causal preemption and counterfactuals

Causal Preemption and CounterfactualsAuthor(s): Martin BunzlSource: Philosophical Studies: An International Journal for Philosophy in the AnalyticTradition, Vol. 37, No. 2 (Feb., 1980), pp. 115-124Published by: SpringerStable URL: http://www.jstor.org/stable/4319357 .

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MARTIN BUNZL *

CAUSAL PREEMPTION AND COUNTERFACTUALS

(Received 30 October, 1978; in revised form 16 August, 1979)

Cases of genuine causal preemption may be rare but they are nonetheless interesting. They are rare because it is difficult to arrange the physics of events so that one event (C1 ) can cause another E, while preempting the efficacy of a third (C2), that would have had the identical effect (E) if C1 had not occurred. But rare as they mat be, genuine cases of causal preemption can be cooked up. ' Such cases are interesting because our intuitions about them are reasonably clear. As such they fonn a good test for proposed analyses of causation. In particular, they pose a challenge for any account of causation which requires that a cause be necessary for its effects. In this paper I shall argue that one such account, David Lewis' counterfactual conditional approach, fails to meet this challenge.

Lewis' proposed analysis of causation is that one event (C) is cause of another (E) if and only if E depends counterfactually on C or there is a causal chain from the first to the second; where, a causal chain is a finite sequence of particular events (C, D, E...) such that D depends counterfactually on C, E on D and so on; and, an event E is counterfactually dependent on an event C in world co if some non-C world that is a non-E world is nearer to co than all non-C worlds that are E worlds.2

Now suppose that Cl causes E and preempts C2 which would have caused E if C1 had not occurred. Then, it seems that on the proposed Lewis analysis, Cl is not the cause of E, since if Cl had not occurred, E would still have occurred. Lewis' defense against this line of attack is to deny the claim that if Cl had E, C2 would have occurred but had failed to cause/caused E. His argument runs as follows:3 Not every causally connected pair of events need exhibit the counterfactual dependence ofthe effect on its cause since counterfactual dependence need not be transitive. (If E depends counterfactually onD, andD on C, it does not necessarily follow that E depends on C counterfactually.) Assume that E depends counterfactually on D, which is in tum counterfactually dependent on C1, where C1 preempts C2 . It might seem that without D, E would still

Philosophical Studies 37 (1980) 115-124. 0031-8116/80/0372-0115$01.00 Copyright ? 1980 by D. Reidel Publishing Co., Dordrecht, Holland, and Boston, U.S.A.



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happen, since if D did not happen, C1 would not have happened, and hence, C2 would have happened, causing E. But Lewis replies that if D had not happened, C1 would still have happened, and would have merely failed to cause D and thus E, even though C2 would still have been preempted. Hence, if D had not happened E would not have happened. Hence, the counterfactual analysis preserves the claim that D is the cause of E.

But why should we say that if D had not happened, C1 would have happened, but would have failed to cause D? Lewis assumes that determinism holds, and argues that if D had not happened then (assuming that causes precede their effects) the whole of the past causal chain that culminates in the occurrence of D would have to be different, unless there was a breakdown in the causal laws which connect that chain somewhere along it.4 Consider possible worlds in which D does not happen. The causal chain that culminates in the occurrence of D in our world does not exist in some of those possible worlds. In others there has been a breakdown in the lawful connections at some point along the chain so that they are similar to our world up to the point of the breakdown, and different thereafter. Consider different possible worlds in which such breakdowns occur at different points along this causal chain. In (at least) one of these possible worlds the breakdown will occur at the last possible moment, that is in the connection between C1 and D. Compare the past of this world (a) to past of the other worlds in which there is a breakdown in this lawful connection as well as those in which the whole causal chain has been changed. Surely this possible world (oa) will be closer to our world than any of these other worlds. But that is just to say that the closest possible non-D worlds are in fact C1 worlds. The lesson that Lewis wants to draw from this is that similarity between possible worlds includes perserva- tion of facts and preservation of laws, but that a small breakdown in laws is worthwhile of the whole of the past can be preserved between the worlds.

My objections to this argument are threefold: S first, it restricts considera- tion of cases of causal preemption to examples involving causal chains. But cases of causal preemption can also arise in the context of direct causal dependence. Second, in order to preserve his possible worlds analysis of counterfactual dependence, Lewis needs to argue that in every case of causal preemption (where in co Cl preempts C2 and causes D which causes E) some C1, non-D world is closer to co than every non-C1 , non-D world. But it tums out that merely assuming determinism to hold (as Lewis does) is not enough to make this claim plausible. Third, once differences in the laws governing



CAUSAL PREEMPTION AND COUNTERFACTUALS 117

other possible worlds and our world (co) have been marshalled in an attempt to show how some C1, non-D world is closer to X than every non-C1, non-D world in cases of preemption, Lewis must prevent a similar kind of appeal to differences in laws from undermining the usefulness of his possible worlds analysis of the counterfactual dependence involved in forward directed cases of causation that involve no preemption. His attempt to do this is unconvonc- ing. I shall consider each of these objections separately:

(1) The problem set was to show that C1 is a cause of E on the counterfactual analysis, even if it preempts C2. Lewis' argument is designed to show that it is because there is a causal chain connecting C1 to E via D. But what is the justification for introducing D in the first place? Suppose that C1 causes E directly, preempting C2. Then E would be counterfactually dependent on C1 itself since there is no intervening event in het causal chain to undermine such direct dependence. Lewis has to block such an example because under such circumstances, if C1 had not happened, C2 and hence E would have happened. Lewis cannot argue against such an example by claiming that for and two events there is a third event that intervenes between them because, on his own definition, a causal chain that connects two events consists of a finite number of particular events. What then justifies the restriction of the argument about preemption to cases where the causal chain connecting C1 and E consists in at least two steps? Perhaps Lewis thinks that cases of preemption cannot exist unless such a state of affairs obtains. But suppose that a poison can be mixed to form a compound with other chemicals some of which make the poison faster acting and some of which block the effect of samples of the pure poison. Let C1 be the ingestion of such a compound and let C2 be the ingestion of the poison simpliciter. Suppose C1 kills the person ingesting it. Then let E be the first event along the chain that connects the event of the ingestion to the event of death. Suppose that C2, the ingestion of the slower acting version of the poison, occurred before C1, and suppose that it would have been connected to E by a chain of two or more events, but that C1 interrupts this chain by chemically blocking it at some point along it. That is to say, C1 plays a role in two causal chains: one that kills the ingestee, the other which blocks the chain from C2. Perhaps Lewis would simply deny that C1 dauses E. But, given our relatively clear intuitions about preemption, such a response would surely smack of question begging.

(2) To reconcile cases of causal preemption with his possible worlds analysis of counterfactual dependence, Lewis cannot allow that any non-Cl, non-



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D world is closer to w than the closest C1 , non-D worlds (where C1 causes D in w). His device for ensuring this is to assume determinism, and to argue that any non-C1 world is a world in which the past has been changed and is thus a world much different from one in which C1 occurs but simply fails to cause D by way of some minor difference in laws. But even if there is a long chain that would have to be changed if D failed to occur and there was no breakdown in the laws, why must the breakdown occur at the last possible moment? Suppose law L 1 connects C1 tot D, but law L2 connects C1 to its predessor B in the causal chain. Now if L1 and L2 were the same law, it would be surely preferable to have the violation occur later rather than sooner and Lewis' argument would hold. But suppose now that L1 is central to a deductive systemization of laws while L2 is a comparatively low level nomological generalization, so that giving up L 1 will entail a much greater cost than giving up L2 because ofL1 's more complicated interconnections in the nomological network.6 Of course, if all laws are considered on a par with one another this argument will cut no ice. But I do not think this is a view that Lewis would ascribe to given his conception of lawhood. 7

Once it is allowed that giving up different laws will involve different costs, the question of how much backtracking to trade off for any law we want to preserve becomes much more complicated. Even though he thinks that laws as well as world lines are part of the measure of the degree to which worlds differ,8 Lewis' argument requires that we never trade any backtracking to preserve a law. I see no justification that would support this strong preference for the preservation of events over laws. Consider the counterfactual: if Nixon had been born in Russia, he would have been a communist. Now consider the nearest possible worlds to our world in which Nixon was born in Russia. Are these worlds that are identical to our world up to the point of Nixon's birth? That is to say, are these worlds in which Nixon's mother lies in Whittier, California just up to the point at which Nixon is about to be bom? Are they then worlds in which, by some mysterious law, Nixon is born in Russia, but his mother gives birth in Whittier? Or, is she moved at the speed of light from California to Russia just at the point of birth? Surely the possible worlds in which Nixon is born in Russia that are closest to our world are worlds in which the past is not identical to ours, but ones in which the past has been changed in certain relevant (causal) respects to minimize the difference in the laws governing the two worlds. And one difference between the pasts of the worlds is that Nixon's mother was in Russia just before she




gave birth in the closest possible worlds in which Nixon is born in Russia. Even assuming determinism (with Lewis), infinite backtracking need not occur for this change to occur: all that needs to be different (for example) is some low level law governing Nixon's mother neuron forings. The result is that virulent anti-communist propaganda in Whittier convinces her to serve

'9 the Revolution by moving to Russia before giving birth to 'Nixon' (3) Appealing to small differences between the laws that govern our world

and those that govern other possible worlds to preserve the counterfactual approach to causation in the case of causal preemption is arbitrary. Lewis argues that given C1 preempts C2 while it causes D which causes E, from the fact that D failed to occur it does not follow that C2 would have occurred. Rather C1 would have occurred and merely failed to cause D due to a breakdown in the laws. For this world is surely closer to w than worlds in which the past is changed. But if some worlds in which laws break down are closer to our world than those in which the laws are the same and the past world lines are different, why aren't they closer than those worlds in which the future world lines are different from ours? Of course, if they are, then the general analysis of forward directed causal dependence will collapse in that if E occurs, then the closest non-C worlds to cX will not be non-E worlds even if C caused E in o. Rather, the closest non-C worlds will be E worlds in which miracles have occurred. Lewis makes a general argument to block this kind of move: where causation is from 'past' to 'future', the closest possible worlds are those worlds where the facts in the past are preserved at the costs of miracles (i.e. differences in laws), but facts in the future are not.10 (The opposite holds when the direction of causation is from 'future' to 'past.') The basis of this is that preservation of facts in the future requires a much greater miracle than that required to preserve facts of the past. Consider a roulette wheel governed by deterministic laws that stops on black.11 Now consider the nearest possible worlds in which the wheel stops on red instead of black. Shall we say that all of the past in these worlds is different from ours? Lewis thinks that a small miracle will allow the pasts to be identical up to the point just before the wheel stops. But once the wheel has stopped, if we wish the futures of these possible worlds to coincide with our own, all of the traces of the wheel stopping will have to be removed by miracles, as well as the traces left by the removal of these traces and so on. And worlds with such a pletho- ra of miracles will surely be further from out world than ones in which the future is different.



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But now consider another possible world (e); the world in which C does not occur but just one of its many traces, E, does. Here a miracle occurs, but it is restricted to E. There seems no reason to think it need be different in size from the miracle that prevents E from occurring when C has. 12 Even if these two miracles are the same size, Lewis would endorse the latter but not the former because with the latter we retain the past identical to our past, while in the former the future is not likewise preserved: 13 though E occurs, it does so without the other traces of C. But is this small miracle worthless? Suppose (modifying an example of Kit Fine14) that in world co Nixon did press the button (C) and there was an ensuing thermonuclear explosion (E). Of course, this is not the only trace of Nixon's action, but the other traces are either obliterated by E or pale in its shadow. Shall we not say that a world with the explosion, even if it lacks the traces of Nixon's sweat on the button, is much closer to world co than a world in which both are absent, even if the former world contains a small miracle? If we allow small miracles to preserve the past identical to our own, why not by parallel reasoning allow small miracles to preserve the future very close to our own? Now while worlds with the miracles needed to make their futures identical to our own could be ruled out because of the numbers of miracles required, here only one small miracle is needed to precipitate a world in which the cause C does not happen but at least some of its effects (E) do. In order to preserve his analysis of causal dependence in terms of counterfactuals, Lewis must claim that this world is further from out world than the nearest worlds in which neither C or E occur. That is to say, he must deny that the possible world in which there is a nuclear explosion by way of a miracle is closer to world C (in which there is a nuclear explosion by way of the button being pushed) than the world in which neither occur.

Lewis' answer to this problem is that a consequence of his analysis of counterfactuals is simply that we should prefer small violatons of law to preserve world lines of possible worlds identical to our own, but should not do so if all we do is preserve world lines close to our own, (however close they may be.)'5 And while he does not "claim that this pre-eminence of perfect match is intuitively obvious", Lewis does believe that it is a feature of at least "some relations of overall similarity, and it must be a feature of any similarity relation that will meet" the needs of his analysis.'6 With the argument for the pre-eminance of a perfect match in hand, Lewis thinks that he has enough to explain why small violations of laws are to be preferred over




changing the past world lines but not the future world lines (when the direction of causation is from the former to the latter): the past, unlike the future, can be kept identical under such circumstances.

But, even if Lewis does have an argument in hand, as I have argued above (see point 2), it is by no means clear that violations of our laws to preserve the past of world lines in possible worlds as identical to our own are preferable to small deviations in the past if this can be accomplished with a small violation of the laws. (The mira2les may be less drastic if they occur before the last possible point in time). Yet if such cases are plausible, then we should prefer small violations of laws that preserve the past of some world lines as merely close rather than identical to our own. Lewis might insist on main- taining the claim of the pre-eminence of a perfect match as the crucial feature of the similarity relation that will meet the needs of his analysis. But to do so would bring the analysis into serious dissonance with our counterfactual practice, when (with Lewis), we assume determinism to hold.

These considerations lead me to be pessimistic about the prospects for a counterfactual conditional analysis that can successfully accommodate cases of preemption, where the analysis is designed to capture a necessitarian approach to causation.

Livingston College Rutgers University

NOTES

* I am grateful to my colleagues in the Department of Philosophy at Rutgers, to Nancy Cartwright and to an anonymous referee, for commenting on earlier drafts of this paper. ' Consider a light bulb that is placed in two identical electrical circuits. Suppose a switch is placed in both circuits at the same distance from the bulb in each case. Now suppose that this switch operates in such a way that whichever position it is in, one of the circuits is closed and the other is open. Then when the switch is in one position it completes one of the circuits and the bulb lights op. Let the event of the switch being in that position at time (t) be C,, and the subsequent lighting up of the bulb be at time (t+1) be E. Then C1 blocks the causal efficacy of a host of events that would have produced E if the switch had been in the other position; the battery in the second circuit having the charge that it did at time (t), the wire in the second circuit having the co- efficient of resistance it had at time (t), and so on.

Most examples of alleged preemption offered in the literature turn out to be cases in which Cl causes E1 and preempts C2 which would have caused a different event E2 if C1 had not preempted it. (Thus suppose one poison which is fast acting is alleged to preempt the effect of a slower acting poison when both are administered to a victim at



122 MARTIN BUNZL

the same time. Here the death that would have resulted from the slow acting poison will be different from the death that occurred because at the very least it would have occurred at at different time.) Such cases of 'preemption' abound since any event that occupies a location of space and time preempts all other events from occupying that location where if they had other effects would have resulted. 2 See D. Lewis, 'Causation', Journal of Philosophy LXX (1973), pp. 556-567.

Ibid., P. 567. 4 See, 'Causation', p. 567, and 'Counterfactual dependence and time's arrow',Nous, forth- coming. (In cases of backward causation it will be the future causal chain that would have to be different. Like Lewis, for the purposes of exposition, I will only consider cases of forward directed causation in this paper. To apply the arguments to cases of backwards causation simply interchange 'past' and 'future' throughout the paper.) 5 The last two apply with equal force to a parallel argument used by Lewis ('Causation', p. 566) to support the claim that if C could not have failed to cause E it does not follow that if E had not happened C would not have happened (because the nearest non-E worlds are C worlds in which a law connecting them has broken down). 6 An example suggested by Peter Klein: suppose L1 connects C en E by subsuming the (appropriately described) under Newton's Second Law, while L2 connects B (C's immediate predecessor in the causal chain) and C (appropriately described) under New- ton's Third Law. 7 Though there are innumerable true deductive systems (so that Li may be more basic than L2 in some, but L2 more than L, in others), Lewis thinks that only some of these systems will have the properly balanced combination of strength and simplicity (Coun- terfactuals (Blackwell, Oxford, 1973), p. 73). In these systems some laws will be more informative than others and hence the worlds in which we give them up will make for greater differences than the worlds in which we give up less informative laws. (See also, 'Causation', p. 560). 8 Ibid., p. 75. 9 As Bob Weingard has pointed out, not every kind of determinism will do the job that Lewis has in mind, since only some forms of determinism allow all that the present determines the future but is itself compatible with only one past. Lewis needs to assume that non-Markovian determinism holds. 10 Ibid., pp. 75-77. 1 Ibid. 12 In this world (,B) it is not all of C's traces that occur, but just one, E. Consider all of the necessary causes that are jointly sufficient for E in our world (w). If one of them (C) fails to occur in this world, we must precipitate what would be violation of the laws of our world (a miracle), to make up for C's absence. But why should this violation be any smaller or larger than the violation to prevent E from occurring when all of the causes sufficient for it occur? Let E be the event of the roulette wheel stopping on black and let C be one of the causes of this event (in w). In some worlds C and all of E's other causes occur, but E fails to. In such worlds the laws are momentarily different from those in w. In other worlds, all of E's causes save C occur and E occurs, although none of the other traces that accompany its occurrence in w occur. Here too there is a mo- mentary difference between the laws of such worlds and w. Is there any reason to think that these two miracles need be any dofferent in size? It is hard to see why. For in both cases they involve a small nudge in the roulette wheel: in one case to prevent E in spite of C, in the other to precipitate E in spite of the absence of C. It might seem that there is a reason to think that the size of the miracles is different because one only involves preventing something from happening while the other requires the creation of something. But this way of picturing things is misleading. For in both cases all that is being changed are the laws that govern these worlds. In one case the law is changed to make the set of




sufficient conditions insufficient, while in the other, the law is changed to make the set of sufficient conditions redundant. 13 See 'Counterfactual dependence and time's arrow', p. 17. 4 K. Fine, 'Critical notice of Counterfactuals', Mind LXXXIV (1975), p. 452.

1 'Counterfactual dependence and time's arrow', p. 17. 16 Ibid., p. 17.

ADDENDUM

Since the original submission of this paper, Marshall Swain has published an article in this journal (34, 1978, pp. 1-19) that raises some of the same com- plaints about Lewis's analysis of comparative similarity as I have discussed in point 3 above. Swain has suggested an alternative account of the causal relation which makes use of a possible worlds analysis of counterfactuals but without appeal to 'miracles'. His intuition is that if C and E are specific events that occurred and C caused E, then there will be at least one difference between the sort of world we would need to imagine in which C occurs without E and the one we would need to imagine in which E occurred without C. The difference is that in the world with C but without E we would need to imagine that some event (other than C) upon which E depended failed to occur; however, in the world with E but not C we would need to imagine two sorts of events. In such a world we would need something (other than E) upon which C depended to fail to occur, but we would also need something present to cause E in that world in the abscence of C. Swain proposes to use this difference in defining the causal relation in such a way as to guarantee asymmetry. (The fonnal account is unfortunately marred by a printer's error. His condition (iii) (2) in D7' (p. 11) ought to read:

some event g occurs in w2 such that e is not causally dependent upon g in w but e is causally dependent upon g in w2 .)

But now consider two light switches (S1 and S2) which are both wired to the same electrical source independently, as well as to the same light bulb. Suppose further (in the manner of Swain's 'Case 2' (p. 13)) that SI can overide S2, but not vica-versa. Now, instead of considering a straight forward case of preemption, suppose that S2 is closed while SI remains open. (Let us further suppose that when SI overrides S2, it does so by preventing the latter from closing. Parallel to the case discussed in point I above, let us also suppose that the relevent causal chains between S1, S2 and the light bulb



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contain only one step each.) Now imagine a world with the light on (E), but with S2 open (not C). What do we need to imagine for such a world? Imagin- ing that SI is closed would seem to do the trick. For SI's being closed both provides what we need for E in the abscence of C, as well as providing us with what we need for C in the abscence of C, as well as providing us with what we need for C to fail to occur - the failure of SI to be open. But now we seem to have a case in which we only have to imagine one sort of thing in- order to have a world in which E but not C occurs. The case therefore seems tot constitute a counter-example to the feature that is meant to guarantee asymmetry.

It may, however, be objected that the above is not a counter-example for the following reason: when we imagine SI to be closed we thereby imagine a state of affairs in which something upon which C causally depends (in the real world) fails to occur, and at the same time we imagine something (other than C) upon which E is causally dependent (in our imaginary world). Si is just doing double duty for two forms of causal dependence that must obtain for a world in which E but not C occurs.

But this objection can only be exercised on pain of circularity. The relevant difference we seek is as Swain puts it,

between the closest worlds we would need to imagine in order to imagine that c occurred but e did not occur and the closest worlds we would need to imagine in order to imagine that e occurred when c did not occur. (p. 11)

The above hypothetical reply to the proposed counter-example assumes that the number of instances of causal dependence (rather than events) that differ between two possible worlds provides a measure of their closeness. But causal dependence depends on counterfactual dependence. And counterfactual dependence in tum depends on claims about some worlds that are judged to be close to our world.



causal preemption and counterfactuals

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