CHAPTER III. The Meaning of Law

THE MEANING OF LAW

§ 1. The popular conception of the physical order as exhibiting a rigid mechanical conformity to general laws, conflicts with our metaphysical interpretation. § 2. Our interpretation would, however, admit of the establishment of averages or approximately realised uniformities by the statistical method, which deals with occurrence en bloc to the neglect of their individual detail. § 3. “Uniformity” in nature is neither an axiom nor an empirically verifiable fact, but a postulate. A consideration of the methods actually employed for the establishment of such uniformities or “laws” of nature shows that we have no guarantee that actual concrete cases exhibit exact conformity to law. § 4. Uniformity is a postulate arising from our need of practical rules for the control of nature. It need not for this purpose be exact, and in point of fact our scientific formulae are only exact so long as they remain abstract and hypothetical. They do not enable us to determine the actual course of an individual process with certainty. § 5. The concept of the physical order as mechanical is the abstract expression of the postulate, and is therefore essential to the empirical sciences which deal with the physical order. § 6. Consideration of the character of genuine machines suggests that the mechanical only exists as a subordinate aspect of processes which, in their full nature, are intelligent and purposive.

§ 1. In our view of the underlying reality of the physical order, as explained in the last chapter, we have scarcely gone further, except in the explicitness of our phraseology, than we should be followed by many who profess a complete disbelief in metaphysical construction and an exclusive devotion to positive natural science. From the side of positive science we have often been reminded that no hard-and-fast line can logically be drawn between the organic and the inorganic, that we are not entitled to assume that the continuity of evolution ceases when we are no longer able to follow it with our microscopes, that we are, with the eye of scientific faith, to discern in the meanest particle of matter the “promise and potency” of all life, and so forth. All which statements seem to be confused ways of suggesting some such conception of the physical order as we have attempted to put into more precise and logical form. It is not until we come to deal with the problem indicated by the title of this chapter that our most serious difficulties begin. We have to face the objections which may be urged against our view of the physical order on the strength of the principle known in inductive Logic as the “Uniformity of Nature.”

The events of the physical order, it may be urged, cannot be expressions of the more or less conscious purposes and interests of individual centres of experience, and that for a simple reason. How a purposive agent will behave is always a mystery, except to those who actually understand his purposes. It is impossible, apart from actual insight into those purposes, to infer from the mere examination of his past behaviour what his behaviour in the future will be. For the special characteristic of purposive action is its power to find new ways of response to stimulus. Hence it is that we rightly regard the power to learn by experience, that is, to acquire more and more appropriate reactions to stimulus, as the test of a creature’s intelligence. Where there is no progressive adaptability there is no ground to assume intelligence and purpose. Hence again the impossibility of calculating beforehand with any certainty what course the behaviour of an intelligent being will take, unless you are actually aware of the purposes he is seeking to realise.

Now, except in the case of the organic world, it may be urged, we do not find progressive adaptability in Nature. The inorganic constituents of the physical order always react with absolute uniformity in the same way upon the same environment. Their behaviour exhibits absolutely undeviating conformity to general routine laws of sequence, and can therefore be calculated beforehand, provided that the resources of our mathematics are adequate to deal with the problems it presents, with absolute exactitude and certainty. That this routine uniformity exists in physical nature is, in fact, a fundamental principle in the logic of inductive science. Every indication of sentience and purpose is thus absent from physical nature, outside the world of living organisms; it is a realm of rigid conformity to laws of sequence. And these sequences, because absolutely without exception and incapable of modification, are purely mechanical, i.e. non-purposive and non-intelligent. Nature is, in fact, a complicated mechanism, in which every event follows from its conditions with undeviating necessity.

Views of this kind are often supposed to be logically necessitated by the principles of physical science. It is manifest that if they are sound our whole preceding interpretation of the physical order is invalidated. For this reason, as well as because of the far-reaching consequences often drawn from them as to human freedom and moral responsibility, it will be necessary to examine their foundation in some detail.

§ 2. The main problems confronting us in this examination will then be—(1) How far is calculable uniformity of sequence really incompatible with the presence of purpose and intelligence? (2) Have we any real ground for ascribing such uniformity to the actual sequences of physical nature? (3) if not, What is the real logical character of the principle of the so-called uniformity of nature? (4) and What amount of truth is contained in the conception of the physical order as a mechanism? Into the problem suggested by the popular contrast between the necessity of mechanical sequence and the freedom of purposive action, it will be needless to enter at any length. For, as we saw in dealing with the popular view of necessary causal relation, the necessity of a mechanical sequence is a purely subjective and logical one. The sequence is necessary only in the sense that we are constrained, so long as we adhere to the purpose of thinking logically, to affirm the consequent when we affirm the antecedent. True necessity is always compulsion, and therefore, so far from being opposed to purposive action, can only exist where an actual purpose is overruled or thwarted. So long as we are dealing solely with phenomenal sequence in the physical order, necessity is a mere anthropomorphic name for routine undeviating uniformity of sequence.

(1) Calculable Uniformity and Intelligent Purpose. It is sometimes assumed that all successful prediction of a thing’s behaviour is incompatible with the ascription of intelligence or purpose to the thing. Thus it has been argued, and continues to be argued in moral philosophy of a popular type, that if we are intelligent beings with purposes of our own, it must always be impossible for an onlooker to predict how we shall behave in circumstances which have not yet arisen. This extreme view of the incompatibility of calculability with intelligent purpose, however, manifestly rests on a double confusion. To begin with, those who assert this view commonly make the mistake of supposing that prediction of the future stands somehow on a different logical level from calculation of the past from present data. Prediction of my future behaviour is supposed somehow to conflict with my character as a purposive being in a way in which inference as to my past behaviour does not. This is, of course, an elementary fallacy in Logic. The conditions required for the successful inference of the absent from the present are identical in the two cases, as we have already seen in dealing with the problems of Causality. Precisely the same kind of insight is requisite to judge how a given man must have behaved in a certain situation in his past history as are needed to determine how he will behave in a situation which is yet to arise. We may thus dismiss from consideration the special case of prediction, and confine ourselves to the general question, how far the general calculability of the course of a process is incompatible with its purposive and intelligent character.

An answer to this question is at once suggested by reflection upon our ordinary attitude towards such attempts to calculate the course of our own behaviour. It is by no means every such calculation that we resent. So far from being affronted by the assumption that our conduct exhibits sufficient uniformity to admit of calculation, we expect our personal friends to have sufficient reliance on its uniformity to assume with confidence that we shall certainly do some things and refuse to do others, that we must have acted in certain ways and cannot have acted in others. “You ought to know me better than to suppose me capable of that” is between friends a tolerably keen expression of reproach, “I know I can count on you to do it,” a common expression of confidence. On the other hand, we should certainly resent the assumption on the part of a comparative stranger of such a knowledge of our character as would warrant confident calculation of our conduct, and if the calculation was avowedly drawn not from personal knowledge at all, but from general propositions of Psychology or Anthropology, we should pretty certainly feel that a more than accidental success threatened our moral individuality.

Now, what is the explanation of this difference of feeling? Manifestly it must be sought in the great difference between the grounds on which the calculation is based in the two cases. In the first case we expected and welcomed the calculation, because we felt it to be founded upon our friend’s personal acquaintance with the guiding interests and purposes of our life; it was an inference based upon insight into our individual character. In the other case we resented the success of the calculation, because we assumed it to be made in the absence of any such personal insight into our individual purposes and interests, on the basis of mere general propositions about human nature. We rightly feel that the regular success of calculation of this second sort is inconsistent with the ascription of any reality to our individual character. If all our actions can be calculated from general theorems in a science of human nature, without taking individual purpose into account, then the apparent efficacy of individual interests and purposes in determining the course of our history must be an empty illusion; we cannot be truly intelligent agents, seeing that we never really do anything at all.

Thus we see that it seems necessary to draw a marked distinction between two types of calculability. Calculation based on insight into individual character and purpose is so far from being inconsistent with purposiveness and intelligence, that the more coherent and systematic the purposes by which a life is controlled, the more confident does such calculation become. Calculation without such special knowledge, and based upon mere general propositions, on the other hand, cannot be regularly successful where one has to deal with the behaviour of individual purposive beings.

Now, the difficulty as to our interpretation of the physical order as the presentation to our sense of a system of intelligent purposive beings, is that the successes of physical science seem at first sight to show that just this “mechanical” calculation of the course of events from observed sequence, without insight into underlying individual purpose, is possible when we are dealing with physical nature. For, on the one hand, we ourselves admitted that if physical nature is permeated by individual purposes, we do not know what those purposes in detail are; and, on the other, it is undeniable that physical science, which systematically disregards their presence, has been signally successful in the past, and may be expected to be even more successful in the future, in detecting uniformities in physical nature, and so submitting it to exact calculation. Hence it might be thought that the actual success of the empirical sciences cannot be reconciled with the principles of our metaphysical interpretation of the course of nature.

We must, however, draw a very important distinction. There is one method by which uniformities of a certain kind can be detected in the behaviour of purposive intelligent beings, without insight into the nature of their individual purposes—the method of statistical averages. Thus, though it would be quite impossible to say with certainty of any individual man that he will shoot himself or will get married, except on the strength of insight into his individual character and interests, we find by experience that it is possible to say, within a certain narrow range of error, what percentage of Englishmen will shoot themselves or will get married in the year. The percentage is, of course, rarely or never precisely realised in any one year, but the longer the period of years we take for examination, the more exactly do the deviations from the average in individual years compensate one another. The explanation is, of course, that on the whole the incentives to marriage or suicide, in a reasonably stable state of society, remain constant from year to year, so that by taking an average of several years we can eliminate results which are due to individual peculiarities of temperament and situation, and obtain something like a measure of the degree in which the general conditions of social existence impose a certain common trend or character on the interests and purposes of individuals.

Two things are at once noticeable in connection with all uniformities obtained by the method of averages. One is that the result formulated in the statistical law is always one to which the actual course of events may reasonably be expected to conform within certain limits of deviation, never one to which we have a right to expect absolute conformity. Not only is the actual number of marriages, e.g., in any one year, usually slightly above or below the average percentage computed, e.g., for a ten years’ period, but as we compare one longer period with others, the average percentage for the longer period itself fluctuates. It is only in the “long run,” that is, in the impossible case of the actual completion of an interminable series, that the computed average would be exactly realised. As every one who has to deal with averages in any form knows, precise realisation of the computed average within a finite series of cases would at once awaken suspicions of an error somewhere in our calculations. Thus the uniformities of this kind are never absolutely rigid; they are ideal limits to which the actual course of events is found to approximate within certain limits of divergence.

The second point is that the existence of such a uniformity never affords logical ground for confident affirmation as to the actual event in a particular concrete case. To revert to our illustration, just as we have no right to infer from the approximately constant percentage of marriages per year in a given society, that this precise percentage will be realised in any one special year, so we have still less right to infer that a particular member of that society will or will not marry. Nothing but insight into the character, situation, and interests of this special member of society can give me the right to judge with confidence how he will actually behave. Similarly, it is possible to say within certain limits of error how many persons over sixty years of age may be expected to die in the next twelve months, but it would be the height of logical presumption to infer that a particular man will die during the year, except on the strength of special information about his pursuits, habits, and general state of health. Thus our general conclusion must be, that calculation and the establishment of uniformities is possible, without insight into individual purpose, but that the uniformities thus obtained are always variable and approximate, and afford no safe ground for inference as to special concrete cases.

§ 3. (2) Uniformity in Physical Nature. The existence of ascertainable uniformities in physical nature, then, will not conflict with our general interpretation of the physical order, provided that these uniformities are of the type just illustrated by reference to ordinary social statistics. On the other hand, the exact and rigid conformity of the actual course of concrete events with such uniform general “laws,” would certainly be inconsistent with the presence of teleological adaptation to ends. A reign of rigid routine conformity to general law cannot co-exist with individual purposive life. Now, it is commonly assumed, and we shall shortly see that the assumption is both necessary and justified as a practical methodological postulate, that the “reign of law” in physical nature is absolute. But are there any grounds for recognising this assumption as more than a possibly unrealised postulate made for human practical purposes? I think it is easy to show that there are none whatever, and that the conception of a nature devoid of purpose and sentience, and swayed absolutely by mechanical “laws,” is simply a metaphysical nightmare of our own invention.

To begin with, it is clear that the undeviating conformity of the actual course of any concrete process to scientific “law” cannot be verified as an empirical fact by observation or experiment. For in no observation or experiment can we ever deal with the whole of any concrete actual event or process. We have always, for the purposes of our observation, to select certain of the general aspects of the process, to which we attend as the “relevant factors” or “conditions” of the result, while we disregard other aspects as “immaterial” or “accidental” circumstances. And this artificial abstraction, as we saw in discussing Causality, though indispensable for our practical purposes, is logically indefensible. Again, within the aspects selected for attention, all that experiment can establish is that the deviation from uniform law, if there is any deviation, is not sufficiently great to affect our measurements and calculations. But how far our standards of measurement are from rigid precision may be readily learned from the chapter on physical standards in any good work on the logic of the inductive sciences. Our failure to detect deviation from law is absolutely worthless as evidence that no deviation has taken place.

Thus, if the absolute uniformity of natural processes is more than a practical postulate, it must be an axiom, that is, it must be implied in the very notion of those processes as elements in a systematic whole. But it should at once be clear that we have no more ground for asserting such uniformity as an axiom, than we had for treating the causal postulate as axiomatic. It is by no means implied in the concept of a systematic whole that its parts shall be connected by uniform law. For the unity of the system may be teleological, that is, the parts may be connected by the fact that they work together to realise the same end, to execute the same function. In that case the behaviour of any one part will depend on the demands laid upon it by the plan which the working of the system fulfils. As these demands vary from time to time, the behaviour of the part under consideration will then vary correspondingly, though to all appearance its surroundings may, for a spectator who fails to grasp the end or purpose realised by the system, be identical. This is actually the case with those systematic wholes in which human insight can directly detect unity of purpose or aim. A man with definite purposes before him does not react in a uniformly identical way upon situations which, apart from their relation to his purpose, would be pronounced identical. He learns, for instance, from previous failure in the same circumstances, and so acquires the power to react on them in a way better adapted to the obtaining of his end. Or his progressive execution of his purpose, where there has been no failure, may require different conduct on the two occasions. To speak with strict logical accuracy, the situations, relatively to his special purpose, are never identical, though it may be no difference could be detected in them apart from that relation to this peculiar purpose. Relatively to the system of intelligent purposes which realises itself through the circumstances, every situation is, properly speaking, unique.

Now, if we consider the methods by which the uniformities called “laws” of nature are actually formulated, we may see ground to conclude that they may one and all be uniformities of the approximate non-exact type. In many cases, if not all, these uniformities have manifestly been obtained by statistical methods. Thus, for example, when it is said that all the atoms of a given chemical element are absolutely alike, e.g., that every atom of oxygen has the atomic weight 16, there is absolutely no valid ground for regarding this uniformity as actually realised without deviation in individual cases. If the atom should prove, as it may, to be no more than a convenient device of our own, useful for computing the behaviour of sensible masses but with no real existence of its own, it is of course evident that there can be no question of the real conformity of individual cases to the law. But even if there really are indivisible bodies answering to our conception of atoms, still we have to remember that we have no means of dealing with the individual atom directly. We infer its properties indirectly from the behaviour of the sensible masses with which we can deal more directly. Hence, at most, the statement that the atom of oxygen has a certain weight means no more than that we can for our practical purposes disregard any possible individual divergences from this value. The oxygen atoms, if they really exist, might actually fluctuate in individual atomic weight about an average; yet, so long as we cannot deal with them individually but only in bulk, these fluctuations, if only sufficiently small, would produce no appreciable effect on our results, and would therefore properly be treated in our science as non-existent. Conceivably, then, such chemical uniformities may afford no safer ground for precise statements about the weight of the individual atom, than anthropological statistics do for precise statement about the actual height, weight, or expectation of life of an individual man. And we can readily see that a non-human observer with senses incapable of perceiving the individual differences between one man and another, might be led from the apparent uniformity of behaviour exhibited by large collections of human beings to the same sort of conclusions which we are tempted to make about atoms.

Similarly with other cases of apparently rigid uniformity. As any one who has worked in a laboratory knows, such results are in actual practice obtained by taking the mean of a long series of particular results and treating the minor divergences from this mean as non-existent because they are negligible for all practical purposes. In other words, the apparently rigid conformity of natural processes to uniform law is an inevitable consequence of the fact that we are debarred by various limitations of a subjective kind from following the course of any process in its individual detail, and have therefore to make all our inferences from the observation and comparison of series of processes sufficiently extended for individual differences to neutralise each other. But in all this there is absolutely no warrant for the conclusion that the course of any one individual process is absolutely uniform with that of any other. There is room within the uniformity got by these methods of comparison for an infinite variety of individual detail, of which our scientific constructions take no account, either because our means of observation are insufficient to detect it, or because, when detected, it is of no significance for the original object of our science—practical success in interference with the course of events.

It is easy to point out some of the conditions upon which failure to detect actually existing individual deviations from uniformity may depend. Professor Royce has, in this connection, laid special stress upon one such condition, the limitation of what he calls the time-span of our attention. We are unable, as the student of Psychology knows, to attend to a process as a whole if its duration exceeds or falls short of certain narrow limits. Now, there seems no foundation in the nature of the attentive process for the special temporal limitations to which it is subject in our own experience, and we have no means of denying the possibility that there may be intelligent beings whose attention-span is much wider, or again, much more contracted, than our own. One can even conceive the possibility of a being with a power of varying the span of attention at will. Now, it is clear that if we could so vary our attention-span as to be able to take in as single wholes processes which are at present too rapid or too slow to be perceived by us in their individual detail, such a purely subjective change in the conditions of our own attention might reveal individuality and purpose where at present we see nothing but routine uniformity. In the same way, we can readily understand that a being with a much wider attention-span than our own might fail to see anything but purposeless routine in the course of human history. Supposing that we are placed in the midst of a universe of intelligent purposive action, it is clear that we can only hope to recognise the nature of that action in the case of beings who live, so to say, at the same rate as ourselves. A purposive adaptation to environment with consequent deviation from uniformity in reaction would necessarily escape our notice if it took place with the rapidity of the beat of a gnat’s wing, or again, if it required centuries for its establishment.

Other similar subjective conditions which would necessarily cut us off from the recognition of purposive fresh adaptations widely different from those which occur in our own life, are the limitations of our power of attending to more than a certain number of presentations simultaneously; and again, the restriction of our sense-perception to a few types, and the impossibility of perceiving contents belonging to those types when they fall below or above the lower and upper “thresholds” of sensibility. These considerations do not, of course, positively prove that the routine uniformity of natural processes is only subjective appearance, but they are sufficient to show that there is no valid reason for taking it to be more, and in conjunction with our previous positive argument for the sentient individuality of all real existence, they suffice to bring our general interpretation of the physical order under Mr. Bradley’s canon that “What must be and can be, that is.”

§ 4. (3) What, then, are we to make of the principle of the “Uniformity of Nature”? Any principle which does actual work in science must somehow be capable of justification, and if our interpretation of the physical order really conflicts with a fundamental scientific principle, it must contain fallacy somewhere. Fortunately, there is no real conflict. In dealing with the principle of Uniformity, we must distinguish very carefully between the sense in which it is actually required for the purposes of science and the sense which has been put upon it in the set of metaphysical doctrines popularly but illogically deduced from the actual procedure of the sciences. As we have seen already, it is impossible to affirm the principle of Uniformity as an axiom of systematic thought. It is also not capable of verification as an empirical truth. Its logical character must therefore be that of a postulate, an assumption defensible on the ground of practical usefulness, but only so far as it actually succeeds.

Now, this is precisely the place which the principle fills in the actual procedure of the sciences. We have absolutely no means of showing that the concrete course of Nature is strictly uniform, as has already been seen. But also, we have no need, for our scientific ends, that it should be uniform. All that we require is that natural processes, when dealt with in the bulk, should exhibit no divergence from uniform routine except such as we may neglect for the purposes of practical calculation and control of the course of events. The actual success of the empirical sciences shows that this demand for approximate uniformity is actually fulfilled with sufficient closeness for all our practical purposes. That it would be so fulfilled we could have had no theoretical means of divining before putting it to the actual test. In this sense the principle, like that of Causality may be said to be a postulate made a priori and in advance of experience. But, once more like the principle of Causality, it could not be presumed to be trustworthy unless the subsequent results of its employment vindicated it; it cannot, therefore, be a priori in the Kantian sense of being known to be true independent of empirical verification.

This result is confirmed by consideration of the way in which the principle of uniform law is actually applied to concrete cases. Scientific laws, as we all know, are purely general and abstract. They state not what will happen, but what would happen providing that certain specified conditions and no others were operative in determining the result. In this abstract form they are, of course, statements of exact and absolute uniformities. But in this abstract form they cannot be directly applied to the calculation of the actual course of any process. To take, for instance, an example which has been used by Professor Ward. We learn in Mechanics that equilibrium is maintained on the lever when the moments of the weights about the fulcrum are equal and opposite. As an abstract generalisation this is a statement of a rigid uniformity. But in order that it may be universally true, we must suppose the conditions implied in the formulation of the proposition to be fulfilled. The lever itself must be absolutely rigid, and must be weightless; it must be of absolutely uniform structure, the fulcrum must be a mathematical point, in order that friction may be excluded, and so forth. Similarly, the weights must be thought of as mere masses without any further difference of quality, and thus only capable of affecting the lever through the one property of their weight; their attachments, again, must be of ideal tenuity, or fresh complications will be introduced. But when all these conditions have been taken into account, the principle has become so abstract as to amount to the tautology that what only operates by its mass and its distance from the fulcrum will not operate by any other property.

In any actual case, the course of events will be liable to be affected by all the conditions which had to be excluded from the abstract formulation of the principle. No actual lever will be weightless or incapable of being bent or broken; its construction will never be uniform. Actual loads, again, may influence the behaviour of a lever differently according to their bulk, their chemical composition, the nature of their attachments. At an actual fulcrum there will be some degree of friction between the lever-bar and its support, and so on. In actual fact, any or all of these circumstances may affect the behaviour of the lever bar when the loads are suspended from it. Consequently, it is quite impossible to apply the mechanical generalisation with certainty to determine the course of events in a concrete case.

What holds good in this instance holds good in all similar cases of the “laws” of nature. In so far as these laws are really exact they are all hypothetical, and deal only with the problem. What would be the course of a physical sequence, assuming its complete ground to be contained in the conditions enumerated in the enunciation of the law? That is, they all, in so far as they are absolute, are different forms of the tautological proposition, that where there is nothing to make any difference between two cases, there will be no difference. But the moment we apply our laws to the calculation of the actual course of an individual process, we have to recognise that the condition for their rigid exactness is absent; in the individual process there are always aspects not comprised in the conditions for which the law was enunciated, and nothing but actual experience can inform us whether the presence of these aspects will perceptibly affect the result in which we are interested. As applied to the study of an individual process, the principle of Uniformity is thus a postulate, like the principle of Causality, which can only be justified by its actual success.

Again, like the principle of Causality, the principle of Uniformity may be successful to different degrees, according to the special nature of the processes for which it is assumed. As the causal postulate rested on the assumption that a selection from the antecedents of an event may for practical purposes be treated as equivalent to its complete ground, so the more general postulate of Uniformity rests on the assumption that individual purpose may be left out of account in assigning the ground of a process. It does not follow that these postulates will receive the same amount of empirical justification for all departments of the physical order. There may well be certain processes in which the individual purposive character is so prominent that, even for our practical purposes, we cannot safely calculate their course without taking their end or purpose into consideration. In that case the principle of Uniformity and that of Causality would, for this part of the physical order, lose their practical value. It is a popular belief that such a failure of these practical postulates actually takes place where we come to deal with the conscious volitions of human agents. The problem is one which must be kept for fuller consideration in our next Book, but we can at present make two general statements.

(1) Such a failure of the postulates of Causality and Uniformity in application to a particular sphere would not involve a breach of the fundamental logical principle of Ground and Consequence, since, as we have seen sufficiently already, both postulates impose special restrictions on that principle for which the nature of the principle itself affords no warrant. It would thus not be an unthinkable or logically untenable position to hold that no general laws of human action can be formulated.

(2) While this extreme denial of the possibility of laws of human action is logically possible, the actual success of those sciences which deal with human behaviour in the statistical way forbids us to accept it. The success of these sciences shows that human behaviour, considered in the gross, does exhibit certain approximate uniformities. But there seems to be no means of proving that all aspects of human behaviour would show such uniformity if considered in gross in the same fashion. It is at least conceivable that some social activities would fail to exhibit approximation to an average value, no matter how extended the area and period taken as the basis of investigation. We might conceivably have to admit that there are departments of social life for which no “laws” can be formulated. If we disregard this possibility in practice, the reason is a methodological one. It is our interest to discover such uniformities, and therefore, as failure may only mean a temporary check to the success of our investigations, we properly make it a rule of method to assume that it is no more than this. We treat all sequences as capable, by proper methods, of reduction to uniformity, for the same reason that we treat all offenders as possibly reclaimable. We desire that they should be so, and we cannot prove they are not so, and we therefore behave as if we knew they were so.

A word may be said as to the nature of the practical need upon which the postulate of Uniformity is based. As we have previously seen, the allied postulate of Causality arose from the practical need of devising means for the control of natural processes. But the causal postulate alone is not enough to satisfy this need. For even if we can assume that every event is determined, sufficiently for practical purposes, by its antecedents, and thus that the knowledge of those antecedents, when obtained, is a knowledge of the means to its production, our practical command over the production of the event is not yet assured. For we can have no general confidence in our power to produce the event by employing the ascertained means, so long as it is possible that the result may on each occasion be affected by variations too minute for our detection, or for other reasons not accessible to our perception. We need to be assured that what seems the same to us is, for practical purposes, the same, and so that the employment of the same means may be trusted to lead to the same result. This is the condition which is expressed in an abstract form by the principle of Uniformity, which states that the course of natural processes conforms to general laws; in their actual application to the concrete processes of actual nature these laws are properly practical rules for the production of effects, and their inviolability means no more than that we may successfully treat as the same, in their bearing on the results in which we are interested, things which appear the same in relation to certain standards of comparison. As we have seen, the validity of this assumption could never have been known a priori; it can only be said to be actually valid where actual use has justified it. At the same time, it is clearly a principle of method to assume the universal applicability of our practical postulates wherever it is to our interest that they should be applicable, as explained in the last paragraph. This is why we rightly assume the applicability of the postulates in spheres where the successful establishment of general uniformities has not hitherto been effected, so long as no positive reason can be shown why they should not apply. We shall find this last reflection suggestive when we come to deal with the ethical difficulties which have been felt about the application of the postulates of Uniformity and Causality to voluntary action.

It is of course clear that our reduction of Uniformity to a mere practical postulate does not introduce any element of pure “chance” into the actual order of existing things. “Chance” is a term with more than one meaning, and its ambiguity may easily lead to misapprehensions. Chance may mean (a) any sequence for which our actual knowledge cannot assign the ground. In this sense chance, as another name for our own mere ignorance, must of course be recognised by any theory which does not lose sight of the fact of human ignorance and fallibility.

Or again, chance may mean (b) a sequence of which the ground is partially understood. We may know enough of the ground of the sequence to be able to limit the possibilities to a definite number of alternatives, without knowing enough to say which alternative completely satisfies the conditions in a special case. It is in this sense that we speak of the “chances” of any one of the alternative events as capable of computation, and make the rules for their computation the object of special mathematical elaboration in the so-called “Theory of Probability.”

(c) Finally, chance may mean “pure” chance, the existence of something for which there is no “ground” whatever, as it stands in no organic interconnection with a wider system of real existence. Chance in this last sense is, of course, absolutely excluded by our conception of the systematic unity of the real as expressed in the principle of Ground and Consequence, as an ultimate axiom of all consistent thought. Our denial of the absolute validity of the principles of Causality and Uniformity would only amount to the admission of “pure” chance into things if we accepted those principles as necessary consequences of the axiom of Ground and Consequence. If they are mere practical postulates, which present the axiom of Ground under artificial restrictions for which there is no logical justification in the axiom itself, the admission that they are not ultimately true in no way conflicts with full recognition of the thorough systematic unity of existence; it merely means that the view of the nature of that unity assumed by our practical postulates, though eminently useful, is inadequate.

We may here conveniently recapitulate our results. On metaphysical grounds, we felt compelled to regard the physical order as the manifestation to our special sensibility of a system of interconnected beings with sentient and purposive experiences like ourselves. The apparent purposelessness and deadness of the greater part of that order we explained as intelligible on the supposition that the subjective purposes and interests of many of its members are too unlike our own for our recognition. We then saw that if nature consists of such sentient experiences, the apparent domination of it by absolute law and uniformity cannot be the final truth. Such uniformity as there is must be approximate, and must result from our having to deal in bulk with collections of facts which we cannot follow in their individual detail, and will thus be of the same type as the statistical uniformities established by the anthropological sciences in various departments of human conduct. Next, we saw that the uniformities we call the “laws” of nature are, in fact, of this type; that they represent average results computed from a comparison of large collections of instances with which we cannot, or cannot so long as we adhere to our scientific purpose, deal individually, are only absolute while they remain hypothetical, and never afford ground for absolute assertion as to the course of concrete events.

We further saw that the only uniformity science requires of the actual course of nature is uniformity sufficiently close to enable us, for our special purposes, to neglect the individual deviations, and that the principle of Uniformity itself is not a logical axiom but a practical postulate, expressing the condition necessary for the successful formulation of rules for practical intervention in the course of events. Finally, while we saw that we have no a priori logical warrant for the assumption that such rules can be formulated for all departments of the physical order, we are bound on methodological grounds to assume that they can, unless we have special positive reasons for believing the contrary. Thus the universality of a postulate of uniformity does not mean that it is universally true, but that it has universally to be made wherever we have an interest in attempting the formulation of general rules.

§ 5. (4) The Conception of the Physical Order as a Mechanism. The conception of nature as rigidly conformable to general laws, finds its completest expression in the view of the whole physical order as a complicated mechanism.

It is not easy to say just how much is always implied when we hear of a “purely mechanical” theory of the world or of physical processes. Sometimes all that is meant is that the theory in question treats the principle of rigid uniformity according to general laws as an ultimate axiom. Sometimes, again, a “mechanical view” of the world is taken to mean, in a narrower sense, one which regards all the chemical, electrical, and other processes of the physical order as merely complicated cases of change of configuration in a system of mass particles. In this narrower sense the “mechanical” theory of the physical world is another name for the somewhat crude form of realist Metaphysics according to which nothing exists but moving masses, everything in the form of secondary qualities being a subjective illusion. Both the wider and the narrower form of the mechanical view agree in treating the processes of physical nature as unintelligent and unconscious, and regarding them as completely determined by antecedent conditions, without reference to any end or purpose which they effect. The theory owes the epithet “mechanical” to the analogy which is then supposed to subsist between the physical order and the various machines of human construction, in which the various constituent parts similarly execute movements determined by relation to the remaining parts, and not by any consciousness of an end to be attained.

It is of course manifest that, so understood, the mechanical view of physical processes is forced upon us by our practical needs wherever it is requisite to formulate rules for successful intervention in the course of nature. If we are to intervene with success in the course of events, that course must, as we have already seen, be capable of being regarded as approximately uniform, otherwise we can have no security that our intervention according to rule and precedent will have a uniform and unambiguous result. Hence, if we are to formulate general rules for practical intervention, we must be able to treat the course of things as—to all intents and purposes—mechanical. And, on the contrary, if there are processes which cannot be even approximately regarded as mechanical, our power of framing general rules for the practical manipulation of events cannot extend to those processes. The limits of the mechanical view of events are likewise the limits of empirical science and of the general precepts of the practical arts.

We see this admirably exemplified in the study of human natures. The behaviour of large aggregates of human beings, as we have already learned, exhibits approximate uniformity, at least in many respects, and may thus be treated as to all intents and purposes mechanical in those respects. Hence it is possible to have a number of empirical sciences of human nature, such as Ethnology and Sociology, in which those uniformities are collected and codified, and to base on these sciences a number of general prudential maxims for the regulation of our behaviour towards our fellow-men considered in the abstract. But when we come to deal with the actual conduct of concrete human individuals, the mechanical view, as we have seen, fails us. What a concrete individual will do can only be inferred with certainty from the knowledge of his interests and purposes; there can thus be no general science of individual character, and consequently no general rules of prudence for behaviour towards an individual fellow-man. It is not to the so-called sciences of human nature, but to personal experience of the individual himself, we have to go for the knowledge how to regulate our conduct towards the actual individuals with whom life brings us into direct and intimate personal relation. Philosophical reflection upon the nature and limits of scientific knowledge fully confirms the verdict passed by the practical sense of mankind on the doctrinaire pedantry which seeks to deduce rules for dealing with actual individuals from anything but concrete understanding of individual character and purpose.

The mechanical view of physical processes is thus an indispensable postulate of the various empirical sciences which seek to describe those processes by the aid of general formulæ. Hence the protests which are sometimes urged against the use of mechanical interpretations in descriptive science are really in spirit no more than the expression of a personal distaste for the whole business of scientific generalisation and description. If there are to be sciences of physical processes at all, these sciences must be mechanical, in the wider acceptation of the term. It does not, however, follow because the mechanical view of physical processes is a necessity for our empirical sciences, that this view is consequently ultimately true. As we have learned already, when we pass from the statement that the processes of the physical order may, for the purpose of description by general formulæ, and the invention of practical methods for their production, be treated as to all intents mechanical, to the very different assertion that the physical order really is rigidly mechanical, we have deserted empirical science for dogmatic Metaphysics, and our metaphysical dogma must stand or fall by its own ultimate coherency and intelligibility as a way of thinking about Reality. The usefulness of the mechanical interpretation for other purposes is no evidence whatever of its value for the special purpose of the metaphysician.

§ 6. Our previous discussion has already satisfied us that, as Metaphysics, the postulate of Uniformity upon which the mechanical view of the physical order rests, is unintelligible and therefore indefensible. But we may supplement the discussion by one or two reflections which throw into striking relief the inadequacy of that concept of the physical order as a huge self-acting machine which is so often offered us to-day as the last word of scientific thought. In the mechanical metaphysical theories two points always receive special emphasis. The physical order, according to the thorough-going exponents of the doctrine, is a mechanism which is (a) self-contained and self-acting, and (b) entirely devoid of internal purpose.

Now, in both these respects the supposed world-machine differs absolutely from the real machines upon analogy with which the mechanical theory is in the last resort based. Every real machine is, to begin with, the incarnation of the internal purpose of a sentient being. It is something which has been fashioned for the express object of attaining a certain result, and the more perfect its structure the greater is the impossibility of understanding the principle of construction without comprehension of the result it is devised to effect. Why the various parts have precisely the shape, size, strength, and other qualities they have, you can only tell when you know what is the work the maker of the machine intended it to do. In so far as this is not the case, and the structure of the machine can be explained, apart from its specific purpose, by consideration of the properties of the material, the patterns of construction consecrated by tradition, and so forth, it must be regarded as an imperfect realisation of its type. In a perfect machine the character and behaviour of every part would be absolutely determined by the demands made on that part by the purpose to be fulfilled by the working of the whole; our inability ever to produce such a perfect mechanical structure causes all our actual machines to be imperfect and inadequate representations of the ideal we have before us in their construction.

Thus a true machine, so far from being purposeless, is a typical embodiment of conscious purpose. It is true that the machine, once set going, will continue to work according to the lines embodied in its construction irrespective of the adequacy with which they effect the realisation of the maker’s purpose. A watch, once wound up, will continue to go, though the indication of the lapse of time may, under fresh circumstances, cease to meet the interests of its maker or owner; and again, if the construction of the watch was faulty, it will not properly execute the purpose for which it was made. The machine has in itself no power of fresh purposive adaptability by which to modify the purpose it reflects, or to remedy an initial defect in its execution. But this merely shows that the purpose exhibited in the machine’s construction originated outside the machine itself, and that the originator had not the power to carry out his purpose with complete consistency. It does not in the least detract from the essentially teleological and purposive character of the machine quà machine.

This brings us to our second point. Just as no true machine is purposeless, so no true machine is self-acting. Not only are all machines in the end the product of designing intelligence, but all machines are dependent upon external purposive intelligence for control. They require intelligence to set them going, and they require it equally, in one form or another, to regulate and supervise their working. However complicated a piece of machinery may be, however intricate its provisions for self-regulation, self-adjustment, self-feeding, and so forth, there is always, if you look carefully enough, a man somewhere to work it. The obvious character of this reflection has unfortunately not prevented metaphysicians from drawing strange inferences from their own neglect of it.

Closer reflection upon the true character of machinery would thus suggest a very different interpretation of the analogy between the uniformities of the physical order and the regular working of our machines from that adopted by the “mechanical” view of nature, as elaborated into a metaphysical doctrine. It would lead us to conceive of the apparently mechanical as playing everywhere the same part which it fulfils in our own system of social life. We should think of the mechanical as filling an indispensable but subordinate place in processes which, in their complete character, are essentially teleological and purposive. Teleological action obviously depends for its success upon two fundamental conditions. It requires the establishment of types of reaction which remain uniform so long as their maintenance satisfies the attainment of the end towards which they are directed, and at the same time the power of modifying those types of reaction from time to time so as to meet fresh situations encountered or created in the progressive attainment of that end. In our own individual physical life these two conditions are found as the power to form habits, and the power to initiate spontaneously fresh response to variation in the environment. In so far as our dominant interests can be best followed by the uniform repetition of one type of reaction, attention is diverted from the execution of the reaction which becomes habitual, semi-conscious, and, as we correctly say, “mechanical,” the attention being thus set free for the work of initiating the necessary fresh modifications of habitual action. Our various industrial and other machines are devices for facilitating this same division of labour. The machine, once properly constructed and set in action, executes the habitual reaction, leaving the attention of its supervisor free to introduce the requisite relatively novel variations of response according to new situations in the environment.

There is nothing to prevent our interpreting the mechanical uniformities exhibited by the physical order in terms of this analogy. We should then have to think of the “laws” or “uniformities” in physical nature as corresponding to the habitual modes of reaction of the sentient beings of whose inner life the physical order is phenomenal; these uniformities would thus be essentially teleological in their own nature, and would also stand in intimate interrelation with the spontaneous initiation of fresh responses to variations in the environment on the part of the same sentient beings. Habit and spontaneity would mutually imply each other in nature at large as they do in our own psychical life, and the “mechanical” would in both cases be simply the lower level to which teleological action approximates in proportion as attention ceases to be necessary to its execution.

This conception would harmonise admirably with the result of our previous inquiry into the kind of evidence by which the existence of uniform “laws of nature” is established. For it would be an inevitable consequence of those subjective limitations which compel us to deal in bulk with processes we are unable to follow in their individual detail, that our observation of the physical order should reveal the broad general types of habitual response to typical external conditions, while failing to detect the subtler modifications in those responses answering to special variations in those conditions. Just so the uniformities ascertained by the statistical study of human nature are simply the exhibition on a large scale of the leading habitual reactions of human beings upon typical external situations, as disentangled from the non-habitual spontaneous responses to fresh elements in the external situation with which they are inseparably united in any concrete life of individual intelligent purpose.

There seems no objection to this conception of “laws of nature” as being the formulæ descriptive of the habitual behaviour of a complex system of sentient beings, beyond that based on the allegation that these “laws” are absolute, exact, and without exception. We have seen already that physical science has no means of proving this allegation, and no need whatever to make it, the whole doctrine of “rigid,” “unvarying” conformity to law being a mere practical postulate falsely taken by a certain school of thinkers for an axiom. We have also seen that the notion of rigid unvarying law is fundamentally irreconcilable with the only intelligible interpretation we were able to give to the conception of the real existence of the physical order. Thus we have no reason to accept it as true, and the fullest ground for dismissing it as false. But for the unintelligent superstition with which the “laws of nature” are worshipped in certain quarters, it would indeed have been unnecessary to deal at such length and with such reiteration with so simple a matter.

One suggestion, already made in slightly different words, may be once more emphasised in conclusion. Even among human beings the relative prominence of fresh spontaneous adaptations and habitual reactions in the life of the individual fluctuates greatly with the different individuals. The “intelligence” of different men, as gauged by their power of fresh adaptive modification of established habits of reaction, ranges over a great variety of different values. If we could acquire the same kind of insight into the individual purposes of non-human agents that we have into those of our immediate fellows, we should presumably find an even wider range of differences in this respect. In principle we have no means of setting any definite limits to the range in either direction. We can conceive a degree of attentive control of reaction so complete that every reaction represents a fresh stage in the realisation of an underlying idea, so that intelligence is everything and habit nothing; and again, we can conceive a state of things in which mere habit is everything and intelligent spontaneity nothing. Somewhere between these ideal limits all cases of finite purposive intelligence must be comprised, and it would be easy to show that neither limit can be actually reached by finite intelligence, though there may be indefinite approximation to either.

Consult further:—H. Lotze, Metaphysic, bk. i. Introduction X. (Eng. trans., vol. i. p. 18), bk. ii. chaps. 7, 8 (Eng. trans., vol. ii. pp. 66-162); E. Mach, The Science of Mechanics, pp. 481-504 (Eng. trans.); K. Pearson, Grammar of Science, chaps. 3 (The Scientific Law), 9 (The Laws of Motion); J. Royce, “Nature, Consciousness, and Self-consciousness” (in Studies of Good and Evil); J. Stallo, Concepts and Theories of Modern Physics, chaps. 1, 10-12 (metaphysical standpoint, “Phenomenalist”); J. Ward, Naturalism and Agnosticism, part 1, lects. 2-5.

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Footnote 127:

Speaking strictly, all necessity would appear to arise from the presence of conflicting purposes or interests in the same experience. E.g., the logical necessity of affirming the conclusion when the premisses are affirmed, implies (1) the presence of the general purpose to think logically; (2) the presence of some purpose or interest which, if gratified, would demand the affirmation of a result inconsistent with the previously affirmed premisses; (3) the repression of this affirmation by the dominant purpose (1). I believe that careful analysis will reveal these same elements in every genuine case of necessitation. I.e. the mere defeat of my purpose is not true necessitation unless it is defeated by a second interest or purpose which I also identify with myself. Thus all necessity would ultimately be self-imposed. This is not without its bearing on Ethics, as we shall see.

Footnote 128:

Compare with what follows, F. H. Bradley, Ethical Studies, Essay 1, and infra, Bk. IV. chap. 4.

Footnote 129:

Our ordinary calculations as to the behaviour of our fellow-men, beyond the circle of our own intimates, seem to involve a mixture of the two types. We base our conclusions partly on conjectures drawn from the observed past acts of our fellows as to their special interests and purposes, partly on generalisations as to the purposes and interests which are most widely operative in human life. Practical men never allow themselves to forget that the conclusions thus obtained are problematical in the highest degree. The whole course of our investigation will go to show that the notion of a deductive science of human nature, by which the concrete conduct of an individual man might be inferred with certainty from physiological and psychological generalities, is a ridiculous chimera. See infra, Bk. IV. chap. 4.

Footnote 130:

It will be recollected that the approximate constancy of such social statistics has been, foolishly enough, brought forward as an alleged disproof of moral freedom. The more vulgar forms of the necessitarian argument have even been pushed to the inference that, if the number of suicides up to December 31 has been one less than the average in some given year, some one must kill himself before the day is out to make up the percentage. What must happen if the number has been one more than the average we are never told.

Footnote 131:

Compare Mach, Science of Mechanics, p. 280 ff. (Eng. trans.); Jevons, Principles of Science, chaps. 13, 14.

Footnote 132:

Compare Lotze, Metaphysic, bk. i. Introduction X., chap. 3, § 33 (Eng. trans., vol. i. pp. 18, 90-93); bk. i. chap. 7, § 208 ff. (Eng. trans., vol ii. pp. 88-91).

Footnote 133:

See the full exposition of this view in Ward, Naturalism and Agnosticism, vol. i. lecture 4, on which the present paragraph is founded. Cf. J. T. Merz, History of European Thought, vol. i. pp. 437-441.

Footnote 134:

My remark is founded more particularly upon the methods by which quantitative uniformities are obtained in the investigations of Psychophysics. I have no direct acquaintance with first-hand experimentation in other spheres, but the method by which it is made to yield general uniformities seems to be of the same kind.

Footnote 135:

Cf. Mr. H. G. Wells’s tale, The New Accumulator.

Footnote 136:

Compare once more the passage already quoted from Lotze, Metaphysic, i. 3. 33.

Footnote 137:

See Naturalism and Agnosticism, vol. i. lecture 2, and compare the elaborate proof given by Mach, Science of Mechanics, pp. 9-23, that all the so-called demonstrations of the general theory of the lever are mere reductions of the more complicated to the simplest cases of a relation which ultimately depends for its recognition on nothing more cogent than the evidence of the senses.

Footnote 138:

For some comments upon the “mechanical view” in the narrower and more special sense, see Chapter VI. of the present Book. It may be convenient, for the sake of precision, to call this more special form of the mechanical view the “mechanistic” theory of nature.

Footnote 139:

Psychology ought probably to be excluded from the sciences for which the mechanical view is fundamental. But Psychology does not deal with any part of the physical order. See the present writers review of Münsterberg’s “Grundzüge der Psychologie” in Mind for April 1902; and cf. infra, Bk. IV. chaps. 1, 2.

Footnote 140:

Compare with the argument of this chapter, Royce, “Nature, Consciousness, and Self-consciousness,” in Studies of Good and Evil; and “Mind and Nature,” by the present writer in International Journal of Ethics, October 1902. The inveterate prejudice that “laws of nature,” to be of scientific use, must be rigidly exact uniformities is so strong, that it may be worth while, even after the preceding discussion of general principles, to assist the reader by reminding him of the elementary fact that the most familiar quantities involved in our scientific formulæ (π, e, the vast majority of second and third roots, of logarithms of the natural numbers, of circular functions of angles, etc.) are incapable of exact evaluation. This of itself renders a scientific law, in the form in which it can be applied to the determination of actual occurrences, merely approximate, and thus shows that exact uniformity is unnecessary for the practical objects of the empirical sciences.

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