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The Metaphysics of Causal Models

Where’s the Biff?

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This paper presents an attempt to integrate theories of causal processes—of the kind developed by Wesley Salmon and Phil Dowe—into a theory of causal models using Bayesian networks. We suggest that arcs in causal models must correspond to possible causal processes. Moreover, we suggest that when processes are rendered physically impossible by what occurs on distinct paths, the original model must be restricted by removing the relevant arc. These two techniques suffice to explain cases of late preëmption and other cases that have proved problematic for causal models.

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  1. More sophisticated counterfactual accounts, such as David Lewis’s influence theory (2000), do manage to account for cases such as Billy and Suzy, but this success appears to be in virtue of closely tracking the symptoms of causation, rather than the causal relation itself. Consequently, the account remains vulnerable to counterexamples (Schaffer 2001).

  2. It is not clear who coined the term, but it is strongly associated with D. M. Armstrong. The first occurrence in print of which we are aware is Lewis (2004). Leading biff theorists have been David Fair (1979), Wesley Salmon (1984), and Phil Dowe (2000).

  3. Causal models have been elegantly explained for a philosophical audience by Christopher Hitchcock (2001). Here we give only a very brief review of models, and direct unfamiliar readers to Hitchcock’s paper.

  4. We here ignore the subtle differences between Halpern and Pearl’s and Hitchcock’s analyses of token causation in causal models. See Korb et al. (2005) for a more thoroughgoing attempt to analyse token causation in terms of processes. Here we aim simply to illustrate the benefits of incorporating the metaphysics of causal processes into our theory of modelling.

  5. See Woodward and Hitchcock (2003) and Korb et al. (2005: 5).

  6. Hitchcock himself does not offer a model for this case, but implies that he too would use a model like that given in Fig. 2.

  7. Note we are using “fact” to refer to something like truths, and thus as things that can have truthmakers. Not everyone adopts this terminology, as for some—such as Russell—“fact” refers to the truthmakers themselves.

  8. Important historical examples of the struggle to account for negative truths are Russell (1972: 67–72) and Wittgenstein (1922: §2.06). More recently, see Molnar (2000).

  9. For instance, it could be said that the event of the rock being in Suzy’s hand at t′ is incompatible with Suzy’s having thrown the rock at t. And moreover, the event of the rock being in Suzy’s hand at t′′ is incompatible with the bottle’s having smashed, because given the laws and facts about Suzy’s throwing powers, she could not have thrown the rock so as to smash the bottle, and retrieve the rock again in such a short time.

  10. In the first, it is a process that runs from Suzy’s catch to the ball being in her hand at a later time. In the second, a process that runs from the ball flying past Suzy at t to the later smash.

  11. We leave it as an exercise for the reader to confirm that both the model in Fig. 2 and the time-indexed model preferred by Halpern and Pearl contain vulnerable arcs.

  12. It might be wondered why anything needs to be done more than simply setting C to its actual value. This will then get the result, however, on most analyses, that Suzy’s throw is not a cause of the bottle smashing. See Korb et al. (2005) for further discussion of a strategy to proceed beyond a wounded model to a complete analysis.

  13. Note that our account does not, on its own, explain the tendency to rule Suzy as a cause more often for some backups than others. For instance, if the backup is a human, rather than a brick wall, it is more common to judge that Suzy is a cause. However, strategies that have been suggested by others to explain such phenomena (e.g. Collins’s “dependence prevention” account (2004)), appear to be compatible with our preferred approach.


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This research was supported by a Monash University Arts–IT Grant. Handfield’s work on this paper was supported, in part, by a Monash University Research Fund Postdoctoral Fellowship and, in part, by an Australian Research Council APD Fellowship. Thanks for helpful comments or suggestions to two anonymous referees and to audiences at Oxford and at the Australasian Association of Philosophy Conference, Sydney, 2005.

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Handfield, T., Twardy, C.R., Korb, K.B. et al. The Metaphysics of Causal Models. Erkenn 68, 149–168 (2008).

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