Elements of metaphysics

by A. E. Taylor

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.[^[164]] 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.[^[165]]

§ 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.[^[166]] 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.[^[167]] 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.