Abstract
I argue that causation is a contrastive relation: c-rather-than-C* causes e-rather-than-E*, where C* and E* are contrast classes associated respectively with actual events c and e. I explain why this is an improvement on the traditional binary view, and develop a detailed definition. It turns out that causation is only well defined in ‘uniform’ cases, where either all or none of the members of C* are related appropriately to members of E*.
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Notes
Contrast classes are to be understood as non-empty sets of contrast events. For ease of exposition, I shall use ‘contrast class’ to refer to both singleton and non-singleton sets. I shall denote actual events by c and e and associated contrast classes by C* and E*. Later, I shall denote generically by C0 and E0 specific contrast classes that are members of the broader sets C* and E*. Where helpful, numerical suffixes such as C1, E2 etc will be used to denote different choices of C0 and E0.
For ease of exposition, often in what follows I shall follow normal usage by speaking of causation as if it held solely between two actual events, but in all such cases a specification also of contrast classes should be taken to be implied as appropriate. I shall argue in Sect. 6 that such linguistic ellipsis is in any case readily explicable and normally harmless. Also for ease of exposition, I shall frequently speak of counterfactual entailment holding between the contrast events themselves rather than between the propositions of their occurrence. Finally, except where stated otherwise, I examine only cases of token deterministic causation.
Thus I disagree with Hitchcock’s comments (2003, 10) that:
We do not need an answer to this causal question to answer the standard barrage of questions. Does Captain deserve praise for saving Victim’s life? Clearly he does not. If Captain actually wanted Victim to survive, did he pursue a rational course of action? No more rational than the alternative of withholding the order”. But my view, as the main text argues, is that in some circumstances invoking causation might be very informative precisely with respect to questions such as these.
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Exceptions include realist theories such as those of Tooley and Armstrong, and physical connection theories such as those of Salmon and Dowe. Although formally consideration of contrast classes could be grafted onto these too, there is more natural motivation to do so with difference-making accounts.
Humphreys (1989, 38) defines the neutral level of a cause to be that level at which “the property corresponding to that variable is completely absent”. But although useful for other purposes, this cannot help us here. For such a neutral level in effect already presupposes some specification of E* (‘the property … completely absent’). In our terminology, the specification of C* is objective only once given an E*, so there inevitably still remains one degree of freedom, as it were, for contextual considerations.
As Woodward remarks, on such a view the causal relata can be viewed as changes in the values of variables. More precisely, the relevant changes here are those between c and C0, and between e and E0.
I omit discussion here of how we might incorporate a contrastive sensibility on the effect side too.
Formally, proscribing e = E* is equivalent to Woodward and Hitchcock’s demand that causation be defined only via ‘testing interventions’ (Woodward and Hitchcock 2003, 17). Informally, it is just the demand that any cause make a difference.
Some Lewisian formulation such as requiring, roughly speaking, that C*&E* obtain in a closer possible world than any in which either of c&C* or e&E* do, will be too weak again. For this does not imply counterfactual entailment between C* and E*—for instance, because the conjunction of C* and some other contrast class, E1 say, might be in a yet closer possible world even than C*&E*. I am also reluctant to build in from the start a commitment to any particular semantics for counterfactuals, Lewisian or otherwise.
What determines the selection of these C0 and E0? In brief, the answer is context. It will follow that our causal judgment is correspondingly context-sensitive, just as in the two assassins case (Sect. 6).
If C0 and E0 are taken to be respectively c and e’s negations (more strictly, the negations of the propositions of their existence), formally (D2) reduces to Lewis’s original definition of causal dependence (1973). But recall our earlier caveat that the causal properties of such negations are in general underdetermined save by smuggling in contrastive considerations.
It does so, at least, as long as we assume determinism. Otherwise, a single C0 might lead to either E1 or E2, where only one of the latter is in {E0}. For example, suppose that an alternative defense minister taking office could chancily have led to a budget of either 0.5 or 1.5 bn. For the first figure, the actual minister taking office was therefore the cause of a higher budget, for the second the cause of a lower one. In this now indeterministic world, causation would then presumably depend on the two outcomes’ relative probabilities. But this paper will concentrate only on the deterministic case.
Notice that continuous contrast classes, such as {E0} in the defense minister example, do not seem to pose any particular difficulty. The conditions for causation can be taken to apply simply to every element in the relevant set, regardless of whether those elements are countable.
Schaffer (2005, 318) proposes an extra requirement, namely that every Ei in {E0} must be entailed by some Ci in {C0}. But I think this addition is unnecessary. Consider the case of the defense minister in the text, for example. Clearly, the minister taking office is still a cause of a higher budget even if there exists some budget figure below 1 bn dollars that, it turns out, would have been obtained by none of the possible alternative ministers. There is an asymmetry here between cause and effect: whereas every Ci in {C0} must entail an appropriate Ei, not every Ei in {E0} must be entailed by an appropriate Ci. This asymmetry, it seems to me, is just reflecting the logical asymmetry of the entailment relation: ‘X entails Y’ requires that all X’s must indeed entail Y’s, but not that all Y’s must be entailed by some X.
Perhaps some account of ‘group’ causation could also be attempted by formulating a definition for when c and e are themselves non-singleton. Such a definition would be necessary for assessing cases of, in manipulationist terminology, complex interventions (Sect. 3). Let {c} = {c 1 , … , c n } and {e} = {e 1 , …, e m }, and let the respective contrast classes, one for each element of {c} and {e}, be denoted by {C0} = {C1, …, Cn} and {E0} = {E1, …, Em}. Then my initial suggestion would be: {c}-rather-than-{C0} causes {e}-rather-than-{E0} iff O(C1 & … & Cn) counterfactually entails O(E1 & … & Em). This new definition could itself be generalized, in the manner of (D4), to cases where individual c i and e i have non-singleton contrast sets.
Note that the nomological stipulation that generates {C*} and {E*} is independent of the operation of context. In principle, context is thus also free to select C0 and E0 that are not members of respectively {C*} and {E*}, in which case we would not have causation.
Indeed, so easily can this be done that it is perhaps thereby explained why it could become natural even to believe that causation is a relation solely between actual events—such mistaken reification is hardly unprecedented in human psychology. In principle, the contrastive view thus has a ready explanation for this mistaken belief, and accordingly that belief’s existence loses force as a counterargument.
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Acknowledgements
This paper has had an unusually long history. Ancestor versions benefited greatly from extensive comments from Jonathan Schaffer, Phil Dowe and anonymous referees for this and one other journal, to all of whom I am very grateful. I would also like to thank Craig Callender, Jonathan Cohen, Carl Craver, Jan Plate, Elliott Sober, Jim Stone, and audiences at: University of California, San Diego, the London School of Economics Metaphysics and Methods Research Group, University of Delaware, and Washington University in St Louis.
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Northcott, R. Causation and contrast classes. Philos Stud 139, 111–123 (2008). https://doi.org/10.1007/s11098-007-9105-0
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DOI: https://doi.org/10.1007/s11098-007-9105-0