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Supervenience and Singular Causal Statements*

Published online by Cambridge University Press:  08 January 2010

James Woodward
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In his recent book, Causation: A Realistic Approach, Michael Tooley discusses the following thesis, which he calls the ‘thesis of the Humean Supervenience of Causal Relations’:

(T) The truth values of all singular causal statements are logically determined by the truth values of statements of causal laws, together with the truth values of non-causal statements about particulars (p. 182).

(T) represents one version of the ‘Humean’ idea that there is no more factual content to the claim that two particular events are causally connected than that they occur, instantiate some law or regularity, and perhaps bear some appropriate non-causal (e.g. spatio-temporal) to each other. This is an idea that is tacitly or explicitly assumed in most familiar accounts of singular causal statements. For example (T) is assumed by many probabilistic theories of singular causal statements, by theories which attempt to analyse singular causal statements in terms of necessary and sufficient conditions, and, as I shall argue below, by David Lewis' counterfactual theory.

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Papers
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Royal Institute of Philosophy Supplements , Volume 27 , March 1990 , pp. 211 - 246
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Copyright © The Royal Institute of Philosophy and the contributors 1990

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References

1 Tooley, M., Causation: A Realist Approach (Oxford University Press, 1987).Google Scholar

2 I have in mind here probabilistic theories of causation which attempt to characterize particular causal sequences or actual causal connections between particular events (so-called ‘token’ causation as in Eells, E. and Sober, E., ‘Probabilistic Causality and the Question of Transitivity’, Philosophy of Science 50 (1983): 35–57)CrossRefGoogle Scholar, in terms of the idea that a cause must raise the probability of its effect in suitably characterized background circumstances. Such theories should be distinguished from theories which attempt to give a probabilistic characterization of generic or population-level causal connections (what Eells and Sober call ‘property-causation’). These last theories are not touched by the criticism advanced in this paper. The falsity of (T) undermines both reductionist ‘Humean’ theories of token-causation which attempt to characterize token causation purely in terms of facts about probabilities, and non-reductionist theories of token causation which permit reference to generic causal facts but not singular causal facts in their specification of background circumstances.

Theories which attempt to characterize particular connections in terms of necessary and sufficient conditions include various variants of the idea that a cause is a necessary or non-redundant condition in a set of conditions which are jointly sufficient for some effect as in Hempel, C., Aspects of Scientific Explanation (New York: The Free Press, 1965)Google Scholar and Mackie, J. L., ‘Causes and Conditions’, American Philosophical Quarterly 2 (10 1965) 245–64.Google Scholar

3 Reasons of space preclude a detailed discussion of the relationship between (T) and the claim (N) that a (deterministic or probabilistic) law of nature must underlie or otherwise be associated with every true singular causal claim. It is perhaps worth adding, however, that while the truth of (N) is logically compatible with the falsity of (T), my view is that the considerations advanced in this paper against the truth of (T) also help to undermine the plausibility of (N). They do so by making the assumption that (N) is true look gratuitous and unmotivated. First, the belief that singular causal statements are analysable in terms of facts about laws of nature and non-causal facts about particulars has been, historically, an important motive for believing that every true singular causal statement ‘must’ have a law of nature associated with it. The idea has been that by providing such an analysis, one renders the opaque and mysterious notion of a particular causal connection metaphysically and epistemically acceptable. In denying (T), we deny the possibility of such an analysis, and thus undercut this motive for belief in (N).

Secondly, (and relatedly) if the arguments of this paper are successful, they show that to state the truth conditions for a singular causal claim, it is not enough just to make reference to facts about an associated law and non-causal facts about particulars—reference to an additional fact F, having to do with the obtaining or non-obtaining of particular causal connections, is also required. It then becomes natural to wonder whether the holding of this further fact F is not by itself a sufficient condition for the truth of the singular causal claim in question, even when there is no associated law. Once we recognize that reference to facts about particular causal connections is unavoidable, reference to laws as well in stating truth-conditions for singular causal claims begins to look superfluous. This does not of course show that it is false that a law is associated with every true singular causal claim, but it does again raise the question of what positive reasons we have for believing that (N) is true. Facts about particular causal connections seem by themselves sufficient to distinguish causal from non-causal sequences, provide support for appropriate counterfactuals, and so forth.

Third, (and again relatedly) the methods we use to establish whether singular causal claims are true or false—and in particular, the use of the eliminative method described below—do not seem to require or to depend upon the truth of (N); there is nothing in those methods which commits us to (N). In particular, to establish that c1 is a possible cause of e and to eliminate other possible candidates for the cause of e, and in this way to establish that c1 is the cause of e, we do not need to rely on the assumption that there is a law of nature linking c1 and e. Here too, while this does not show that (N) is false, it again makes the assumption that it ‘must’ be true look gratuitous and unmotivated.

4 I claim no originality at all for this general observation, which appears in various forms in many, different writers. Discussions which are at least loosely related occur in Kim, J., ‘Causation, Nomic Subsumption, and the Concept of Event’, Journal of Philosophy 70 (1973) 217–36CrossRefGoogle Scholar and in Achinstein, P., The Nature of Explanation (Oxford University Press, 1983)Google Scholar in the context of a criticism of the covering-law model of explanation. More recent and closely related discussion occurs in a series of papers by E. Eells and E. Sober including ‘Probabilistic Causality and the Question of Transitivity’, Sober, E., ‘Causal Factors, Causal Inference, Causal Explanation’, Aristotelian Society Proceedings 1986Google Scholar and Eells, E., ‘Probabilistic Causal Levels’, in Skyrms, B. and Harper, W., (eds.) Causation, Chance and Credence (Dordrecht: Kluwer Academic Publishers, 1988)Google Scholar. As noted above, Eells and Sober distinguish between what they call ‘property causation’ and ‘token causation’ and give examples having essentially the same structure as my (Ex. 1) below to show that the inference from property causation within a population to token causation between individual occurrences within that population is less straightforward than one might suppose. On their view, probabilistic theories of causation are most plausibly construed as characterizations of property causation rather than token causation. My claim in what follows is the (I believe) different and more radical claim that no characterization of token causation, probabilistic or otherwise, -which just makes reference to regularities or generic relations between events and to non-causal facts about particulars will be adequate. I would thus reject the account of token-causation suggested in Eells' ‘Probabilistic Causal Levels’. For reasons which will become obvious below, I am also sceptical of the ‘Connecting Principle’ between property and token causation proposed by Sober in his ‘Causal Factors, Causal Inference, Causal Explanation’.

5 I take both of these features—that the law D1 has counterfactual import and that it describes the difference which the factor C1 taken in isolation makes to the occurrence of E—to be characteristic of laws in general and not just probabilistic laws. Our stipulation that D1 has these features is thus not ad hoc.

The tendency in a great deal of recent philosophical discussion has been to represent or analyse probabilistic laws as claims about conditional probabilities or differences between conditional probabilities. In what follows, I do not assume that the probability P1 will in general coincide with any of the obvious candidates constructed from conditional probabilities such as P(E/C1), P(E/C1)–P(E/) or P(E/C1)–P(E/). My reasons for resisting this assumption include, among other considerations, the fact that a probabilistic law like Dt can be true in a situation in which the relevant conditional probabilities are not well defined, whether because the denominators P(C) (or P(), etc.)=O or because C or (or , etc.) does not have a well defined probability distribution or is not a random variable at all. More generally, I would distinguish sharply between the conditional probability P(E/C) and the probability of E, given a counterfactual condition C. Probabilistic laws have to do with the latter notion, not the former. I should also emphasize that I take the law D1 to specify the probability P1, with which C1causes E. Even putting aside the above problems, this will not, for example, equal P(E/C1) – P(E/) if other causes of E are also present and cause E, or if E sometimes occurs spontaneously. For reasons which I lack the space to discuss here, I do not think that the strategy of trying to deal with this difficulty by conditionalizing on the absence of other causes of E will always work.

6 I have generally followed the convention of using upper case letters to refer to types of events and lower case letters or locutions like ‘particular occurrence of (type) C’ to refer to particular event-tokens. However, at a few points at which it seemed awkward, distracting, or intolerably pedantic to explicitly distinguish between type and token, I have run roughshod over the distinction, thinking that it would be clear enough how to sort things out.

7 One may, if one likes, think of this assumption as implicit in the stipulation that C1 and C2 act independently, but it is useful to make the assumption explicit. I have excluded the possibility of pre-emption to avoid certain irrelevant complications and not because I think that such cases create difficulties for the treatment of singular causal claims I shall defend. In fact, I think that cases of pre-emption provide additional reasons for rejecting (T).

8 Cf. Lewis, Philosophical Papers, Vol. II (Oxford University Press, 1986), 193 ff.Google Scholar

9 I should emphasize that my claim is simply that (1), (2) and (3) entail the above counterfactuals. I do not claim that the above counterfactuals exhaust the meaning of (1), (2) and (3) or that the truth of these counterf actuals is a sufficient condition for the truth of (1), (2) and (3). In fact, I do not think it is possible to give an analysis of causal claims in terms of a notion of counterfactual dependence which does not presuppose causal notions. Moreover, I also do not claim (in fact I think it is false) that all causal claims entail counterfactuals parallel to those given above. Instead, the form of the counterfactual entailed by a causal claim will depend upon the details of the claim and upon which other causal claims are true in the situation under investigation. For example, if (Ex. 1) were instead a case involving pre-emption or linked overdetermination in which if C1 had not caused e, c2 would have, the counterfactual (1) would not hold.

10 For a concrete case, consider an example in which someone has a serious illness. Suppose that he is treated with a drug (c1) which has probability P, of causing recovery (e), but that there is also a non-zero probability of recovery (e) occurring spontaneously.

11 In fact, I believe that both of these claims are false. My point here, however, is that even if true, they are generalizations of form (S2) rather than form (S1).

12 See, for example, the remarks on the limitations of information about temporal relationships in deciding among conflicting causal claims in Cook, T. and Campbell, T., Quasi-Experimentation (Boston: Hough ton Mifflin, 1979).Google Scholar

13 It may be responded that these observations bear only on epistemological and methodological issues relating to causal inference, and not on the metaphysical issue of whether spatio-temporal facts, in conjunction with other noncausal facts about particulars and facts about the laws, are as (T) claims, sufficient to fix the truth of every singular causal statement. The observations show only that generalizations of form (S2) are not (widely) known for many causes or that they are not used or appealed to in causal inference, not that such generalizations are not true. I concede this point. Still, I think that the above observations help to shift the burden of proof onto those who think that we can always appeal to spatio-temporal facts in defence of (T). What positive reasons are there to believe this claim, given the above methodological and epistemological observations?

14 It is true that it follows from energy/momentum conservation and the requirement that physical laws must be Lorenz-invariant that energy/momentum transfer must be local and that there can be no causal action at a distance in the context of fundamental physical explanation. See, for example, Ohanian, H., Gravitation and Spacetime (New York: W. W. Norton and Co., 1976)Google Scholar. But at the level of analysis characteristic of sciences like psychology and economics, the imposition of a similar no-action at a distance requirement seems misguided. Moreover, even in physics, it seems to me that the fact that there is no causal action at a distance is not plausibly viewed as a characterization of what causality is or must involve. Rather, this fact is a quite contingent physical fact which stands in need of more fundamental physical explanation. Insofar as there is a common core to the notion of causation, it seems to me to involve the idea of counterfactual dependence emphasized above, rather than the idea of action by contact. See my ‘The Causal/Mechanical Model of Explanation’, in Kitcher, P. and Salmon, W. (eds.), Minnesota Studies in The Philosophy of Science, Vol. 13 (Mineapolis: The University of Minnesota Press, 1989)Google Scholar for further discussion.

15 I owe this point to David Ruben.

16 In Lewis, D., Philosophical Papers, Vol. II, (Oxford University Press), 159–213.Google Scholar

17 (L2) may seem less plausible than the narrower claim made in Lewis' remarks. And this is perhaps why Lewis does not formulate or endorse a principle like (L2). However, a satisfactory account of causality which might be used to defend (T) obviously must be more general than the account explicitly asserted by Lewis; it must say something consistent with (T) about which causal claims are true in cases (like those represented by (Ex. 1) and (Ex. 2)) in which c raises e's chance of occurring but in which e's chance without c need not be small. Indeed, given that one subscribes to (T) (as I believe Lewis does), it is not easy to see how one could consistently defend the view that c causes e only when the chance of e, given c is sufficiently greater than the small chance of e without c, but not in the other kinds of cases covered by (L2). This restriction looks ad hoc and motivated only be a desire to avoid difficulties to which the more general (L2) may be subject. The fact that (L1) is vague (how much less is ‘very much less’?) in a way in which the notion of causation is, I would argue, not vague, is one reflection of the ad-hoc character of this restriction.

18 I take it that Lewis intends (L1) as a conceptual truth about causation.

19 It is worth emphasizing that this argument and the similar arguments which follow on pp. 224–226 require the understanding of laws and their relation to conditional probabilities sketched on pp. 214–215 and in footnote 5. For example, it is because the law linking C1 and E gives the probability P1 with which C1 would cause E and the law linking C2 and E gives the probability P2 with which C2 would cause E that the probability of production of E in (Ex. 1) is P1 + P2–P1P2. If instead P, were, say, P(E/C1) –P(E/) this result would not follow. More generally, the idea about the link between causation and invariance on which my argument relies requires that the law linking C1 and E specify the contribution made to E by Cu acting alone. It is this contribution which should remain invariant when we move to contexts like (Ex. 1) in which other causes of E may be present. I am very grateful to Paul Humphreys for impressing on me the importance of being explicit about this point.

20 A rather similar idea is developed in Cartwright, Nancy, Nature's Capacities and Their Measurement (Oxford University Press, 1989)Google Scholar which appeared just as I was completing this paper. Cartwright also emphasizes the idea that causal capacities (rather than causal laws) must be stable or context-independent; however her understanding of what such conduct-independence involves seems to be rather different from mine. In particular, Cartwright links the notion of context-independence to the notion of unanimity as it occurs in discussions of probabilistic theories of causation: she requires that a cause must increase the probability of its effect across all homogeneous background contexts. I have argued elsewhere (in Woodward, , ‘Laws and Causes’, The British Journal for the Philosophy of ScienceGoogle Scholar, forthcoming) that this requirement is too strong and that a factor may have a stable causal tendency even if it does not produce an effect with any fixed probability at all.

21 I offer no general account here of what it is for a factor or type of event to be a possible cause. I will, however, remark that if C is a possible cause of E, it need not be the case that there is a deterministic or probabilistic law linking events of type C to events of type E, but that it must be the case that C exhibits the sort of stable, context-independent tendency or capacity to produce E's discussed in Section II above. That is to say, C's must be capable of causing E's accross a range of different circumstances and background conditions. (We thus must make use of the notion of a particular causal connection or a true singular causal claim to explicate the notion of a possible cause.) We can think of this as (one form of) an invariance or resiliency requirement; invariance is in general a distinguishing mark of causal or nomological relations.

22 What I mean by rendering a claim implausible or unlikely is illustrated both by the examples considered below, and by the following case, which is adapted from Paul Humphreys, The Chances of Explanation (Princeton University Press, forthcoming). According to classical statistical mechanics, a container of water has a very small, but non-zero probability of freezing spontaneously. Suppose that such a container is placed in a refrigeration unit and freezes. There are two singular competing causal hypotheses regarding the freezing: (1) the freezing was caused by the placement within the refrigeration unit; (2) this was one of those very rare occasions in which the freezing occurred spontaneously. In this sort of case, although (2) is a genuine physical possibility, it is known to be extremely unlikely or implausible on the basis of theoretical considerations. As I shall construe the eliminative requirement, we are entitled to regard (2) as ruled out, because of its great implausibility.

23 The eliminative strategy thus fits with a general account of science and inductive inference in which hypotheses are ‘accepted’ or ‘rejected’ and are not just assigned degrees of belief between zero and one. I lack the space to defend such an account here, and merely remark that it seems to correspond to scientific practice. The eliminative strategy also reflects the idea that warranted causal inference is not, as is sometimes claimed, a matter of inference to the best explanation; it is rather a matter of inference to the only acceptable explanation among some range of alternatives.

24 As a general rule, the burden of proof for showing causation rests with the plaintiff but in tort law, unlike the criminal law, the evidence required to establish a causal claim need only show that is ‘more likely than not’. (See Prosser, W., Law of Torts (St. Paul, Minnesota: West Publishing Company, 1971)Google Scholar. While the standards of evidence required to show that it is reasonable to accept or reject a causal claim are thus different from and in some respects less demanding than those often imposed in science, the basic point remains that providing grounds for accepting a causal claim requires providing grounds for rejecting competing hypotheses. A demonstration that a causal factor was present and that the factor was a possible or frequent cause of the effect, or that it raised the probability of the effect is not taken to show that the factor in fact caused the effect.

25 See Muller, R., Nemesis (New York: Weidenfeld and Nicolson, 1988).Google Scholar

26 Many philosophers of science, heavily influenced by recent emphasis on the fallible and conjectural character of all scientific knowledge will smile at this talk of ‘proving’ a scientific theory. In fact, although I lack the space to argue for this claim here, I think that the phrase is quite appropriate. Often scientists really can (a) delimit a set of possible theories which (modulo some agreed upon level of idealization and approximation) exhaust the plausible alternatives regarding some phenomena of interest and (b) obtain evidence which rules out all possibilities from this set except for one. When this can be done it is perfectly appropriate to describe the remaining possible theory as proved or established beyond a reasonable doubt.

27 The central role in causal inference of ruling out alternative explanations of an observed association and the differences among research designs in how effectively they accomplish this end are emphasized by many writers in the social and behavioural sciences. In addition to Cook and Campbell, Quasi-Experimentation, see, for example, Asher, H., Causal Modeling (Beverley Hills: Sage Publications, 1983).CrossRefGoogle Scholar

28 In saying this, I do not mean to claim that in every case having the structure of Lewis' example, we are somehow assured on a priori grounds that there is a determinate fact of the matter about whether e would or would not have occurred without c. My claim is rather that it is a mistake to hold that merely because supervenience fails, it follows on conceptual grounds that there could not be a determinate fact of the matter regarding which of these counterfactuals is true. In fact, I think that it is very plausible that there are quantum-mechanical cases having the structure of Lewis' example, in which the above counterfactuals lack a definite truth value, and in which nothing corresponding to Lewis' hidden feature can be present. However, I think that this is so for empirical reasons peculiar to quantum-mechanical phenomena (reasons summarized in the various no-hidden-variables theorems) and not merely because of conceptual considerations having to do with the failure of supervenience. My point is thus a conditional one: that if there is to be a determinate fact of the matter about whether c has or has not caused e, then there must also be a determinate fact of the matter about whether e would or would not have occurred without c and the case must be one in which Lewis' hidden feature might be present.

29 Glymour, C., Theory and Evidence (Princeton University Press, 1980).Google Scholar

30 Indeed, I suspect that something stronger is true: not only is it permissible or legitimate to test or support causal claims by the use of other assumptions which are causal in character it is usually (perhaps always) necessary to do this. It is typically (perhaps always) unwarranted to draw causal conclusions just on the basis of evidence and assumptions which are non-causal in character. For an argument in support of this claim in connection with the use of statistical techniques like regression analysis to establish causal conclusions, see my ‘Understanding Regression’, PSA 1988 (Philosophy of Science Association, 1988), 255–69.Google Scholar