lewis on causal dependence

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Lewis on causal dependenceMichael McDermott aa University of SydneyPublished online: 02 Jun 2006.

To cite this article: Michael McDermott (1995) Lewis on causaldependence, Australasian Journal of Philosophy, 73:1, 129-139, DOI:10.1080/00048409512346441

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Australasian Journal of Philosophy Vol. 73, No. 1; March 1995

LEWIS ON CAUSAL DEPENDENCE

Michael McDermott

The purpose of this note is to suggest a way in which certain undesirable features of Lewis' analysis of causation may be eliminated. Lewis' theory may be summarised as follows: '(1) Causal dependence is counterfactual dependence between distinct

events . . . (2) Causation is the ancestral of causal dependence: event c causes event e iff either e depends on c, or e depends on an intermediate event d which itself depends on c, o r . . 71 If we assume determinism, as Lewis mostly does, counterfactual dependence may be defined as follows: ~

D1 e counterfactually depends on c

=df O(c) [3---,O(e) and -O(c) [3--~~O(e) .

If c and e are actual events, the first clause is automatically true. [O(c) is the propo-

sition that c occurs.] The undesirable features of the theory which I hope to eliminate are: (i) it

requires a profligate theory of events; (ii) it requires the acceptance of counterintu- itive verdicts on the truth of certain counterfactuals. I will suggest that these conse-

quences of the theory can be avoided by a fairly small change in the definition of counterfactual dependence.

There are no doubt other undesirable consequences of Lewis' theory which the suggested amendment does nothing to remove. It is merely intended to be neutral on these further questions: as far as I have been able to discover, it does not affect

the plausibility of the various proposals which have been made to amend Lewis' theory in other respects. I hope, of course, that my suggestion does not create new troubles itself.

Profligacy In 'Events' , §4, Lewis accepts a profligate theory of events. Consider

(Case 1) John greets Fred. Because he is tense, John says hello loudly. If he had not been tense, he still would have said hello, but softly. Fred jumps, and

then returns John's greeting. If John had said hello softly, Fred would not have jumped, but he still would have returned John's greeting.

In this case, Lewis says, two events of greeting by John occur. They have different essences. One (Strong) would not have occurred if John had said hello softly - it is

' [2, p.2421 2 [2, p.166-167]

129

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130 Lewis on Causal Dependence

an essentially loud greeting. The other (Weak) still would have occurred if John

had said hello softly - it is a loud greeting also, in actuality, but it is merely accidentally loud.

Lewis evidently finds such a theory of events unwelcome, and I assume we con- cur. He argues - correctly, I think - that it is forced on him by his theory of causation. We will need to be quite clear what the argument is.

The argument is not, as Lewis emphasises, from the fact that we have the two descriptions 'John's saying hello' and 'John's saying hello loudly'. Both descrip-

tions might refer to Strong, or both might refer to Weak. There is no reason why a

name of an event should give all and only its essential features.

Here is what Lewis regards as the real reason why we need both events:

The real reason why we need both events, regardless of which description

denotes which, is that they differ causally. An adequate causal account of what happens cannot limit itself to either one of the two. The first event (the weak one) caused Fred to greet John in return. The second one (the strong one) didn't. If the second one had not occurred - if John hadn't said 'Hello' so loudly - the first one still might have, in which case Fred still would have returned John's greeting. Also there is a difference on the side of causes: the second event was, and the first wasn't, caused inter alia by John's state of

tension?

This passage, however, is capable of two different interpretations. I think the

most obvious reading would be a misinterpretation. What Lewis seems to be saying

is as follows. We assent to the sentence

(1) It was John's saying hello which caused Fred's reply, not his saying it loudly.

To analyse this sentence we must take 'John's saying hello' and 'John's saying

hello loudly' to refer to Weak and Strong respectively, since the former caused Fred's reply and the latter did not. Similarly, we assent to

(2) John's saying hello loudly was caused by his state of tension, but his saying

hello was not.

To analyse this sentence we must take 'John's saying hello' and 'John's saying

hello loudly' to refer to Weak and Strong respectively, since the latter was caused by his state of tension and the former was not. In this kind of case - sentences

which (as we might naturally put it) distinguish the causally relevant features of a

cause or effect from its causally irrelevant features - we must take the different event-descriptions as giving the essences of different events.

But if this was what Lewis meant, he would face immediate refutation over the sentence

[2, p.255]

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Michael McDermott 131

(3) It was not John's saying hello which caused Fred's jump, but his saying hello loudly.

If we apply the analysis just described to this sentence, it says that Strong caused Fred's jump, and Weak did not. But this is false on Lewis' theory: certainly Strong caused Fred's jump, since if Strong had not occurred, i.e., if John had not said hello loudly, Fred's jump would not have occurred; but Weak also caused Fred's jump, because if Weak had not occurred, i.e., if John had not said hello at all, Fred's jump

would not have occurred. I think the correct interpretation of Lewis' argument is as follows. Firstly, the

sentence

(4) John's saying hello caused Fred's reply

must come out true. But, however much slack there may be in the connection between expressions which refer to events and the events' essences, (4) obviously can't be true unless there is an event which caused Fred's reply. And for this purpose only Weak will do. Secondly, the sentence

(5) John's saying hello loudly was caused by his state of tension

must come out true. And again, whatever the details of the analysis, (5) obviously can't be true unless there is an event which was caused by John's state of tension. And for this purpose only Strong will do.

On this reading, Lewis is concerned to have enough events to make true all the positive causal statements we want. He is not saying that we need Strong because the sentence

(6) John's saying hello did not cause Fred's reply

comes out false if ' John's saying hello ' refers to Weak; or that we need Weak because the sentence

(7) John's saying hello was not caused by his state of tension

comes out false if 'John's saying hello' refers to Strong. As we saw above, Lewis

must analyse negative causal statements in some less direct way: (3) comes out false if 'John's saying hello' refers to Strong, and false if it refers to Weak.

It is plausible to argue that we must admit certain purported events because we need them as causes or effects. But it would be implausible to argue, and I do not think Lewis is arguing, that we must admit certain purported events because, if they exist, they will fai l to be causes or effects.

To sum up Lewis' argument, as I think it should be understood, there are two premises, imposed by his analysis of causation:

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132

(P1) (P2)

Strong will not do as the cause of Fred's reply; Weak will not do as the effect of John's tension.

Lew& on Causal Dependence

And the conclusion is:

We need to acknowledge both Weak and Strong.

I think this argument is correct - Lewis' theory really does require the undesirable profligate theory of events. On the revised definition of counterfactual dependence which I shall suggest, (P1) will no longer be true.

The Fragile Bunzl Event

The next trouble for Lewis I want to look at comes up in his discussion of overdeter- mination, in Postscript B to 'Causation'. We have

(Case 2)

U The four neurons all fire. B fires vigorously, but would have fired feebly if stimulated by C 1 or C 2 alone. E still would have fired, and in the same way, if B had fired feebly.

Lewis thinks that

(8) The firing of C 1 caused the firing of E

is true (and similarly for C2). He tries to get this result from his theory as follows:

The vigorous firing of B that actually occurs depends on both of the simulta-

neous firings of C 1 and C 2. Without either one of these causes it would not have occurred. The feeble firing of B that would have occurred with only one of them would not have been the same event. But also the firing of E depends on the firing of B. So each of our redundant causes is connected to the final effect by a two-step chain of causal dependence. 4

The weak point here, in my opinion, is the justification for the claim that the firing of E was counterfactually dependent on the vigorous firing of B that actually occurred. Lewis is assuming that the counterfactuat

4 [2, p .210]

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Michael McDermott

(9) If B had not fired vigorously, it would not have fired at all

133

is true. But common sense objects, 'No, it might have fired feebly'. Lewis address- es this conflicting intuition in the following paragraph:

My solution depends on assuming that if the intermediate event - the vigorous firing of B - had not occurred, then B would not have fired at all. It isn't

that the vigorous firing would have been replaced by a feeble firing, differing only just enough not to be numerically the same. That may seem to go against a similarity theory of counterfactuals - wouldn't the minimal change

to get rid of an event be one that replaces it with a barely different event? Not so; a similarity theory needn't suppose that just any sort of similarity we can

think of has nonzero weight. It is fair to discover the appropriate standards of similarity from the counterfactuals they make true, rather than vice v e r s a . . .

And we certainly do not want counterfactuals saying that if a certain event had not occurred, a barely different event would have taken its place. They sound false; and they would make trouble for a counterfactual theory of causation not just here, but quite generally. 5

This seems very weak to me. Firstly, Lewis argues for ' I f B hadn't fired vigor-

ously it wouldn't have fired at all ' by arguing against ' I f B hadn't fired vigorously it

would have fired feebly'. But the alternative which common sense favours is that it might have fired feebly, not that it would. Secondly, he argues that we should not let our verdicts on counterfactuals be dictated by independent judgements of similarity. But what he is opposing here is a direct intuitive verdict on a counterfactual, not one derived from an intuitive judgement of similarity.

So it still looks as if the counterfactual (9), which Lewis' theory forces him to accept if he wants to endorse the intuitively acceptable (8), is itself contrary to common sense.

I think this is indeed the correct moral to be drawn from the case. But unfortu- nately there are some complications we must explore, to be sure that this view can be maintained.

It is a surprising feature of Lewis' discussion here (and indeed throughout the

Postscripts to 'Causation') that it takes no account whatever of the profligate theory

of 'Events' §4. Lewis talks here of 'The vigorous firing of B that actually occurs'. A little earlier he discusses whether the vigorous firing of B is a different event from

the feeble firing that would have occurred if either C 1 or C 2 had fired alone; his answer is that it depends on vague or shifty standards of fragility. He seems to

explicitly reject the idea that there are two actual firings, one more fragile than the other: 'Don' t say: here we have the events - how fragile are they? Instead it should be: here we have various candidates, some more fragile and some less - which ones do we call the events? '6

s [2, pp.210-211] [2, p.196]

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The crucial difference between the passages presently under discussion and the argument for profligacy is that Lewis relies on different intuitions - conflicting intuitions - about the truth values of the key counterfactuals. We have

(10) If John hadn't said hello loudly, he still might have said hello softly

and

(11) If B hadn't fired vigorously, it still might have fired feebly.

In arguing for profligacy, Lewis accepts (10). But in arguing for the truth of (8), he rejects (11).

How would Case 2 look if Lewis accepted both (10) and (11), in conformity with common sense? As in Case 1, he would need to acknowledge two simultaneous firings of B, one essentially vigorous, the other merely accidentally vigorous. The former is needed as the effect of the firing of C1: the accidentally vigorous firing will not fill this role, since it would have occurred if C 1 had not fired. But the latter is needed as the cause of the firing of E: the essentially vigorous firing of B will not fill this role since, by (11), E still might have fired if it had not occurred. Neither firing of B both causes the firing of E and is caused by the firing of C1, so there is no chain of counterfactual dependence linking C 1 with E. The common-sense verdict on (8) is abandoned.

I maintain that (10) and (11) are both true. Consistency, if not agreement with common sense, could also be achieved by rejecting both. And such a position, as well as upholding (8), has the virtue that it would undermine the argument for profligacy. The argument was that (i) only Weak will do as the cause of Fred's reply, but (ii) only Strong will do as the effect of John's tension. But if we reject (10), we are saying that if Strong had not occurred, i.e., if John had not said hello loudly, then John would not have said hello at all; so we may say that if Strong had not occurred, Fred's reply would not have occurred. Strong will now do as both the cause of Fred's reply and the effect of John's tension.

Avoiding profligacy is a good thing, but is it worth the cost of rejecting (10) and (11)? Let me leave this question unanswered, since I hope to show that we can avoid profligacy while accepting (10) and (11).

The Sum of Overdetermining Events as Cause I turn now, for my final example of trouble for Lewis, to his discussion of the causal role of the sum of redundant causes. The simplest case will do:

(Case 3) ( ~

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C1, C 2 and E all fire. If either C 1 or C 2 had fired alone, E would still have fired, in just the way it actually did fire. E would not have fired if neither C 1

nor C 2 had fired.

On Lewis' theory, neither the firing of C 1 nor the firing of C 2 was a cause of the firing of E. Many people find this result unintuitive, but that is not our present con-

cern. Assuming that neither the firing of C 1 nor the firing of C 2 was a cause of the

firing of E, must we say that the firing of E was uncaused? No, says Lewis:

[C]onsider the larger event composed of the two redundant causes. (I mean

their mereological sum. Not their d is junct ion . . . ) Whether or not the redun-

dant causes themselves are genuine causes, this larger event will be there to

cause the effect. For without it - if it were completely absent, with neither of

its parts still present, and not replaced by some barely different event - the

effect would not occur. For ex hypothesi the effect would not occur if both

the redundant causes were absent, and to suppose away both of them is just

the same as to suppose away the larger event that is composed of them. 7

The causal sentence Lewis defends is

(12) The larger event caused the firing of E.

I agree that this is true, according to common sense. But to get this result, Lewis is

forced by his theory to accept the counterfactual

(13) If the larger event had not occurred, the firing of E would have not occurred.

That is, he has to accept

(14) If C 1 and C 2 had not both fired, neither would have fired.

And (14) is clearly contrary to common sense. Indeed (14) has an even more serious defect than that: it implies that the firing

of C 1 caused the firing of C2! For (14) implies

(15) If C 1 had not fired, C 2 would not have fired.

Intuitively, this can be seen as follows: if C 1 had not fired, C 1 and C 2 would not

both have fired, and hence, by (14), C 2 would not have fired. If this is not suffi- cient, we can verify that (15) follows on Lewis' theory of counterfactuals. Suppose

(14) is true. Then, according to the theory, there is a world w such that C 1 and C 2

do not both fire in w, neither fires in w, and there is no closer world in which they

do not both fire but one of them does fire. It follows that there is a world, namely w,

[2, p.212]

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such that C 1 does not fire in w, C 2 does not fire in w, and there is no closer world in which C 1 does not fire but C 2 does. Hence (15) is true.

The Amended Definition

These three examples of trouble for Lewis have come from his discussions of a vari- ety of independently controversial issues. To help us focus on what I take to be the common source of the trouble, let me give an example of my own.

(Case 4) There are three buttons. If I press A or B, Victim gets an electric shock. If I press C, or none of them, Victim does not get a shock. I choose at random and press A.

Consider

(16) My pressing A was the cause of V 's getting shocked. (17) If I had not pressed A, V would not have got shocked.

The common-sense view, I take it, is that (16) is true and (17) is false. Then we may argue as follows. Since there are no intermediate events to provide a chain of counterfactual dependence, the truth of (16) implies that V 's shock was counterfactually dependent on my pressing A, according to Lewis' theory. But the shock was

counterfactually dependent on the pressing, according to the theory, iff (17) is true. Hence Lewis cannot accept the common-sense verdict on both (16) and (17).

There are of course numerous ways in which Lewis might try to avoid this conclusion. But all carry a cost.

Appealing to the profligate theory of events, Lewis might say that I actually per- formed several simultaneous pressings of button A, and the one which caused V's shock was essentially a pressing of A or B. The shock would be counterfactually dependent on this event, in virtue of the truth of

(18) If I had not pressed A or B, V would not have got shocked.

But, as Lewis himself argues, we should not admit such overly disjunctive events. There is also the unwelcomeness of profligacy in general.

One might argue, I suppose, that V's actual shock was counterfactually dependent on my pressing A, despite the fact that he would have got shocked if I had pressed B instead, because in that case V would have got a different shock. It might have been an intrinsically identical shock, but it would have differed in its relational properties, for example, by being preceded by my pressing B rather than A. But I agree with Lewis that our common-sense judgements of causation are not based on such extreme standards of event fragility as that.

Alternatively, Lewis might argue (somewhat as he does with respect to overde- termination) that if we examine the case in detail we will find an intermediate event which would not have occurred if I had not pressed A, and such that V would not have got the shock if it had failed to occur. Perhaps there would turn out to be some

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action of the internal mechanism of button A which would serve. The trouble with this line is that such a putative intermediate event is irrelevant, even if it really exists, since it was not mentioned or implied by the initial description of the case, on which our common-sense judgement of causation is based.

No doubt there exist still other possible responses, similarly ingenious and artifi- cial. But, I suggest, the overwhelmingly natural and obvious response is simply to allow that V 's shock was directly counterfactually dependent on my pressing A, even though the shock might have occurred without the pressing. All we need, to establish the direct counterfactual dependence, is that it is not true that the shock would have occurred whatever I did. We don't need it to be true that the shock would not have occurred without the pressing; we just need it to be false that it would have occurred without the pressing. Although (17) is false, the following is also false:

(19) If I had not pressed A, V would still have got shocked.

And it is the falsity of (19) which establishes the truth of (16).

In general, I propose that we replace Lewis' D1 by D2:

D1 e counterfactually depends on c =dr O(c) []--~O(e) and ~O(c) [:l--,NO(e) .

D2 e counterfactually depends on c =dr O(c) []--,O(e) and -(~O(c) []---,O(e) ).

If Conditional Excluded Middle was true, ~(-O(c) [t---O(e) ) would be equivalent to ~O(c) I:]--~-O(e) , and D2 would be equivalent to D1. [The principle of CEM is: (qb IS]--- ap) v (dp [:]--- .-ap).] And, as Lewis notes, s CEM is quite plausible. But I think Lewis is right to reject CEM, despite its plausibility. The reason CEM is a plausible principle is, presumably, that very many of its instances are true. This accounts also for the plausibility of Lewis' definition of counterfactual dependence. Most of the time, certainly in most of the examples Lewis discusses, the alternatives to c are similar in relevant respects: either we don't get our e on any of them, or we get it on all. The special feature of Case 4 is that among the alternatives to my pressing A some would have had the effect in question and others would not. So we can't say that e would have occurred in the absence of c, and we can't say that it would not; all we can say is that e might have occurred in the absence of c, and it might not.

This special feature is shared also by the three troublesome cases we extracted from Lewis. (Case 1) If John had not said hello loudly, he might have said hello softly (so (21) is false), and he might have not said hello at all (so (20) is false):

(20) If John had not said hello loudly, Fred would have replied; (21) If John had not said hello loudly, Fred would not have replied.

[1, §3.4]

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(Case 2) If neuron B had not fired vigorously, it might have fired feebly (so (23) is false), and it might not have fired at all (so (22) is false):

(22) If B had not fired vigorously, E would have fired; (23) If B had not fired vigorously, E would not have fired.

(Case 3) If C 1 and C 2 had not both fired, just one might have fired (so (25) is false), and neither might have fired (so (24) is false):

(24) If C 1 and C 2 had not both fired, E would have fired; (25) If C 1 and C 2 had not both fired, E would not have fired.

On the replacement definition of counterfactual dependence, the three troubles go away. (Case 1) John's essentially loud saying hello will now serve as the cause of Fred's reply, since Fred might not have replied if it had not occurred - (20) is false. We can get enough events to be the required causes and effects by admitting Strong alone, so the argument for profligacy collapses. (Case 2) We can preserve the common-sense view that the firing of C 1 caused the firing of E, without having to accept that if the linking neuron B hadn't fired vigorously it wouldn't have fired at all. All we need to accept is

(26) If B hadn't fired vigorously, it might not have fired at all,

and that is not contrary to common sense. And similarly (Case 3), we can preserve

the common-sense view that the combined firings of C 1 and C 2 caused the firing of E, without having to accept the disastrous (14). All we need to accept is

(27) If C 1 and C 2 hadn't both fired, neither might have fired,

and that is not contrary to common sense.

Indeterminism

In most of Lewis' discussion of causation he makes the simplifying assumption of determinism. The analysis of causation we have been looking at is only supposed to work under determinism, and the troubles arose in discussions conducted under that

assumption also. Likewise my suggested amendment to the definition of counterfactual dependence is only supposed to work under determinism.

Lewis has a more general analysis which is intended to work whether we assume determinism or not. Causation still consists in a chain of causal dependence, but he now says that e causally depends on c if the chance of e would have been much lower in the absence of c. The parallel generalisation of my suggested redefinition of causal dependence would be that e causally depends on c if it is not the case that

the chance of e would not have been much lower in the absence of c. As far as I can see, the two accounts give different results only in the case where

c has several significantly different alternatives - i.e., where the chance of e would

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have been much lower if this alternative to c had occurred, but not if that alternative to c had occurred. In this kind of case, I think the reasons for preferring D2 under determinism still apply. Consider an indeterministic version of Case 4: if button A or B is pressed the chance of Victim getting a shock is 88%; if C is pressed, or no button, the chance is 3%; as before, I press A (at random) and V gets a shock. We take for granted the intuitions which, in the simple indeterministic case, support the idea that a cause increases the chance of its effect. The same intuitions tell us here

that my pressing A caused the shock, even though the chance of shock might have been the same if I had not pressed A. The relevant point is rather that it is not the

case that the chance would have been that high whatever I did. I conclude with a note on my use of 'might'. Lewis' favoured view of 'might'

counterfactuals is that ' If a had occurred, b might have occurred' means 'Not (if a had occurred, b would not have occurred)'. He notes, however, 9 that there is per-

haps also another use, under which it means 'If a had occurred, b would have had some chance of occurring'. I agree that the former is the most natural sense in ordi- nary language, and have used 'might' solely in that sense in the foregoing. TM

University of Sydney Received January 1994 Revised July 1994

REFERENCES

1. Lewis, D., Counterfactuals (Oxford: Blackwell, 1973). 2. Lewis, D., Philosophical Papers: Volume I1 (New York: Oxford University Press, 1986).

9 [2, p.64] ~0 I have profited (insufficiently, he will think) from correspondence with David Lewis.

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lewis on causal dependence

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