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Common causes and the direction of causation

Abstract

Is the common cause principle merely one of a set of useful heuristics for discovering causal relations, or is it rather a piece of heavy duty metaphysics, capable of grounding the direction of causation itself? Since the principle was introduced in Reichenbach’s groundbreaking work The Direction of Time (1956), there have been a series of attempts to pursue the latter program—to take the probabilistic relationships constitutive of the principle of the common cause and use them to ground the direction of causation. These attempts have not all explicitly appealed to the principle as originally formulated; it has also appeared in the guise of independence conditions, counterfactual overdetermination, and, in the causal modelling literature, as the causal markov condition. In this paper, I identify a set of difficulties for grounding the asymmetry of causation on the principle and its descendents. The first difficulty, concerning what I call the vertical placement of causation, consists of a tension between considerations that drive towards the macroscopic scale, and considerations that drive towards the microscopic scale—the worry is that these considerations cannot both be comfortably accommodated. The second difficulty consists of a novel potential counterexample to the principle based on the familiar Einstein Podolsky Rosen (EPR) correlations in quantum mechanics.

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Notes

  1. While Good (1961a, b) is a much ignored early proponent of probabilistic causation, my own ignorance is for present purposes justified, as he assumes the temporal orientation of causation from the outset. Suppes (1970), a much more widely known treatment, does likewise.

  2. There are at least two reasons why this is the case. First, the various causal discovery algorithms on offer typically deliver a set of compatible causal models (a so-called markov equivalence class) rather than a unique causal model for any set of probabilistic data—and so additional information is required to select the correct model. Second, for any reasonably complex system the algorithmic search space will be extremely large—and so again, any available information which could reduce the search space will normally be employed. Temporal order is an obvious candidate in both cases. On the face of it, the latter poses less of a problem for the metaphysical reductionist, since the role of temporal information can here be reasonably construed as pragmatic or heuristic. Such a strategy sits less easily with the former, however; this will be discussed further in what follows.

  3. For example, why should we concede that the conceivability of simple worlds with uninstantiated causal laws as brute simples entails that in our world, causal laws can not be reduced?

  4. Unfortunately, I know of no comprehensive survey of the differences and similarities between the theories, though Hausman (1998) provides some detailed criticism of each of the others.

  5. When I presented this paper at Konstanz without this qualification, Chris Hitchcock and Iain Martel were quick to point out that Reichenbach explicitly disallowed probabilities of unity, since this prevents the disambiguation of causal asymmetry by the principle of the common cause. The remainder of the paper should be read with this qualification implicit—it does not alter the structure of the argument.

  6. In fact, Reichenbach appealed to networks of probabilistically related events rather than global predominance. I will return to this point in what follows.

  7. Of course (5) and (6) follow trivially, since there was no correlation in need of screening off—the point here is that any instance of record keeping establishes the probabilistic relations (7) and (8).

  8. I leave to one side here issues concerning the possibility of simultaneous causation—even if simultaneous causation is possible in some circumstances, it certainly isn’t going to apply to all cases which fall under the principle of the common cause.

  9. Tooley (1987, p. 237; 1993, p. 22) has pressed the objection that to rely on causal nets makes causation unacceptably extrinsic. Appeal to intuitions concerning the intrinsic nature of causation has also been made by, for example, McDermott (1999, p. 303) and Lewis (1986a, pp. 205–207). A somewhat related concern is raised by Price (1993). Price points out that in order for temporal asymmetry not to be smuggled into the account (what he calls disguised conventionalism), the probabilities used must be temporally symmetric. But, he claims, if we use a naïve actual frequentist interpretation of probability, we become committed to only talking about causation where we have enough correlation to speak of statistical dependence—committed, that is, to the impossibility of single-case causation. It seems to me that this is a worry about probabilistic or regularity theories of causation in general rather than about their prospects for explaining causal asymmetry, however—Hume’s account of constant conjunction is open to the same sort of objection, after all. The way out is, obviously, modal, and Price further charges that whatever modal notions are appealed to here will be as difficult to provide a temporal asymmetry for as the causal asymmetry we are seeking to ground. But this has no purchase on the theories under consideration, since the probabilities involved are all atemporal—if they were not, we would have been cut short at the very first step in the proposed reduction.

  10. On the other hand, if our theory of the causal relation is not itself a probabilistic one, we might have problems justifying why probabilities should matter for the asymmetry. This point is made by Dowe (1992b) with respect to the causal process theory of Salmon—the problem is why it should be that a causal process, which is an intrinsic property of a physical system, should be given its direction by extrinsic, de facto relations with surrounding causal processes. This point carries over to other theories which attempt to use the common cause principle as a plug-in solution for causal asymmetry, but needn’t concern us here.

  11. While this is correct, the analogy shouldn’t be pressed too hard. While we have a clear idea of what it would take for thermodynamic and radiative asymmetries to be reversed, it is less clear what criteria we should use to adjudicate cases of backwards causation. So for the former asymmetries, we have clearly defined asymmetric phenomena which stand in need of explanation; while in the latter case I take it that we are still attempting to explain the sense in which the phenomena is asymmetric in the first place.

  12. Dowe (1992a) suggests both strategies in the context of process theories, while Collins, Hall, and Paul (2004) suggest the entropic strategy for fixing counterfactual dependence.

  13. This consequence of the approach ought to appear striking to those philosophers used to formulating causal exclusion arguments premised on causation being the province of fundamental physics.

  14. See Hausman and Woodward (1999) for the details.

  15. Hausman himself makes essentially this point when he points out that in the deterministic case, “the probability of y conditional on the direct causes of x will be the same as the probability of y conditional on x and all the direct causes of x” (1998, p. 215).

  16. I am indebted to an anonymous referee for prompting me to make this conclusion explicit.

  17. I use the phrase for the time being to refer not only to the specific theorem first given by Bell, but to the family of theorems inspired by Bell that purport to prevent any local-realistic interpretation of quantum mechanics. Later in the paper I will focus on one particular theorem.

  18. A brief comment here on a recent series of papers (Hofer-Szabó, Rédei, & Szabó, 2000, 2002; Rédei, 2002; Szabó, 2000) claiming that Bell’s Theorem does not in fact rule out a common cause explanation of the EPR correlations, but rather only a common common cause, namely, an event that functions as the common cause of each set of measurement outcomes. Once we allow that a different common cause may be operating for different measurements, it is claimed, we can construct a common cause explanation for the correlations after all. In my view this is an ignoratio elenchi. Suppose such uncommon common causes are operative in the EPR case. The complete set of these uncommon common causes forms a common common cause, and is therefore ruled out by Bell’s Theorem. But if there is only an incomplete set of uncommon common causes, then the only way to recover the correlations is via dependency of this incomplete set on measurement choices, that is by violating autonomy. Either way we do not have an explanation that escapes Bell’s Theorem (this is effectively conceded by Szabó (2000, p. 910)). I do not mean to discourage work on constructing uncommon common cause models of the EPR correlations, but merely to point out that such models, like all hidden variable theories, must violate one of the Bell-Wigner premises. Thanks to Iñaki San Pedro Garcia for prompting me to address this literature.

  19. A different strategy for criticising the conditional formulation of the principle is to attempt to provide causal models of the EPR correlations, showing that there can be causal explanations in the absence of common causes in the sense discussed in this paper. There is a large literature evaluating the prospects for projects of this sort, and as an anonymous referee pointed out, the consensus seems to be that it has shown that the conditional formulation fails. Nevertheless, the EPR enthusiast provides a far more direct path to this conclusion, and has the advantage of not requiring any specific proposals about how the correlations are to be explained. For a sample of this literature see Redhead (1986, 1987, 1989, 1990); Cartwright and Jones (1991); Elby (1992); Healey (1992a, b); Chang and Cartwright (1993).

  20. I owe this observation to Huw Price.

  21. This bears noting in this context since van Fraassen (1982, p. 32) takes a failure of autonomy to entail a failure of the principle of the common cause in general. The availability of backwards causation models of quantum mechanics in the context of common cause theories of causation shows this to be false—see for example Dowe (1997), clearly a coherent if in my view untenable interpretation. See Suárez (2004) for further discussion.

  22. The most plausible development of the former option appeals to variable detector efficiency, first proposed by by Pearle (1970) and most fully developed in the so-called prism models of Fine (1982a, b). The latter option dates back to O. Costa de Beauregard and has been physically most highly developed by Cramer (1997), and philosophically most developed by Huw Price—see Price (1984, 1994, 1995, 1996b); Price (1994) is criticised by Dowe (1996), with a reply by Price (1996a). See also Dowe (1997).

  23. As Arif Ahmed pointed out to me, the conjunction of any two effects of the two measurement results, respectively, would provide a screening off event. The advantage of localising these effects together in a single recording event serves to avoid appeal to such gerrymandered alternatives. We could easily construct a recording device to cause one distinct event for each possible combination of measurement outcomes.

  24. See Cartwright (1999) for a similar though differently motivated view of the status of the principle of the common cause. Cartwright (1989) argues that the principle is not a necessary condition for establishing the direction of causation.

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Acknowledgements

Thanks to audiences at Konstanz and Sydney, to the Russellian Society Discussion Group, and to Huw Price, Hartry Field, Miklós Rédei, Malcolm Forster, Iain Martel, Dave Lagnado, Tevye Krynski, John Cusbert, Iñaki San Pedro Garcia, Arif Ahmed, and three anonymous referees.

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Weslake, B. Common causes and the direction of causation. Minds & Machines 16, 239–257 (2006). https://doi.org/10.1007/s11023-006-9042-2

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  • Asymmetry of causation
  • Backwards causation
  • Causal markov condition
  • Causality
  • Causation
  • Common cause
  • Direction of causation
  • Reichenbach
  • Quantum mechanics