Lewis's 'causation as influence'

Australasian Journal of Philosophy

Volumn 79, Issue 3, 2001, Pages 409-421

  Kvart, Igal ^a  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

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EID: 61449554932     PISSN: 00048402     EISSN: None     Source Type: Journal    
DOI: 10.1080/713659268     Document Type: Article

References (17)

1. The Journal of Philosophy XCVII (2000), pp. 182-97.
2. 'Causation', Journal of Philosophy 70 (1973), reprinted in his Philosophical Papers, Vol. 2, (Oxford University Press: 1986), and its 'Postscripts to "Causation "' there.
3. Another option that might be considered if one wishes (as one should, in my opinion) to opt for an outcome whereby the preempted cause is not a cause, is to adopt a threshold constraint (Lewis is fully aware of this option) so as to rule out as causes cause candidates (i.e., ones with some influence) with too little influence, where the threshold presumably is (at least, it seems, it should be) context-dependent. But then it doesn't seem that context yields the requisite threshold, that is, so that Billy's throw here (or in similar cases where the preempted cause has more, even much more, influence) would come out as below the threshold, and yet in other cases, in the same context, events with as much influence (or less) which intuitively count as causes, wouldn't. (See the counter-examples in section II, which illustrates how the preempted cause might have a lot of influence, which substantiates the point that the threshold option is not promising.) Setting aside redundancy cases as special cases as part of the analysis is one thing, whereas expecting context to differentiate them regarding the threshold from non-redundancy cases is another. The above option of adopting a threshold would, moreover, bring out further the non-objectivity of the notion of cause under this account, which reflects Lewis's position in previous accounts as well, primarily through the use of similarity for the counterfactual construction which serves as the corner stone of all of Lewis's conceptions of cause, earlier ones as well the present one, since the similarity relation (which underlies the closeness relation) is taken to be context-dependent, which therefore also renders Lewis's account of counterfactuals context-dependent . (This remains so even when the properties in question are taken to be natural properties, since they need to be assigned weights or ordering.) For an approach on which the cause relation comes out objective (as do the core-cases of the counterfactual construction), see my 'Cause and Some Positive Causal Impact', Philosophical Perspectives 11, Mind, Causation and World, J. Tomberlin (ed.), 1997, pp. 401-32; my 'Causation: Counterfactual and Probabilistic Analyses', in Counter/actuals and Causes, J. Collins, N. Hall, L. Paul (eds.) (Cambridge, MIT Press, forthcoming); my 'Causal Relevance', in New Studies in Exact Philosophy: Logic, Mathematics and Science (selected contributions to the Exact Philosophy conference, May, 1999), Vol. II., Bryson Brown (ed.) (London, Hermes Scientific Pub. Co., 2000, pp. 59-90); and my A Theory of Counterfactuals (Indianapolis, Hackett, 1986), esp. chs. 2 and 9.
4. In addition, the gravitational pull that Billy's rock applied to Suzy's rock also had an influence, though a very slight one, on the window's shattering; and similarly so did other material objects in the area. If there is no cutoff point below which having influence does not yield being a cause, the presence of each of such objects was also a cause of the bottle's shattering, an absurd result. See note 3 above for more on the option of introducing a threshold for influence.
5. Thus, assume that both vehicles were allotted an acceleration period just prior to the official starting time. They were at liberty to select their acceleration pattern, but were required to arrive at the starting point right at the starting time, which they in fact did.
6. The condition for influence, i.e., that some of the values of the counterfactual mapping differ is not met.
7. 1 and V' respectively, which map into distinct alterations of e, are two dimensional alterations spaces. Insofar as c is concerned, this 2-dimensional space is the entire space of alterations off c that map into distinct alterations of e. But for the sports car there is another whole dimension-the velocity dimension, and specifically velocities within the (V+, V+ΔV) interval. Those three parameters, we can plausibly assume, are mutually independent, and thus there are 2-dimensional spaces of alterations of b and c respectively that confer distinct alterations of e, which are isomorphic. But then there is another dimension, that of the velocity parameter, with lots of values in the above interval each of which yields an alteration space of b isomorphic to the entire alteration space of c. In that respect there is a clear intuitive sense in which b has more influence on e than c does. In order to drive this point home further, assume that the pertinent values of the two parameters of the colour and texture of the front bumper, regarding b and c, and of the velocity, regarding b, are well ordered in the neighbourhoods of b and c respectively. This can be fleshed out by way of putting restrictions in terms of the competition on how many different variations the contesters are allowed to vary those parameters through, which the participants in fact adhered to, and where violation of such a restriction would yield disqualification and thus the victory of the other participant. (On top of that, this is also an obvious conceptual possibility, and Lewis's analysis is designed to be a conceptual analysis, not limited to our actual physical confines.) In that case, the number of alterations in question is finite, and, in view of the isomorphism between the pertinent alteration spaces for b and for c regarding the colour and shape of the front bumper that can be assumed to be built into the example, the extra dimension of the velocity for b yields more alterations for b over c in a precise finite sense.
8. In particular, Ned Hall's and Hartry Field's. For my counter-example, see 'Cause and Some Positive Causal Impact', section 5, and 'A Counterfactuals Analysis of Cause', Synthese (forthcoming), section 1. For the diagonalisation argument against transitivity of causal relevance and thus of cause, see my 'Transitivity and Preemption of Causal Impact', Philosophical Studies 64 (1991), pp. 125-60, section 5.
9. If intermediate events are allowed to play a role in the determination of influence, influence theory would be more, possibly a lot more, complicated than the account Lewis provided. Call the account of influence in terms of counterfactual dependence between alterations of the effect candidate and alterations of the cause candidate, as Lewis presented it, direct influence. If intermediate events are to play a role, two problems arise: first, for a chain (of, say, 3 elements) c, d and e, what is the influence of c on e conferred by the chain given the direct influence of c on d and of d on e? Second, what is the influence of c on e (call it influence simpiiciter) given two or more such chains? Lewis does not offer answers to these problems (though his conclusion that influence is not transitive yields certain constraints). In his discussion of the example of late preemption as well as the examples he uses to argue that influence is not transitive he proceeds as if only direct influence is involved. I followed suit and so did I in the examples above. But if influence simpiiciter is not direct influence, then Lewis's discussion of these examples doesn't establish the conclusions he reaches regarding them since there is, in his paper, no account of influence simpiiciter (if other than direct influence). If this is indeed the case, Lewis's theory of causation as influence is, as presented in this paper, inapplicable by and large to particular examples (i.e., so long as there are intermediate events), and thus is by-and-large not testable and has no predictive power. This paper, therefore, is best considered, it seems, as a theory of direct influence, since there is no theory of indirect influence in this paper.
10. I assume here and below that the parameters involved are one-dimensional parameters whose values can be considered on a linear scale.
11. Note that in order to verify that the influence of b on e is not sustainably reducible, one needs to select a lively sub-neighbourhood. To ensure that the sub-neighbourhood is lively, it's enough to find out two values of a certain parameter in an interval that is lively in the neighbourhood in question. That is, that there be two points in the neighbourhood in question that have different values for this parameter, have the same value for all other parameters, and are counterfactually mapped into different values in the neighbourhood of c. But although the sub-neighbourhood in question must include the interval of the parameter in question in order to be lively, it need not include the two points of the neighbourhood in virtue of which this parameter is lively in that interval.
12. I have presented this example in my 'A Counterfactual Theory of Cause' as a counter-example against Lewis's previous theory of cause.
13. For a discussion of aspects, see my 'Cause: Time and Manner' (forthcoming). See also Daniel Hausman, Causal Asymmetries (Cambridge University Press, 1998), ch. 2, sec. 2.3; and L.A. Paul, 'Causal Aspects', The Journal of Philosophy XCVII (2000), pp. 235-56.
14. To further tighten the point that the influence of c on e was minimal, consider the indirect influence off c on e, namely, via a, through cause transitivity. The influence of a on e was minimal: all the alterations of a map into just the actual alteration of e (the shattering of the window). This should be enough to yield that the influence of c on e via a was minimal (and so should come out the sustainably reducible influence, mutatis mutandis). If further tightening of this conclusion is desired, though it doesn't seem necessary, then boost the example in the following way so that the influence of c on a will be minimal and thus the indirect influence of c on e will be at most minimal. Thus, assume that Suzy had to throw her stone through a filter that lets the stone through only if it has certain precise specifications involving the manner of Suzy's throw, which had been determined prior to the throw. In fact, Suzy's throw met those specifications, and the filter let Suzy's stone through, though it wouldn't have otherwise. The point of introducing the filter in this example (analogously to the resort to the barrier) is to have the effect that different alterations of Suzy's throw map into only two alterations of a, namely the actual alteration of the barrier's being impacted at t or the alteration with its non-occurrence (but still with the impact of Billy's rock), which yields minimal influence of c on a, namely, influence yielded by a counterfactual mapping that has only two values-only two distinct alterations of a. Further, in addition to the direct influence of c on a's being minimal, so is the influence on a of the filter's letting Suzy's rock through-again, it is minimal. These wrinkles on the example are designed to maximise the contrast of the influence of b on c vs. that of c. One need not quibble over the details, however, so long as it is appreciated that b's influence is very considerable and that the example can be tailored so that c's influence is appreciably less. Then the point of the example carries over even if the influence of c on e is not recognised as minimal (i.e., yielding a mapping with only two distinct alterations of e as values).
15. See my 'Causes: Manner and Time'.
16. The account is designed for an indeterministic world. See my 'Causal Relevance'; my 'Causation: Counterfactual and Probabilistic Analyses'; and especially my 'Causes: Manner and Time'.
17. I thank Alex Byrne and Michael Fara for comments on the content of early drafts of the first part of this paper. I also thank Carl Posy for comments on the latter part.