Chapter V (1)

THE WORLD OF THINGS—(2) CHANGE AND
CAUSALITY

§ 1. The conception of things as interacting leads to the two problems
of Change and Causality. The paradoxical character of change due to
the fact that only what is permanent can change. § 2. Change is
succession within an identity; this identity, like that of
Substance, must be teleological, _i.e._ must be an identity of plan
or end pervading the process of change. § 3. Thus all change falls
under the logical category of Ground and Consequence, which becomes
in its application to succession in time the Principle of Sufficient
Reason. § 4. _Causality._ Cause—in the modern popular and scientific
sense—means the ground of a change when taken to be completely
contained in preceding changes. That every change has its complete
ground in preceding changes is neither an axiom nor an empirically
ascertained truth, but a postulate suggested by our practical needs.
§ 5. In the last resort the postulate cannot be true; the dependence
between events cannot be one-sided. The real justification for our
use of the postulate is its practical success. § 6. Origin of the
conception of Cause anthropomorphic § 7. Puzzles about Causation.
(1) _Continuity._ Causation must be continuous, and yet in a
continuous process there can be no distinction of cause from effect.
Cause must be and yet cannot be prior in time to effect. § 8. (2)
_The indefinite regress_ in causation. § 9. (3) _Plurality of
Causes._ Plurality of Causes is ultimately a logical contradiction,
but in any form in which the causal postulate is of practical use it
must recognise plurality. §10. The “necessity” of the causal
relation psychological and subjective. §11. Immanent and Transeunt
Causality: Consistent Pluralism must deny transeunt Causation; but
cannot do so successfully, §12. Both transeunt and immanent
Causality are ultimately appearance.

§ 1. The fourth of the features which characterise the pre-scientific view of the world we found to be the belief that things act and are acted upon by one another. The problems to which this belief gives rise are so vast, and have been historically of such significance for Metaphysics, that they will require a separate chapter for their discussion. In the conception of the interaction of things as it exists for the naïve pre-scientific mind, we may distinguish at least two aspects. There is (1) the belief that things _change_, that within the unity of the one thing there is a succession of different states; and (2) the belief that the changes of state of various things are so inter-connected that the changes in one thing serve as occasions for definite changes in other things. We thus have to discuss, first, the general notion of change as an inseparable aspect of the being of things, and next the concept of systematic inter-connection between the changes of state of different things.

(_a_) _Change._ The problem presented by the apparently unceasing mutability of existence is one of the earliest as well as one of the most persistent in the whole range of Philosophy. In itself it might seem that the successive presentation in time of various states is neither more nor less noteworthy a feature of the world of experience than the simultaneous presentation of a like variety, but the problem of mutability has always appealed with special force to the human imagination from its intimate connection with our personal hopes and fears, ambitions and disappointments. Tempora mutantur, _nos_ et mutamur in illis; there is the secret of the persistence with which our philosophic thought has from the first revolved round this special problem. There, too, we may find a pregnant hint of the central paradox implied in all mutability—namely, that only the identical and permanent can change. It is because the self which changes with the flux of time and circumstance is still in some measure the same old self that we feel its changes to be so replete with matter for exultation and despair. Were we completely new-made with each successive change in our self, there would no longer be ground for joy in transition to the better or grief at alteration for the worse.

The thought that only what is permanent can change has affected Philosophy in different ways at different periods of its history. At the very dawn of Greek Philosophy it was the guiding principle of the Ionian physicists who sought to comprehend the apparent variety of successive phenomena as the transformations of a single bodily reality. As the difficulties inherent in such a materialistic Monism became more apparent, the felt necessity of ascribing unity of some kind to existence led Parmenides and his Eleatic successors to the extreme view that change, being impossible in a permanent homogeneous bodily reality, must be a mere illusion of our deceptive senses. While yet again the later Ionian physicists, and their Sicilian counterpart Empedocles, sought to reconcile the apparent mutability of things with the criticism of Parmenides by the theory that what appears to the senses as qualitative change is in reality the mere regrouping in space of qualitatively unalterable “elements” or “atoms”—μεῖξις διάλλαξίς τε μιγέντων.

At a more developed stage of Hellenic thought, the necessity of taking some account of the mutability as well as of the permanence of existence impelled Plato to draw the momentous distinction between two worlds or orders of being—the real, with its eternal unvarying self-identity, and the merely apparent, where all is change, confusion, and instability. In spite of Plato’s manifest failure to make it intelligible how these two orders, the eternal and the temporal, are ultimately connected, this distinction in one form or another has continued ever since to haunt all subsequent metaphysical construction. Even our modern scientific Materialism, with its loudly avowed scorn for all merely metaphysical questions, shows by its constant endeavour to reduce all material existence to a succession of changes in a homogeneous medium, both the persistence with which the intellect demands a permanent background for change, and the difficulty of finding logical satisfaction for the demand.

Yet there have not been wanting attempts to get rid of the paradox by denying its truth. As the Eleatics sought to escape it by reducing change itself to a baseless illusion, so some at least of the disciples of Heracleitus seem to have evaded it by refusing to admit any permanent identity in the changeable, and they have not been entirely without imitators in the modern world. Incessant change without underlying unity has had its defenders in the history of Metaphysics, though they have not been numerous, and we must therefore briefly consider what can be urged for and against such a concept. Apart from the general difficulty of seeing how what changes can at the same time be permanently identical with itself, the only special argument in favour of the doctrine that only incessant change is real seems to be the appeal to direct experience. In any actual experience, it is contended, however contracted its limits, we are always presented with the fact of change and transition; we never apprehend an absolutely unchanging content. Even where the object before us exhibits no succession, self-examination will always detect at least alternating tension and relaxation of attention with the accompanying fluctuations of bodily sensation.

Now there can, of course, be no gainsaying these facts of experience, but the conclusion based on them evidently goes much further than the premisses warrant. If experience never gives us mere persistence of an unchanging content, neither does it ever give us mere change without persistence. What we actually experience always exhibits the two aspects of identity and transition together. Usually there will be, side by side with the elements which sensibly change in the course of the experience, others which remain sensibly constant throughout it. And even when, through inattention, we fail to detect these constant elements, the successive states of the changing content itself are not merely momentary; each has its own sensible duration through which it retains its character without perceptible changes. Experience thus entirely fails to substantiate the notion of mere change apart from a background of permanent identity.

The positive disproof of the notion must, however, be found in its own inherent absurdity. Change by itself, apart from a background of identity, is impossible for the reason that where there is no underlying identity there is nothing to change. All change must be change of and in some thing. A mere succession of entirely disconnected contents held together by no common permanent nature persisting in spite of the transition, would not be change at all. If I simply have before me first A and then B, A and B being absolutely devoid of any point of community, there is no sense in saying that I have apprehended a process of change. The change has been at most a change in myself as I passed from the state of perceiving A to the state of perceiving B, and this subjective transition again can only be called change on the assumption that the I who am qualified first by the perception of A and its various emotional and other accompaniments, and then by that of B and its accompaniments, am the same. And where you have not merely a change of perception but an actual perception of change, the case is even clearer. What we perceive in such a case is “A changing into B,” the two successive states A and B being held together by the fact that they are successive states of some more permanent unity [gamma]. Apart from the presence of this identical [gamma] in both the earlier and later stages of the process, there would be no meaning in speaking of it as one of change.

§ 2. Change, then, may be defined as succession within an identity, the identity being as essential to the character of the process as the succession. In what way, then, must we think of this identity or common nature which is present throughout the whole succession of changes? It should be clear that this question—how that which changes can be permanent?—is simply our old problem of quality and substance, how the many states can belong to one thing, considered with special reference to the case of states which form a succession in time. Thus, whatever is the true nature of the unity to which the many states of one thing belong, will also be the true nature of the identity which connects the successive stages of a process of change.

Now we have already seen in what the unity to which the many states belong must be taken to consist. We found that this unity is essentially teleological; that group of states, we saw, is one thing which functions as one in regard to an end or interest, or, as we may also say, is the embodiment of coherent structure. The same is true of the process of change. The earlier and later stages of the process are differences in an identity precisely because they constitute one process. And a process is one when it is the systematic realisation of a single coherent end. To be one process means to be the systematic expression in a succession of stages of a single coherent plan or law. The succession of stages is thus welded into a unity by the singleness of the plan or law which they embody, and it is this systematic connection of each stage with all the rest which we express by saying that whatever changes possesses an underlying permanent identity of character. It would amount to precisely the same thing if we said the successive states of anything that changes form a connected system.

We must be careful here, as we were in dealing with the problem of Substance, not to be misled by taking symbolic aids to imagination for philosophical truths. Just as it is easy to imagine the “substance” of things as a sort of material substratum, it is easy to imagine the identity which pervades all changes as that of a number of pieces of matter, and to think of the changes as constituted by their motion through space. But such a representation must not be taken for anything more than an aid to imagination. It helps us to make a mental diagram, but it throws absolutely no light upon the real nature of the connection between the identity and the succession. For the same problem breaks out within each of the “self-identical” pieces of matter; we have to say what we mean by calling it one and the same throughout the series of its changing positions, and the necessity of answering this question shows us at once that the identity of a material particle throughout its motion is only one _case_ of that identity pervading succession which belongs to all change, and in no sense affords any explanation of the principle it illustrates.[100] As a recent writer puts it, “it seems to be a deeply rooted infirmity of the human mind ... that it can hardly conceive activities of any sort apart from material bases, ... through habitually seeking to represent all phenomena in mechanical terms, in terms of the motion of little bits of matter, many of us have come to believe that in so doing we describe the actual events underlying phenomena.”[101] This “disease of the intellect,” as the same writer aptly calls it, is nowhere more insidious than where we are dealing with the problem of Change.

Change, then, involves two aspects. It is a succession of events in time, and these events are connected by a systematic unity in such a way that they form the expression of a plan or law of structure. The series of successive states which make up the history of a thing are the expression of the thing’s nature or structure. To understand the thing’s structure is to possess the key to the succession of its states, to know on what principle each gives way to its successor. And similarly, to have complete insight into the nature or structure of Reality as a whole would be to understand the principles according to which every transitory event in the history of the Universe, regarded as a series of events in time, is followed by its own special successor.

It is evident that, in proportion as our knowledge of any thing or system of things approaches this insight into the laws of its structure, the processes of change acquire a new character for us. They lose their appearance of paradox, and tend to become the self-evident expression of the identity which is their underlying principle. Change, once reduced to law and apprehended as the embodiment in succession of a principle we understand, is no longer change as an unintelligible mystery. We should bear this in mind when we reflect on the doctrine of Plato that the physical world must be unreal because the scene of incessant change. Such a view is only to be understood by remembering that before the invention of the mathematical methods which have enabled us with such conspicuous success to reduce physical phenomena to orderly sequence according to law, the physical world necessarily appeared to the philosopher a scene of _arbitrary_ change following no recognisable principle. Change, so far as understood in the light of its principle, has already ceased to be mere change.[102]

§ 3. _Ground and Consequence._ In the technical language of Logic, the underlying principle of any system is called its _Ground_, the detail in which the principle finds systematic expression is called its _Consequence_. Ground and Consequence are thus one and the same systematic whole, only considered from two different points of view. The Ground is the pervading common nature of the system, thought of as an identity pervading and determining the character of its detail; the Consequence is the same system, looked at from the point of view of the detail, as a plurality of differences pervaded and determined by an identical principle. The understanding of a process of change thus clearly consists in bringing it under the principle of Ground and Consequence. In so far as we are successful in detecting a principle in the apparently arbitrary succession of events, these events become for us a system with a common principle of structure for its Ground, and a plurality of successive states as its Consequence.

Change is not, however, the only instance of the principle of Ground and Consequence. These two aspects may also be found in systematic wholes which contain no element of succession in time, _e.g._ in a body of logical deductions from a few fundamental premisses. The special peculiarity of the case of Change is that it is the principle of Ground and Consequence as applied to a material which is successive _in time_. As thus applied, the principle has received the special name of the _Principle of Sufficient Reason_, and may be formulated thus: _Nothing takes place unless there is a sufficient reason why it should occur rather than not_. It is clear that such a proposition is a mere result of the application of the conception of Reality as a systematic whole to the special case of the existence of the successive in time. It is therefore simply one case of the fundamental axiom of all knowledge, the axiom that what truly exists is a coherent whole.[103] We must of course observe that the principle does nothing to solve the perhaps insoluble problem _why_ succession in time should be a feature of experience. This is a question which could only be answered if we could show that succession in time is a logical consequence of the existence of any multiplicity forming a systematic whole. Until we are able to establish this result, we have simply to accept succession as a datum of our experience. (Yet for some light upon the problem, see _infra_, Bk. III chap. 4, § 9)

§ 4. _Causality._ So far we have said nothing of a concept which is much more familiar in the popular treatment of the problem of Change than that of Ground and Consequence, the concept of _Cause_. In proceeding to discuss this concept, it is necessary in the first place to explain which of the numerous senses of the word we are taking for examination. There was an old scholastic distinction, which still reappears occasionally in philosophical writings, between the _Causa cognoscendi_, or reason for affirming a truth, and the _Causa existendi_ or _fiendi_, the cause of the occurrence of an event. It is this latter meaning of the word “cause,” the meaning which is predominant wherever the term is used in modern scientific language, that we shall have in view in the following sections.

The _Causa cognoscendi_, or logical _reason_ for the affirmation of a truth, as distinguished from the psychological factors which lead a particular individual to affirm it, is clearly identical with what modern logicians call the _Ground_. A given proposition must logically be affirmed as true in the last resort, because it fills a place in a wider system of truths which no other proposition would fill. Thus, _e.g._, a special proposition about the relation between the sides and angles of a triangle is logically necessitated, because it is an integral element in the development of a system of geometrical ideas which repose as a whole upon certain fundamental assumptions as to the character of spatial order. The original presuppositions cannot be worked out to their logical consequence in a body of internally coherent geometrical notions unless the proposition in question is included in that body. And reciprocally, the logical justification for regarding these presuppositions rather than any others as sound, lies in the fact that they yield a body of internally consistent consequences. Incidentally, we see by means of this illustration that Ground and Consequence are mutually convertible, which is what we might have inferred from the way in which we defined them as mutually complementary aspects of a single systematic whole.

What we are concerned with in the everyday and scientific treatment of Causation, is not this purely logical relation of Ground and Consequence, but something partly identical with it, partly different. The _Causa fiendi_ has no significance except in connection with occurrences or events in time, and may roughly be said to correspond with what Aristotle denotes the “Source of Change”—ἀρχὴ κινήσεως or ὅθεν ἡ κίνησις—and his mediæval followers named the Efficient Cause. Cause, in the popular sense of the word, denotes the attempt to carry out the principle of the interconnection of events in a system along special lines by regarding every event as completely determined by conditions which are themselves previous events. Widely as the popular and the scientific uses of the term “cause” diverge in minor respects, they agree in the essential point. That every event has its cause is understood, both in everyday life and in the sciences which use the concept of causation, to mean that the occurrence and the character of every event in the time-series is completely determined by preceding events. In more technical language, causation for everyday thought and for the sciences means _one-sided dependence_ of the present on the past, and the future on the present.

It is, of course, obvious that the principle of Causation as thus understood is not a necessary logical deduction from the principle of Ground and Consequence. It might be the case that all occurrences form a coherent plan or system, such that if you once grasped the principle of the system you could infer from it what precise occurrence must take place at any one moment, and yet it might be impossible to discover this principle by an examination of the course of events up to the present moment. In other words, the principle of the systematic interconnection of events might be valid, and yet the events of the present might depend on those which will succeed them in the future no less than on those which have preceded them in the past. In that case it would be impossible with absolute logical certainty to infer what will occur at a given moment from the mere examination of what has preceded, _i.e._ the principle of Causation as used in the sciences would not be logically valid.[104]

Cause, as currently understood, is thus identical not with the whole true logical ground, but with the ground so far as it can be discovered in the train of temporally antecedent circumstances, _i.e._ cause is _incomplete_ ground. This point is important, as it shows that the principle of Causation is not, like the principle of Sufficient Reason, axiomatic. It is no necessary logical consequence of the knowability or systematic character of the Real that an event should be completely determined by temporally antecedent events; for anything that is implied in the systematic character of the Real, the event may be equally dependent on subsequent occurrences. Again, the principle of Causation cannot be empirically established by an appeal to the actual course of experience. Actual experience is certainly not sufficient to show that every event is absolutely determined by its antecedent conditions; at most the success of our scientific hypotheses based upon the assumption of causality only avails to show that events may be inferred from their antecedents with sufficient accuracy to make the causal assumption practically useful.

Regarded as a universal principle of scientific procedure, the causal assumption must be pronounced to be neither an axiom nor an empirical truth but a _postulate_, in the strict sense of the word, _i.e._ an assumption which cannot be logically justified, but is made because of its practical value, and depends upon the success with which it can be applied for confirmation. In the sense that it is a postulate which experience may confirm but cannot prove, it may properly be said to be _a priori_, but it is manifestly not _a priori_ in the more familiar Kantian sense of the word. That is, it is not a necessary and indispensable axiom without which systematic knowledge would be impossible. For, as we have already seen and shall see more fully in the immediate sequel, it may not be, and indeed in the last resort cannot be, true.

§ 5. This last statement will possibly appear startling to the reader who is unacquainted with the history of metaphysical investigations into Causality. But it is easy to show that it is really the expression of an obvious truth. For the causal principle, as we have just seen, is an imperfect expression of the really axiomatic principle of Sufficient Reason or Ground and Consequence. And it is readily seen that the expression it gives to that principle, because imperfect, must be partially false. What the principle of Ground and Consequence says is, that the whole of existence is a single coherent system in which every part is determined by the nature of the whole as revealed in the complete system. But if this is true, each constituent of the system can only be completely determined by its connections with all the rest. No constituent can be entirely determined by its relations to a lesser part of the whole system, in the way presupposed by the notion of one-sided causal dependence. The “cause” must, if the principle of Ground and Consequence be valid, be determined by the “effect” no less than the “effect” by the “cause.” And therefore the causal postulate cannot be the whole truth.

How this fatal logical defect in the principle of Causation makes itself felt in the logic of the inductive sciences, and how logicians have sought without success to avoid it, we shall incidentally see as our discussion proceeds. At present we must be content to note that, owing to this flaw, Causation, wherever it is asserted, can only be Appearance and never complete Reality, and that no science which works with the concepts of cause and effect can give us the highest truth. Of course, the logical defects of the concept need not impair its practical usefulness. Though it can never, for the reason given already, be ultimately true that any event is absolutely determined by antecedent events, the assumption may be sufficiently near the truth to yield useful deductions as to the course of occurrences, precisely as a mathematical approximation to the value of a surd quantity may, without being the exact truth, be close enough for practical use. Also, it might well be the case that the causal postulate approximates more nearly to the truth in some spheres of investigation than in others, a consideration which is not without its bearing on the ethical problems of freedom and responsibility.

If we ask how the causal postulate, being as it must be only imperfectly true, comes to be made, the answer is obvious. The whole conception is anthropomorphic in origin, and owes its existence to our practical needs. To take the latter point first, logically there is no better reason for treating an event as determined solely by antecedents, than for treating it as solely determined by subsequent events. Yet when the latter supposition is made, as it is by all believers in omens and presages, we all agree to condemn it as superstitious. Why is this? Two reasons may be assigned. (_a_) Even granting that an event may be determined by subsequent events, yet, as _we_ do not know what these events are until after their occurrence, we should have no means of inferring by _what_ particular events yet to come any present event was conditioned, and thus should be thrown back upon mere unprincipled guess-work if we attempted to assign its, as yet future, conditions.

(_b_) A more important consideration is that our search for causes is ultimately derived from the search for _means_ to the practical realisation of results in which we are interested. We desire to know the conditions of occurrences primarily, in order to produce those occurrences for ourselves by setting up their conditions. It is therefore essential to us for our practical purposes to seek the conditions of an occurrence exclusively among its antecedents, and the causal postulate which asserts that the complete conditions of the event are comprised somewhere in the series of antecedent events is thus the intellectual expression of the demand made by our practical needs upon Reality. We postulate it because, unless the postulate is approximately realised, we cannot intervene with success in the course of events. We refuse, except as a pure speculation, to entertain the notion that an event may be determined by subsequent as well as by antecedent events, because that notion leads to no practical rules for operation upon our environment.

§ 6. As might be expected of a postulate so obviously originated by our practical needs, the concept of cause on examination reveals its anthropomorphic character. This is particularly obvious when we consider the concept of Causation as it figures in everyday unscientific thought. The various scientific substitutes for the popular notion of cause all exhibit traces of the endeavour to purge the conception of its more anthropomorphic elements. In the popular use of the concept this anthropomorphism comes out most strikingly in two ways. (_a_) A cause, as popularly conceived, is always a person or thing, _i.e._ something we can imagine as a whole, and into which we can mentally project a conscious life akin to our own. To the scientific mind it seems obvious that causes and effects are alike _events_ and events only, but for popular thought, while the effect is always a quality or state (_e.g._, death, fever, etc.), the cause is regularly a thing or person (the bullet, the poison, the tropical sun, etc.).

(_b_) Closely connected with this is the emphasis popular thought lays upon what it calls the _activity_ of the cause. The cause is never thought of as merely preceding the effect as an “inseparable antecedent”; it is supposed to _make_ the effect occur, to bring it about by an exercise of activity. According to the most coherent expositions of this type of thought, in causation one thing is always _active_ in producing a change in another thing which is _passive_. The origin of this notion is sufficiently obvious. As all philosophers since Hume have recognised, the “activity” of the cause results from the ascription to it of the characteristic feeling of self-assertion and self-expansion which accompanies our own voluntary interference in the course of events. Similarly, the “passivity” of the thing in which the effect is produced is only another name for the feeling of coercion and thwarted self-assertion which arises in us when the course of nature or the behaviour of our fellows represses our voluntary execution of our designs.

Science, in its attempt to extend the concept of causal determination over the whole domain of existence, has naturally felt these anthropomorphic implications as obstacles. From the effort to expel them arises what we may call the common scientific view of causation, as ordinarily adopted for the purposes of experimental investigation and formulated in the works of inductive logicians. The concept of a thing, except as the mode of interconnection of states, being unnecessary for the sciences which aim simply at the reduction of the sequence of occurrences to order, the notion of causation as a transaction between two things is replaced in the experimental sciences by the conception of it as merely the determination of an event by antecedent events. Similarly, with the disappearance of things as the vehicles of causal processes falls the whole distinction between an active and a passive factor. As it becomes more and more apparent that the antecedent events which condition an occurrence are a complex plurality and include states of what is popularly called the thing acted upon as well as processes in the so-called agent, science substitutes for the distinction between agent and patient the concept of a system of reciprocally dependent interacting factors. These two substitutions give us the current scientific conception of a cause as the “totality of the conditions” in the presence of which an event occurs, and in the absence of any member of which it does not occur. More briefly, causation in the current scientific sense means sequence under definitely known conditions.

Indispensable as this notion of the determination of every event by a definite collection of antecedents and by nothing else is for practice, regarded as a logical formulation of the principle of the systematic unity of existence, it is open to grave objections, most of which will be found to have made themselves felt in the logic of the inductive sciences quite independently of conscious metaphysical analysis. In dealing with these difficulties, we shall find that their general effect is to place us in the following dilemma. If we wish to state the causal principle in such a way as to avoid manifest speculative falsehood, we find that it has to be modified until it becomes identical with the principle of Ground and Consequence in its most universal form, but as thus modified it is no longer of any service for the purposes of the experimental sciences. You seem driven to take it either in a form in which it is true but practically useless, or in one in which it is useful but not true. To illustrate the way in which this dilemma arises, we may examine three of the main problems which have actually been created by the scientific use of the principle,—(_a_) the puzzle of continuity; (_b_) the puzzle of the indefinite regress, (_c_) the puzzle of the plurality of causes.

§ 7. (_a_) _The Puzzle of Continuity._ Continuity is, strictly speaking, a property of certain series, and may be defined for purposes of reference much as follows. A series is continuous when any term divides the whole series unambiguously into two mutually exclusive parts which between them comprise all the terms of the series, and when every term which so divides the series is itself a term of the series. From this second condition it obviously follows that a number of intermediate terms can always be inserted between any two terms whatever of a continuous series; no term of the series has a _next_ term. This is the peculiarity of the continuous with which we shall be specially concerned. Thus the series of points on a straight line is continuous because (1) any point P on the line divides it into two collections of points in such a way that every point of the one is to the left of every point of the other, and every point of the second to the right of every point of the former; and (2) every point which divides the line in this way is a point on the line. Again, the whole series of real numbers is continuous for the same reason. Every member of the number-series divides it into two classes, so that every number of one is less than every number of the other, and every number which thus divides the series is itself a term of the number-series.

But the series of _rational_ real numbers is not continuous, because it can be divided into mutually exclusive classes by terms which are not themselves members of the series. (_E.g._ √2 is not a member of the series of rational numbers, but we can exhaustively divide all rational numbers into the two mutually exclusive classes, rational numbers _less_ than √2 and rational numbers _not less_ than √2.)[105] From the continuity of the series of real numbers it follows that any other series which corresponds point for point with the terms of the number-series will be continuous. Now one such series is that of the successive parts of time. Every moment of time divides the whole series of moments into two mutually exclusive classes, the moments _before_ itself and the moments which are _not before_ itself. And whatever thus divides the time-series is itself a moment in that series. Hence from the continuity of the time-series it follows that any puzzles created by this property of continuousness will apply to the case of Causation. In what follows I shall not discuss the general problem of the continuous, a problem which requires special mathematical equipment for its efficient handling, but shall confine myself to the difficulties introduced by continuity into the scientific concept of causal relation.

We may conveniently attack the problem by taking it up in the form in which Hume bequeathed it to modern science. As any careful reader of Hume must perceive, Hume’s whole doctrine of Causation is based on the assumption that the causal process is not continuous. Experience is supposed by him to come to us not in an unbroken stream, but in isolated separate pieces which we subsequently proceed to link together artificially by the notion of Causation. We are supposed to begin by observing the sequence of an event B on a previous distinct event A, and the problem of Causation thus becomes that of discovering the nature of the link by which the originally distinct A and B are connected in our scientific thought. In more technical language, Hume thought of the series of events as one in which every member has a next term, and this way of conceiving it has coloured the whole subsequent treatment of Causation by the inductive logicians who have commonly got their metaphysical doctrines from Hume.

Now, recent Psychology, in deserting the old notion of the atomic sensation for that of the “stream of consciousness,” has completely destroyed the supposed empirical foundation for this Humian theory of the discontinuity of the course of events. The real problem for the inductive logician we can now see to be not to discover the link by which an originally separate A and B have got joined together in thought, but to find the source of the distinction we habitually draw within what comes to us as one continuous process between an earlier stage A which we call cause, and a later stage B which we call effect. We are not, however, concerned here with the psychological weakness of Hume’s doctrine, but with the logical difficulty to which it gives rise.

We may state the difficulty thus: (1) Causation cannot possibly be thought of as discontinuous, _i.e._ as the sequence of one distinct event upon an assemblage of other events without gross contradiction. To think of it as discontinuous, we must conceive the _cause_ A to exist first in its completeness, and then to be suddenly followed by the effect B. (That the cause A consists of a number of conditions, _a_, _b_, _c_ ... which themselves come into existence successively, and that A is not there until the last of these conditions has been realised, makes no difference to the principle.) Now this seems to be what is actually implied by the language of those inductive logicians who insist that in all Causation the cause must _precede_ the effect. But what can such precedence mean? It can only mean that after the complete realisation of the conditions included in the cause A, there must intervene a space of empty time _before_ the effect B enters on the scene. However brief and “momentary” you take this gap in the stream of events to be, the gap must be there if your language about the cause as being _before_ the effect is to have any meaning. For if there is no such gap, and the entrance of B is simultaneous with the complete realisation of its conditions A, it is no longer true to say that the cause A is _before_ the effect B. A does not exist as A until _a_, _b_, _c_ ... are all present, and as soon as they are present B is present too. And thus the relation between A and B is not that of the sequence of a later event on an earlier. They are actually _together_.

In fact, the doctrine that the cause precedes the effect rests upon the notion that the time-series is one in which each member has a next term. And this seems inconceivable. For not only can you subdivide any finite time, however small, into two mutually exclusive parts, but the point at which the division is effected is itself a moment in the time-series lying _between_ the beginning and the end of the original interval. Time therefore must be continuous, and if causation is not equally continuous, we must suppose that gaps of empty time are what separate the first event, the cause, from the subsequent event, the effect. Yet _if_ this could be regarded as a defensible doctrine on other grounds, it would then follow that the assemblage of events A is not the totality of conditions requisite for the occurrence of B. The “totality of conditions,” _i.e._ the _cause_ as previously defined, would be the events A _plus_ a certain lapse of empty time.[106] And so the cause would once more turn out not to precede the effect, or we should have to suppose the end of the interval of empty time included in it as separated from the beginning of B by a second lapse, and so on indefinitely.

(2) These difficulties, in a more or less clearly apprehended form, have led many recent writers on inductive Logic to modify the definition which was still satisfactory to Mill. Cause and effect, we are now told, are not distinct events, but earlier and later stages in a continuous process. The real business of science is not to discover “laws of connection” between distinct events or “phenomena,” but to invent general mathematical formulae by the aid of which we may trace the course of continuous processes. The discovery of causes, from this point of view, is reduced to the construction of formulæ which exhibit some quantity as a function of a time-variable. Fully worked out, this view of the nature of experimental science leads to the so-called “descriptive” ideal of scientific explanation, advocated by such eminent thinkers as Kirchhoff, Mach, and Ostwald among physicists, and, with various modifications, Avenarius, Münsterberg, Royce, and James Ward among recent philosophers. According to this doctrine, the ultimate ideal of science, or at any rate of physical science, is simply the description of the course of events by the aid of the fewest and simplest general formulæ. _Why_ things happen as they do, it is now said, is no proper question for science; its sole business is to enable us to calculate _how_ they will happen. With the general epistemological questions raised by this doctrine we must deal later in our third and fourth books. At present we are concerned only with its bearing on the notion of Causal Relation.[107]

The important point for our immediate purpose is that the reduction of all events to continuous processes really does away with Causation altogether, as is recognised by those adherents of the theory who openly propose to expel the word “cause” from the language of science.[108] For in a continuous process it is purely arbitrary where we shall mentally draw the dividing line which is to mark the boundary between the “earlier” and the “later” stage. What the descriptive formula, with the aid of which we trace the course of the process by giving a series of successive values to our time-variable presents, is not the “cause” of the process but the “law” of it. Instead of looking upon the later stages of the process as determined by the earlier, we are now looking upon the process as a whole as the expression in detail of a single principle. We have, in fact, abandoned the category of cause and effect for that of Ground and Consequence. We are seeking the ground of the whole process not in a set of temporally preceding events, but in its own pervading principle.

From this point of view the one-sided dependence of effect on cause, characteristic of the causal relation, disappears. Whether we shall infer the later stages of the process from the earlier, or the earlier from the later, depends simply upon our choice of positive or negative values for our time-variable. For “descriptive” science, what we suggested at first as a paradoxical possibility is the actual fact. The past is determined by the future in precisely the same sense in which the future is determined by the past, namely, that as both are stages of the same continuous process, if once you know the principle of the process you can start equally well with either and reason to the other.[109] Thus, within the limits of experimental science itself, the conception of causal relation has given way to the conception of events as logically connected into a system in virtue of their underlying ground or principle. For practical purposes experimental science has, in its application of this conception, to be guided by two postulates, neither of which can be metaphysically justified. It has to assume (_a_) that the course of events is composed of a plurality of more or less independent continuous processes, each of which has its own ground within itself, at least to such an extent as to be capable of being treated for our purpose as independent of others; (_b_) that the underlying ground or grounds of all events can be adequately expressed in terms of mathematical symbolism.

As to the first of these points, our discussion of the unity of Reality convinced us that there must in the end be a single ground of all existence, and therefore the complete reason of any partial process cannot be entirely within itself. The independence of the various processes must be relative, and even the belief that it is sufficient to enable us to treat them for our own special purposes as self-contained and independent, must be a postulate prompted by our practical needs, and justified in the end by its success. The second point will engage our attention more fully in subsequent chapters. At present one remark upon it must suffice. The calculability of the laws of continuous processes depends upon our ability to reduce them to numerical and quantitative forms. Wherever we have the appearance, at any stage in a process, of a new quality, we have in fact an apparent breach of continuity, and it ceases to be in our power to exhibit the new stage of the process as a mere transformation of what was already expressed in former stages. Hence the success of natural science in reducing all sequences of events to continuous processes depends upon the assumption that we can establish equations between qualitatively different magnitudes.

Now this assumption is even more evidently than the preceding a postulate. We have to make it, if we are to calculate the course of events, but we have no guarantee that it will succeed beyond the fact of its actual success. If it fails anywhere, as we shall hereafter contend that it does in the critical case of the sequence of psychical on physical events, and _vice versâ_, two results will follow, one practical, the other speculative. The practical consequence of the failure is that in such cases we cannot apply the concept of continuous process, and have to fall back upon the cruder notion of causal sequence. Thus, in attempting to create a science of Psychophysics we cannot hope to exhibit the whole of a psychophysical process as the continuous realisation of a single principle; we must be content to establish laws of causal connection between the physical and the psychical sides of the process. The speculative consequence is that the principle of Ground and Consequence is only imperfectly represented by the conception of a continuous process, inasmuch as that conception is only applicable where qualitative differences within the consequences of a single ground can be disregarded. This hint will prepare us for subsequent criticism of the concept of continuity when we come to deal with the metaphysics of the time-process.[110]

#§ 8 (_b_). _The Indefinite Regress._ The defects of the causal postulate as a principle of explanation may also be exhibited by showing the double way in which it leads to the indefinite regress. The indefinite regress in the causal series is an inevitable consequence of the structure of time, and, as we please, may be detected both outside and inside any causal relation of two events, or two stages of a continuous process. For it follows from the structure of the time-series (_a_) that there are an indefinite number of terms of the series between any two members, between which there is a finite interval, and (_b_) that there is also an indefinite number of terms before or after any given member of the series. Like the series of real numbers, the time-series, because it satisfies the definition of a continuous infinite series, can have neither a first nor a last term, nor can any member of it have a next term.[111] Applying this to the case of Causation, we may reason as follows:—

(1) The same reasons which lead us to demand a cause A for any event B, and to find that cause in an assemblage of antecedent events, require that A should be similarly determined by another assemblage of antecedent events, and that this cause of A should itself have its own antecedent cause, and so on indefinitely. Thus the causal principle, logically applied, never yields an intelligible explanation of any event. Instead of exhibiting the transition A-B as the logical expression of a coherent principle, it refers us for the explanation of this transition to a previous instance of the same kind of transition, and then to another, and so forth without end. But it is impossible that what is not intelligible in one instance should become intelligible by the mere multiplication of similar unintelligibilities.

(2) Similarly if we look within the transition A-B. This transition being continuous must have its intermediate stages. A becomes B because it has already become C, and the transition A-C-B is again “explained” by showing that A became D which became C which became E which became B. And each of the stages A-D, D-C, C-E, E-B can be once more submitted to the same sort of analysis. But in all this interpolation of intermediate stages there is nothing to show the nature of the common principle in virtue of which the stages form a single process. We are, in fact, trying to do what we try to do wherever we establish a relation between terms, to answer a question by repeating it. And we decided at the end of our last chapter that this kind of repetition is never an answer to any question. How entirely it fails to answer the question we ask whenever we look for a cause is obvious. We want to know why B exists, and we are told that B exists because it is determined by the previous existence of A. But why does A exist? Because of the previous existence of C. And so ultimately the existence of everything depends on the existence of something else, and this again on the existence of still something else. If this is so, since nothing can exist until its cause has existed, and the cause again not until its cause has existed, then, as this unending series has no first term, nothing can ever come into existence at all. This inevitable introduction of the indefinite regress whenever we try to think out the causal principle to its logical consequences, has sometimes been treated as proving the inherent defectiveness of the human mind. What it proves rather is that Causality is not a proper formulation of the real principle of the unity of all experience.

A word may be said about the attempts which philosophers have made to extricate themselves from the difficulty without giving up Causality as an ultimate principle of explanation. The least philosophical method of escape is that of arbitrarily postulating a first cause with no preceding cause, which amounts to the same thing as a beginning of existence or a first moment of time. This way out of the difficulty obviously amounts to an arbitrary desertion of the causal principle at the point where it becomes inconvenient to remain faithful to it. Whatever the nature of the event you pitch upon as your “first cause,” the causal principle, if logically valid at all, is just as applicable here as anywhere else Your “first cause” must have had a previous cause, or else the whole causal scheme must be, as we have contended that it is, the illogical and imperfect perversion of a genuine principle of systematic connection, useful and indeed indispensable in practice, but quite indefensible in theory.

It would not help you out of the difficulty to distinguish between a first event and a first moment of time, by postulating a first cause with an indefinite lapse of empty time before it. For the causal principle would then require you to look for the determining conditions of the first event in the preceding lapse of empty time. But this lapse, because merely empty, cannot contain the determining conditions for any special occurrence in preference to others. This is why the conception of a beginning of the causal series in time, with an empty lapse before it, has always led to the insoluble riddle, “Why did God create the world when He did, rather than at some other point of time?”