C. D. Broad, Perception, Physics, and Reality, 1914

CHAPTER II

ON CAUSATION; AND ON THE ARGUMENTS THAT HAVE BEEN USED AGAINST CAUSAL LAWS

    In this chapter we propose to discuss Causation, and more particularly certain problems connected with it on which objections to causation have been based. It is clearly quite useless to discuss the causal theory of perception and its bearing on the reality of what we perceive until we at least know whether there is any reason to believe that causal laws are necessarily invalid. At the same time this chapter will omit some considerations which, though vitally necessary for a complete view of causation, are beyond our present scope. I shall assume in fact the belief that the results of proceeding upon the theory of probability are correct without exhaustively discussing the nature and validity of the axioms on which it is based. This practically means that I shall assume what everybody does assume that the ordinary processes of induction do lead to propositions which are probably true; though we might find it very hard to say on precisely what grounds we believed this.

    What then does Causality mean? This question has, of course, been discussed ad nauseam, but the discussion has lead to so little agreement that it is worth while to enter upon it again. There are two characteristics about which most people would agree that they are essential to causality:

  1. It deals with the existent, and
  2. it deals with it so far as it is regarded as changeable.
Unfortunately this happy agreement is somewhat marred by the facts that existence is a very vague term, and that some people do not believe that anything that changes exists. This difference, however, is largely verbal. In the first place, although people cannot define existence and do use the term with some looseness, yet it is possible to give an extensive definition by pointing to the sorts of things that everyone believes to exist. It is still easier to point to the sort of entities that people agree in believing not to exist, and happily, this is really what concerns us most. People mean by saying that causation only applies to things that exist that it applies, if at all, to what can change; and they believe that, if anything can change, it is things like chairs and tables and minds, and not those like the propositions of Euclid and the multiplication table. What would be agreed then is that, if causal laws apply to anything it is to what can change in so far as it changes.

    Then, however, we have the trouble that some people think that only the changeless is real. They then proceed to identify reality with existence, and so there ceases to be any genuine agreement as to that to which causality applies. But this is an unnecessary mystification. We have already tried to show that all the characteristics that appear must at least qualify appearances and be true of them in order that we may be able to argue from these characteristics of appearances that they are not realities. Hence, even if change be self-contradictory, and therefore all that changes be appearance, yet these things that are condemned as appearances because they change must truly change if the argument against their reality is to be valid. Thus it might be true that what changes can never be more than appearance and that whatever is real must be changeless; but this does not alter the fact that there is a whole world of appearances which truly change. In as far as these appearances and the supposed timeless reality are alike in differing from such entities as the propositions of Euclid and the multiplication table, we can say that both the truly changing appearances and the truly changeless reality exist. And then the person who does and the person who does not consider that change is a mark of appearance will be able to agree that, if there be any causal laws, they apply to that part of the existent that changes in so far as it does change. They will only differ in that the former will have to say that causality only applies to appearances, whilst the latter will not see any reason to doubt that it may also apply to reality. There will remain for both the question: Are there any causal laws, and, if so, what precisely do they claim to tell us?

    What is the characteristic of what we agree to call cases of causation? I throw a stone, we will suppose, and it breaks a window. Here we say either that the stone breaks the window or that I do so. And this is said to be a causal action between me or the stone and the window. The first point on which we must be clear is what is to be called the cause. Reflexion would be held to tell us that, although I may be called the cause of breaking the window, this is at best an elliptical way of speaking. It will be said that accurately I am the cause of the motion of the stone, and the stone is the cause of the breaking of the window. But, so put, there is a distinction which is, I think, generally made between the sorts of things that are causes and the sort of things that are effects. The stone is a substance, in the sense that it is a subject and cannot be made a predicate. But the breaking of the window is not a substance; it is attribute of the window. It can be both a subject and apparently a predicate too. Not, however, a predicate in quite the ordinary sense. If we say that a window is red we no doubt generally mean that it is red now, but we do not bring in any explicit reference to time. It may have been red ever since it was a window. On the other hand a window breaking is an event which implies a definite beginning in time; the window cannot always have been breaking. (There are, of course, other differences between a window being red and being broken. The latter state is analysable and the former is not; but these differences are not relevant for our present purpose.)

    The effect here then is an event, but it is also an event that, as we put it, 'happens to' the window. On the other hand, the cause, if taken to be the stone, is not an event, but the sort of thing that has qualities and to which events 'happen.' Are people prepared to maintain this distinction between causes and effects, which is undoubtedly implied in their habitual usage of the terms? I do not see that they can do so. There is always more to be said about the stones that break windows than that they are stones. In fact whilst there are many stones that are moving which do not break windows, there are no stones that break windows that are not moving. Hence, it seems necessary to hold that it is not merely the stone that is the cause of the breaking of the window, but either

  1. the motion of the stone, or
  2. the moving stone.
Either the cause is a substance qualified by the fact of a certain event happening to it, or it is the event taken as happening in a certain substance. The effect, so far as I can see, would always be said to be an event happening to a certain substance and not a substance qualified by the occurrence of a certain event in it. No one would say that the effect was a window in the act of breaking in the same sense as he might say that the cause was a stone in the act of moving. For this would seem to imply that the cause produced the window as well as its state of breaking, which nobody believes.

    Can we decide then, whether the cause ought to be called the moving stone or the motion of the stone? We must first see what exactly is the difference between the two. When we talk of the motion of anything the phrase is ambiguous. We may mean either

  1. merely the fact that at different moments of time the same thing is at different places, or
  2. we may mean a supposed quality which all bodies of which (a) is true possess so long as (a) is true of them.
If (a) be all that is meant by the motion of a body, then all the actual facts involved about it are its relations to certain moments of time and to certain points of space. It is at one point at one moment and another point at another moment, and that is all that there is to be said about it. On the other hand, if (b) be true it also possesses a quality all the time for any two moments of which it is in different positions; viz., a state of motion which may be greater or less at different times. Now, if causes be particular existents, as is commonly supposed, the only particular existents involved in the motion of the stone are the relations to different points of space and time. Now it might be a true account of causality to say that the cause of the breaking of the window is the stone at- s1-at-t1. the stone at- s2-at-t2, . . . ; but I do not think that this is what people suppose themselves to mean when they say that the motion of the stone causes the breaking of the window. I think they mean that, although all these relations exist, they are not the cause of the breakage, but rather that they involve in the stone the existence of an intensive magnitude of some quality which is the real cause.

    On the other hand, the people who think that it is the moving stone that breaks the window and not the motion of the stone would say that it seems absurd to make a quality or state the subject of an active verb. They would say that a state of motion no more breaks windows than fair words butter parsnips, that it is only a thing that has this quality or state to which the active verb can be applied, and that the very fact that those who hold the opposite view cannot take their state of motion in the abstract as a cause but must make it the state of motion of the stone gives away their case.

    The foregoing discussion as to what common-sense takes to be the cause in interactions which it believes to be causal may seem trivial, but it is really important as introducing us to a duality of view whose further elaboration leads to the conflicting philosophic notions about causality. These two aspects are

  1. that of activity, and
  2. that of regularity and predictability.
Activity may be a very discreditable category and we may ultimately have to reject it, but the fact remains that people do believe until they become sophisticated that there is something more in causal laws than mere uniformities. The activity view leads us to say that a cause is always a thing in a certain state, and its elaboration often leads to idealistic theories of the universe. The uniformity view leads to a theory of causation like that of Mach or of Mr Russell. Since it is uniformity that interests science it is not surprising that those who have approached causation from the side of physics should have laid stress on that side of it. Still we have no right to neglect the other side which is historically more primitive and is certainly believed to be equally essential by common-sense. If it leads us into difficulties we must reject it, but we must not reject it unheard.

    We will begin then by attempting to understand what is meant by the activity view. In the first place we must notice that, when the law of causality is stated in general -- as distinct from particular causal laws -- in the form that every event has a cause, this may indeed be meant in the uniformity sense of causation, but probably most of the assent that it gains is received from the activity view. That to which people think they are assenting when they agree that every event has a cause would seem to contain two quite distinct but often confused propositions. One is a law of causation in the activity sense, and one is a law of uniformity; but neither is really the law of causality in the sense that it must have if all causal laws be mere uniformities. People mean (a) that they do not think that things that are quiescent suddenly explode into change unless something other than themselves forces them out of their quiescence. If such an explosion has apparently happened you will find, they believe, on investigation either that they were not really quiescent, or that they were not really let alone by other things. And, even if you cannot find evidence for either of these alternatives, they would still say that it was certain that one or other of them had been fulfilled. That a thing genuinely did nothing for five minutes or five seconds and then exploded into change without being acted upon from outside, common-sense refuses to admit, whatever the appearances may be. (b) People are also prepared to admit that if A forces B to have the state C at one time it will force it to do so at any other time so long as nothing else is forcing it in another direction on the second occasion which was not acting on the first. But neither of these propositions, which I think must be what common-sense believes when it accepts the general law of causality, are what the uniformity theory of causal laws must mean by this general law. The uniformity theory can only mean by the law of causality

  1. that there are causal laws; and
  2. that every event is so connected with other events by one or more laws that if enough events had been known its happening might have been predicted.
Now I do not think that common-sense would hold that the proposition (b) here was self-evident in its own right. It would agree to it because it would hold that every event must have been forced to happen by something else and that something acts uniformly. Thus (b) is only admitted by common-sense, because of the proposition of which it is immediately certain that every event must be forced to happen; without this neither proposition of the pure uniformity theory would be held to be certain a priori. Common-sense would say that, if it were offered the uniformity theory alone, it would be prepared to admit that the law of causality as offered would be very useful if true, that clearly a great many events are connected by laws of uniformity which allow of prediction, and that experience proves that the best way to discover such particular uniformities is to take the view that they always can be discovered if we only look carefully enough as a methodological postulate.

    Can anything be made of this activity view? Let us take the law of causality first. All that is actually open to investigation in it can be stated in terms of the uniformity view. For all that possibly could be observed on any theory is the changes in various things and their temporal relations to each other. If, then, the activity view were right all that could actually be observed would be that, when a body A has not been noticed to change at all for a finite interval and when it suddenly begins to do so, we can always find either that some other body has changed, or that A really was changing during the interval when we supposed it to be quiescent. But, taken as it stands, this amount of observation gives a ridiculous law. Of course, whether A has changed or not, we shall always be able to find plenty of bodies that have changed during the time in which we have been observing A. If we know what forced A to become A' the activity view would admit that we had discovered a causal law, but since we can only decide that it was X and not Y that acted upon A by observing uniformities in X and A, it is no thanks to the activity view that the causal law has been discovered. Everything that can be observed would have been the same if nothing but the uniformity view were correct. Thus we reach two conclusions about the activity view :

  1. it is perfectly useless to science, and
  2. no kind of observation of external things and their changes could prove it.

    Some people have thought that the observation of our volitions and their effects could prove it. This opinion, however, is ridiculous. No doubt, when I will to move my body I do have a peculiar feeling of effort, and so too when I try to remember something that I have forgotten. But then I am a spirit which has to use a body to exercise its volitions, and it is not at all surprising that the use of my body should give me feelings which I call feelings of effort, since I know on other grounds that the changes in my body are capable of producing feelings in me. If other things that apparently interact causally were spirits, interacted voluntarily, and had to use bodies to do so, there might be some reason to suppose that they had the same sort of feelings. Otherwise there is none. For we differ from billiard balls in precisely that respect which makes it probable that when billiard balls hit each other they do not have feelings of effort.

    I suppose that the answer to this will be as follows. No doubt if billiard balls are not conscious they are not conscious of feelings of effort. Still we are conscious, and our feeling is not a mere feeling, but is indicative of something which is present in all cases of genuine causation. It is not the feeling that is activity, nor does being active just mean that we have this peculiar feeling, but the feeling is an indication of some real quality in us when we exercise causality. This real quality, it will be said, can be assumed to be present in all cases of causality. Over volitional causation, there would be just the same controversy between the two schools as to what precisely is to be called the cause, as there was over what was the cause when the stone breaks the window. The believer in activity would say: I, with this state of volition, am the cause of the motion of my arm. The descriptionist would say : From this particular state of volition the motion of my arm at some later moment can be inferred.

    Supposing that my feeling of effort really were an indication of some quality in me when I exercise volition, the question remains: What exactly is that quality, and is it of such a kind that it can be supposed to be present in stones, and billiard balls, and other non-voluntary causal agents? What, in fact, is really meant by transitive verbs? Clearly they imply a relation, though not necessarily to a different term from their subjects. If I say 'I hurt,' the statement is incomplete because we need to know what I hurt. But what I hurt may be myself. In fact, the difference between active and reflexive forms of transitive verbs expresses on the activity theory the difference between transeunt and immanent causation. It appeals then, that the same thing can be both active and passive with regard to the same action. But it might be denied that the same thing is ever active and passive at the same time with regard to the same action. I may stick a pin further and further into my body for some seconds, and there will be pain contemporaneously with the motion of the pin. It would seem that in this case I was active and passive at the same time with regard to the same events. But this depends on whether one accepts or rejects the view that causes must always precede their effects in time, which has not yet been discussed. If they must be earlier then the position and qualities of the pin at earlier moments [they] will determine the pain at some later moment, and [at] no moment shall I be active with respect to the cause and passive with respect to its effect, though I may be passive with respect to an effect of a previous cause which is very like the one at present operating.

    Again, it is an old truism that nothing can be perfectly passive; the way in which it reacts depends as much on its own nature as on that of what is said to be active and is called the cause. The believer in activity might say: No doubt the object in which the effect is being produced is affected differently according to its nature by the same cause. But this does not make it active in the same sense in which we hold that the cause must be so. For the cause is constraining it to do something which, though definite and determined by its own nature, is yet not what its own nature would have determined had the cause not acted. You could only say that the body affected was active in the same sense as the cause, if it actually modified the cause. Now, in a great many cases, we know that no effect is produced by the object in which the original effect occurs in the object that causes it, and in these cases it is reasonable to say that the object affected is, with respect to the cause, purely passive. Thus, to take Lotze's illustration of the style writing on wax, no doubt if the wax were not soft the style would not write on it, but if the style, unlike the wax, remains unchanged throughout the whole process we can still say that with regard to this causal action, the style is active and the wax passive.

    Can this answer be accepted? Let us begin by remembering that, on the present view of causation, the cause is the style in a state of motion. But in what state of motion? Is it the state in which it would have been if it had not touched the wax or anything else, or the state in which it is when it is actually writing on the wax? If the former, then clearly the wax is as active as the style; in fact there is reciprocal causation. The style is supposed to be active because it determines states in the wax which its own nature would not have determined alone. But the wax determines states of motion in the style which ex hypothesi it did not have before it touched the wax, and therefore it is active in precisely the same sense as the style. If, on the other hand, we choose to say that the cause of the writing on the wax was the motion of the style as it was actually determined to move when it was in contact with the wax, then, indeed, the wax was not active with respect to the immediate cause of the writing. Still, it was just as active in changing the original motion of the style to that which is now taken to be the immediate cause of the writing. It would seem then, that if a thing is said to be active in so far as its nature determines changes in something else which, had the latter been left to itself, would not have happened, the object in which the effect is produced must in general also be said to be active with respect to the cause.

    It is worth while to point out how the above discussion as to the implications of the terms 'active' and 'passive' agrees with what has already been said as to the usual distinction that is made between the sorts of things that are causes and those that are effects. We said that by effects common-sense always means the states of things, but that by causes it never means the states of things alone, but always things in certain states. Common-sense does not say that the motion of a style makes marks on wax except elliptically, for the statement that the style in motion makes the marks. It does not say that the wax with marks on it is the effect, but that the marks on the wax are the effect. And when we come to discuss activity and passivity it does not say that the marks on the wax are the cause of the change of the style in motion, but that the wax with its marks is the cause in the change of motion of the style. In fact it holds that objects with their states are active or passive, and, as effects are the states of things but are not things, it does not say that effects are passive, but only that the objects whose states are effects are so.

    We have now seen that if all causes are active and all objects in which effects are produced are passive the converse also holds. But this is no reason for rejecting the activity view. No doubt if A be active with respect to B, and B with respect to A, it will follow that A is both active and passive with respect to B. And this may appear impossible, since activity and passivity with respect to the same object appear to be incompatible. But when we examine a particular case we see that there is no particular harm in such couples of propositions. The style is said to be active with respect to the wax, because, if it were not for the style, the latter would not of its own nature change in the way that it does. The wax is at the same time active with regard to the style because the style if not in contact with the wax would have moved differently. At best this could only prove that causal action is always reciprocal, by which it is meant that A never affects B in any way without B affecting A in some way (which may, of course, as an unusual particular case be the same way as that in which A affected B).

    The whole question of activity then, seems to come to this one of a thing forcing another to do that which, if it were left alone, it would not do. The question is: Can anything more be made of this notion of 'forcing' than what the descriptionist makes of it, viz., that there are synthetic laws of the successive states of things in accordance with which from a knowledge of the states at a certain number of times those at any time can be determined, and that generally the states of more than one object have to be considered in order to determine those even of one object? To answer this question we need to find out what is meant by what things would or would not do 'of their own nature.' We generally suppose that a thing left to itself will not suddenly go out of existence or come to pieces. But we cannot build very much on this. A shell appears to be a thing with a nature. It does not cease to be a thing with a nature when its fuse is lighted. But after a while it explodes without further external interference. But this is not really a fair example. A shell with a fuse is not one thing, and it is not really quiescent when it seems to be so. It has several parts, one of which is the fuse, and the fuse has been lighted from outside and continues to burn till it produces that effect on the other parts of the shell that causes the disruption. It would seem, therefore, that the thing that is expected to keep quiescent of its own nature for ever must either be perfectly homogeneous or really have been undergoing no change for a finite time.

    It is the latter that is the important characteristic. It would be held to be just as surprising for a shell with the fuse unlighted suddenly to explode as for a shell with no fuse at all to do so, providing nothing affected it from the outside. I think, then, that common-sense would deny that homogeneity is essential, and would hold that even a huge system, like the solar system, ought to do nothing if it were once quiescent and even then left to itself. This belief apparently contradicts the law of gravitation. No doubt if the planets were all stopped dead for a finite time and then let go, they would begin to move under their mutual attractions; but then the letting go of them is an external event, and so the belief of common-sense is compatible with the law of gravitation. Thus the first point on which common-sense is certain as to what things can do from their own natures and what they have to be forced to do, might be put as follows: If any system, whether under the influence of other objects or not, has been quiescent for a finite time it can only be through the action of external objects and not through its own nature that it ceases to be quiescent. Such a system will neither change its qualities nor move as a whole or in parts, nor cease to exist as a whole or in parts unless it is forced to do so by changes in objects external to it.

    This opinion is closely bound up with the question of the continuity of causation on which it is customary for philosophers to base an antinomy with which we shall later have to deal. The point is that, if what I have said be what common-sense really holds, then it may believe that within any system, so long as there is no moment after which all the qualities and relations of all the parts of it remain unchanged for a finite interval, changes might proceed 'of its own nature' without assistance from outside. But as soon as all changes have ceased during a finite interval however short, they cannot start again except by the action of objects not contained in the system. Now this belief sets a limitation on the kind of causal laws that are possible. It cuts out immanent causal laws in which the only condition is lapse of time. Such a law as: After being quiescent for ten seconds the system A will again begin to change is logically a possible one, but it would be ruled out of court by the present view.

    When we pass from changes from quiescence to merely continuous states of change we find it much harder to decide what a thing or system is supposed to do 'by its own nature,' and what has to be forced on it from outside. The distinction clearly assumes that we can know what a thing's nature is, and what it can do independently of the effects of other things on it. Now this might be possible if we could consider systems which are isolated and are not quiescent, and find out their characteristics. We might then say that the changes that went on in this period were due solely to the nature of the system. But then the only guarantee that you can have that the system is isolated would be the knowledge that, as a matter of fact, nothing outside it had acted upon it during the time of observation. And the only way of judging on this point brings us straight back to the other view of causation. We can be sure that a system is isolated when and only when we find that a selection of data within it at various times will enable us to infer that which we actually can observe at other times in it. Of course, the fact that we cannot do this in a particular case does not prove that the system is not isolated, for we may merely be ignorant of the law of the changes of the system. But until you have actually found such a law immanent within the system you have no right to suppose that the changes in that system are expressions of its own nature in the sense required. But even so, the isolation is only known to be relative. Under the supposed conditions we can conclude that the system has not been acted upon from outside while we observed it, but we cannot assume that the section of its history which we observe, and are able to bring under purely immanent causal laws, was not begun by action from outside which happened before we started our observations. In fact, to be perfectly sure that the changes that we observe in a system are wholly the expression of its own nature we should

  1. have to discover purely immanent causal laws which would give, as the state at any moment during the time of observation, the state that is actually observed at that moment; and
  2. to be certain that at no moment ex parte ante would those laws fail to give what might have been observed.
When both conditions (i) and (ii) are satisfied we may say that the changes of a thing or system are purely the expressions of its own nature1. It follows, however, from the conditions that it is practically always impossible to be certain that the changes in any system are expressions of its own nature, and, therefore, impossible to tell how much is forced upon it by other things.

    I think, then, we may sum up our discussion of the activity theory of causation as follows.

  1. Activity certainly cannot be observed in the external world. We can only observe those regularities from which we infer causal laws in the sense of the uniformity theory. Hence, if you put activity into causation as an essential element it must be something discovered by thought and not based by the ordinary processes of induction on what can be observed.
  2. With regard to the so-called feeling of activity it seems almost certain that it depends on the fact that we are minds and in volition produce states in our bodies which are causally connected with certain feelings in our minds. Hence, if activity be identified with feeling of activity, there can be no reason to believe that it is a general characteristic of all causation unless we are already convinced on other grounds of an idealism like that of Leibniz or Lotze or Dr McTaggart, which holds that all substances are minds.
  3. On the other hand, if we take the more promising position that the feeling in the case of agents with minds and organic bodies is not a mere mental event, but the sign of a real quality of activity which exists whether felt or not in all causal agents, we must be prepared to state what we mean by this quality and what can be known about it. We found that it was no objection to it that in many and perhaps in all cases it would have to be found both in the cause and in the effect; because this would merely mean that most or all cases of causation are cases of reciprocal causation, which is a perfectly harmless proposition.
  4. But when we come to ask what activity and passivity mean we are referred to the notion of one thing forcing another to do what it would not do of its own nature. When we came to enquire into this we found that the only way to decide what anything could do of its own nature was by the introduction of causal laws in the uniformity sense of the word. We can express everything that is conveyed by saying that one thing is forced to do something which it would not do by its own nature by the statement that its changes can only be inferred by laws that make use as data of events in other things. And we can state the belief of common-sense that all systems that begin to change after being quiescent for a finite time have to be forced from outside in terms of the rival theory by saying that a law of causation that is immanent to a system can only be found for continuous changes. Thus the notion of forcing things to do what their nature alone would not let them do is perfectly compatible with and explicable by the view of causation that reduces the latter purely to causal uniformities. But this is the only meaning that has been proposed for the terms active and passive, and therefore there seems no reason to suppose that they stand for qualities involved in all cases of causation over and above causal regularities.
  5. So far as I can see the only way to retain activity would be to say that it is just an unanalysable quality, like red or green, to the reality of which our feeling when we exercise volition bears witness. With regard to this modest claim we can merely say that there, seems little reason to believe that our feelings do attest the existence of such a quality even in the case of causation by volition, that there is still less to believe in it in other cases of causation, and that anyhow the important part of causation has now been shown to lie wholly in the causal regularities.

    We shall therefore assume for the future that the essence of causality is causal laws and that these are laws of a certain kind about change. We want in the rest of this chapter to discuss the nature of these laws and the objections which philosophers have brought against them, with a view to seeing how far they can be trusted. The first important question is: How exactly are causal laws related to things?

    Causal Laws and Things. This question keeps us very close to our old discussion about what things do by their own nature and what they are forced to do by other things. Just as the activity view overrated the importance of substances in causality by saying that all causes are substances in certain states, so the descriptionist view is liable to underrate it by talking as if causal laws merely connected events in general and not events in particular substances. Take for instance the law that successful volition is followed by pleasure. The descriptionist is, no doubt, right in saying that this law means that whenever successful desire occurs it will be followed by pleasure. But what is also important to notice is that the general law only holds when the volition and the pleasure are supposed to be states of the same person, whatever that may mean. Smith's successful desire may very well cause pain in Jones. The notion of cause then is very closely connected with that of things, since it is necessary to state to what things the events that are connected as cause and effect happen.

    What then is meant by one thing independently of causation? This depends on whether the thing in question be a mind or a body. In our case it is more important to consider bodies. With regard to them I think that we are simply forced to deny that there is anything ultimate or recondite in the notion of one thing. There are two different points to note in the definition of one thing: (i) What distinguishes it at a given moment from other things at that moment? and (ii) What makes us call a certain succession of states the states of one thing that persists through time? And the answers that I would suggest to these two questions are (i) Homogeneity at a given moment of sense qualities within a definite boundary in space, and (ii) That the changes that these qualities and this boundary undergo are sensibly continuous. Both these crude statements will need discussion and qualification. We will take them in order.

    (i) What precisely do we mean by saying that at a given moment one thing is an aggregate of qualities in various relations and all within one definite boundary which is closed? On this view a state of a thing is a quality which is a member of such an aggregate. The assertion that P is a state of a thing S, which is generally put in the form S is P, means that P is a member of that aggregate of related qualities within a closed boundary to which we give the name of the thing S.

    Various objections can be brought against this view. The main ones are (a) that qualities themselves have qualities and relations, and clearly they are not aggregates of qualities in relation and within a boundary; and (b) that the account that I have just given of what is meant by predicating a quality of a thing is not what is meant, but that it is essential to introduce the notion of a substance distinct from the qualities.

    (a) We do not deny that qualities have qualities and relations and that these can be predicated of them. Nor do we deny that the same form of words is used to denote the two sorts of predication; e.g. there is no difference of form between 'this table is red' and 'this colour is red.' But we shall do well to remember that a great many different meanings are covered by the same word -- 'is.' For example, by implicitly assuming that 'is' means 'is identical with,' Mr Bradley comes to the most startling conclusions about substantives and adjectives; but surely no one supposes that because the same form of words is used to express identity and inherence, therefore they must mean the same thing or else nothing at all. In fact, the argument that our account of the predication of qualities of substances does not cover the predication of qualities of qualities comes very ill from the supporters of substance, since they are in precisely the same position. For their theory of the first sort of predication is that it asserts the inherence of a quality in a substance, whilst their theory of substance being that it is that which can be a subject but not a predicate, it is clear that the inherence view cannot also apply to the predication of a quality of a quality.

    I do not think then that the fact that qualities can have predications made about them helps the substantial account of the states of things as against ours. What ours requires is merely a further discussion of the nature of the relations between the qualities and of the aggregate of which they are elements in those cases in which the aggregate is said to be a thing with the elements as its qualities.

    We said that a closed boundary is the essential characteristic of one thing at each moment. As long as there is a perceptible gap between a candle and a candle-stick no one would think of calling them one thing ; but, as soon as the candle is stuck into the candlestick it is felt to be reasonable for many purposes to call them one thing. Of course, as it is also known that they can be put apart, and quite frequently are so, it is also reasonable to call this one thing an aggregate of two things. But even this is mainly because the old spatial boundaries are still visible. People would say that whiskey in one glass is one thing and water in another glass is another, but, when they are mixed, they would be much more likely to call the whole one thing.

    Thus, if our theory be right, one of the main circumstances in constituting one thing of which qualities can be predicated is the possession by those qualities of the quality of extension and their standing in spatial relations. The qualities of one thing at a given moment are extended sense-qualities like colour, temperature, the objects of tactual sensation, etc., which together occupy an extension outside the boundary of which there are either no or very different perceptible qualities for a finite distance. Some of the qualities may occupy the whole extension and more than one can do this provided they be not synthetically incompatible. Others again may occupy only part of the extension as do the coloured flowers that form the pattern of a carpet. The great condition is that there should be as much continuity within the boundary as possible and as much discontinuity without it. It is to be noted that extension and shape occupy a different place in this notion of a thing from the other qualities like colours, etc. Primarily, extension and shape are qualities of the other qualities. But the bounding shape and the extension contained within it are predicated of the thing as its shape and extension. Thus, what is fundamental is the notion of certain sensible qualities having extension and shape. I do not think that this notion can be analysed further. Without some extended quality we have no definite shape or extension, and these qualities can only exist in some shape and extension. Whilst this appears to me to be all that common-sense means by one physical thing at a given moment, it is important to remember that in any particular case a great deal is involved beside direct perception. Direct perception may give us colours in a continuous visible boundary, and it may give us temperatures in a continuous tactual boundary; but we need more than direct perception to tell us that the coloured surface and the hot surface are one and the same thing. For, as we have already noted, it is partly a matter of inference, and partly a matter of definition, to identify a seen with a felt boundary, either as to position or to shape. And then the identification is not a 'finding identical' of the objects of two different sense-perceptions, but a correlation of them with a third unperceived common shape through their correlation with each other.

    (b) We can now turn to the other objection that at any rate what I have suggested as being what is meant by one thing and the states of that thing at a given moment is not what we do mean, but that it is necessary to introduce the notion of substance and inherence. As we are now talking about the predication of qualities of things it would seem that by 'substance' is to be understood that which can be a subject but not a predicate. Now let us consider a red thing. On our view, to say that it is red merely means that an instance of redness occupies the whole or part of certain bounded extension within which are a number of other extended qualities and without which for a finite distance there are not perceptible extended qualities of at all the same kind. It also allows us to say that the thing in question is a subject and not a predicate. For, as a matter of fact, the thing never does stand in the same sort of relation to other things in which the qualities that constitute it stand to each other. If it did they would cease to be other things.

    But I grant at once that not all propositions that assert qualities of physical things can be interpreted in the way I suggest. To say 'this thing is red and hot' is of the same form as to say 'this thing is triangular.' But if we make the former mean that redness and temperature exist within a certain boundary, we can hardly make the latter mean that triangularity exists within a certain boundary. Yet I do not see that we are forced to say that, since something must be triangular and since we cannot interpret the proposition in the same way as 'this thing is red,' therefore we are forced to appeal to substance. For if we ask what is triangular it is not a substance but the qualities. It is the red and the temperature that are triangular. There are, however, some important points to notice about this. In the first place the 'is' here does not mean the same as in 'this is red or hot' when we take the shape as fundamental. Another point to notice is that in the case of extended qualities the 'is' is in a certain sense reciprocal. 'This triangle is red' and 'this red is triangular' are equivalent to each other. And the further development of this brings us to another consideration. It is probably not the universals redness or temperature that are triangular, but 'this red' and 'this temperature.' Of course it is not a completely cogent argument in favour of this view to say that since, e.g., there are red circles and red triangles and since the same thing cannot be both circular and triangular at once, therefore it cannot be redness that has these spatial qualities. Some such complex statement as 'redness is triangular here' and 'redness is circular there,' would meet this objection. If these were analysable into 'redness is triangular' and' redness is here,' etc., the difficulty would no doubt recur, but there is no reason to assume this. But I do not see that we can possibly avoid introducing particulars somewhere and it is the insistence on particulars which seems to me to be what is true in the substance theory. I would analyse 'this red is triangular' and 'this triangle is red' into this is an instance of red and an instance of triangularity, and it seems to be an a priori certainty that any instance of any colour is an instance of some shape, and any instance of any shape must also be an instance of some other universal, such as colour or temperature. What is true in the substance theory then has no special reference to the unity of a thing with a number of qualities but refers to the relations of instances to their universals, a relation which would equally hold in a case of a particular which was an instance of only a single universal.

    There is one other point to be mentioned before leaving this subject. Objections have been brought against substance which, if valid, would be equally fatal to particulars. Have they any weight? The objection is that substance is meaningless, that nothing can be said about it. If this be true we could object that particulars are meaningless and nothing could be said about them. The objection is not well expressed. Strictly, a thing has meaning when acquaintance with or knowledge about it either enables one to infer or causes one by association to think of something else. I see no reason why everything should have meaning in this sense. What I suppose to be intended is that the word substance has no meaning because no propositions can be known about substance in abstraction, and, therefore, the hearing or seeing of the word does not cause one to think about anything definite. To see whether there is anything in this objection we must consider for a moment what is meant by 'vicious abstractions' which (like most vicious characters) have furnished an inexhaustible theme of conversation especially in Hegelian circles.

    The attacks of Berkeley and Hume on abstraction rested on mere mistakes, on the confusion of ideas with images. You cannot have an abstract image, and since ideas were confounded with images, it was thought that you could not have an abstract idea (by which they meant the idea of an abstraction, for of course all ideas as such are concrete particulars). There is then no general objection to abstraction. But there is a common mistake that can be made over abstraction and that is to assume that whenever two things can be conceived separately they can exist separately. And even this must not be rejected without further analysis as a sheer mistake, for it has three forms. The most serious form is to abstract an universal and then expect it to be able to exist like a particular. I should suppose that it was a very rare error. A less culpable form is the following. There seem to be universals so related that an instance of one is always also an instance of the other, and this connexion can be judged a priori. For example, to say that there might exist a triangle which had nothing but geometrical qualities would not be to expect triangularity to exist like a particular, for we are talking of particular triangles and making no confusion. Where we err is in forgetting what seems to be an a priori law that nothing can be an instance merely of triangularity. Finally there are universals that are found in practice always to have gone together, thus giving rise to empirical laws of coexistence. Such are ruminance and cloven-footedness. In these cases it would not be termed a vicious abstraction to assert the possibility of the existence of instances of one that are not also instances of the others. Here 'possible' has the fairly definite meaning of contradicting no a priori law.

    Now substances and particulars are certainly not vicious abstractions in the sense that anyone supposes that they could exist apart from their qualities and relations. As a matter of fact I think people have been unduly timid in this direction, for I see no obvious objection to the existence of terms that stand in relations but have no qualities except those of standing in the relations in which they do stand. This does not mean that they have no nature; they are what they are and they differ immediately from other terms. I have already suggested that we approach (though we certainly do not reach) such terms in tastes and smells. But where people find an objection seems to me in the following place. Where we make an abstraction and it is justifiable, although it may be that the abstracted terms cannot exist apart and are not supposed to be able to do so, yet in order to make the abstraction it is essential that each element abstracted should have a definite nature and that something can be said about it in separation from the other elements. Thus, no one supposes that triangles can exist without colour or something equivalent; yet quantities of propositions can be asserted about triangles owing to the definite nature of triangularity without any reference to the other element which must be present in any existent triangle. But this condition, it will be said, is not fulfilled in the case of substance in abstraction or particulars in abstraction; for, by abstracting their qualities and relations, you have removed all that could be said of them. And it is useless to reply that there is no need to consider them in abstraction because they exist and are given only with their qualities and relations. For this very statement assumes that what exists and is given is a complex in which qualities and relations and that which has qualities and stands in relations can be separated in thought. When I say: 'This is red and triangular,' I do not mean that redness is red or triangular or that triangularity is red or triangular and I must therefore be talking about some third thing different from both redness and triangularity.

    But does all this really involve any objection to particulars? When we say that we take a particular in abstraction all that we mean is that we leave out of account all the true propositions such as 'X is red,' or 'X is triangular,' or 'X is more virtuous than Y,' and confine ourselves to the single proposition 'X is a particular.' All the other propositions which are true of X at all remain so whether we choose to consider them or not. So it is false to say that nothing can be said about X; and what must be meant when people say that nothing can be said about X in abstraction is that when you confine yourself to saying that 'X is a particular' you convey no information at all. And this seems to me to be false. Particularity is as good an universal as redness or triangularity; and it is as possible to recognise it. Probably people make a confusion of the following kind. In the first place many universals imply the presence of other universals in any instance of them either in accordance with a priori or empirical laws. Thus if X be triangular we know that it must also be an instance of some other universal like colour and also that if it be a Euclidian triangle the sum of its angles will equal pi. Now the statement that X is a particular does not have many interesting implications like this; at best it leads to some not very certain propositions about its relations to space and time, as, e.g., that it cannot be at two places at once. But it cannot be an objection to the reality of an universal that it is not connected by a priori laws with many other universals, though this fact may make it difficult to recognise and impossible to describe. Secondly, many universals are analysable and can be defined, and people have a tendency to think that there is something disreputable about anything that cannot be analysed and defined; forgetting that if you are to be able to grasp anything at all you must be able to grasp something without further analysis. Now particularity cannot be analysed. The result of these two facts is that it can neither be defined nor described, but must be either directly recognised or missed altogether; though I can hardly suppose that anybody has really missed it, yet the fact that they cannot describe or define it, accompanied by false logical theories which overrate these two processes, has led many to deny that there is such an universal at all.

    We can therefore turn to --

    (ii) Here we have to discuss the theory that the unity of a thing through time depends on the sensible continuity of the boundary and the qualities within it throughout their changes. It is sometimes said that every change demands something permanent and that this permanent is substance. If the thing at one moment was nothing but sense-qualities in a boundary, how can you say that it changes continuously or discontinuously, it will be asked? A good deal of unnecessary difficulty has been found in change owing to the fact that the proposition 'X changes' has been taken too rigidly. ' changes' seems to present the following difficulty: Whatever else it may mean it implies that X had some2 'quality x1 at a certain time and that it has now ceased to have it, and either replaced it by another quality x2 or not at all. Now it is said: Either a thing at any moment is identically the same as its qualities in relations of a certain kind, or we mean by X a permanent substratum. But, if we mean the former, then it is clear that the X of which x1 was a quality is not the same X which has the quality x2 and not the quality x1 so that if, in the proposition 'X has changed,' you refer either to the X that had x1 or the X that has x2 your statement is false. The X that was x1 has not changed; it has absolutely ceased to exist. And the X that is x2 has clearly not changed, for here it is at the moment of predication. Hence people suppose that they are forced by the fact of change to say that the X that they mean is something different from the qualities in their relations as they are at any moment, that it is, in fact, the common substratum of these successive sets of qualities in relation.

    But there is a very short way with this view as a solution of the difficulties. For, if 'X has changed' refers to the substance common to the two successive states, it is clearly false, since ex hypothesi the substance is the same in both cases. To this the answer will be that the full statement of the substantial view of change is as follows: 'X has changed' means that there is one substance underlying two successive states, but that these states differ. This, however, does not really help us. For the only way to recognise identity of substance is by identity of qualities; hence, since the qualities at two different moments are, ex hypothesi different in part at any rate, what right have you to assert that the substance is the same?

    Accordingly some people thought that they could have change neither with substance nor without it, and so they rejected it altogether. It is clear that the whole question turns on how much sameness is needed to allow us to say that two things perceived at different times and in part different from each other, the same. If people had reflected they would have seen with Hume that nothing like complete identity of qualities is needed to make two things observed at different times to be regarded as the same thing. All that is necessary is that the successive objects of observation should be continuous with each other. By this we mean that, the shorter the interval between the successive observations, the more nearly will the objects perceived at the two moments be found to resemble each other in position, configuration and sensible qualities. When no difference can be found in two successive observations we say that what is observed has not changed in the interval. When we have perceived successive differences and yet continuity in the sense which I have mentioned we say: Such and such a thing has changed. By this we do not mean that any sort of substance has remained permanent all through, but we mean that we have either observed or have reason to believe that we could have observed that the whole process was continuous in the sense mentioned above from that stage which we now observe to that one which we observed some time ago and called 'This X.' Thus our theory is perfectly competent to account for the statement that a thing changes and yet is permanent; whilst the substance theory adds nothing useful to our own.

    We can now return to the subject of the relation of causal laws to things, since we now know what is meant by things and their states. We find from our discussion of the meaning of one thing a considerable support for our rejection of the view that causation means that one thing forces another to act in a way in which its own nature would not let it act if it were left to itself. For we now see that what constitutes one thing in the physical world is nothing of a deep or recondite character, and that its nature is just its qualities from moment to moment in the relations in which they constitute a thing. These successive qualities in relation still remain precisely what is meant by the nature of the thing even though they would be different if it had different relations to other things. We saw that, so far from causation involving two separate natures and the forcing of one by another, it was ultimately only after the introduction of causality and by means of it that we could theoretically define what a thing does of its own nature, and that even then this definition is doomed to remain purely theoretical. In spite of this, since the notion of thing is of great importance, it is in general true to say that it is necessary to state causal laws not merely as holding between successive qualities, but rather between the successive qualities of definite sorts of things, that phrase being defined in the sense that we have given. For in general it will not be irrelevant to the truth of a causal law whether the various states mentioned in it occur in the same or in different complexes.

    We can now express what is meant by the distinction between immanent and transeunt causality and can see that there is no difference in principle between the two that would justify the immense distinction that Leibniz and Lotze make. Immanence is in the first instance always relative to a definite system, and a definite set of events. A causal law is immanent to a given system S when all the data that are required by it are to be found within S at various times and all the states that can be inferred are states of parts of S. But S may be a system with many different parts. Then relatively to the same causal law that law will be transeunt with respect to any part of S that we like to choose, because to infer its states we shall have to consider the states of other parts of S.

    Thus an isolated system of particles in Mechanics is a system all of whose configurations are determined by causal laws immanent to the system, but the position of any particular particle in it is determined by laws which are transeunt with respect to it. This is the true distinction between transeunce and immanence. But the notion of one thing enters in the following way. The isolated system under immanent causality may also under our definition be one thing and then we come to the more common-sense of immanence as Lotze and Leibniz use the term. On the other hand the system in which immanent laws of causation hold may very well be a selection of separate things in our sense, as indeed is the case with the isolated mechanical system of particles. In such a case Leibniz and Lotze would have overlooked the immanence in the whole system, just because the system was not one thing, and fastened on the transeunce within it with respect to its various elements. But our discussion as to what is the criterion of one thing will enable us to see that both sides are equally valid and that there is no possible ground in the nature of thing to make causality immanent with respect to it intelligible and causality transeunt with respect to it a mystery or a contradiction. Our main conclusion then in this section is that anyone who can accept immanent causality has no right to strain at transeunt causality; and when it is remembered that it is the straining at transeunt causality that is one ground of Leibniz's monadism and the sole ground of Lotze's belief in M, this result will be seen to be of some importance.

    I now pass to a second question about Causation, viz.: --

    Causal Laws and Time. On this relation of causation to time many of the arguments against causal laws have been based. It was asserted by Hume that cause must be prior to effect and contiguous to it in time. The latter phrase however implies that there are contiguous moments in time and this contradicts the general belief that the time series is continuous. Thus if there were reason to suppose that in any causal law cause and effect must be contiguous there would be some grounds for denying that there can be any causal laws. Hume, however, offers no argument for his position. He just says quite bleakly, that 'nothing can operate in a time or place which is ever so little removed from those of its existence3.' For a person who was so convinced of the value of Newton's law of gravitation as to wish to introduce something like it into the mental world the statement with regard to space seems an odd one, and, as that with regard to time has no evidence for it and is incompatible with that continuity of time in which most people believe, we need not consider that we have here an antinomy. We need not reject causation, but only Hume's doctrine that cause and effect must be contiguous.

    This leaves us with the alternatives that they are continuous with each other, that they are contemporary, or that they are separated by finite intervals. At this point Bradley appears on the scene with an argument against causation which attempts to prove that cause and effect both must and cannot be continuous with each other. The arguments are (i) Cause and effect must be continuous with each other, for otherwise there will be a blank time between them during which the cause does not operate. And, if it does not operate for a finite time however short, why should it ever do so? (ii) Cause cannot be continuous with effect, for, if so, then if we take an infinitely thin section across the stream of events it will contain the cause of all that follows; and yet, since it will occupy no time at all, it will not be an existent4.

    (i) The thesis must either be supposed to assume the activity view of causation, which we have rejected, or it will need to be greatly modified. As it stands it assumes that the cause forces the event to happen as soon as it is strong enough to do so. If then it was not strong enough to do so at the beginning of the interval and nothing happened to it in the interim it is impossible on the activity theory, to understand how it came to be more successful at the end of the interval. If, on the other hand, it became strong enough at the end of the interval then the last cause is the state at the end and not at the beginning and so the cause once more is continuous with the effect. After our rejection of the activity view of causation such arguments will leave us very cold. It is of interest to note that Sigwart has an almost identical argument which is so honestly and clearly put that its futility becomes obvious to the most casual reader. He says; 'If effect consists in a change, and if we can speak of causation only in so far as a change occurs, if therefore nothing is effected until the change occurs, then the action of the cause and the resulting effect must necessarily be simultaneous5' This is word for word what we have made out of Bradley's argument for the thesis. It comes simply to this, that a thing is not a cause unless it produces an effect and therefore you have no right to call it a cause until it has produced its effect. It is clear that such an argument is merely verbal, and it is not worth while to consider it any further.

    Since the thesis, when stated on the activity view, becomes a mere play upon words we will see if any better fate awaits it when stated in terms of a descriptionist theory of causation such as we are trying to defend. Stated in terms of the latter view, Bradley's argument would be: No state that persists for a finite time can be a datum in a causal law from which the state which begins when that time is over can be inferred. The first thing to be said of this proposition is that if it happened to be true, it would be a very miraculous thing that people should ever have thought that they had discovered and verified causal laws. For it is tolerably certain that no one has ever been acquainted with a state that lasted for no time at all. At best he can only have taken a kind of average over a short duration. The second point is that the proposition gets such plausibility as it has by being confounded with the other proposition that nothing that has been completely quiescent for a finite time can have its subsequent changes accounted for by purely immanent causation. But that does not at all mean that a persistent state in a system may not be one of the data in a law of transeunt causation connecting this state and those of other systems with future states of the at present quiescent system. If a billiard ball be at rest there is no purely immanent law of causation connecting its quiescent states with any future movements that it may have. But its mass and position, though they have persisted for a finite time unchanged are all-important elements in a transeunt causal law connecting its future positions with those of another billiard ball that I have just hit in its direction.

    I think the above discussion will enable us to see exactly what is to be accepted in the doctrine that cause and effect are continuous, and subject to what assumptions it is to be accepted. (i) It is assumed by common-sense that no system that has been completely quiescent for a finite time can have its future changes, if any, predicted by purely immanent causal laws. This I think must be taken to be a belief about causation which most people would consider self-evident. (ii) It is quite admitted that the change in B which is one of the data from which the states of A subsequent to its quiescence can be inferred by a transeunt causal law need not happen at the moment at which A starts once more to change. (Indeed, if time be continuous there is not a moment at which A starts to change. A is alpha for all moments after t and before t' and beta at t' and moments after it; so that there is either no last moment at which it is alpha or no first moment at which it is beta.) But if there be a finite gap between the occurrence of the event in B and of the new one that can be inferred in A, then taking the systems A and B together they will be a system within which this particular causal law is immanent. Hence the whole system A + B will have been quiescent for a finite time and we shall have to seek a third system C for a law transeunt with respect to A + B which shall account for its emergence from quiescence. To put it in symbols the maxim (i) holds that if a system A in which there has been no change for a finite time tau takes on the new quality beta at the end of that time then we must go outside of A to another system B and a state b in it to account for the occurrence of beta. But if b occurs some time within the interval tau and B remains quiescent for a finite term in the state b then, if we take A and B together as one system, that whole system will be quiescent with the states b and alpha for a finite time. If the original maxim be true this demands an appeal to a third system C to account for the emergence of A + B from this quiescent state. Hence the maxim (i) compels you to press forward until you have reached a system which includes A in which something is happening through the whole of the interval tau which in A alone is blank and part of which in A+ B is blank and so on. Thus if we accept the maxim that the future changes of any quiescent system that follow its quiescence can only be explained by transeunt causal laws, we have to say that the complete account of any case of causation compels us to proceed until we reach a continuous causal series immanent in a larger system which includes A. I must confess that the maxim does seem to me self-evident. I cannot believe in an immanent causal law of the form: When the system A has been in the state alpha for 2½ minutes we can infer that it will become beta independently of anything that happens in the rest of the universe. I therefore have to accept the conclusion of Bradley's thesis, though not his argument for it, and to suppose that in the end all causation is continuous. Let us pass then to

    (ii) This attempts to prove that causation cannot be continuous. This is much wider in scope than the thesis; and here again Bradley's argument seems to rest entirely on the activity view of causation for its plausibility. Each infinitely thin section is to cause the next and yet, being infinitely thin it will occupy no time and so not exist. In the first place we must not put the argument as I have just done in the form that each section causes the next, for that would be to revert to the theory of contiguity which we have rejected. We are assuming continuity of time and so there will be no next. But I suppose that the real point of the argument is that all your data will be states without duration and that this is a vicious abstraction. We must distinguish two different sorts of objection to states without duration: (a) Metaphysical objections, and (b) Epistemological ones.

    I have already hinted at the epistemological objection in discussing the thesis. How could you discover causal laws, if their data are states without duration, since you certainly cannot directly experience such states? But here we have the metaphysical objection: How could such abstractions be the causes of anything? (a) It seems to me that the metaphysical difficulty which is the only one on which Bradley touches is not really a serious one. It is only when you take the view that the cause must be an active substance with all the solidity of chairs and tables that there is any difficulty in the fact that events without duration claim to be causes. When you merely mean that if you know enough events at enough moments you can infer some events at all moments the relation all through is a semi-logical one between these thin events which are at a moment but do not endure for a time, and there is nothing very startling about it provided you can persuade yourself that there can be states without duration and that you can know them. But certain metaphysical questions about change are raised. This question is evidently a general one connected with change and not with causality in particular. We may best approach it from the point at which we left change when we discussed what was meant by one thing and by its altering and yet remaining the same thing. For our explanation of the changes of things which are complexes of qualities in relation assumed the changes of qualities and relations, and questions may arise over the latter as well as the former. A piece of iron, let us suppose, was black; it is heated and it becomes red. This we explained to mean that a certain complex of qualities altered in a certain well-defined sense. But we did not discuss what was meant by the black changing to red and all the time remaining a colour. Change of qualities and relations may be of two kinds. Either a quality is a member of a complex for a time and then ceases altogether to exist in it, or else we have continuous change of a quality. As examples of the two sorts of change of quality we may take (alpha) an overcooled liquid suddenly crystallising, and (beta) a body steadily rising in temperature. (alpha) With the overcooled liquid the quality of fluidity has been present for a finite time. A crystal is introduced and suddenly it solidifies. The quality of fluidity has thus ceased to be a quality combined with the other members of the complex and has been replaced by that of solidity. To avoid complications we will confine ourselves to the change of tactual qualities that has thus suddenly taken place. The two successive tactual qualities are synthetically incompatible; they cannot be attached at the same time to the whole of the same bounded extension. The extended fluid quality has ceased to occupy the given boundary and it has not appeared anywhere else. This kind of change then involves that a quality may exist for a finite time in a given boundary and then cease to exist there altogether. And another quality that did not exist there before may begin to do so at a moment such that at all moments before it and after an earlier one the other quality was there. I do not think that any analysis can be made of what is meant by existence with a certain boundary during a certain time. The only question then is whether there is any difficulty in saying that a certain quality exists for a certain time at a certain place and that at other times it does not exist there. It will be said: if you really mean the same quality how can it have different relations at different times? How can it both exist here and not exist here? This difficulty is I think met by Mr Russell's6 position that there can be no objection to a quality having a relation to certain moments of time and points of space which it does not have to other moments of time and points of space, just as there is no objection to the Senate House being to the left of King's and to the right of Trinity when viewed from the river. It is proper to note that it is not necessary to drag in absolute time with moments in order to recognise this as the correct solution of the problem. The temporal relations of events have magnitude. Hence we can say that there is no objection to fluidity having that complex relation to existence and the Norman Conquest and a certain boundary which is called 'existing here from a time tau after the Conquest to a time tau' after it' and not having the relation to the same terms called 'existing here from a time tau' after the Conquest to a time tau'' after it.' For there can be no reason why the same set of terms should not have some relations of a kind and not others of that kind. Thus the principle of Mr Russell's solution remains the same whether we have an absolute time series as he supposes or only relative time. On the former assumption change means that a quality has the same relation to existence and various moments of time and does not have it to other moments of time. On the latter the same entities have some but not all of the relations of a certain kind to each other.

    (beta) We can now, therefore, leave the question of sudden changes from a quality that has persisted for a finite time, and come to continuous change which leads to Bradley's difficulty. We are going to take as our example a body steadily rising in temperature. This involves that at no moment is the degree of temperature the same as at any other moment however near. Now only definite degrees of temperature exist. But if the change be continuous no definite degree persists for any time at all. If it exists it only does so at a moment and not through a duration. And so far as I can see the plausibility that is left in Bradley's antithesis after we have rejected the activity view of causation rests on the belief that if none of the successive degrees persist none can be said to exist. But if none of the particular degrees existed then clearly there was no temperature in existence throughout the whole of the interval during which it was said to be changing continuously. The argument then rests on the assumption that anything that exists in time must persist for a finite time. Can this axiom be maintained?

    The result of holding it would be that we should have to believe that all changes are of the kind discussed in (alpha), i.e. that each state lasts for a finite duration and is then succeeded by another. When the duration of each is less than a certain amount the change has for perception that peculiar character which we call perceptual continuity. If space be continuous this will mean that a moving body cannot pass through all the points on a straight line. For motion would involve that a body was at A for all moments not before t and before t + tau say, at B for all moments not before t + tau and before t + 2tau, etc. If then it were at all the points of a straight line and the line were continuous it would take an infinite time to cover any distance however short. But it is perfectly possible to assume either that physical straight lines are not continuous but consist of large numbers of contiguous points very close together. Or we can assume that the lines are continuous but that a moving body only visits a selection of their points. Similarly we can deal with temperature or any other physical magnitude that seems continuous. They may be only a large but finite number of different degrees of temperature, or else any given body rising in temperature may only touch a finite selection of the infinite number of possible intermediate temperatures each of which perhaps actually exists in some body at some time.

    Would this give as much continuity as the acceptance of the axiom about immanent causality which we discussed in the thesis seems to necessitate? That axiom forced us to hold that the total state of the universe could not be the same for any finite time. Now the present axiom would hold that every state of everything in the universe persists unchanged for a finite time. For these to be compatible it would be necessary that every moment should be the last of some state in the universe though all states endure for a finite time. Now there is no objection to this being the case if there be enough states in the universe. If the time series be compact and there be 2Aleph° states then each state can endure for a finite time and yet the universe never is in the same total state for a finite time however short. Hence the supposition that the states of every particular thing in the universe change discontinuously is not incompatible with the result deduced from our earlier axiom about causation if only there be enough states in the universe.

    It would follow, however, from our original axiom that no immanent causal laws for the causation of continuous changes of position or degree of quality would be possible. Thus, if motion be really discontinuous, so that a body moving with a fixed velocity really stays for a short but finite time at the consecutive points of a discontinuous space and then without any lapse of time is at the next point and so on, the first law of motion which is apparently immanent must really be pseudo-immanent and the result of a more fundamental law of transeunt causation. For taken as an immanent law it would be of the form: After the material point X has been at a point of space Pn for a short but finite time t it will be at the consecutive point Pn+1. This form of law our axiom rejected as pseudo-immanent. Hence the assumption that motion is discontinuous is incompatible with the belief that the first law of motion is an immanent law and as such applies to an isolated system. There are not of course the same objections to the assumption that the change of physical qualities, like temperature, are really discontinuous, because their changes are not supposed to be subject to immanent causal laws.

    There is, so far as I am aware, only one way of dealing with a very fundamental proposition such as: 'Whatever exists in time must persist for a finite time,' which is neither obviously true nor obviously false; and that is the rather tedious one which we have pursued of seeing what would follow if it were true and then trying to judge whether these results make that which implies them probable or improbable. Our investigation has shown (1) that the argument has no particular relevance to causality when we drop the activity view of causation, but is an argument that really deals with the continuity of change. (2) But an axiom which seemed self- evident about causation did imply that at any rate the states of the universe as a whole must change continuously. We saw, however, that if the universe only has enough states this is compatible with the view that the states of all that is in it last for a finite time. Hence there is no antinomy whether we assume continuity or discontinuity in the changes of particular things. (3) As the proposition does not appear to me to be in the least self-evident, and as it is incompatible with the view that the first law of motion is the truly immanent law of an isolated system I see no reason to accept it. But we have seen that there is no antinomy over causal laws whether we accept or reject it.

    We can therefore turn to --

    (b) This it will be remembered is the alleged epistemological difficulty raised on p. 111 against the statement of causal laws in terms of momentary states. The difficulty was that the laws of causation are supposed to be about the existent and to be found by observing the existent and yet there is not only the doubt whether momentary states exist, but the certainty that they cannot as such be observed. But surely, even if we accept the view that the laws of causation are stated in terms of momentary states and that these cannot be observed and do not exist, we have no reason for concluding that causal laws may not be true of the existent and be deduced from observations upon it. Granted that no one perceives momentary states it must also be remembered that no one perceives causal laws, any more than he perceives states that do not endure for a finite time. Both causal laws and the momentary states into which perceptually continuous change of quality is analysed are discovered by reflecting upon and reasoning about what we do perceive. It then becomes quite irrelevant to the validity of causal laws whether the states in terms of which they are formulated really exist, so long as it is always possible to retrace one's steps from these durationless states to what we actually do perceive which, for that reason, exists and endures. Now this, I take it, we always can do. We know how we have reached the momentary states from the enduring ones that we perceive and hence we know how to get back from the former to the latter. The argument would run somewhat as follows. We can get a conceptual account of what is meant by continuity or compactness by considering the series of real numbers or the series of rationals respectively. And here we are on safe ground because we are acquainted with the elements and can define them. Now there is no ground for thinking that time is more continuous than the series of real numbers, in fact there is no reason for attributing to it anything more than compactness which the series of rationals possesses. We cannot become directly acquainted with moments of time, but if we suppose that finite durations consist of terms without duration and that the relation of before and after among them has the same logical qualities as that which generates the compact series of the rational numbers we know that we cannot have erred on the side of attributing too little continuity to time. Hence we can define moments as terms having the same kind of relation to finite times as rational numbers have to certain classes of them. Suppose then that we do attribute this kind of continuity to the time-series. What then are we to say of states that remain unchanged for a finite time? Clearly they can be analysed into the same state at each of the infinite number of moments within the finite stretch. Hence we get to the notion of momentary states. Now the important point to notice is that no logical exception can be taken to any of these steps if rightly understood. Time is held to be continuous in the same general kind of way as the rationals, hence it cannot be wrong to get clear ideas about the continuity of time by analogies with the rationals where we actually know what the elements are. The assumption that time consists of moments arranged by the same kind of relation as the rational numbers will certainly account for all the continuity that is perceived. This being granted, no exception can be taken to the analysis of existence through a finite time into that of existence at each moment within the stretch. It is never necessary in the case of causal laws to think of this analysis as being any more than a form of statement which can always be translated back into the only form in which we do perceive states, viz., as lasting for a finite time.

    Clearly most if not all causal laws are discovered from our perceptions. In the case of states that last for a finite time the momentary state is precisely the same as that which persists and can be observed, and so no difficulty ought to be felt. In the case of continuously varying states what we mean by the momentary state is that which would have persisted if the process could have been stopped at the moment at which the state is said to exist. In practice we try to take permanent records and thus shift the impossible problem of directly determining a momentary state into the soluble one of determining a momentary state when precisely similar ones exist at all the moments of a finite duration.

    The upshot of the whole discussion is that, although we admit that causal laws apply to the existent, and though they are certainly stated in terms of momentary states which cannot be directly observed, it is quite unimportant for our theory of causation whether momentary states really exist or not. Momentary states are the product of a theory of time which (a) will account for the facts, and (b) is internally consistent. The theory connects its momentary states with the enduring ones that can be observed in a perfectly definite and unambiguous way. Hence it is perfectly possible to interpret laws connecting momentary states in terms of states that can be observed and vice versa. And so, whether momentary states exist or not, it is perfectly possible (a) from observations on the changes that can be perceived to pass to laws stated in terms of momentary events; and (b) to pass back from these laws to foretell what states will actually exist in the world.

    We can pass then to another question as to the relation of causal laws to time, viz., Is Causation always successive? It has been held by many philosophers that the cause must always precede the effect in time. Hume attempts a proof of this, and Lotze has a similar argument. Hume's argument runs as follows: ' 'Tis an established maxim both in natural and moral philosophy that an object that exists for any time in its full perfection without producing another is not its sole cause; but is assisted by some other principle which pushes it from its state of inactivity . . . . Now, if any cause may be perfectly co-temporary with its effect, 'tis certain according to this maxim that they must all of them be so; since any one that retards its operation but for a single moment exerts not itself at that very individual time at which it might have operated, and therefore is no proper cause. The consequence of this would be . . . the destruction of that succession of causes which we observe in the world, and indeed the utter annihilation of time. For, if one cause were co-temporary with its effect, and this effect with its effect and so on, 'tis plain that there would be no such thing as succession7.'

    We have seen in what sense the 'established maxim' is to be accepted. We must now see precisely how Hume's argument depends upon it, and whether it would be valid with the form of the maxim that we have accepted. The essential point is the attempted proof that, if any cause be contemporary with its effect, all must be so. This is supposed to follow from applying the maxim to a given cause supposed to be contemporary with its effect. We must remember that Hume believes that there are contiguous moments in time. Hence the alternative for him is between a cause producing its effect at the next moment, or at one separated from it by several moments, or at the same moment. The maxim as stated by him cuts out the middle alternative. He evidently does not think that it cuts out the first alternative, because that is as a matter of fact his own view. He wishes to prove that, if any cause produces its effect at the same moment as itself the maxim will show that all causes must do so. Now he only does this by assuming that there is no alternative between a cause producing its effect at the same moment as itself or at several moments later. This of course is true if time be continuous, but is inconsistent with his own position, since he accepts the view that the cause 'does not retard its operation for a single moment,' which means that it produces its effect at the next moment. But whether we accept next moments in time or not it is obvious that his argument is formally vicious. It is perfectly obvious that the two premises 'Some causes produce their effects at the same moment as themselves' and 'No cause produces its effect at a moment later than the next' cannot possibly lead to any conclusion about all causes. Yet Hume makes them lead to the conclusion that all causes produce their effects at the same moment as themselves. Hence his argument is invalid whether we accept his premises or not.

    It is interesting to compare Lotze's argument with Hume's. Lotze8 is trying to produce an antinomy, about Becoming, and he does this by way of simultaneous causation. He argues as follows. If causes be simultaneous with their effects their relation reduces to logical connexion. This is similar to Hume's position. But as the antithesis of his antinomy he takes the argument: If causes be not simultaneous with their effects then a cause would be able to exist for a finite time without producing its effect. On contraposing this antithesis we see that, for the same maxim, Lotze deduces that all causes must be simultaneous with their effects, whilst Hume concludes that, if any cause be simultaneous with its effect all must be so. We can now see the reason for the difference. Hume's argument is sheerly wrong and Lotze is right on his own premises. Lotze's premises are that two events must either be separated by a finite time or be contemporary and Hume's maxim. These two do lead to the conclusion that all causes must be simultaneous with their effects.

    But it is easy for us, after our previous discussions, to see that any argument for or against simultaneous causation based on the maxim cannot be accepted as it stands. It is perfectly clear that both Hume and Lotze assume in their arguments the activity view of causation that we have rejected. The former seems hardly justified in doing this in view of his final conclusions. But the form in which we have accepted the maxim leads to no conclusion whatever about successive or simultaneous causal laws. The phrases 'the cause' and 'its effect' lose most of their meaning when we turn all causality into causal laws by which inferences can be made from a certain number of data to others at different times. The maxim as accepted by us merely assured us that a causal law of the form: 'X remains in the state alpha for the time tau unchanged and then passes into the state beta' is not an ultimate law immanent to the system X but will always be found to depend on laws transeunt to X. But this does not tell us that the data in causal laws whether immanent or transeunt must be contemporary with that which is to be inferred. In fact it is quite clear that as a rule they are not. The only question then for us is whether causal laws ever connect states that happen at the same moment.

    Lotze and Hume both seem to think that this is impossible; but they both hold, though on different grounds, that all causes would be contemporary with their effects and discuss the question on that basis. Since we have no need to accept this view, and indeed no possibility of doing so we cannot accept the reductio ad absurdum of these philosophers that there would then be no process in the world. On the other hand the thesis of Lotze's antinomy would apply to all cases of simultaneous causation if it were valid, even though not all cases of causation were simultaneous. We must therefore consider it. Lotze's argument is that simultaneous causation would be nothing but logical connexion. When we say that there is simultaneous causality we recognise that there is also a process in time, and if the causality be really simultaneous there could not, Lotze thinks, be a process in time. If this argument be true it will be fatal to any case of simultaneous causality that offers itself. It is most certainly true that when we commonly hold that there is simultaneous causation we also hold that there is a process, just as much as where we believe the causation to be successive. Thus it would commonly be said that the heat of a fire is the cause of water's boiling, and that once the water has started to boil it is the heat of the fire that causes by simultaneous causality the continued boiling. And the fire's burning and the water's boiling are both continuous processes that occupy a finite time. Now is it true that if the causation were really contemporaneous with the corresponding evaporation of the water there would be no process? On our view of causation to say that there is simultaneous causality would be to say that there is a law connecting each momentary state of the fire with the state of the water at the same moment. If then the change in the fire and in the water that goes on through a finite time be nothing but the succession of their momentary states there can be no objection to the statement that there is at once simultaneous causality and a continuous process in the fire and the water. Hence the burden of the argument rests on the old question: 'Can the process in the fire and the water be resolved into the fact that they have different states at each moment of time, states that do not themselves occupy any duration?' This question we have already discussed in reference to Bradley's argument about the continuity of causation, and we saw no reason to answer it in the negative when once we understood its meaning.

    But Lotze has an argument of his own on the subject which we must just notice. Lotze attempts the same solution as we have offered and then says that it will not do. His argument is as follows: 'If we assume, as was assumed, that C (i.e. the cause in Lotze's notation and the fire with its successive states in our example) traverses the series c1, c2. . . then, as the order of the series is supposed to be fixed, each term must be the condition of the succeeding one, and, as in the previous case (i.e. the problem of which this account is offered as a solution) two adjacent terms can neither have any blank interval of time between them nor can they be simultaneous9.' Thus the argument against the attempted solution is that the same difficulty breaks out inside the successive series of states which are supposed to be causes in the simultaneous causation. The argument assumes that in any continuous change each state causes the next one. But, as we saw, if the change be continuous there can be no next states. Further we saw that there is no need to suppose that if the continuous change were subject to immanent causation that causation must be simultaneous. No doubt, if it were simultaneous there would be no process; or to put it in another way the successive states of a system could not be accounted for by immanent simultaneous causality. But, since we saw no reason to suppose that the amount of continuity that causation demands precludes causal laws connecting states that are separated by finite intervals of time, we are not faced by Lotze's dilemma. I conclude then that, if our earlier discussions about the continuity of causation be accepted, there is no need for us to deny that there may be laws of simultaneous causality and that they may be perfectly compatible with a continuous change of state in what is called the 'cause' in common language.

    It being granted that there is no objection to simultaneous causality two questions remain about it: (i) Suppose that there is such causality how do we distinguish cause and effect in it? and (ii) Is there much reason to suppose that there is such causality?

    (i) With regard to the first question it is obvious that people do claim to distinguish cause and effect even when they believe themselves to be dealing with cases of simultaneous causality. Thus no one would say that the evaporation of the water caused the heat of the fire. With the theory that causation reduces to causal laws we must remember that the use of the term 'a cause' differs very much from that which is implied by the activity view and is therefore the usage of everyday life. Here we just have laws that unite the existence of states in certain aggregates and relations with that of other states at the same or different times in the same or different aggregates. Which of the states then are to be called the causes and which the effects?

    The distinction I think depends on the fact that many causal laws are not convertible. We may know that if x and y occur at t1 and t2 in A and B respectively then z will occur in C at t3 whatever moments t1, t2, t3 may be, so long as t2-t1 and t3- t2 are fixed. On the other hand the occurrence of z in C at t3 will not in general enable us to infer x and y in A and B at t1 and t2 respectively. When there is this lack of reciprocity we can call x and y in A and B the cause of z in C. But all this is really very unimportant and there are plenty of cases where it cannot be employed, as will be seen when we come to discuss the actual nature of causal laws. So far as it holds at all it applies equally to simultaneous causality, which only differs from the more general example given by its relation to time. Thus we do say that the fire boils the water because given the fire in the proper relation to the water we can infer the boiling of the kettle, but given boiling water we can only argue to a fire as one among a number of other possibilities. On the other hand when the causal law becomes strictly reciprocal I doubt if it be possible any longer to give a reasonable meaning to the distinction between cause and effect.

    Perhaps one that agrees more closely with common usage for the case of simultaneous causality than the one that I have offered would be the following. Suppose that a system, like the water, has been quiescent for some finite time and it then begins to change. Then we know that the law of causation for these changes must be transeunt to the quiescent system. If the causality be simultaneous but leads us to states in another system which was changing with respect to these states while the first system was still quiescent we shall generally call the changes in the latter system the cause of those in the former. Thus the water was at a certain temperature for some time. It changed and the law of this change leads to another system, viz. the fire, states in which produce the changes in the water by simultaneous causality. But the process in the fire was going on while the water was still in its quiescent state. Hence we say that the fire causes the changes in the water and not vice versa.

    (ii) The second question is whether there is any strong reason for believing that simultaneous causality takes place. It is clear that, if there be any causality at all, some of it must be non- simultaneous, and therefore it would be an aesthetic advantage if the apparent cases of simultaneous causality could be reduced to those of successive causality. I do not think that it would be possible to offer any proof of the existence of simultaneous causality, because all the supposed cases might really be examples of non-simultaneous causality in which the interval between cause and effect was so short as not to be perceptible. We do not, I think, use the term causality unless there be a change going forward. Thus when we say that all ruminants are cloven-hoofed we do not generally mean to assert that one characteristic causes the other by simultaneous causality. Nevertheless, if we accept simultaneous causality at all there is no difference in principle between the connexion of cloven-footedness with chewing the cud and that between the momentary states of the fire and the water. The only difference is that in the former case the cloven-footedness is the same at all moments within a finite time, whilst, in the latter, the states of the fire differ at every different moment. In both cases the actual connexion between momentary states is that one state at one moment can be inferred from the other state at the same moment. The resemblance between what is believed to be simultaneous causality and one attribute being a mark of the presence of another is so great that it will hardly be possible to insist that the former cannot really be simultaneous without holding that the latter cannot be so either. I do not think that anyone supposes that constant connexion between attributes in the same thing apparently at the same moment is really a case of a connexion between momentary states separated by a very short interval of time. But this inferrability of one attribute from another at the same moment in the same thing is precisely what would be meant by simultaneous causality immanent with respect to that thing. Hence unless they make this assumption in the case of constant coexistence of attributes in one thing there seems to be no ground for making a similar assumption when we are faced with what is prima facie transeunt simultaneous causation. It is never absolutely certain that what appears to be simultaneous may not really be separated by a short interval of time, but, as there is no theoretical objection to simultaneous causality, and as what amounts to immanent simultaneous causality is commonly supposed to be really simultaneous, there seems to be no good ground for rejecting simultaneous causality in general.

    We can pass then to another quite general question about causal laws: What is meant by the Necessity of Causal Laws? Causal laws have been reduced by us to regularities connecting together the simultaneous or successive states of things. (1) But it seems clear that there are some regularities of this kind that are not held to be causal. (2) Again we constantly find that causal laws as stated are not obeyed. Something, we say, has 'interfered.' In what sense then can those laws that are admitted to be causal be held to be universal and necessary or indeed even true? We will discuss these questions in order, and we shall find that they have a good deal of connexion with each other.

    (1) With regard to simultaneous causality we should hesitate to say that chewing the cud was the cause of cloven-footedness in animals or vice versa; and, with regard to successive causality we should not say that the night causes the day or conversely. Yet we saw that the connexion between chewing the cud and cloven- footedness was, in our sense of causality, apparently a case of simultaneous immanent causation. There is much less certainty about the sequence of night and day even seeming to be a case of causation in our theory. It may be doubted whether the occurrence of darkness is a datum from which that of light can be inferred without a good many further data.

    We must expect that, as our account of causation drops activity and so differs from that of common-sense, we shall sometimes differ from common-sense in our application of the term. In the example of cloven-footedness and ruminance I think that we must admit that we have a very specialised case of a causal law. But it remains true that a great many regularities are not held to be directly causal, and it will be valuable for us to investigate this point.

    The important thing to notice is that we deny the term causality to regularities which are known or believed to be analysable into other regularities. The fact that day follows night is not thought to be an instance of a causal law because it is analysed into

  1. the fact that the earth turns round on its axis once in twenty-four hours,
  2. the fact that the light on the earth is due to the sun, and
  3. the fact that the earth is opaque to light.
This is not of course an analysis in the sense that all these characteristics can be found in the mere fact that darkness and light regularly follow each other. On the contrary, the various propositions are got from various facts which they explain or from direct experiment, and together they account for the observed regularity. The facts to be explained are the successive appearances and disappearances of the sun which is observed to travel across the sky from east to west and ultimately to disappear below the horizon. We know by analogy with other opaque bodies and other sources of light that this can be explained by supposing that the earth turns round relatively to the sun. The point to notice is that our original regularity has been analysed into a regularity in the relative notions of the earth and the sun, and another as to the invisibility of sources of light through bodies like the earth. Further considerations lead us to believe that the successive positions of the earth depend on its past positions. The analysis cannot, so far as we know, be carried further and so these regularities are finally taken as causal.

    Thus we seem to find that a regularity is not held to be causal unless it cannot be analysed into other regularities, but it is always held that the products of the analysis will be one or more laws of causation. On the face of it this distinction between causal and other regularities seems to raise more questions than it answers. It may be reasonably asked whether

  1. it does not become purely subjective in view of the fact that we never know whether a given regularity may not be further analysable; and
  2. some further account of analysis is clearly demanded.

    (a) The first objection is not of importance. No doubt all our knowledge is subjective in the sense that we do not know how much we have yet to learn. But here this is unimportant because, whilst we may learn that something which we took to be a causal regularity is really analysable and therefore not truly one, we shall not learn that what we judged not to be a causal regularity really is one. If we can give some account of analysis which will stand criticism, then we can say that every further step in our analysis of regularities brings us nearer to truly causal laws, even if we can never be quite certain that we have got them. It is right to remark in passing that a good many physicists (including Helmholtz), and some philosophers (including Sigwart) seem to have held that there were marks by which causal laws, in the physical world at any rate, could be recognised. Such laws, they thought, would be ones connecting homogeneous terms with permanent qualities which only differed by their relative positions in space. Even if this were true of the physical world we can hardly call it a complete account of the nature of causal laws in general. For it assumes that the real world of matter is much less varied than what we perceive, and for the qualities dropped out we shall need laws connecting that world with our minds. And it is clear that the latter cannot be reduced to regularities among homogeneous things with permanent qualities which only differ by their relative spatial positions.

    (b) The question of what precisely is to be understood by analysis of regularities in the present connexion is a more serious one. There are several ways in which a regularity may be analysed.

    (alpha) By splitting it up into two or more regularities which occupy successive stretches of time into which the period of the original regularity may be split. Thus, take the regularity that, if gunpowder be hit hard enough, it will explode. There is strong reason to believe that the period between the blow and the explosion is the scene of two successive regularities:

  1. the blow is followed by rise of temperature; and
  2. the rise of temperature, if it passes a definite limit -- a fact which itself depends in part on the violence of the blow -- is followed by an explosion.
Those subsidiary regularities approach much more nearly to the causal ideal than the regularity which is analysed into them. For the blow may not be hard enough to give the requisite rise in temperature or the heat may be conducted away too quickly, and then the complex regularity will fail although the simpler ones will still hold.

    (beta) The second way in which a complex regularity may be analysed is into contemporaneously operating causal laws, with each cause producing its own effect. Here what was originally taken as cause and as effect are both complex. One part of what was taken as cause produces one part of what was taken as effect, and the rest of the original cause produces the rest of the original effect. Thus sun-rays focussed by a burning-glass on a piece of paper saturated with a silver salt will scorch the paper and change the colour of the silver salt. Now it is easy to take the light as the cause and the whole change as the effect. But the proper analysis shows that the true cause is light + heat and the true effect is scorching of paper + change of silver salt. Now both these laws hold independently of each other, and it is only when what is lumped together under the name of light and treated as a single cause really has both long and short waves in it that what is taken as effect, viz. scorching + change of colour, will happen.

    It is important to notice that such an analysis as this cannot always be made even when the cause and the effect are recognisably composed of parts that are separately connected by causal laws. When A is connected causally with B and C with D we are inclined to suppose that AC must be followed by BD. So strong is this belief that, when the actual sequent is E, we think that B must really be a complex with B and D as elements even though B and D cannot be directly detected in E. Now it is true that there are cases in which when A is followed by B and C by D, AC is followed by BD; to such cases the form of analysis (beta) applies. But it is not true that if A is followed by B and C by D, AC must be followed by BD. Something -- E -- entirely different from BD may follow and we have no right to suppose that B is BD in disguise unless we can prove this to be so. Here no real analysis is possible.

    (gamma) The last form of analysis is hypothetical explanation. And this raises the question: Is any observed regularity to be degraded from the rank of a causal law just because human ingenuity can invent hypothetical laws that will account for it? Clearly this is not what is intended. It is meant that the hypothetical laws shall have been verified. i.e. rendered probable by the large region of facts that they coordinate. But it may be said: At best they can only be probable whilst many of the regularities which they are supposed to oust from the position of causal laws are practically certain. For instance, it is as certain as anything can be that light is always refracted on passing at an angle to the surface of separation between two media of different density. Yet this is not held to be a causal law. It is, on the other hand, analysed into hypothetical laws which connect terms that are merely assumed ad hoc. Thus it is assumed that light, as a physical phenomenon, consists of wave-motions which travel with different velocities through different media, and that these wave-motions when they afflict the retinas of normal people produce perceptions of colour which depend on the wave-length. It is then deduced from the laws of wave-motion that there will be the phenomena which we call the refraction of light, and what the laws of those phenomena will be. Now it might be objected that the laws of refraction are all obvious and certain whilst the explanatory hypotheses are all precarious. Why not accept the observed regularity then as an ultimate causal law and drop all these assumed causal laws that are needed when we degrade the observed regularities to mere consequences of really causal laws? The answer to this is that, if we had to deal merely with the refraction of light, it would be most unreasonable to try and get behind the observed regularities in this way. But then phenomena that have such close resemblances to those of refraction as to be equally called optical have also regularities of their own with which the regularities about refraction, if taken as ultimate, seem to have nothing in common. On the other hand the hypothesis which explains the laws of refraction explains without further assumptions those of the remaining optical phenomena. The position then is that, whilst the theory is more complex and less certain a priori than any of the regularities which it is supposed to explain taken by themselves, yet by accounting for all these regularities that can be observed to hold it gains a high degree of probability for itself, and its laws are justly regarded as causal rather than the observed regularities.

    But it may still very well be objected that there is no difference of principle between the complex regularities which are not held to be causal and those hypotheses which account for them and are held to be causal laws. The answer to this objection turns on the second subject to be discussed in this section, viz. the necessity of causal laws. This vague phrase has several possible meanings which we must separate, but, for the present purpose, the following is the important one. It is believed that a real causal law would assert an unconditional regularity in some sense; in fact, how can you talk of a law when there are exceptions, since a natural law just means what things of a certain kind as a matter of fact do? But as soon as you have reason to believe that a given regularity is analysable into several others there enters a ground for believing that its regularity is only conditional. There is, of course, first of all the residuum of doubt which attaches to any alleged causal sequence and therefore even to the regularities discovered or inferred in the analysis. But, over and above this, there is in any admittedly complex regularity the further doubt as to whether the whole of the elementary sequences can be trusted always to fall together. If any of them fail, then, although each may be truly regular, the complex regularity will break down. As an example of this we may take Kepler's Laws and the Newtonian Planetary Theory. As long as we consider the planets moving steadily and comfortably round the sun Kepler's Laws are all that we need, and they seem to be unconditional regularities. But when we consider the falling of bodies to the earth, the motions of the moon, the Cavendish experiment, etc., we analyse Kepler's Laws and find them to be the results of the First Law of Motion and the Law of Gravitation. These we believe to be unconditional causal laws, and we accept them as we did the results of the hypothetical account of optics because they explain such quantities of seemingly unconnected regularities and apparent irregularities. But, when we have once made this analysis and believe it to be true, our whole attitude towards Kepler's Laws alters. We now know that, instead of being unconditioned regularities, they are merely special cases of the consilience of the new regularities which we believe to be unconditioned. We know, too, what kind of departures to expect from them and where and when to expect them; and, when we look for them we actually find them in the perturbations of one planet by the others.

    We are thus led to see how it is that no regularity which there is good reason to believe analysable into several others is accepted as a causal law. And, whatever be the upshot of our enquiry into the meaning and truth of the belief that ultimate causal laws are unconditioned regularities we see that the products of such analyses are at least less conditioned than the complex regularities from which they are discovered, and, as such, approach more nearly to the ideal of a causal law.

    We are not however even yet in a position to discuss the question of what is meant by a causal law being unconditional and what is meant by its being 'interfered with.' We must first consider certain points connected with the analysis of regularities, since we now see that it is of the products of such analyses that this question will have to be asked and answered. We will then discuss certain points that arise in connexion with the kinds of analysis that I have called (alpha) and (beta).

    A cause in the most general sense is a set of successive sets of contemporary events from which other sets of events can be inferred. The question with regard to (alpha) is: What is the least number of successive sets that is wanted for a complete cause and a complete effect? With regard to (beta) the question is how many distinguishable aspects or events are needed in each successive set to constitute a complete cause and a complete effect? It must he remembered that we are already supposed to have found a certain regularity and to be trying to analyse it into truly causal ones. We find that a certain set of sets of events is regularly followed by another set of sets, all within a certain interval of time. What we do in (alpha) is to make a rearrangement of these successive sets. In virtue of other experiments we know that some that come in the middle of the interval follow regularly on others that come earlier in it, whilst these sequents under certain circumstances have other sequents, as we learn from a fresh set of experiments. The essence of this kind of analysis is that some of the later sets of events in what was formerly taken as the cause are found to be effects of the earlier sets in it, or some of the earlier sets in what was formerly taken as the effect are found to be causes of the later sets in it. Finally the parts of the old supposed cause that are now taken as effects are also part causes of those parts of' the old supposed effect which are now taken as causes of the later sets in it. This form of analysis might be called Vertical, because it analyses the successive sets of sets of contemporary events which were taken as whole causes or effects into fewer successive sets which are both causes and effects, but does not trouble about analysing the sets of contemporary events themselves at each moment under consideration.

    The kind of analysis mentioned under (beta) may be called Horizontal. Here we shall find it necessary to distinguish certain aspects in events. If an event be the occurrence of a sense-quality at a certain moment we must distinguish in that quality

  1. the general aspect that makes it the sort of quality that it is (e.g. sound or colour);
  2. what I shall call 'characteristics,' i.e. certain independent variables by which the particularity of the quality is fixed. These are generally few in number, e.g. in sound they are pitch, loudness and quality. They generally have intensive magnitude and the range of their possible values is believed to be continuous;
  3. the particular values of these variables.

    In an Horizontal Analysis of any regularity we have to see whether, out of the sets of contemporary events successive sets of which constitute 'causes' and 'effects' in our regularity so long as it is supposed to be unanalysable, we cannot make selections which constitute smaller sets known to be related as causes and effects.

    This brings us to the question: Is there any relation that holds generally between the complexity of an effect and the complexity of its cause? This is important as bearing on the question of how complex the real world must be if we hold that it causes our perceptions but do not hold that the objects of those perceptions are the real world. Must every distinguishable event and characteristic in the effect have a differentiation in the cause to correspond to it? Let us begin with events as wholes. If in an effect a (beta) analysis can be made so that every distinguishable event is the effect in a different causal law there must of course be at least as much distinction in the cause as there are events in the effect, for the cause of any event must be at least one event. But in general such an analysis is not possible, and then no conclusion can be drawn from the number of distinct events in an effect to that in its cause.

    Now let us consider the case of characteristics, which is more fundamental. An event is not fixed till all its characteristics are fixed. Hence the causal laws that determine the occurrence of a definite event must determine all its characteristics too. Let us consider an event like a particular sound with its three characteristics of pitch, loudness and quality all determinate and let us suppose that it is the complete effect of some cause. Must that cause have at least three differentiations? I do not see why it should. We could only conclude that the cause must contain at least one event, but not that no cause can be less complex than its effect either in the number of events in it or the number of variable characteristics. There might perfectly well be an ultimate causal law connecting one event with two characteristics with four events with three characteristics apiece. I think this view is contrary to the usual opinion or at any rate to the opinion that ought to be held if many applications of causality be valid. I fancy that common-sense would probably use the following argument about characteristics at any rate. Suppose that A causes B in the sense that B's occurrence at a certain moment is inferable from A's occurrence at a definite period earlier. Suppose that B is an event with three characteristics whilst A is a single event with only one. Then it will be said: 'Each occurrence of A with its characteristic with a certain value is a definite event and as such will allow of the inference of a B event. Moreover, if the B event is what is inferred from the A event there will be one B event to each different A event and therefore just as many different B events as there are different A events. But the number of possible B events is one for each value of each of the three characteristics that define such events. Hence there will be quantities of B events left over uncaused by A events.' This argument is invalid, and that for two reasons.

(1) It assumes that because all B events are alike in being B's, therefore if one B event is caused by a particular A event all B events must be caused by A events. This cannot be proved. At the same time it seems probable and is certainly true in most cases. If it be set aside there is the possibility that only a certain selection of possible B events are caused by A events, and that all the B events which are supposed to be left over when all possible A events have been considered are caused by a different set of events which are not A events at all.

(2) But, setting this suggestion aside, there remains another and a fatal criticism. The argument is only true if the range of values of the characteristics be discontinuous and there be only a finite number of possible values for each. For the argument rests on the assumption that a compact series defined by the values of one variable cannot have as many terms as a series defined by the values of three independent variables whose range of values is compact. Now if the series be really compact this assumption is a sheer error, and with it the argument falls to the ground. It follows then that, even if we grant that the causes of events that only differ by possessing the same characteristics to different degrees, will themselves only differ in this respect, still the cause need not be as differentiated as the effect. One set of events that are defined by a single characteristic and only differ by the particular values of the latter may, if the values form a compact series, cause any finite number of events with any finite number of characteristics apiece.

    We can now pass to the question

    (2) In what sense are causal laws universal and necessary? We now know that the question must be asked not of any regularity that chances to appear, but only of the products of analysis where that is possible. Any of the ordinary regularities which are stated as causal laws in common life are found to have exceptions. And there is no avoiding the fact that a natural law that has exceptions is not as such a natural law but a mere mistake. We say that arsenic is a poison, or more accurately that if a man takes arsenic he will die with certain symptoms; but we know quite well that not all people who take arsenic die with those symptoms, since, if they take an emetic soon enough they recover. We might put the matter thus. The set of events that constitute a cause are generally separated by a finite interval from that which constitutes its effect. And it is found that the effect depends on what takes place within that interval. Hence what we said was the cause was not the complete cause. On the other hand if you have to take account of what happens at every moment up to that at which what is called the effect happens causal laws are quite useless. Nothing at all is inferred; for there is no moment immediately before that at which the effect happens and our causal law comes to nothing but a mere observation of what has happened at every instant of a finite stretch of time. And again there is a difficulty about the breadth of each momentary state. We have seen that horizontal analyses are not by any means always possible. A alone might cause B. But then the other events are always happening contemporaneously with A and there is no reason why, if AX produces B, AY should do so. Hence causal laws seem doomed to the barren tautology that if A has once been followed by B after a time tau, then if the whole state of the universe with A in it recurs and all the other states that formerly intervened between A and B also recur B will happen again after a time tau.

    This is the essence of Bradley's attack on causality; and if it be valid it is fatal. We must therefore examine it carefully. We will begin with the Horizontal difficulty. Bradley's position really amounts to a denial that in any case horizontal analysis is possible. Now we must begin by distinguishing two different kinds of uncertainty which are often confused. They are

  1. uncertainty whether you have found a certain law and whether it is really true, and
  2. that the law is uncertain in its operation.
A law that is uncertain in its operation is not a law, and there we must leave the matter. But I take it that the argument with which we have to deal is different from this. It would take the form: Every causal law to be of any use must connect only parts of the total states of the universe at various moments. But when the laws are stated in these terms they frequently are found to be false. A appears under different circumstances and you infer B and B does not take place. Now you only can infer the laws that are supposed to connect partial state from observations on what are really total states, and you assume that the part of the state not mentioned in your law is irrelevant. But the constantly proved falsity of your laws proves that this is at any rate often a mistake. What right have you to believe that it is ever anything but a mistake? And, if so, you never can state laws with confidence, for they must always connect partial states to be of any use, and those partial states are always abstractions from what you now admit is quite likely to be relevant.

    This objection forgets the fact that causal laws are not merely read off from the book of nature without further trouble, but have to be sought and tested with precisely the object of seeing what is and what is not relevant. Certainly you cannot tell beforehand what is going to be irrelevant, but then the process of discovering causal laws just is the process of discovering what is irrelevant. If I shoot a gun at a person's heart he will generally fall down and be found dead with a hole in his heart. But if he is wearing a metal plate over his heart it is very likely this will not happen. Now certainly there is no a priori reason why the wearing of a metal plate should be more relevant than the question of what horse wins the Derby. But an investigation of what actually happens shows that the one is relevant and the other not. And, if we investigate the matter more closely, we can see why the plate is relevant, because we can make a vertical analysis of the process of killing a man by a gunshot, though we cannot see why it should be irrelevant what horse wins the Derby.

    The fact is that, so far from it being true that no occurrence in the universe can be known to be irrelevant, whole masses of the universe are shown to be irrelevant every time the law is verified under different circumstances10. The real objection is that there do always remain masses of possible events that might be relevant. If you do not take them into consideration you cannot be at all confident that your proposed law is true; but if you do your law will more and more come to connect unique states of the whole universe and so cease to be a general law. Among the circumstances that cannot be proved to be irrelevant there is one important group for which this fact does not greatly matter. That is the relatively permanent features of the material universe. All the regularities that we observe and from which ultimately all our supposed causal laws are gotten take place in presence of these permanent features, and we cannot tell whether they may not be relevant circumstances in laws which, because of their invariable presence, do not need to mention them. But the same circumstances that make it impossible to tell whether these permanent characteristics be relevant or not make it unimportant to decide, I do not see how we could be sure that arsenic kept for the usual time in a man's stomach would poison him if the planet Mars were annihilated, since all our experiments have been performed in presence of that planet. But then it is so very unlikely that the planet Mars will be annihilated that this possibility is not an objection to a causal law about arsenic poisoning which makes no reference to the planet. We must I think assume in our causal laws a tacit admission that the permanent features of the universe are supposed to be pretty well the same at all times for which they are supposed to hold.

    It is not then the possible relevance of relatively permanent characteristics that troubles us, but that of the constantly changing circumstances under which every new case to which the law is supposed to apply must take place. Now it is quite clear that we are not as a matter of fact reduced to the impasse that Bradley suggests. We can foretell certain classes of events with almost absolute certainty without taking into account everything in the universe. For the fact is that, beginning with a few obvious regularities which are seen to hold in spite of any change of circumstances that we can compass, we are led to recognise in the world a system of practically independent causal series and to see that it is very improbable that events of the type A should be relevant to causal laws connecting events of the type B. At the present stage of our knowledge of the structure of the world we can confidently rule out the possibility that the result of a horse-race should affect the question of whether a bullet aimed at a man's heart will kill him. We know enough about the 'make' of the universe, subject to its hitherto permanent structure remaining permanent, to know the kind of events to which the results of horse-races are and are not relevant. But when we are still in the dark as to the phenomena under investigation we cannot lay down these rules about relevance and irrelevance of certain classes of events to other classes with any confidence and our position is much more like that which Bradley seems to think it ought to be everywhere. Thus we are practically certain that the strength of illumination is perfectly irrelevant to the motion of a billiard ball after it has been hit with a cue, but it would be radically unscientific to begin by assuming its irrelevance to the telekinetic motion of objects by Eusapia Paladino, supposing that it actually happens. There is no a priori necessity that the universe should be thus divided into causally water-tight compartments, but experience shows that this is largely the case and that, by assuming as a methodological principle that there are such compartments even when they are not immediately obvious, they can be discovered and separated. The universe might have been as unified as some Idealists would wish us to believe, but, by a merciful ordinance of Providence (for which the true scientist will be more thankful than for his 'creation, preservation,' and the other 'blessings of this life') it is not so, and other people beside the Absolute have some chance of disentangling its structure.

    But, granted that things are not as hopeless as Bradley suggests; that we can discover in the universe mutually irrelevant groups of events; and that the permanent characteristics of the universe, whilst their permanence precludes our proving that they are irrelevant, are for the same reason negligible in practice; we are still by no means clear of the general Bradleian objection. We still have to admit that within a given isolated group, any cause being given, you cannot with certainty infer an effect because other events of the same group may intervene in the time between cause and effect and so replace the supposed causal law by a new one with a vertically more complex cause. And similarly there is the question of the breadth that is to be given to the cause within that group.

    How then must a causal law be stated for the events of a group when it is admitted that in general a finite time elapses between cause and effect and that your law is useless unless the momentary states mentioned are less than the total momentary state of the group? The two difficulties are closely connected. Suppose that the regularity is not found to be analysable vertically but that the intervening events coalesce with the ones that have gone before to give a new cause with a new causal law. Then, if the general law of causality be true, those intervening effects could have been predicted. But in order to predict them we should have needed a wider knowledge of the earlier states in the total isolated group than we actually had. In the most general case we should need for a completely certain prediction

  1. a wider knowledge of the momentary events in the group that are contemporary with what we at first took to be the cause,
  2. a knowledge of the causal law by which we could predict from them the intermediate states that we had formerly left out of consideration, and
  3. a knowledge of the new causal law connecting the new cause, which consists of what was originally taken as cause + the intervening events which (i) and (ii) have enabled us to foresee, with the new and actual effect.
And it is clear that the causal law mentioned in (ii) will be open to the same criticisms as the original one to supplement which it was introduced. Thus it seems that you will never be able to stop till you have taken in all the events at all the moments under consideration in the group, and then you will no longer have inference but mere statement.

    I think that so long as we insist that causal laws shall be capable of giving us certainties about the occurrence of events this reasoning is fatal to them. But I think that they can be defended if we hold that they give us certainties about the probabilities of the occurrence of events. The line of argument that I wish to suggest is that a causal law is not properly of the form 'the occurrence of X at t makes it certain that Y will occur at t + tau no matter what moment t may be' --which amounts to saying no matter what other events may be contemporary with X. For this I would substitute: 'It is certain that the occurrence of X at any moment increases the probability of Y's occurrence at a moment tau later over what it would have been if X had not happened.' This is the suggestion that we must now consider for a moment.

    Of any event that can be proposed to us as happening at a certain moment it is evident that it is eternally true that it will happen then or that it will not. By this I mean that the alternative is settled one way or the other eternally whether we know or suspect or do not know or suspect which way it is settled. It is also evident that this amount of certainty has nothing to do with causal laws, although it sometimes seems to be thought that it has. It would be equally true that of the two propositions: I shall die on the 22nd of September, 1913 and I shall not die on the 22nd of September, 1913, one definite one is true without reference to time whether there were causal laws in the universe or not. Hence causal laws and probabilities must have to do with something beside the truth or falsehood of propositions. Again, one of the propositions being true and the other being false independently of our knowledge, we may suspect that the probability of the two will have something to do with knowledge. The first point on which to be clear will be just what the connexion is between truth, probability and knowledge. A proposition does not have probability, though it does have truth or falsehood, when taken in complete abstraction from other propositions. Probability arises from the fact that propositions are so related that the knowledge of certain ones alters the expectation that we ought to have of the truth of one of the alternatives of which as we saw we know a priori that one definite one is eternally true, but not which one it is.

    Now, since the question of knowledge thus enters, we may ask whether the probability of a given proposition depends on the other propositions that have this relation whether they be known or not or on the knowledge of these propositions. If we take the latter alternative it might seem that the probability of a given proposition would become purely subjective, which no one believes to be the case. But this is not necessarily so. You might say that 'the probability of the proposition p' is an elliptical phrase, which taken by itself has no meaning or only a conventional meaning. Thus it might be held that the proper statement would always be 'the probability of p given the knowledge of q, r, etc.'; and that by the phrase 'the probability of p' used by itself all that was meant was 'the probability of p given that amount of knowledge that may be assumed in all sane people or in all the people to whom my remarks are addressed.' Would this make probability objective in the sense that is needed? When A and B say 'the probability of p is alpha' and 'the probability of p is beta' respectively ; they might both be correct on this theory. For one might mean the probability given the knowledge of q, and the other the probability given the knowledge of r. But would this give us any more than the sort of statement that 'sugar in tea is pleasant' gives; where apparent contradictions are avoided by substituting for this elliptical phrase: A finds sugar in tea pleasant and B finds it unpleasant? This is not as much objectivity as is wanted for probability propositions, because it is held that people can make mistakes about the probability of propositions, whilst they can hardly do so about their likes and dislikes.

    But this objection could easily be met on the view under discussion. It might be said, whilst A and B may certainly both be right in their judgments of probability, it is equally true that they may both be wrong. This may happen in two ways. When A says 'the probability of p is alpha' he means the probability of p relative to his present knowledge. Now he might think that the only relevant bit of knowledge that he had was q whilst really he knew r which was also relevant. Or he might be right in supposing that the only relevant piece of knowledge that he had was q, but wrong in his estimate of the probability of p given q. It is tolerably obvious that the two kinds of mistake come to the same. To suppose that r is irrelevant is just to make an erroneous judgment about the probability of p given r.

    But, if this defence of the possibility of making mistakes about probability, although the correct probability is always that relative to the knowledge of the person who makes the probability- judgment, is to be tenable, we must clearly assume that the knowledge, of the person in question as to how far what he knew, is relevant to the probability is not a part of the knowledge that has to be taken into consideration in saying what is the true probability relative to his state of knowledge. It is clear in fact that the opposite view would lead to a vicious circle fallacy; since then the true probability of p relative to a person's knowledge would be the probability relative -- among other things - - to the knowledge of the true probability. Hence if this position is to be held at all we must put it in the form that to every amount of knowledge there corresponds a true probability of any proposition relative to that knowledge, but the knowledge of what the true probability is cannot be one of the data on which it depends.

    But there remains a serious objection to it. Everyone will admit that we ought to prefer a probability calculated on a wider to one calculated on a narrower basis, even though the man who only had the narrower basis of knowledge had made his calculations properly. But if probability is to be reckoned relatively to people's knowledge of propositions and not to the propositions themselves it is difficult to attach any meaning to this preference. You cannot get over the difficulty by saying that the knowledge that A has given the probability alpha to p relative to his knowledge of q and B has given the value beta to p relative to his knowledge of q and r is itself a relevant piece of knowledge for you and one relative to which the probability of p is beta and not alpha. For, whatever else this may or may not explain, it does not explain the fact that A himself will want to increase his knowledge as much as be can before he is confident of the value of the probability of p. On the present theory the only doubt that A ought to have is whether he has ascribed the right probability relative to what he does know. If so, his probability is correct; and B's probability relative to a wider basis of knowledge is no better than it. But no one really does believe this to be the case. We feel that, although A and B have both calculated rightly and attributed the right weight to what they know, B's value of the probability of p is in some sense preferable to A's; and this belief seems incompatible with the statement that you can only state probabilities relative to what is known by someone.

    Hence we must adopt a different theory as to the relation between probability, truth, and knowledge. We shall still say that a proposition p has not a probability taken in abstraction, but that the probability depends on other propositions. But we must now say that it depends on the propositions and not on the knowledge of them. The state of affairs then is this. To every proposition stating the occurrence of an event at a certain moment there are other proposition making similar statements and the probability of the first depends on the latter whether they are known or not. We must not suppose that even though all these propositions were known the proposition in question is one about which we ought to be certain one way or the other. The probability of p is that value which persons who knew all these other propositions would ascribe to the probability of p if they made their calculations properly. What then are we to say about the probabilities rightly calculated by persons who do not know all the relevant propositions? I think the following is what should be said. When A says that the probability of p given q is alpha he may be perfectly correct; but we must not suppose that when he speaks of 'the probability of p' he means the probability of p given q, even if q is the only relevant proposition that he knows. For there may be other relevant propositions that he does not know, and the probability of p is that relative to all these + q. But supposing that q is the only relevant knowledge that he possesses, whilst someone else -- B -- has the knowledge of r which is relevant, B's value of the probability (if properly calculated) is to be preferred, because lie is nearer the position of knowledge in which the probability could be calculated, viz,, that in which the whole of the relevant propositions are known.

    This however is only a rough first approximation to a proper theory. This is easily seen from the following considerations. It may often happen that when p only is known the probability of X happening is very high. As time goes on we may learn the additional relevant proposition q and the probability of X relative to pq may be quite small. Yet X may actually happen. In this case we seem to have gone wrong by taking in more relevant information. For instance p may be the proposition that someone has taken poison, X may be his death within a certain time. The probability of X given p alone will be large. Suppose we learn q -- that he has taken an emetic -- then the probability of X given pq is pretty small. Yet he may actually die. So the probability relative to the wider range of relevant propositions is not always in practice a safer guide than that relative to a narrower selection. I do not profess to offer a perfectly satisfactory theory of the relations between knowledge, probability and truth. At present the best suggestion I can make is the following, and I offer it for what it is worth.

    Every proposition is eternally either true or false. The law of causality is perhaps the assertion that to every true proposition that asserts the happening of an event at a time there is a set of relevant true propositions such that relative to the whole of them the probability of the event happening is 1. (In this case an uncaused event like a free volition on the indeterminist view would be one that actually happens, but whose probability is not 1 relative to any set of other true propositions.) The part played by our minds is a selective one due to our partial ignorance. The result is that we know selections only of all the propositions that are relevant to the occurrence of any given event. Different people know different selections at the same time, and the same person knows different selections at different times. Now what we want for practical purposes of prediction is that when an event is actually going to happen its probability relative to the relevant propositions that we know shall be high, and when it is actually not going to happen the corresponding probability shall be low.

    Now, while we must admit that with any selection less than the whole of the relevant propositions the probability may be low though the event is actually going to happen, or high though it is actually not going to happen, still we shall less often go wrong if we expect an event to happen when its probability is high relative to a larger selection than if we base our expectations on probabilities relative to smaller selections. For the larger the selection the nearer it approaches to that group of propositions relative to which (if the law of causation be true) the probability of an event that actually happens happening is 1. Very often we may go wrong by following this injunction to maximise our selection, for we may acquire our knowledge in such an unfortunate order that we start with a set of propositions that make what is true very probable and then keep on acquiring knowledge that decreases the probability whilst we fail to reach at all the few remaining ones that would once more make it high. For all that the maxim remains the most reasonable one to follow; just as it is reasonable to argue logically, although you might come to wrong conclusions by arguing correctly from false or insufficient premises and to right ones if you had only simply converted enough A propositions and had enough undistributed middles. Very often the worst that will befall you in following it will be that the probability of a true proposition which, relative to a smaller selection, was nearly 1, hovers about ½ relative to the wider selection that you can reach. But this will lead to no error, for you will simply not feel justified in predicting at all. You will then miss some truth, but you will have no expectation disappointed.

    I think that we can now see our way to a proper statement of a causal law and to the answer to Bradley's objections. A causal law subsists between two sets of events when they are so related that the proposition asserting the occurrence of one of the first set strengthens the probability of the occurrence of one of the second set. Now it is to be noted that the strengthening is the same whatever other events may happen; the only point is that the other events may weaken more than the given one strengthens. Thus let us take the proposition: Smith will die in the next quarter-of-an-hour -- it being assumed that this is asserted at some definite moment so that it is definite with respect to time and is therefore a genuine proposition. Then this proposition is eternally true or false whether there be causal laws in the universe or not. But, if there be causal laws, there may be, and, if the Law of Causality be true, there will be propositions asserting the occurrence of certain other events and such that the original proposition has a definite real probability depending upon these whether they be known or not. Suppose, for instance, that Smith has taken arsenic within the last few minutes. Then this proposition largely increases the probability over what it would be if this were not true. But it does not follow from this that the probability is large, because another proposition that may be true is that he will take an emetic immediately. But the point to notice is that it remains true in spite of this that the proposition that he has taken arsenic does strengthen the probability that he will die within the next half-hour whether other propositions be true that weaken it or not. Causal laws then as laws about the strengthening of the probability of the occurrence of one event by the occurrence of another remain on any view. The only question is whether we can go further than this and whether it is ever reasonable to suppose that we have actually arrived at the true probability of the occurrence of an event.

    In our actual application of causal laws we do not attempt to calculate numerical probabilities. What we want to know is whether an event is very probable or very improbable. Bradley's criticism assumes that we expect causal laws to give us absolute certainly; but no scientist would demand this and the laws cannot be defended if such a demand is made. The question then for us is: Are we ever justified in holding on the data that we can have that the occurrence of an event is practically certain? Consider what this means. It means: Granted that relative to the relevant propositions that we know other than the knowledge that all our knowledge is limited, the proposition p is very probable, have we any right to hold that its probability relative to all actually relevant propositions is 1? It seems to me clear that we often have a good right to do so. Our right depends on how far we are justified in holding that the propositions that we do not know, if there be any that are relevant at all, are either few or have very little influence on the probability compared with those which we do know. Now we have already seen that we soon learn to cast aside whole masses of the universe as irrelevant to certain aspects of it. Thus the field within which relevant data are likely to lie is often a very restricted one as to breadth. And within this it is often possible to arrange so that the occurrence of any relevant events other than those which we have taken into account is most unlikely. If Smith in the example be locked up in a room and plenty of arsenic administered I think he will exhibit unreasonable optimism if be finds any comfort in Mr Bradley's argument from the complication of the universe.

    We may bold then, I think, that Bradley's argument does not apply in our world to causal laws when they are stated in terms of the strengthening of probabilities. Causal laws it may be admitted at once do not give us complete certainty, but this does not prevent their being laws, and it does not conflict with any belief that anybody who uses them has held about them. We can pass then to the last objection to Causality with which we shall have to deal, viz.

    The alleged Antinomy of a First Cause. We shall not have to spend much time with this venerable friend, who, like most elderly antinomies, has the misfortune to be lame in one leg. The argument for the thesis is that causation claims to explain events, and, as it only does so by referring to other events which need just as much explanation, it involves a vicious infinite regress, unless we assume a first cause. The argument depends on using 'explanation' in the sense of proof. The propositions of Euclid follow from the definitions and axioms. The axioms are also propositions, but they do not need a proof because they are supposed to be self-evident. Similarly it was thought that causal series must end with an uncaused cause. But difficulties at once break out in such an analogy. The axioms of Euclid differed from the propositions by the fact that they were self-evident whilst the propositions were not. But the first cause was either an event or not. In general it was taken to be the first event in a certain substance, viz. God. But this event, unlike the axioms of Euclid, had no distinguishing characteristic like that of self-evidence in their case to differentiate it from the other events which were supposed to need causes as self-evidence differentiated axioms from propositions that needed proof. Hence it required a cause as much as any other event, and this must be events in the same or a different substance, and so the old regress broke out again. It was impossible, as Schopenhauer put it, to 'take the Cosmological Argument as if it were a cab and drop it when it had taken one as far as one wished to go.' Thus the antinomy is weak on the side of the thesis. The analogy of causal explanations with logical proofs which started the regress breaks down at just the point at which we wanted it to stop the backward journey.

    On our view of causation, however, there is no reason even to begin the regress, because we do not hold that there is any analogy between proof and causation. The possibility of causal laws merely means that there is a certain amount of' unity in the world, which, on further investigation, is found to take the form of a set of more or less isolated groups within which laws hold. In virtue of this fact the world is not a perfect chaos in which nothing can be legitimately expected at one time rather than another, but it is subject to certain laws such that the happening of one event or set of events, when known, has a legitimate influence on our expectation of the occurrence of other events. The fact that our knowledge of the occurrence of the events B strengthens our expectation of the occurrence of the events C and that there were events A which had they been known to have happened would have strengthened our expectation of the events B and so on presents no vicious regress. In fact there is no real analogy between causal explanation and logical proof. The only sense in which causal laws explain is that they simplify. They do not show us why an event happens in terms of some event or law that is self- evident, for one event has no distinction from another to correspond to degrees of self-evidence among propositions. What they do tell us is that we can hope to know with some certainty what will happen where and when we cannot have or do not wish to have direct experience. It is in this sense that it is right to insist with Mach that their value is an economic one, whilst at the same time we definitely take our stand against the Pragmatists and deny

  1. that this is what is meant by their truth, and
  2. that it is a test of their truth.
It is because it is true that they are of a certain definite nature that they are of economic value to thought, and it is because predictions made by them are found to be verified by experience that they are believed to be true. In this sense of explanation, which is the only one that causal laws will bear, the Kantian antimony leaves them untouched.

    But it may be said: This is no doubt true of your causal laws, but what about your axiom that a system that has been quiescent for a finite time can only have its emergence from quiescence explained by a causal law transeunt to the system in question? Suppose we accept the axiom as I have done, what will happen? The sole difficulty that can arise will be over the beginning of change in the universe. If this axiom be true it is clear that the whole universe (meaning the world + God, if there be one) can never have been completely quiescent. For it certainly is not so now, and if it ever had been it would only have got out of that state through a transeunt causal law which, with respect to the whole universe, is a contradiction in terms. But really there is no difficulty about this whatever. Why should the whole universe ever have been quiescent for a finite time? Apart from the axiom the question is a perfectly open one and with it we must decide that it never has been quiescent for a finite time. The only argument that could be brought against this view must be based on the supposed difficulties of infinity and continuity. But, since these difficulties are at an end, arguments based on them alone may be relegated to that cave in Pilgrim's Progress where Giants Pope and Pagan mumble the bones of their past victims and growl at the passersby whom they can no longer hurt11.

    We have now discussed all the classical objections to causal laws, and have tried to show that none of them are of weight against the view of such laws as which we have offered and which suffices for natural science. It only remains to close this chapter with a word about the Law of Causality as opposed to particular laws of Causation. The Law of Causation is that every event has a cause and it is often supposed to be an a priori truth. Now we have admitted as an a priori truth the law that a system that has been quiescent for a finite time can only be set in change by a causal process transeunt to itself. The certainty of this law may cover two certainties, (a) that such a system will only be set in motion by causes, and (b) that those causes will be partly transeunt to the system. Now are (a) and (b) both equally self-evident? It seems to me that (b) is self- evident; on the other hand (a) is a particular case of the general Law of Causality that every event has a cause. Of course the particular case might well be self-evident without the general law being so too. That every event has a cause means on our theory that to every true proposition asserting the occurrence of an event at any given time there is a number of true propositions asserting the occurrence of other events at different (and perhaps, to be in accord with tradition, we should add earlier) times such that relative to this set the probability of the event's occurrence is 1. This proposition does not seem to me self-evident, nor do I know of any means of proving it. At the same time it obviously cannot be disproved and it is advantageous to assume it as a methodological postulate. So far we have found that by assuming it even in the most unpromising cases we can find laws such as it suggests. But we never know when it may break down, and some persons hold that it does so over volition. I do not know that there is nearly such good reason to think that it breaks down over volition as over the occurrence of earthquakes, but as some people take an innocent pleasure in believing that their volitions are not even theoretically predictable, it will be pleasant not to have to rob them of that harmless opinion.

    Is the particular case of this supposed law which we see forms a part of the axiom about causality self-evident? That takes the form, that whenever a system that has been quiescent for a finite time ceases to be so there is an event or events so related to the new one in the system that the knowledge of them strengthens the probability of the latter. I am inclined to believe that this is self-evident. If I enter a room and find that a chair which was by the fire, is now by the window I invariably hold that if I had been present I might have had knowledge of events which would have strengthened the probability of this change, In fact, apart from the knowledge that such events may have happened in my absence, or, to put it more strongly, with the certainty that they have not happened, the change of position of the chair has no probability at all.


Notes

1 Even so there may be necessary external conditions, and our apparent ability to find a purely immanent law may be merely due to their permanence.

2 I am using quality in a very wide sense here; it will of course include relations.

3 Treatise on Human Understanding, Part III, § 2.

4 Appearance and Reality, pp. 60-61.

5 Logic, Vol. II, p. 104.

6 Principles of Mathematics, Chap. LIV.

7 Treatise of Human Nature, Part III. § 2.

8 Metaphysic, Vol. II. § 207.

9 Loc. cit.

10 This is not strictly true. If X happens ones in the presence of P and the absence of Q and then again in the absence of P and the presence of Q you cannot decide offhand that P and Q are irrelevant. All you can say is that P is not essential and Q is not essential, but P or Q may be essential.

11 It most be noted that the fact that the universe can never have been quiescent for a finite time is perfectly compatible with its having a beginning in time. The universe began at t means that nothing existed at any moment earlier than t, whilst at t and all later moments up to now something has existed. The universe has been quiescent for a finite time means that if t and t' be any two moments there is always an intermediate moment such that what existed at it differs either from what existed at t or from what existed at t'.


Contents -- Chapter 3