SpringerLink
Log in

An Internal Limit of the Structural Analysis of Causation

  • Original Paper
  • Published:
Axiomathes Aims and scope Submit manuscript

Abstract

Structural models of systems of causal connections have become a common tool in the analysis of the concept of causation. In the present paper I offer a general argument to show that one of the most powerful definitions of the concept of actual cause, provided within the structural models framework, is not sufficient to grant a full account of our intuitive judgements about actual causation, so that we are still waiting for a comprehensive definition. This is done not simply by focusing on a set of case studies, but by arguing that our intuitions about two different kinds of causal patterns, i.e., overdetermination and counterdetermination, cannot be addressed using that definition.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (Canada)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Notes

  1. As far as I know, this is the most complete definition now at our disposal. It constitutes a development of the definition given in Halpern and Pearl (2001), and benefits from the analysis provided by Hitchcock (2001).

  2. See, for instance, Menzies (2004b), Woodward (2006), Hall (2004), Hall (2007), Hitchcock (2007), and Halpern and Hitchcock (2014).

  3. This standpoint, adopted with minor modifications by Halpern and Pearl (2001), Hitchcock (2001), Woodward (2003), Halpern and Pearl (2005), can be now considered the standard view about modelling causation using structural equations.

  4. Thus, X = Y and Y = X are indeed different structural equations: the first one states that X has the same value of Y and the value of X is causally dependent on the value of Y, while the second equation states that X has the same value of Y and the value of Y is causally dependent on the value of X. Hence, the order of occurrence in a structural equation is crucial for distinguishing causes and effects.

  5. Thus, in a sense, the proposed theory is a counterfactual theory of causation, capturing many aspects of Lewis’ first theory. See Lewis (1973a, b, 1979), Yablo (2002), and Menzies (2004a) .

  6. The present definition is a slight modification of the original Definition 3.1 in Halpern and Pearl (2005). In Definition 1.3 only basic events are allowed as actual causes, but this limitation is only apparent. The original definition includes a further condition stating that the set of events identifying the actual cause has to be minimal; given this condition, it can be proved that such a set can only be a singleton.

  7. The same basic idea constitutes the starting point for the substantially similar definitions proposed in Hitchcock (2001), pp. 286–290, and Woodward (2003), pp. 77–85.

  8. By the way, the classical examples suggesting that causation is not in general transitive are cases of counterdetermination. See, for instance, McDermott (1995) and Hitchcock (2001).

  9. Primary overdetermination is also called symmetric overdetermination.

  10. Notice that early preemption, late preemption, and trum** preemption are all species of backup overdetermination.

  11. A classic example of this exception is given in McDermott (1995): a man catches a cricket ball in a context in which the next things in the ball’s direction of motion are a solid brick wall and a window. In this case only few people would say that the man’s action prevented the ball hitting the window.

  12. See Hiddleston (2005) and Halpern and Hitchcock (2014) for a more extended presentation.

  13. See Halpern and Pearl (2005), p. 25. This example is taken into account in Hall and Paul (2003), and exhibits a paradigmatic case of multiplication of causes.

  14. See also Hitchcock (2001), pp. 290–98 and Woodward (2003), ch. 2, § 2.8 on causation, omission, and serious possibilities. The strategy followed by Halpern and Pearl can be considered as a formalization of Woodward’s approach in co** with puzzling examples.

  15. See Halpern and Pearl (2005): “As the examples have shown, much depends on choosing the “right” set of variables with which to model a situation, which ones to make exogenous, and which to make endogenous. While the examples have suggested some heuristics for making appropriate choices, we do not have a general theory for how to make these choices. We view this as an important direction for future research.”. See also Woodward (2003), pp. 88–91, where the subjectivity problem is faced trying to show that at least in part the subjective choice of models and worlds is based on objective facts about how the world works.

  16. The strategy of distinguishing default and deviant worlds, see Hitchcock (2007) and Hall (2007), seem to undergo a similar critique, unless the distinction is made without relying on our causal intuitions.

  17. An analysis of cases of threats, as cases of causation by double prevention, is provided by Hall. See Hall (2007).

  18. See Hall (2007), p. 120: “The family sleeps peacefully through the night, in part because the watchful police have nabbed the thief before he can enter the house”.

References

  • Hall N (2004) Two conceptions of causation. In: Collins J, Hall N, Paul LA (eds) Counterfactuals and causation. MIT Press, Cambridge, pp 225–276

  • Hall N (2007) Structural equations and causation. Philos Stud 132:109–136

    Article  Google Scholar 

  • Hall N, Paul L (2003) Causation and preemption. In: Clark P, Hawley K (eds) Philosophy of science today. Oxford University Press, Oxford, pp 100–130

  • Halpern JY, Hitchcock C (2014) Graded causation and defaults. Br J Philos Sci 66:413–457

    Article  Google Scholar 

  • Halpern J, Pearl J (2001) Causes and explanations: a structural model approach—part I: causes. In: UAI 2001, pp 194–201

  • Halpern J, Pearl J (2005) Causes and explanations: a structural model approach—part I: causes. Br J Philos Sci 56:843–887

    Article  Google Scholar 

  • Hiddleston E (2005) Causal powers. Br J Philos Sci 56:27–59

    Article  Google Scholar 

  • Hitchcock C (2001) The intransitivity of causation revealed in equations and graphs. J Philos 98:273–314

    Article  Google Scholar 

  • Hitchcock C (2007) Prevention, preemption, and the principle of sufficient reason. Philos Rev 116:495–532

    Article  Google Scholar 

  • Lewis D (1973a) Counterfactuals. Basil Blackwell, Oxford

    Google Scholar 

  • Lewis D (1973b) Causation. J Philos 70:556–567

    Article  Google Scholar 

  • Lewis D (1979) Counterfactual dependence and time’s arrow. Nous 13:455–476

    Article  Google Scholar 

  • McDermott M (1995) Redundant causation. Br J Philos Sci 46:523–544

    Article  Google Scholar 

  • Menzies P (2004a) Difference-making in context. In: Collins HN, Paul (eds) Counterfactuals and Causation. MIT Press, Cambridge, pp 139–180

  • Menzies P (2004b) Causal models, token causation, and processes. Philos Sci 71:820–832

    Article  Google Scholar 

  • Pearl J (2000) Causality: models, reasoning, and inference. Cambridge University Press, Cambridge

    Google Scholar 

  • Woodward J (2003) Making things happen: a theory of causal explanation. Oxford University Press, New York

    Google Scholar 

  • Woodward J (2006) Sensitive and insensitive causation. Philos Rev 115:1–50

    Article  Google Scholar 

  • Yablo S (2002) De facto dependence. J Philos 99:130–148

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Philosophy, Catholic University of Milan, Milan, Italy

    Alessandro Giordani

Authors
  1. Alessandro Giordani
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alessandro Giordani.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Giordani, A. An Internal Limit of the Structural Analysis of Causation. Axiomathes 26, 429–450 (2016). https://doi.org/10.1007/s10516-016-9297-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10516-016-9297-z

Keywords

Search

Navigation