Mackie, J L - The Direction of Causation

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The Direction of Causation Author(s): J. L. Mackie Source: The Philosophical Review, Vol. 75, No. 4 (Oct., 1966), pp. 441-466Published by: on behalf of Duke University Press Philosophical ReviewStable URL: http://www.jstor.org/stable/2183223Accessed: 02-04-2015 00:56 UTC

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THE DIRECTION OF CAUSATION

I

O N A simple regularity theory of causation, a cause is both necessary and sufficient for its effect in such a sense that it

follows automatically that the effect is equally sufficient and necessary for its cause, and the only difference between the relation of cause to effect and that of effect to cause is that of temporal order: the cause precedes the effect. Given that two events are causally connected in a direct line with one another, whichever of the two comes first in time is called the cause.

It seems, however, that this cannot be the whole of the difference between causing and being the efect of. A cause is commonly taken to explain its effect in a way in which an effect does not explain its cause, even where we can retrodict the cause from the effect as con- fidently as we can predict the effect from the cause. Consequently, if two events occur close together, this may be explained by their being joint effects of a common cause, but it will not be explained by their being joint causes of a common effect. The same principle applies if two features, or two kinds of events, tend frequently to occur together. A tendency for white hair and pink eyes to go together in various species of animal may be explained by these features being joint effects of a single gene; but we could not explain a tendency for high humidity and falling barometric pressure to go together by their being joint causes of the falling of rain.

Indeed, it is questionable whether temporal order is even part of the difference between causing and being the efect of. Admittedly, we believe that causes always, or nearly always, precede their effects, and we often use temporal order to decide which of two causally connected events is the cause. But on the other hand, we do not rule out the possibility of an effect occurring simultaneously with its cause. What is more, it seems at least conceivable that there should, in special cases, be evidence for backward causation, for an effect preceding its cause in time. For example, it seems conceiv-

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J. L. MACKIE

able that there should be evidence for cases of precognition, and if precognition were anything like ordinary perception it would involve backward causation: the details of the precognized object would be causally responsible for the content of the precognizer's belief and of the description he offers.' It seems, then, that we recognize a relation which we may call causal priority, which holds in one direction only between a cause and its effect, and that this relation is not identical with, and probably does not entail, temporal priority. Even if it turns out that causes always precede their effects-that is, even if backward causation does not occur and, where the two appear to be simultaneous, the cause very slightly precedes the effect in time-so that temporal priority always coincides with causal priority, that the two do so coincide will be a synthetic statement. If this is so, then while we may, as we in fact do, commonly use temporal priority as evidence of causal priority, there must be some more fundamental way in which we can, in at least some cases, recognize causal priority itself.

I have already spoken, and shall continue to speak, of temporal 1 The possibility of backward causation has been and continues to be the

subject of a vigorous controversy, started by the symposium between M. Dummett and A. Flew, "Can an Effect Precede Its Cause ?," in Proceedings of the Aristotelian Society, supp. vol. XXVIII (I954), 27-62. See also Max Black, "Why Cannot an Effect Precede Its Cause?," Analysis, i6 (I955-I956), 49-58, reprinted in Models and Metaphors (Ithaca, i962), pp. I70-i8i; A. Flew, "Effects Before Their Causes?-Addenda and Corrigenda," Analysis, i6 (1955-I956), I04-II0; M. Scriven, "Randomness and the Causal Order," Analysis, I7 (I956-I957), 5-9; D. F. Pears, "The Priority of Causes," Analysis, I7 (I956- I957), 54-63; A. Flew, "Causal Disorder Again," Analysis, I7 (I956-I957), 8i-86; R. M. Chisholm and R. Taylor, "Making Things to Have Happened," Analysis, 20 (I959-i960), 73-78; W. Dray, "Taylor and Chisholm on Making Things to Have Happened," Analysis, 20 (I959-I960), 79-82; A. J. Ayer, The Problem of Knowledge (Harmondsworth, I956), pp. I70-I75; M. Dummett, "Bringing About the Past," Philosophical Review, LXXIII (i964), 338-359; S. Gorovitz, "Leaving the Past Alone," Philosophical Review, LXXIII (i964), 360-37I; R. M. Gale, "Why a Cause Cannot Be Later than its Effect," Review of Metaphysics, XIX (i965), 209-234.

It will be obvious that I have drawn freely on points made by all those who have taken part in this controversy, although I am not in complete agreement with any of them, and although on the central issue in this controversy my final opinion is at variance with that of the majority of the participants. My main purpose, however, is not to decide whether causes could be later than their effects, or could be found to be so, but simply to discover what constitutes causal priority.

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order as something given, something we can take for granted when we inquire into causal order. It might be suggested that this is a mistake, and that temporal order itself depends upon causal order. This suggestion seems to be supported by the fact that discussions that are ostensibly about "the direction of time," "time's arrow," "temporal asymmetry," and so on are in fact often concerned with the detection of causal order within certain types of causal process.2 My way of speaking can, however, be defended by the following considerations. Events in time form a series ordered in one dimension (leaving aside the relativity complications), and once a direction has been given to any segment of this series, a direction has been given to the series as a whole. For example, if events A, B, C, D, E form a series in this order, so that B is temporally between A and C, C is temporally between B and D, and so on, and if, besides, events D' and E' are simultaneous with D and E respectively, then if B is before C, this determines that A is before B, D before E, D' before E', and so on. If, on the other hand, C is before B, but the ordering in terms of "temporally between" remains as before, then this determines that B is before A, E before D, and so on: the direction within each pair of events must be reversed. The direction of time, then, characterizes the ordered series as a whole. The direction of causation, on the other hand, seems to characterize each particular process by itself. Even if the direction of time, therefore, is ultimately analyzable in terms of the causal direction within all, or most, causal processes, we can nonetheless, in considering any particular causal process, take the time direction as determined by the causal directions of other processes, and discuss the direction of causation within this process against a given temporal order of the events in this process. Of course, if the direction of time were thus ultimately analyzable in terms of causal direction, this would show conclusively that causal direction could not be wholly constituted by temporal order; an account which reduced each direction to the other would be viciously circular. But there are plenty of cases where we are

2 See, for example, H. Reichenbach, The Direction of Time (Berkeley, I956); K. R. Popper, "The Arrow of Time," Nature, I77 (I956), 538; A. Grfinbaum, "Temporally-asymmetric Principles, etc.," Philosophy of Science, 29 (i962), I 46- I 70.

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J. L. MACKIE

directly aware of temporal order: we know what it is for one event to occur before another when they come close together in our immediate experience. Whether or not any further explanation can be given of this awareness, we can take it as determining the temporal order of any pair of nonsimultaneous events. I shall, therefore, take the temporal order of events as already determined when we inquire whether one is causally prior to another.

So far, however, "causal priority" is only a name for an as yet unidentified relation. I want to see whether we can give an account of this relation and of how we detect it.

What we might call the time-shape of a causal relationship can, in some cases, be fairly readily determined. For example, by tracing the continuity of causal processes, by identifying inter- mediate links in "causal chains," we may be able to decide whether there is a direct relationship between A and B, as indicated in (i) below, or whether they are causally connected only by a common relationship to a third item C, as in (ii). (The arrows in the diagram represent only temporal order.)

S A A

Diagram I.

But if all that the tracing of continuities could establish were the difference between the line relationship of (i) and the fork relationship of (ii), it would leave unsettled the vital question of direction. Figure (i) would be ambiguous between "A caused B" and (with backward causation) "B caused A." Figure (ii) might equally represent A and B being joint effects of the common cause C, or A and B being joint causes of the common effect C, or A causing C and C causing B-or vice versa-with backward



causation in one arm only. So even where we can decide the time- shape of causal relationships, we need a further account of how to decide the causal priorities they involve.

II

Some asymmetry between cause and effect comes to light as soon as we improve on the simple regularity account of causation (that cause and effect are each both necessary and sufficient for the other). A more accurate account, still within the regularity theory, would run as follows.3 If I say that this short circuit caused this fire, I am claiming only that the short circuit in conjunction with other factors which were actually present formed a sufficient condition for the fire's breaking out, that these other factors alone, without the short circuit, were not a sufficient condition for the fire, and that no other sufficient condition for the fire was present. I should probably admit that quite different sets of factors could constitute sufficient conditions for such a fire. The short circuit, which I describe as the cause of the fire, or as having caused it, is not in itself either necessary or sufficient for the fire; but it is a nonredundant part of a sufficient condition which was also, as it turned out, nonredundant. This sort of condition, an insufficient but necessary part of an unnecessary but sufficient condition, I call for short (using the initial letters of these words) an inus condition. Formally, A is an inus condition of B if there is some set of factors X, and some set of factors or disjunction of sets of factors r, such that (AX or T) is both necessary and sufficient for B, but X alone is not sufficient for B, nor is A. Then to say that A caused B is at least to claim that A is an inus condition of B, that on this occasion both A and the factors summed up as X were present, but that the sets of factors summed up as r were absent. And this statement is, as it stands, asymmetrical as between cause and effect, between A and B. To say that A was thus an inus condition of B is not to say that B was an inus condition of A. This asymmetry, however, cannot constitute the causal priority for which we are looking. For if A is

3 I have developed such an account, of which this paragraph is a summary, in "Causes and Conditions," American Philosophical Quarterly, 2 (i965), 245-264.


J. L. MACKIE

an inus condition of B, then, provided that there is some necessary and sufficient condition for A itself, B will also be an inus condition of A. Since the short circuit was, given the circumstances, nonredundant and also sufficient for the fire, the fire, together with these circumstances, formed a sufficient condition for the short circuit, and of this sufficient condition the fire was a nonredundant part. In other words, given the fire in these circumstances, the short circuit must have occurred, but if the fire had not occurred in these circumstances, the short circuit would not have occurred either; but there are presumably other sets of conditions, not present on this occasion, that would similarly have been sufficient for the short circuit. Thus although the relation "is an inus condition of" is not symmetrical, an effect usually is in fact an inus condition of its cause, just as a cause is an inus condition of its effect. The causal priority which distinguishes them has still to be found.

III

The counterfactual conditional I have just used-"if the fire had not occurred in these circumstances, the short circuit would not have occurred either"-sounds rather odd. We may be inclined to reject this counterfactual, but to accept the converse one-"If the short circuit had not occurred in these circumstances, the fire would not have occurred either"-and then to offer the truth of such a counterfactual as the analysis of the causal priority of (in this example) the short circuit to the fire. This would not be very illuminating, however. The counterfactual conditional is a form of expression which is itself much in need of analysis. Such a conditional seems to be a condensation of an argument from a "belief- contravening supposition."4 If the counterfactual is to be natural, one requirement is that its consequent should be derivable as a conclusion from the supposition which corresponds to the antecedent together with premises which it is plausible to retain when we introduce the belief-contravening supposition. Another

4See N. Rescher, "Belief-Contravening Suppositions," Philosophical Review, LXX (i96i); also Hypothetical Reasoning (Amsterdam, i964); J. L. Mackie, "Counterfactuals and Causal Laws" in Analytical Philosophy, ed. by R. J. Butler (Oxford, i962).




requirement is that this consequent should not conflict with beliefs which it is plausible to retain when we introduce this supposition. Now the second counterfactual-"if the short circuit had not occurred . . . the fire would not, etc."-meets these requirements, for although we believe that the fire actually occurred, this belief can plausibly be abandoned when we suppose the short circuit not to have occurred. But why? Because the fire was an effect of the short circuit. On the other hand, the first counterfactual-"if the fire had not occurred . . . the short circuit would not, etc."- violates the second requirement; the short circuit was the cause, not the effect, of the fire, and supposing the fire not to have occurred gives us no reason for abandoning the belief that the short circuit did. The occurrence of the short circuit was not dependent on that of the fire. But what this means is that the acceptability of the second counterfactual and the contrasting oddness of the first are themselves due to the causal priority of the short circuit to the fire. The contrast between them, then, will not serve as an analysis of this causal priority; this analysis is unillu- minating because it is circular.

IV

A more promising approach is by way of controllability and "effectiveness"* the direction of causation is connected with the way around in which we might use the causal law as a recipe. A cause is effective as a means of bringing about its effect. The rubbing of a safety match on a matchbox is an inus condition of the appearance of a flame, and vice versa. But I can use the rubbing of the match as a means to the producing of a flame (if the other conditions are right), whereas although I can produce a flame independently, I cannot use the producing of a flame as a means to the previous rubbing of the match on the matchbox.

This is associated with one of the queerest features of the hypothesis of backward causation. One might suppose that if there were a time-reversed exact analogue of causation, then one could use a later event as a means to the bringing about of an earlier one: in one of the stock examples, putting up a particular picture on Tuesday would be a way of bringing it about that a precognizer


J. L. MACKIE

should have made, on Monday, a drawing that resembles it. And this seems to be absurd.5

The causally prior item, then, seems to be the one which is effective-the one which I can directly control, and by way of which I can indirectly control the other. Causes are effective; effects are not.

Can we, then, simply equate causal priority with effectiveness? This suggestion would fit in well with one of the main uses to which we put the notion of causal priority. If there is some evidence of a causal connection between two items-for example, if there is a significant statistical correlation between self-confidence and skill in the performance of certain tasks-then until we know the direction of causation we cannot base any practical policy on the causal connection; we do not know, for example, whether measures taken to increase self-confidence will raise the degree of skill.

This suggestion applies also to causal relationships of the functional dependence type, where cause and effect are simultaneous. The law PV - kT can, indeed, be used more than one way around: if the volume of the gas is kept constant and the temperature raised by some external means, the pressure will be increased; alternatively, the pressure may be increased and the temperature kept constant, and the volume will then decrease, and so on. That is, such a law may cover more than one causal relationship, with different directions of causation. But in any actual process there is some definite direction of causation: we can distinguish the cause (or causes) from the effect. And whenever we use the law, the causally prior items are those which we control directly and by means of which we control something else. This distinction will not necessarily coincide with the merely algebraic distinction between independent and dependent variables, and the fact that one variable can be treated algebraically as, say, the

6 This point is used, e.g., by Flew, in Analysis, I7 (I956-i957), 8I-84, to argue that what Scriven offers as an example of backward causation would not be causation because it leaves out "effectiveness." Gale also (op. cit., p. 2I7) takes "effectiveness" to be an essential feature of a cause, saying that "a cause is that which can be used for the purpose of making, or bringing it about that, something else happens," and (consequently) says that "the ordinary concept of causality is anthropomorphic." Contrast note I 2 below.



dependent variable does not necessarily mean that the corresponding quantity can be causally dependent upon the others.

Despite the merits of this suggestion, it cannot provide a full account of causal priority. For, first, we apply this concept to cases where there is no question of human control. The hypothesis that the solar system was produced by the approach of another star to our sun involves the supposition that this approach was causally prior to the formation of the planets; but it would be strange to say that this supposition could be elucidated only by saying that if we could bring one star close to another, and the latter was in a suitable state, we could by this means make a set of planets. We should not assume too readily that our causal concepts are infected with an often inappropriate anthropocentricity. Secondly, even where a causal sequence is more or less under our control, the causal priority of one event in the sequence to another can hardly consist in the fact that we can control the latter by means of the former. There must surely be some relation holding among the events themselves which makes it possible for us to use their causal connection as a recipe one way around but not another. But if so, we have still to identify this relation. Thirdly, if there were novolun- tary agents in the world, would there not still be causal priority? If so, we should be able to describe this relation as it is in itself, without reference to the manners in which voluntary agents can or cannot control things. In short, effectiveness is an anthropocentric concept, but causal priority seems to be a concept that applies objectively to the natural world. It may, indeed, be that our voluntary actions give us our primary, direct, awareness of causal priority.6 But the task remains of saying explicitly what it is that we are then aware of, and there is no need to assume that what we are aware of is necessarily tied to human interventions.

V

Let us try yet another approach, examining a type of experiment that could conceivably be used to provide evidence for backward

6 Cf. Max Black, "Making Something Happen," in Models and Metaphors (Ithaca, i962), p. i62: "when one person acts upon another, so that one action is contiguous and co-temporal with another action, we can still immediately identify the cause as that action of the two that was free."


J. L. MACKIE

causation.7 On Monday a person who claims to have powers of precognition is asked to draw a copy of a pattern that is going to be displayed in a certain place the next day; on Tuesday the pattern is produced by some randomizing device and displayed as promised; and, let us suppose, the precognizer's drawing turns out to be exactly like the random pattern which it was intended to copy. Prima facie, this result is evidence that this person really has precognized the pattern. Of course, several precautions must be taken to give this evidence any serious weight. We must check that the drawing has not changed or been changed, that on Tuesday it is still as it was drawn on Monday. We must exclude various possible ways in which the precognizer, or his drawing, might have fed information into the alleged randomizing device. Again, a single favorable result, however surprising, might be written off as an accident; but if the experiment were repeated a number of times with all the appropriate precautions and continued to give favorable results, then it would begin to constitute weighty evidence that precognition was occurring. And if we conclude that it is precognition, we are not merely saying that if the pattern had been different the drawing would have been different in a sense in which the converse counterfactual-that if the drawing had been different the pattern would have been different-would have been equally true. We are saying also that the pattern is responsible for the details of the drawing being as they are, that it has determined the drawing and not vice versa; in other words, that the pattern is causally prior to the drawing.

In this experiment, nothing depends essentially on the use of a human precognizer. We could describe a conceivable experiment that might give evidence of backward causation without precognition by replacing the supposed precognizer by a machine which included, say, a photographic film. If the film, when developed, regularly showed a picture that closely resembled the pattern subsequently produced by the randomizing device, then, given all the appropriate precautions, we should have evidence that this photographic machine was being affected by the subsequently

7This is based on Scriven, op. cit. An important feature of Scriven's experiment, the use of several precognizers, is temporarily omitted, but is introduced in Sec. IX below.



produced pattern-that is, that a temporally later event was causally prior to a temporally earlier one. I shall, however, continue to discuss this suggestion with reference to a precognizer's drawing.

The central question is: just how would a successful experiment of this sort provide evidence for the conclusion that the pattern is causally prior to the precognizer's drawing? It is not the randomness of the pattern, in any sense in which this is an intrinsic feature of the pattern, which tends to show its causal priority; for the drawing, being just like the pattern, will equally exhibit this sort of randomness. This sort of randomness, in both items, is important only because it helps to show that there is some causal connection between the drawing and the pattern, because it is unlikely that two similar random figures should have come into existence close together but independently.8 But granted that there is some causal connection between the two, what supports the conclusion that the pattern is prior to the drawing? In the first place, it is the excluding of various specific ways in which the drawing might have influenced the production of the pattern; for example, we should have checked that no photograph was taken of the drawing and fed into the device which produced the pattern, that no one who had seen the drawing had anything to do with the operation of the device, and so on. What this means is that there are various already known kinds of directional causal process (about which we already know which part of the process is causally prior to the other), and that we have checked that none of these processes could run from the precognizer or his drawing as the causally prior item to the pattern as the causally posterior one. In the second place, this conclusion (that the pattern is causally prior to the drawing) may be supported by the argument that we know enough about the process that produced the pattern to be able to say either that this process contained an element of pure chance, so that nothing at all was prior to the determination of this particular pattern, or else that what was causally prior to it was such that it could not have been affected by the drawing or by the thoughts of

8 But note that the randomizing device may be regarded as introducing randomness of another sort, which contributes to a different argument discussed in Sec. VI below.

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the man who drew it. Here again we are relying on what we take to be already known cases of causal priority or its absence. (The same would hold if instead of, or as well as, the randomizing device, we inserted free human decisions into the process by which the pattern was produced; again the point would be that we could say that nothing was causally prior to the determination of this particular pattern.) In all cases then, if we appealed to an experiment of this sort as evidence for precognition or backward causation generally, we should be implicitly using an argument of this form: A and B are causally connected, but A is not causally prior to B (either because nothing is causally prior to B or because what is causally prior toB is such thatA could not be connectedwith it), therefore B is causally prior to A. It follows that an experiment of this sort cannot illustrate the primary detection of the direction of causation. Appeal to it involves an argument, not an alleged perception, and this argument uses in its premises supposed previous determinations of causal priority or of its absence, together with the assumption that if two items are causally connected, one of them must be causally prior to the other. So this kind of experiment does not in itself reveal what causal priority is or what is our fundamental way of recognizing it.

Some light, however, is thrown on this if we consider some objections to the appeal to any such experiment as evidence of backward causation and some replies to these objections.

VI

First, we noted that one argument implicit in the appeal to such an experiment rests on the systematic exclusion of various ways in which the temporally earlier item (our drawing) might have influenced the temporally later item (our pattern). But excluding all known ways in which the drawing might have influenced the pattern does not prove that the pattern influenced the drawing. One further possibility is that the drawing influenced the pattern in some mysterious and hitherto unknown way. And since, if the pattern influenced the drawing, this backward influence would have been of an at least equally mysterious and hitherto unknown kind, the hypothesis that the drawing influenced the pattern, by


THE DIRECTION OF CA USA TIOX

some unknown form of forward causation, is at least as plausible as its rival. If the view that the drawing is a product of precognition seems initially the more plausible, this is only because ordinary visual perception is a familiar process which we know to be able to reproduce a complicated pattern in all its detail: it seems plausible to talk of someone "seeing" a future pattern because we know about seeing present patterns. But since precognition would have to be utterly different from ordinary visual perception, which uses normal causal mechanisms, this analogy does not really make the precognition hypothesis any more plausible than its rival, that the drawing influenced the pattern in some undetected and hitherto unknown manner.

To meet this objection, anyone who wanted to use an experiment of this sort as evidence for backward causationwould have to do something more than exclude known possible ways in which the earlier item A might have influenced the later item B. As we have seen, one thing he might do is to show that B has nothing causally prior to it, that some essential aspects of it have arisen by pure chance or from contra-causally free decisions. Another thing he might do is to show that B is produced by causes that have nothing to do with A, either by tracing a series of events causally prior to B back to a time before the occurrence of A, or by tracing the production of B to complex and obscure causes such as would figure in a deterministic explanation of the behavior of gambling instruments like dice, roulette wheels, and the marbles in a lottery barrel. (The suggestion, in our original account of this sort of experiment, that the pattern should be produced by a randomizing device, is ambiguous between the two main possibilities we are now considering: this device might be regarded as incorpo- rating an element of pure chance, or as working by complex and obscure causes. In either case the randomizing is now seen to have a further function-over and above that of helping to show that there is some causal connection between the drawing and the pattern-namely, that of excluding any forward causal influence on B from A, or even from any ordinary cause of A.) 9

9 This is the function hinted at in note 8: this use of a "random selector" is a vital part of Scriven's argument.


J. L. MACKIE

Of these two main possibilities, the former might seem to be of special value to the defender of the experiment. If B could be shown to have arisen, in some essential respect, by chance or free decision, and thus to have nothing causally prior to it, what explanation could there be of a significant resemblance between A and B except that B influenced A by some kind of backward causation? But we shall see (in Section VII below) that there is an objection which pretty well rules out any appeal to considerations of this kind.

The latter possibility, of tracing B to causes that are not dependent on and are in the end prior in time to A, leaves room for another objection. Suppose that there is some set of events and conditions C, which is causally prior to B and temporally prior to A; this makes it possible that C is also causally prior to A, by some unnoticed process of forward causation. In our example, if the causal determination of the pattern could be traced back, even in principle, to some conjunction of factors before the Monday when the drawing was made, this opens the possibility that the drawing should have been determined, by some process of forward causation, by this conjunction of factors and not by the pattern; the drawing and the pattern would then be joint effects with this conjunction of factors as their common cause. But against this the defender of the experiment could argue that a close resemblance, such as we have assumed, between the drawing and the pattern is more easily accounted for by a direct causal relationship between them than by their being joint effects of a common cause which does not resemble either of them. Also, if any specific account were suggested of how this conjunction of factors might have influenced the drawing, this could be tested by repeating the experiment with the conditions so changed as to block this influence. There could therefore be an indirect confirmation of the hypothesis that a later event B had a backward influence on an earlier event A. Admit- tedly, such confirmation could not be conclusive: having traced B to a causal antecedent C which is temporally prior to A, we should have excluded the possibility of even a mysterious forward causal influence from A to BA but we still face the objection that the hypothesis of a mysterious forward causal influence from C to A, rendering A and B joint effects of C, must be at least as plausible



as that of an equally mysterious backward causal influence from B to A. The problem is now one of weighing evidence, since there is no conclusive argument on either side; in a practical case, if a successful experiment of this sort were produced, our judgment about it would depend upon the rarity of such results and the plausibility of the inductive conclusion that since causal priority normally coincides with temporal priority, it always does so.

VII

A second objection is more fundamental. Suppose that the first part of our experiment has been performed, and a certain drawing has been made on Monday. According to the precognition hypothesis, this is literally a copy of the pattern that is to be produced on Tuesday. But then suppose that someone decides to stop the device that would have produced the pattern, so that no pattern is produced after all. The drawing cannot be a copy of a pattern which never comes into existence, and thus on this occasion the precognition hypothesis is false. But on every occasion, after the drawing is made, it is possible that someone or something should intervene so that the corresponding pattern fails to be produced. Consequently, it cannot on any occasion be the pattern that is responsible for the details of the drawing; the precognition hypothesis must be false even for those occasions when the device is not stopped and the pattern actually is produced and turns out to be just like the drawing.10

This objection rests upon the assumption that past (and present) events and states of affairs are fixed and settled and unalterable, whereas at least some future ones are still to be fixed, as yet undecided. The argument is that if at any time event A is fixed while event B is still unfixed, B cannot be causally prior to A, because at this time things might still be so decided that B does not occur. Is there any way in which this objection can be countered? We may dismiss the fantastic suggestion that past events may be not fixed but still subject to decision; but the reply is still available

10 Cf. Flew's three articles mentioned in note I; also Black, "Why Cannot an Effect Precede Its Cause?" This is what Flew refers to as the "bilking experiment."


J. L. MACKIE

that future events, or at any rate those of them which could conceivably be precognized or have other effects that precede them in time, may already be fixed at the time that those effects occur. This objection, in fact, tells only against a supposed case of backward causation where the occurrence of the supposed cause is still undecided at a time when the supposed effect has already occurred. This, however, means that this objection is fatal to what we called the former possibility in Section VI-namely, the possibility of defending, for example, our precognition experiment by showing that the pattern had, in some essential respects, nothing causally prior to it, that it was the product of pure chance or free decisions occurring after the picture had been drawn. For if any future events are undecided, they are those which will result from chance occurrences or free decisions that are yet to come. I suppose the reply could be made that all events, future as well as past- even uncaused future ones-are already fixed, that what is to be is to be in something more than an empty logical sense. But to say this in order to defend the possibility of backward causation is to pile fantasy on fantasy. I conclude, therefore, that this objection does, as I suggested in Section VI, rule out the use of uncaused items as objects of precognition or as the causes in any kind of backward causation. The defender of our precognition experiment must therefore fall back on the latter possibility discussed in Section VI, where the precognized pattern B can, at least in principle, be traced, through a causal series that is independent of the drawing A, to a cause C which precedes A in time. But we have seen that this is a conceivably defensible possibility. The fact that B is already causally fixed, a sufficient cause for it having already occurred when A occurs-so that the proposed "bilking experiment" is blocked-does not mean that we are committed to saying that what causally fixes B is either A itself or some cause of A."1 These

11 Black (Models and Metaphors, pp. 176-I77) states the dilemma: "If we can do this [i.e., arrange for the later event to disagree with the supposed precognition of it], the stipulations for the supposed precognition are logically impossible of fulfillment.... On the other hand, if we find that once Houdini has answered we cannot [do this] ... we shall be compelled to say that the causal antecedents of [the later event] are not independent of [the earlier]." In effect, I have argued against the second horn of this dilemma. I concede that if the later event is to be precognized, it must have a sufficient cause that has



are hypotheses that cannot be excluded a priori, but it is conceivable that the weight of the evidence should be against them.

VIII

What is important for my purpose, however, is the light that this objection and the reply to it throw on causal priority itself: the principle behind them both is that what is unfixed at a given time cannot be causally prior to what is fixed at that time. This suggests the following account of causal priority: if A and B are causally connected in a direct line, then B is causally prior to A if B is fixed at a time when A is still unfixed. It is a point in favor of this account that although it relates causal order to temporal order, it leaves it at least logically possible that there should be backward causation: for it is possible that although A precedes B in time (and therefore A is fixed before B occurs) B should nevertheless be fixed at a time before A occurs, when A itself is still undecided. Also, by introducing the contrast between what is fixed and what is as yet unfixed, this account satisfies our initial requirement that causal order should be at least something over and above temporal order.

This account will not quite do, however, for once a sufficient cause of some effect is fixed, the effect is also fixed automatically: there cannot be a time at which the sufficient cause is fixed and the effect is not, and yet we want to say that even a sufficient cause is causally prior to its effect. The following modification, then, is required: if A and B are causally connected in a direct line, then B is causally prior to A if there is a time at which B is fixed while A is not fixed otherwise than by its causal connection with B.

This account fits in with the suggestion considered in Section IV that causal priority has something to do with controllability and effectiveness, and that we are directly aware of causal priority in our own actions. For in making decisions and putting them into effect we at least appear to be fixing what was previously not fixed, what was literally undecided.

occurred before the earlier event; but there is no a priori reason for excluding the possibility that this cause is independent of the earlier event, and there may be evidence that strongly supports this possibility.


J. L. MACKIE

We can also relate this to what was mentioned in IV as one of the strongest objections to the concept of backward causation: a supposed backward causal relationship could not be used as a way of bringing something about, since at the time when the "cause" might be applied, the "effect" either has happened, or has failed to happen, already. In this respect there cannot be a time-reversed exact analogue of ordinary causation. This objection is not quite as damaging as it appears to be, however. While a backward causal relation could not be used on its own to bring something about, it is conceivable that it should be so used in conjunction with a forward causal relationship. In our scheme, someone could use C to bring about A by means of B. By doing something on Sunday to ensure that a particular pattern was produced on Tuesday, one could bring it about that a corresponding drawing was made by the precognizer on Monday. So although what was brought about (the drawing) necessarily (in view of the fixity of the past) occurs later than the bringing of it about, part of the chain of causation by which it is brought about might be time-reversed. Although backward causation could not have exactly the same relation to ways of controlling things that forward causation has, it could, as we have seen, embody the same causal priority as analyzed in terms of fixity, and this is the objective feature of the direction of causation which is indicated by the use of causal relationships to bring results about.12

This account of causal priority in terms of fixity would also make sense of the principle mentioned in Section I, that a cause can explain its effect in a way in which an effect does not explain its cause. For this principle now means that what is fixed at a

12 Cf. Flew in Analysis, I 7, and GaJe, op. cit. (see note i). If causal priority is identified with effectiveness as Gale defines it (see note 5 above)-and causal priority is, as I agree, an essential part of the ordinary notion of causation- then it follows that if the past is fixed, backward causation cannot occur. But it also follows that the notion of causation is incurably anthropocentric, and not strictly applicable to matters that lie totally beyond human control-e.g., processes that occurred before there were any human beings. If, on the other hand, causal priority is analyzed directly in terms of fixity, its connection with "effectiveness" can be understood, but the notion of causation will be much more widely applicable; but given this analysis of causal priority, backward causation is not ruled out a priori.




certain time can explain something that at that time is not fixed except by its connection with the former item, but not vice versa.

It may be felt that there is still something rather obscure and metaphysical about this contrast between fixity and nonfixity. The following, however, would seem to provide at least a basic elucidation of this contrast: an event E is fixed at time t if, and only if, either E has occurred at or before t, or a sufficient cause of E has occurred at or before t. Whether this is an adequate account of the fixity/nonfixity contrast for all purposes is a further question. But it seems adequate for our present purpose: in particular, if this is taken along with the account given above of causal priority, we still find that causal order is only loosely related to temporal order.

However, I want to leave this fixity analysis of causal priority aside for the present, and consider some other suggestions that have been made about asymmetries in causal processes.

Ix

There is a class of processes, pointed out by Sir Karl Popper as being temporally asymmetrical, of which an example is the system of circular waves spreading out from a center, as when a stone is dropped into a pool. The reverse process, with circular waves contracting to a center, would be equally compatible with the laws of physics, but it never, or hardly ever, occurs, whereas expanding wave systems are extremely common.13 As Popper says, the reverse process with contracting waves "would demand a vast number of distant coherent generators of waves, the coherence of which, to be explicable, would have to be shown . . . as originating from one centre." That is, we have here a situation in which A is a single event (the disturbance of the surface at the center of the pool), B is an occurrence which involves a sort of coherence between a number of separated items (a wave motion all round the circumference of the pool), and there are causal laws in accordance with which A could lead to B, but B could equally well lead to A. B, however, is here in need of explanation in a way in which A is not; conse-

13 See K. R. Popper, "The Arrow of Time," Nature, I77 (I956), 538; also Nature, I78 (I957), 382; and I79 (I958), I297.


J. L. MACKIE

quently A could satisfactorily explain B, whereas before B could explain A the coherence in B itself would need to be explained by reference to some other single event C. Examples of this kind establish a direction of explanation,from some central occurrence to the coherence of a number of separated items: explanation runs to situations involving dispersed order from ones which do not. Let us say that the central disturbance as compared with the expanded circular wave is prior with respect to the dispersal of order. If we add the principle that a cause explains its effect in a way in which the effect does not explain the cause, it follows that there can be a satisfactory explanation only if the causally prior item is also prior with respect to the dispersal of order. If the opposite were the case, if the item exhibiting dispersed order were causally prior to the central one, the two requirements for explanation would be in conflict with one another within the situation as thus far described, and we should obtain a satisfactory explanation only if we could go beyond this situation and find another item which was both causally prior and prior with respect to the dispersal of order to the item exhibiting dispersed order. These points are not directly relevant to the direction of time, however. It is clear that it is logically possible that a particular process which is the reverse of a normal one-that is, one in which what is prior with respect to the dispersal of order comes later in time, in which the order-dispersal direction is opposite to the order-dispersal direction of most other processes in the same time-continuum-could occur without there being any normal process available to explain its starting point. Nor would such a time-reversed process be intrinsically inexplicable. What is true is that such a reversed process would be explicable only if we could establish, or assume, that the item which was prior with respect to the dispersal of order was also causally prior, despite the fact that it came later in time; that is, such a process could be explained only in terms of backward causation. If in fact such a reversed process never occurs without a previous normal process to set up its initial conditions, this is only an exemplification of the general truth that processes that require explanation in terms of backward causation do not actually occur, though they are not logically ruled out.

We can put this in another way. An example of dispersed order,



such as the outer circular wave, is (in virtue of the laws of physics) a set either of joint effects or of joint causes of the central event. Also, because of the complex coherence it contains, it is intrinsically improbable and in need of explanation. Now if it is agreed that a cause can explain its effect in a way in which an effect does not explain its cause, it follows that a common cause can explain the co-occurrence of its joint effects whereas a common effect cannot explain the co-occurrence of its joint causes. Hence we have a satisfactory intrinsic explanation of this example only if the central event is the cause and the dispersed order item is a set of its joint effects.

Conversely, in many cases what is, or could be, a set of joint effects is an example of dispersed order, and therefore in need of the explanation that is provided by tracing them to a common cause. We may consider here a way of strengthening the precognition experiment that we have omitted until now.14 Suppose that instead of just one alleged precognizer we have a number, all making drawings on Monday of the pattern that is to be displayed on Tuesday, and suppose that all the drawings closely resemble the pattern that is later produced. Then the mutual resemblances between the drawings of this set are themselves in need of explanation; the set of drawings is in itself an example of dispersed order. If no common cause occurring earlier in time can be found, then it is plausible to take the subsequently produced pattern as the common cause, and to argue that a successful experiment of this modified form could conceivably give particularly strong support to a hypothesis of backward causation.

On account of the objection discussed in Section VII this defense of the experiment cannot be combined with the suggestion that the pattern is itself a product of pure chance or free decision. We must, therefore, admit that in principle a cause Cofthe pattern can be found which has occurred before the drawings are made on Monday, and C will therefore be a rival candidate to the pattern B for the role of the common cause of the drawings (which we may now call A1, A2, and so forth). The plurality of alleged precognizers and their drawings strengthens the evidence for precog-

14 Cf. Scriven, op. cit.

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J. L. MACKIE

nition because it rules out forward causation from the drawings A1, A2, and so forth to the pattern B: this forward causation would fail to explain the dispersed order among the drawings themselves. But there is still a rival hypothesis to precognition which could in principle explain this dispersed order-namely, forward causation from C which we have had to introduce as a cause of B in order to block the objection of Section VII. (In Diagram 2, higher points represent events later in time; the arrows represent directions of causation; the firm arrow from C to B represents the definitely postulated causation, while the two sets of dotted arrows represent the rival hypotheses which might explain the dispersed order among the A's.)

Diagram 2.

Even when the experiment is thus strengthened, then, it would not be conclusive evidence for backward causation; there would still be the problem of weighing the evidence for and against each of the rival hypotheses, including the inductive evidence for the view that all causation is forward causation.

We have found, however, both that priority with respect to the dispersal of order is evidence for causal priority, and why this is so. The one is evidence for the other, because if they coincide the situation is explicable, whereas if they fail to coincide it is bewildering: we have a situation that is in need of explanation, but no explanation can be given.

This point may help to resolve what would otherwise have been a difficulty: where do we find the data for the inductive conclusion that most or all causation is forward causation? If our detection of




causal priority were limited to experience of our own voluntary actions, then even if causal priority always coincided with temporal priority here, it would be rash to conclude that they coincide in processes of all other kinds. But if, as we have seen, priority with respect to the dispersal of order is evidence of causal priority, we can and do have far more extensive evidence for at least a normal coincidence of causal with temporal priority.

X

It is often suggested that the increase in entropy in any isolated system constitutes a general temporal asymmetry in causal processes. But this is not so.15 Let us consider the stock example of a rigid chamber containing gas, initially with part of the gas, at a higher temperature than the other part, concentrated at one end of the chamber; the two parts gradually mix and the gas ap- proaches a uniform temperature throughout the chamber. If we consider this chamber as persisting for a very long time, we must say that there is an enormous number of possible arrangements of the gas molecules, and that of these the overwhelming majority will be disordered-that is, will represent fairly uniform distri- butions of temperature. Ordered arrangements with a distinctly higher temperature at one end of the chamber than the other will be extremely improbable; nevertheless, given a sufficiently long time they will occasionally occur. It follows that among the (rare) occurrences of order, the change from order to disorder will be practically universal, whereas among the (very common) occurrences of disorder, changes from disorder to order will be extremely rare. Yet in this very long run changes from disorder to order will occur, and will occur with the same absolute frequency as changes from order to disorder. Examples of this sort, then, do not yet exhibit any asymmetry of causal pattern in relation to the direction of time.

But we find something further if we look more closely at the details of a change from order to disorder. The state of the gas a

15 Cf. A. GrUnbaum, Philosophical Problems of Space and Time (New York, i963), pp. 240-242. Griinbaum refers to earlier discussions, and ascribes the resolution of the logical difficulties to P. and T. Ehrenfest.


J. L. MACKIE

short time after the two parts have begun to mix will be, with respect to the general distribution of temperature, a fairly disordered one; nevertheless, it will be different from most equally disordered arrangements of molecules in that it is such that if the velocity of each molecule were simultaneously reversed, the gas would return in a short time to the very unusual distribution with the part at one end of the chamber at a higher temperature. That is, this is a rather special sort of disorder, and while the occurrence of disorder in general is intrinsically highly probable and requires no particular explanation, the occurrence of this special sort of disorder calls for explanation, and is indeed to be explained as the outcome of a recently previous ordered state. In fact, this special sort of disorder is just another example of what I have called dispersed order. The coherence is now concealed within what superficially looks like any other disordered arrangement of molecules; but there is still an intrinsically improbable coherence between the positions and velocities of the various molecules, which is brought out by what would happen if the velocities were reversed; this requires explanation and it is explained by its lawful descent from the recent obviously ordered state. Once again, then, we have a definite direction of explanation, to a dispersed orderfrom a nondispersed order to which it is related by laws. The mixing process, then, is explicable on its own, in terms of ordinary forward causation, because the temporally prior state is also prior with respect to the dispersal of order, so that a coherent explanation can be given if we assume that this temporally prior state is also causally prior. But a change in the opposite direction, a process of separation of two parts at different temperatures, because of the initial improbability of its initial state (its dispersed order), could not be explained on its own without assuming backward causation; yet, since this initial state is only improbable, it could be explained, going outside this process itself, as something that occurs very infrequently in a very long period of time, and this explanation would not require backward causation. In this respect, then, the entropy-increase type of example does yield an asymmetry, but it is strictly analogous to Popper's kind of example and introduces no new principle. These are both covered by the very general principle that otherwise improbable concomitances




and co-occurrences can be explained as joint effects of a common cause, as dispersed order lawfully related to a causally prior nondispersed order.

XI

It would appear, then, that in addition to temporal priority there are two other kinds of priority: causal priority as described in Section VIII with reference to the contrast between what is fixed and what is undecided, and priority with respect to the dispersal of order. In all ordinary cases, the three kinds of priority coincide. But it is a contingent fact that they usually, and perhaps always, coincide. It would indeed be bewildering if causal priority ran counter to priority with respect to the dispersal of order, for the two requirements for explanation would then be in conflict. We should have processes which were obstinately inexplicable; but this is still a logical possibility. But given that causal priority coincides with priority with respect to the dispersal of order, not only is it logically possible that these two together should fail to coincide with temporal priority, but if they did we would not need to find this bewildering: coherent explanation would still be possible. The evidence for backward causation in any particular case (such as even the final form of the precognition experiment) could not be conclusive, and in any single case the backward causation hypothesis would be opposed by the weight of the inductive evidence in favor of the view that all causation is forward causation. But it is conceivable that there should be many cases in which a backward causation hypothesis was prima facie the more plausible, and if there were enough of them they would rebut these inductive considerations. It is conceivable, then, that backward causation should occur, and should be discovered to occur; it appears that it does not, but if so, this is a contingent truth, and I have indicated the sort of evidence on which our knowledge of it can rest.

There is, indeed, another conclusion that could be drawn from this discussion. It might be argued that the contrast between what is fixed and what is not fixed is unsatisfactory, perhaps because at any given time all events, even future ones, are fixed in the sense


J. L. MACKIE

required, and hence that causal priority cannot be satisfactorily analyzed in terms of fixity. If so, we might identify causal priority with priority with respect to the dispersal of order. In place of what I have called the two requirements of explanation there would then be only one, so that there would be no possibility of their failing to coincide. On this view it would still be at most a contingent truth that causal priority coincides with temporal priority, but there would be only one contingent coincidence, not two. However, this conclusion is open to the objection that it would destroy the connection between causal priority and effectiveness, and indeed it would be hard to develop the concepts of voluntary action, control, and effectiveness without using the contrast between what, at any given time, is fixed and what is as yet undecided. The former conclusion, therefore, seems to be the more acceptable.

I have argued, then, that causal priority is something other than temporal priority; it cannot be analyzed in terms of the logical asymmetry of statements about inus conditions, and an analysis in terms of counterfactual conditionals would be circular; causal priority is connected with the way in which we can control things and bring results about, but this does not yield an adequate account of causal priority; discussion of the sort of experiment that could conceivably provide evidence for backward causation, and of some suggestions about temporal asymmetries in physical processes, has brought to light two kinds of priority, one according to which B is prior to A if there is a time at which B is fixed while A is not fixed otherwise than by its causal connection with B, the other being priority with respect to the dispersal of order. It seems that causal priority can be identified with the former of these, but the latter normally coincides with the former, and it would be bewildering if they ran counter to one another. Consequently, priority with respect to the dispersal of order can be and is used as evidence for causal priority; temporal priority is in practice also used as evidence for causal priority. But it is a contingent fact about the world that these three kinds of priority seem always to coincide.

J. L. MACKIE University of rork



Article Contentsp. 441p. 442p. 443p. 444p. 445p. 446p. 447p. 448p. 449p. 450p. 451p. 452p. 453p. 454p. 455p. 456p. 457p. 458p. 459p. 460p. 461p. 462p. 463p. 464p. 465p. 466

Issue Table of ContentsThe Philosophical Review, Vol. 75, No. 4, Oct., 1966Front Matter [pp. 425 - 425]Three Ways of Spilling Ink [pp. 427 - 440]The Direction of Causation [pp. 441 - 466]Consistency [pp. 467 - 495]DiscussionExplaining the Behavior of Entities [pp. 496 - 509]Infinite Causal Regression [pp. 510 - 525]

Book Reviewsuntitled [pp. 526 - 530]untitled [pp. 531 - 534]untitled [pp. 534 - 536]untitled [pp. 537 - 540]untitled [pp. 540 - 545]untitled [pp. 545 - 548]

Books Received [pp. 549 - 557]Back Matter

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Mackie, J L - The Direction of Causation

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