assigned. The complete description of such a movement would require the recognition of its meaning for the being executing it as a step in the realisation of a craving or a design, and would thus merge in what we have called philosophical interpretation. So generally, if all existence is ultimately experience and all experience essentially teleological, such description as can be distinguished from interpretation must always be incomplete from the logical standpoint, though adequate to fulfil certain special purposes.

(2) The descriptions of science, again, must be carefully distinguished from such descriptions as can be effected by the mere multiplication of unanalysed sensible detail. Scientific description, it must be remembered, is always description undertaken with a view to the calculation and prediction of the course of events. This implies that it must be description in general terms, and, wherever possible, by the aid of mathematical analysis. Natural processes are described by the empirical sciences which deal with them, not in their concrete individual detail, but only in so far as they exhibit certain uniform aspects permitting of reduction to formulæ suitable for calculation. Such description is frequently spoken of as explanation, and is expressly contrasted by this difference in nomenclature with the mere accumulation of sensible detail. We must not, however, allow the difference in question to blind us to the essentially descriptive character of all scientific hypotheses. It is sometimes urged that scientific explanation must differ in its logical character from description, because the “substance,” “agencies,” and “media,” in terms of which explanation is couched, are largely of a kind inaccessible to sense-perception. It must be remembered, however, that hypotheses as to such imperceptible objects are only valuable so far as they serve as connecting-links by which we may calculate sensible events from sensible data. Whatever intermediate links empirical science may find it useful to assume, it invariably takes the sensible occurrences of the phenomenal physical order as the starting-point, and again as the goal of its inferences. All its hypothetical constructions are thus subservient to the main interest of the accurate description of the course of sensible events. The only kind of “explanation” which can be reasonably contrasted, in respect of its logical character, with description is teleological interpretation, and even here the contrast, as we have seen, is not final.

§ 2. We have to ask, then, what is the object at which scientific descriptions aim? What purpose do they seek to fulfil, and how does the essential character of this purpose determine the logical character of the descriptive process? Now, it is at once evident that all description has for its immediate object one or other of two practical ends, which are so closely connected as to be ultimately coincident. Historically, it is beyond a doubt that the original purpose of all description of physical events was intercommunication with a view to social co-operation. I have already referred to this function of description with special reference to the use of causal descriptions in science, but may conveniently deal with the same point rather more fully and in a more general way here.

In a society of finite individuals with interrelated aims and objects, each of the individuals can only attain satisfaction for his own subjective interests by some degree of concerted action along with the rest. And concerted action is only possible where the co-operating individuals can reduce their various views of their common external environment to common terms, equally intelligible to all, and similarly indicate to each other their respective special contributions to the common task. There must be a common understanding of the difficulty to be met, and of the precise part each is to play in meeting it. Thus intercommunication between individuals is an indispensable requisite of all effective practical co-operation.

But again, intercommunication is only possible by means of description in general terms. Only in so far as there are identical elements in the experiences of the various individuals can one communicate the contents of his experience to another. Immediate feeling, precisely because of its unique individual character, is essentially incommunicable. Thus in communicating information about my own body to another, I am of necessity forced to speak of my body in terms not of the immediate experience I have of it in organic sensation, but of those complexes of sense-presentations which he and I alike get through our organs of special perception. And so the whole physical order can only serve as a basis of co-operation between individuals so far as it is describable in the last resort as a complex of sense-presentations equally accessible to the observation of all the individuals. Any kind of experience of nature which is uniquely peculiar to myself, and therefore incapable of being got under assignable conditions by any other individual endowed with the same organs of perception, is necessarily incommunicable, and therefore useless as a basis for concerted action. Hence science is restricted by its very purpose to describe the physical order in such a way that its descriptions may be available for the objects of practical art, to the description of it in its phenomenal aspect as a mere complex of related presentations or possibilities of presentation. It is no accident, but a logical consequence of the conditions of intercommunication, that all scientific description must start from and end with occurrences of the phenomenal order which any individual may experience by conforming to the prescribed conditions of perception. Thus we see that it is an epistemological characteristic of the physical order as investigated by science, that it consists exclusively of those objects which are, in principle, perceptible by more than one individual. If there are objects in their own nature incapable of being experienced by more than one individual, such as, e.g., my own inner life, those objects cannot belong to the physical order of science.

§ 3. There is a second purpose of description which arises out of the first as human experiences become more reflective. Description not only enables me to communicate the particular situation of the moment to others, and devise in concert with them means for coping with it; it also enables me to formulate beforehand general rules for my own behaviour in recurrent situations of the same type. The need for the possession of such general views originates, of course, while description is still confined to its original function in assisting social co-operation. From the practical point of view of those industrial arts out of which our various physical sciences have arisen, it is an economical advantage of the first magnitude to be able once and for all to formulate a general rule for dealing with the indefinitely numerous occurrences of typical situations, instead of having to deal with each occurrence separately as it arises.

The advantages of such general rules speedily make themselves felt in the increased power and importance enjoyed by the section of society which is in possession of them, a consideration which may help us to understand why, in early stages of civilisation, such rules are commonly jealously guarded as the hereditary secrets of close corporations. Thus it comes to be the special aim of scientific description to assist the formulation of general rules for the practical manipulation of the objects of the physical order. And, with the progress of reflection, this originally secondary object of the descriptive process becomes to a large extent independent of the primary object of intercommunication. Even where I have no need or no desire for intercommunication and co-operation with my fellows, it becomes my interest to seek generalised descriptions of typical situations in the physical order as the basis of practical rules for my own voluntary intervention in that order.

§ 4. The interest in the formulation of general rules for practical interference with nature, again, necessarily dictates the form which our scientific descriptions will take, and is thus the source of those practical postulates of empirical science with which we have already made some acquaintance. It compels us to assume, in the first place, as an indispensable condition of success in our descriptions, that there are situations in the physical order which may be treated with sufficient accuracy for our practical purposes, as recurring identically; in the second place, that, so long as we abstain from intentional intervention in the course of events, they succeed one another in a fixed routine order, or, in other words, that there are no departures in nature from established routine of such a kind as to interfere with our calculations; in the third place, that every event in the physical order is, within the limits requisite for our successful devising of means to our ends, determined by antecedent events. It is thus our interest in obtaining general rules for the production of effects in the physical order by intentional interference with it which is the source of the three fundamental postulates of empirical physical science, the postulates of uniformity, of the omnipresence of routine or mechanical “law,” and of the causal determination of subsequent by antecedent events.

The dependence of physical science upon these three fundamental postulates thus does not prove their ultimate truth, as we have already shown at length in preceding chapters: it proves only that where they cannot be treated as approximately true, within the limits in which their falsity could be detected by sensible experiment, our special interest in devising rules for the manipulation of events cannot be gratified. Conversely, wherever that interest can be successfully gratified, these postulates must be for all practical purposes equivalent to the truth. Hence, if we remember that the ultimate object of all physical science is the successful formulation of such practical rules for action, we can see that it is a logical consequence of the character of the interests which dominate our scientific descriptions, that the physical sciences should adopt a rigidly mechanical view of the physical order. Only, in proportion as any one branch of physical science succeeds in carrying out in detail this conception of the physical order as an interconnected mechanism of sequences rigidly determined by laws of sequence, does it succeed in effecting the purposes by which all physical science has been called into existence. We may thus call the mechanical conception of the physical order the most general postulate of physical science. Only, we must once more take care to recollect that a fundamental postulate of physical science need not in the least be an ultimate truth; such a postulate is in the end nothing more than a way of stating the nature of the interest which physical science subserves, and, as we have sufficiently seen, that interest is not the purely logical one of consistent thinking, but the practical one of successful interference with nature.

§ 5. It does not, of course, follow that all the sciences which deal in any way with the events of the physical order can as a matter of fact carry out this mechanical view of their objects with equal success. It is only in the various branches of abstract Mechanics that we get anything like complete systematic adherence to the postulates of the mechanical theory of physical nature as previously enumerated. For the physical, chemical, and still more for the biological sciences, it remains an unrealised ideal—and one we have no right to think ever completely realisable—that all the facts of electrical and chemical, and again of physiological process should be ultimately capable of reduction to routine uniformities upon which confident calculation and prediction can be based.

Thus, even in Chemistry, limits are set to the successful adoption of the purely mechanical point of view, by the fact that chemical combination is regularly productive of new qualities in the compound which could not have been predicted from a knowledge of the properties of its constituents, but have to be ascertained a posteriori by actual experiment. It is true, no doubt, that we seem to be increasingly able, as our chemical knowledge advances, to say in general what properties may be expected to result from the combination of given elements, but there is no logical ground for supposing that we shall ever be able to foretell all the properties of an as yet unexamined compound, and in any case such knowledge could only be of a general sort. However much we might know, in advance of the results of the combination of certain elements in certain proportions, it would still be impossible to predict with absolute certainty the precise result of trying the combination in a particular concrete case.

Still less realisable would be the ideal of the reduction of Biology to applied Mechanics. It is not merely that the isolated physiological process regularly exhibits qualitative aspects of a chemical or electrical kind, which we have no right to reduce to mere quantitative changes. Beyond this, as the very terminology of our evolutionary hypotheses is enough to show, it is impossible to state the facts of biological evolution without introducing, under such names as “sexual selection,” continual reference to a subjective factor, in the form of the likes and dislikes, habits and cravings of sentient beings, and this selective factor, being in its own nature incapable of direct presentation in identical form to a plurality of experiences, is not even a member of the physical order. With the case of Psychology we shall be better able to deal in connection with the special discussions of the following Book. (See especially Bk. IV. chap. 1.)

Considerations of this kind seem to necessitate the following general view of the logical character of descriptive physical science. The only science in which the postulates of description are rigidly carried out to their logical consequences is the science of abstract Mechanics in its various branches (Statics, Kinetics, etc.). Mechanics owes its power to follow out these postulates to its abstract character. Precisely because it regards only those aspects of the actual physical order which are consistent with the fundamental postulate of describability by general formulæ, Mechanics is constrained to be a purely abstract and hypothetical science. For since every actual process involves the appearance of the qualitatively novel, and since all concrete quality is in its essence unique, no actual process can be merely mechanical.

Thus the only way of conceiving the physical order which is logically consistent with the postulates of descriptive science in their rigidity, is one which treats all natural changes as reducible to equations. And it is only in abstract Mechanics that this view is systematically carried out. Consequently, it is only in so far as all physical science can be reduced to abstract Mechanics that we can attain the ultimate purpose of our scientific constructions, the calculation and prediction of the course of occurrences by means of general formulæ. This conclusion, derived in the first instance from reflection on the logical nature of scientific description, is fully borne out by our actual experience of the results of our scientific theories. Just because we cannot ultimately reduce all chemical and biological processes to mere quantitative changes in a material of uniform quality, we are unable to predict with absolute confidence the precise result of a concrete chemical experiment, and still more unable to foretell the precise behaviour of a living organism.

Hence follow two very important results. (1) There is a real practical justification for the attempt, as far as possible, to treat the chemical and biological phenomena as if they were simply more complicated instances of the relations familiar to us in Mechanics. For though they are not really purely mechanical, it is only in so far as we can treat them without appreciable error as exactly measurable that they admit in principle of calculation.

(2) At the same time, there is also ample justification for the use of qualitative and teleological categories in Chemistry and Biology. For the interests which chemical and biological knowledge subserve are not limited by our need for practical rules for intervention in the course of nature. Over and above this original scientific interest, which can only be gratified by a mechanical treatment of the subject, we have an æsthetic interest in the serial grouping of processes according to their qualitative affinities, and an historical interest in tracing the successive modifications which have led to the establishment of a relatively stable form of human social existence. In so far as the chemical and biological sciences involve the recognition of qualitative distinctions and the consequent use of categories which are non-mechanical, it is these æsthetic and historical interests, and not the primary scientific interest in the control of natural phenomena, which are subserved by their elaboration.

Hence, while Chemistry and Biology, even apart from the possibility of their conversion into branches of applied Mechanics, are essentially descriptive sciences, the task fulfilled by them, so far as they use qualitative and teleological categories, is one of æsthetic and historical rather than of properly scientific description. And æsthetic and historical description, having another object than that of purely scientific description, are under no necessity to conform to the postulates imposed on the latter by the special character of the interests it aims at satisfying. Thus we can see how the right of Chemistry and Biology to be regarded as something more than mere applied Mechanics, can be reconciled with Kant’s profoundly true assertion that any branch of knowledge contains just so much science as it contains of Mathematics. When we come, in connection with the special problems of the following Book, to discuss the aims and methods of Psychology, we shall find in that study a still more striking example of the way in which the narrowly “scientific” interest may play a markedly subordinate part in determining the procedure of a branch of knowledge which must, because of its systematic character, be called a “science” in the wider acceptation of the term.

§ 6. Since it is only complete and all-embracing knowledge which can be in the last resort a completely self-contained and self-explaining system, we must expect to find that the concepts employed in the mechanical interpretation of the physical order lead us into contradiction the moment we try to treat them as a complete account of the concrete nature of the whole of Reality. This is shown more particularly in two ways. On the one hand, the application of the categories of Mechanics to the whole of Reality leads inevitably to the indefinite regress. On the other, in their legitimate application to a lesser part of existence they are all demonstrably relative, that is, they always appear as one aspect of a fact which has other aspects, and without these other aspects would have no meaning. It is worth our while to consider both these points in some detail.

For the successful application of the mechanical view to the physical order, we need to treat that order as consisting of the changing configurations of a whole of qualitatively homogeneous related parts. Any departure from this point of view would involve the recognition of differences which cannot be treated as merely quantitative, as mere subjects for calculation and prediction, and would thus necessitate the introduction of a non-mechanical factor into our interpretation of the universe. The mechanical view, fully carried out, thus involves the conception of the universe as a system extended and ordered in space and time, and capable of spatial and temporal change, but manifesting a quantitative identity throughout its changes. In the actual constructions of physical science this quantitative identity is represented principally by the principles of the Conservation of Mass and the Conservation of Energy. Both these latter principles are thus, in their general form, neither axioms of knowledge nor verifiable empirical facts, but a part of the general mechanical postulate. There is no ultimate logical principle in virtue of which we are constrained to think of the particular quantities we denote as mass and energy as incapable of increase or diminution, nor again have we any experimental means of proving that those quantities are more than approximately constant. It is, however, a necessary condition of success in calculating the course of events, that there should be some quantitative identity which remains unaffected in the various processes of physical change, and it is chiefly in the special forms of the quantitative constancy of Mass and Energy that we seem at present able to give definite expression to this a priori postulate of mechanical construction.

Now, with regard to spatial and temporal direction and position, we have seen already both that they are always relative, position and direction being only definable with respect to other positions and directions arbitrarily selected to serve as standards of reference, and that, when taken as ultimate realities, they involve the indefinite regress. It only remains to show that the same is true of the other fundamental concepts of the mechanical scheme, mass and energy. Taking the two separately, we may deal first of all with the notion of mass. The mass of a material system is often loosely spoken of as its “quantity of matter,” but requires, for the purposes of logical analysis, a more precise definition. Such a definition may be given in the following way. In order to explain what is meant by the constancy of the mass of a body, it is necessary to consider the mutual relations of at least three different bodies, which we will call A, B, and C. It is found that, at a given distance, in the presence of A, C receives an acceleration m, and in the presence of B a second acceleration n; then the mass of A is said to stand to that of B in the ratio m/n, which is the ratio of the accelerations which they respectively produce on C, and this ratio is constant, whatever body we choose for C. Hence, if we arbitrarily take B as our unit for the measurement of mass, the mass of A as determined by the foregoing experiment will be represented by the number m. By the principle of the Conservation of Mass is meant the doctrine that the ratio m/n as above determined does not alter with the lapse of time. That is, the ratio between the accelerations produced by any pair of bodies or a third body is constant and independent of this third body itself. This proposition is verifiable approximately by direct experiment for a particular pair of bodies, but when affirmed as universally true becomes a part of the general mechanical postulate.

Now, it is obvious from the foregoing explanation of the meaning of mass (1) that mass is a relative term. It is a name for a certain constant ratio which requires no less than three distinct terms for its complete definition. Hence there would be no meaning in ascribing mass to the whole physical order or “universe.” The “universe” could only have a mass as a whole if there were some body outside the universe, but capable of interaction with it, so that we could compare the relative accelerations, in the presence of this body, of the whole “physical universe,” and of our arbitrarily selected unit of mass. But the “universe,” by supposition, contains all physical existence, and there is therefore no such accelerating body outside it. Hence we cannot say, without an implicit contradiction, that the whole of existence possesses the property of mass, nor a fortiori that its mass is constant. It is only subordinate parts of the universe to which the principle of the Conservation of Mass can be intelligibly applied.

(2) It is also clear that the mass of a body is only one aspect of a whole of existence which possesses other aspects, not regarded in our mechanical constructions. The bodies which actually exhibit a constant ratio in their accelerations have other properties over and above the fact of this constant ratio. They have always, in actual fact, qualitative differences from one another and from other things, which we disregard in our mechanical treatment of them because they make no difference to this special property, in which for purposes of calculation we are peculiarly interested. It is by the barest and most palpable of abstractions that, in Mechanics, we treat bodies as if they were masses and nothing more. Thus the facts taken into account by the mechanical interpretation of nature are, so far as its reduction of bodies to masses is concerned, a mere aspect of a fuller reality which we treat as equivalent to the whole for no better reason than the practical one that it suits a special object of our own that it should be so equivalent, and that this object is empirically found to be attained by regarding it as equivalent.

Precisely the same is the case with the complementary concept of Energy. The kinetic energy, or capacity of a body for doing work against resistance, is found experimentally to be measured by half the square of its velocity multiplied by its mass. It is further found by experiment that, so far as we can measure, the energy of a material system not acted upon from without remains constant. That the constancy is absolute is, of course, once more not a matter for direct empirical proof, but a part of the postulate that the physical order shall be capable of a mechanical interpretation. Now we can see at once, from what has been previously said of the concept of Mass, that the physical order or “universe” as a whole cannot be intelligibly said to possess kinetic energy, whether constant or otherwise. What cannot be said to have mass clearly cannot have a property only explicable in terms of mass. We might indeed have inferred the same consequence directly from the definition of energy as capacity for doing “work” in overcoming resistance. The “universe,” having nothing outside itself, can have no source of possible resistance to overcome, and therefore cannot be thought of as doing “work.” Hence, once more, it is only the parts of the physical order, considered as parts, to which energy can be ascribed.

(3) Again, it is even more evident in the case of energy than in the case of mass, that we are dealing with one aspect singled out by abstraction from a whole possessed of other aspects not regarded in a purely mechanical construction. For (a) the capacity for work of an actual body does not always exist in the “kinetic” form of actual motion. There are various forms of non-kinetic energy, such as, e.g., the energy of “position” of a resting body, the heat of a body of higher temperature than its surroundings, which Mechanics treats as equivalent to “kinetic” energy, because they are theoretically capable of being converted into it. And these forms of non-kinetic energy are qualitatively different both from energy of actual motion and from each other. It is by a mere abstraction that we treat them as identical because they are, for certain special purposes, equivalent. The qualitative differences may make no difference with respect to a particular purpose of our own, but they are none the less really there.

Again, the mechanical scheme itself is quite insufficient to explain why or when these different forms of energy are replaced by one another. As has been well said by Professor Ward, the doctrine of the Conservation of Energy asserts no more than that a certain quantitative identity is maintained in all exchanges of energy. But when or in what direction these exchanges shall take place, the principle itself does not enable us to say. Thus, to take a simple example: if I know the mass of a stone lodged on a roof, the height of the roof from the ground, and the acceleration produced by gravity at the spot in question, I can determine the “potential energy” of the stone. But my data tell me nothing as to whether this potential energy will remain for ever in its potential form, or whether the stone will yet be dislodged and its energy converted into kinetic shape, and if so, when. The principles of the mechanical interpretation of nature are thus inadequate to describe the concrete course of events in so simple a case as that of the fall of a stone. If the stone falls, then by the aid of the mechanical postulate I can describe one aspect of the process, namely, the amount of kinetic energy which will be evolved; and again, if certain previous conditions are fulfilled, e.g., if the support gives way, and if the descent of the stone is not previously arrested, the mechanical postulate enables me to infer that the stone will fall and will reach the ground with just this kinetic energy. But I can never escape, so long as I keep within the mechanical scheme, from this necessity of hypothetically assuming as given data which the mechanical scheme itself cannot fully determine.

All these considerations show how the very nature of the mechanical scheme itself justifies our previous conclusion, that it is in all its details simply the expression of a postulate created by our practical need that the course of nature shall admit of calculation with sufficient exactitude for the devising of successful rules for intervention in it, but logically incapable of being without contradiction regarded as the real truth about any concrete natural process. The internal evidence, derived from examination of the fundamental concepts of scientific Mechanism, thus confirms the view we have already adopted on different grounds, that the whole physical order is merely the appearance of a more ultimate reality of a kind akin to our own sentient and purposive life. At the same time, our examination of mechanism may serve to throw some useful light on the often misconceived antithesis between Reality and Appearance. We call the physical order, as conceived by mechanical science, “appearance,” not because we regard it as illusory or deceptive in itself, or because it is not the manifestation of a true reality, but because it takes account only of those particular aspects of Reality which are important and significant for certain very special purposes. What appears to us as the physical order is, indeed, true Reality, and is, in fact, an integral part of the only Reality there is, but it appears to us in this special form and under these special restrictions because we have arbitrarily excluded every other aspect of the concrete facts from our purview by the choice of our initial postulates of descriptive science. By the nature of the special questions we put to our world, in our physical science, we determine in advance for ourselves the general character of the answer we are to receive.

Rigidly scientific investigation, for instance, finds mechanical determination everywhere in the world, and purposive spontaneity nowhere, just because it has previously resolved that it will accept “mechanical explanation” and nothing else as the answer to its questions. So far as we bear in mind the presence of these self-imposed logical limitations throughout our mechanical science, their existence need lead to no illusion or deception. The success of our mechanical postulates shows that, within the sphere of their logical applicability, the course of the world does really conform to them, and thus the results won by their application are genuine truth, so far as they go. It is only when we forget the limits set to the logical applicability of the mechanical postulates, by the special nature of the interests they subserve, and proceed to treat them as logically indispensable conditions of all existence and all knowledge, that the truths of mechanical science are perverted into the illusions and falsehoods of a mechanical philosophy.

Consult further:—F. H. Bradley, Appearance and Reality, chaps. 11 (Phenomenalism), 22 (Nature); H. Lotze, Metaphysic, bk. ii. chaps. 7, 8; E. Mach, Science of Mechanics, chap. 2, § 5, p. 216 ff.; K. Pearson, Grammar of Science, chaps. 7, 8; H. Poincaré, La Science et L’Hypothêse, parts 3 and 4, chaps. 6-10; J. B. Stalle, Concepts and Theories of Modern Physics, chaps. 2-6, 10-12; J. Ward, Naturalism and Agnosticism, vol. i. lects. 2-6.

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Footnote 161:

And, again, the intermediate links themselves, however imperceptible, have always to be thought of as exhibiting properties identical in kind with those of objects given in direct presentation. As Mill said, a hypothesis which assumes at once an entirely unfamiliar agent and an equally unfamiliar mode or law of operation, would be useless. Thus the imperceptibles of scientific hypothesis belong essentially to the physical order.

Footnote 162:

This is the characteristic selected by Prof. Münsterberg as the basis of his own distinction between “physical” or “superindividual” and “psychical” or “individual” objects. See Grundzüge der Psychologie, i. 15-77.

Footnote 163:

Cf. Mach, Science of Mechanics, p. 4. Mach, however, erroneously as I think, makes the intercommunication a secondary consequence of the rise of specialised industrial classes.

Footnote 164:

I.e., the mechanical view of Nature, to be thoroughly self-consistent, must be purely mechanistic.

Footnote 165:

To put the matter more succinctly, as regards the position of Chemistry and Biology, we may say that while chemical and biological facts are never merely mechanical, chemical and biological science, so far as they subserve the strictly scientific interest of calculation and the formulation of general rules, must always be so. The facts only lend themselves to this special purpose in so far as they admit of being, without sensible error, treated as if they conformed to the postulates of universal Mechanism. The special and more difficult case of psychological facts I reserve for separate discussion in the following Book (infra, Bk. IV. chap. 1).

I am glad to be able to refer the reader, for a view of the logical worth of the mechanical postulates which appears in principle identical with my own, to the interesting discussion of Mr. W. R. B. Gibson in Personal Idealism, p. 144 ff.

Footnote 166:

Compare Bradley, Appearance and Reality, chap. 23, note 2 to p. 331 (1st ed.); Lotze, Metaphysic, bk. ii. chap. 7, pp. 209, 210 (Eng. trans., vol. ii. p. 89 ff.); Ward, Naturalism and Agnosticism, vol. i. pp. 84-91 (Conservation of Mass), 170-181 (Conservation of Energy).

Footnote 167:

If we merely desired to fix the sense of the term mass without introducing the concept of constant mass, we might of course consider two bodies only, A and B. Then the ratio

mass of B acceleration of A in presence of B ————- = ————————————————— mass of A acceleration of B in presence of A.

See Mach, Science of Mechanics, p. 216 ff.; and Pearson, Grammar of Science, p. 302 (2nd ed.), on which the above account is based.

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