Lewis’ counterfactual chains analysis [1973]

Lewis’ [1973b] analysis of causation differs slightly from Hume’s naïve counterfactual analysis. Lewis wants to analyse causation in terms of chains of counterfactual dependence (rendering causation a transitive relation) in order to analyse basic cases of early pre-emption correctly (cases we shall come to later). Note that counterfactual

dependence is not itself a transitive relation (i.e. if ~oA →→ ~oC, and ~oC →→ ~oD, then it does not follow that ~oA →→ ~oD). To give an analysis of a transitive causal relation in

terms of counterfactual dependence Lewis gives the truth conditions for causation in terms of counterfactual chains, where the truth conditions for counterfactual chains can be expressed as follows:

 There is a chain of counterfactual dependence from E to C iff there are some actual events (E, D, D1 etc… C), such that E counterfactually depends on D, D on D1 etc…. C.

Lewis’ 1973 analysis of causation can then be expressed as follows; where C and E are distinct actual events, then:

 C causes E iff there is a counterfactual chain of dependence from E to C.

How does the analysis deal with a paradigm case of causation? Suppose I throw a ball, and the window shatters. My throw (C) causes the window shattering (E) as follows: there is a counterfactual chain of dependence leading from the window shattering (E) to my throw (C), i.e. there are some actual events (the shattering (E), my ball in late flight (D), my ball in early-flight (D1), my throw (C)), such that the shattering (E) counterfactually depends on my ball in late flight (D), and my ball in mid-flight (D) counterfactually depends on my throw (C). Note the counterfactual chains analysis implies that counterfactual dependence between distinct actual events is sufficient for causation (i.e., it implies the truth of SC); for if there is a counterfactual dependence between C and E, then there is a counterfactual chain of dependence between C and E (namely, the chain that only includes C and E). Thus the counterfactual chains analysis squares well with our original intuition that SC really was sufficient for causation.

Lewis’ counterfactual chains analysis renders the causal relation a transitive one. Is causation really transitive? It certainly isn’t intransitive. That is, it is clear that there are cases in which C causes D, D causes E, but also C causes E. For instance, the striking of the billiard ball (C) causes the ball’s moving across the table (D), and the ball’s moving across the table causes the ball to be pocketed (E), but also the striking of the billiard ball (C) causes the ball to be pocketed (E). The choice is then between causation being a transitive relation (such that for all C, D, and E, if C causes D and D causes E, then C causes E), and a non-transitive relation (such that there are cases where C causes D and D causes E in which C is also a cause of E, but also different cases where C isn’t a cause of E). But which? Putative counter-examples to the transitivity of causation are common place. Witness:

An example due to McDermott40: Suppose a dog bites off Billy’s forefinger (C), which causes Billy to set off a bomb with his left hand (D), which in turn causes the explosion (E). However, surely the dog biting off Billy’s forefinger (C) is not a cause of the explosion (E)?

An example due to Hall41: Suppose Suzy gives Billy half of a deadly dose of poison (C), which causes Bruno not to give Billy the second half of the deadly dose (D), which in

40_{See McDermott [1995]}

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turn causes Billy’s survival (E). However, surely Suzy giving Billy half of a deadly dose (C) is not a cause of Billy’s survival (E)?

An example due to Field42: Suppose Suzy leaves a bomb outside Billy’s door (C), which causes Bruno to deactivate it (D), which in turn causes Billy’s survival (E). However, surely Suzy’s placing of a bomb (C) is not a cause of Billy’s survival (E)?

An example due to Papineau43: Suppose Billy’s being fat (C) caused him to go on a diet (D), and his going on a diet caused him to be thin (E). However, surely Billy’s being fat (C) was not a cause of him becoming thin (E)?

An example due to Bennett44: Suppose heavy rain in April (C) caused the delayed electrical storm in June (D), and the delayed electrical storm in June caused the forest fire (E). However, surely the heavy April rain (C) was not a cause of the forest fire (E)?

An example due to Lombard45: Suppose Brown’s heroic action (C) causes Jones not to be stabbed one night by Smith (D), and that Jones’ not being stabbed that night (D) causes the persistent Smith to kill Jones a year later (E). However, surely Brown’s heroic action (C) is not a cause of Jones’ death a year later (E)?

42_{Hartry Field, cited from an unpublished lecture, see Lewis, p. 97, [2001]}

43_{See Papineau [1986]}

44_{Bennett, p.222-3, [1987]}

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An example due to Ramachandran46: Suppose Singh was due to detonate a bomb but is instead involved in an accident (C) that prevents this. Patel detonates the bomb instead (D) and the bomb explodes (E). However, surely the accident (C) was not a cause of the explosion (E)?

What are we to make of such putative counter-examples to the transitivity of causation? Some have accepted that the causal relation is indeed non-transitive (see Yablo [2004]), some have resisted such counter-examples (see Lewis [1973b]), others have said that there are in fact two different, but equally useful, concepts of causation- one transitive, the other non-transitive - and it depends on context which concept we are using (see Hall [2001]).

Which reaction should we prefer? Lewis, when he defends a transitive causal relation, understands statements of the form ‘C causes E’ in terms of ‘C is in the causal history of E.’ He writes: “in rejecting the [putative] counter-examples [to the transitivity of causation]… I think I am doing what Historians do. They trace causal chains, and without more ado, they conclude that what comes at the end of the chain was caused by what went before”47. In contrast, the pull against the view that causation is transitive seems to come from the fact that we often understand statements of the form ‘C causes E’ in terms of ‘C causally explains E,’ such that when we address the putative counter-examples above, we find it counter-intuitive to cite C as a cause/causal explainer of E; and this is

46_{Ramachandran, p390, [2001]}

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supported by the fact that E does not counterfactually depend on C in such examples, confirming the view that counterfactual dependence should hold in paradigm cases of causation.

The matter of whether causation is transitive or not then seems to become an issue of what causal concept we are talking about. We should then understand analyses of causation that render the causal relation transitive to be analysing a causal concept about causal histories, and analyses that render the relation non-transitive to be analysing a causal concept about causal explainers. This shall subsequently widen the scope of our investigations for an interesting causal concept.

So far we have discussed Hume’s counterfactual analysis [1948] and Lewis’ counterfactual chains analysis [1973b]. We shall now visit Lewis’ later analyses of a more sophisticated variety.