Abstract
The majority of the currently flourishing theories of actual (token-level) causation are located in a broadly counterfactual framework that draws on structural equations. In order to account for cases of symmetric overdeterminiation and preemption, these theories resort to rather intricate analytical tools, most of all, to what Hitchcock (J Philos 98:273–299, 2001) has labeled explicitly nonforetracking counterfactuals. This paper introduces a regularity theoretic approach to actual causation that only employs material (non-modal) conditionals, standard Boolean minimization procedures, and a (non-modal) stability condition that regulates the behavior of causal models under model expansions. Notwithstanding its lightweight analytical toolbox, this regularity theory performs at least as well as the structural equations accounts with their heavy appliances.
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Notes
There are some regularity theoretic proposals that consider token causation to be primary (e.g. Mackie 1965), but the criticism raised against these token-level accounts (e.g. Kim 1971), in my view, shows that these accounts are beyond repair. I shall not pursue the singularist thread in the regularity theoretic literature here.
There are some analyses of causation referred to as “regularity theories” that draw on such modal notions as nomic sufficiency (Hausman 1998, 42–43) or counterfactual conditionals (Hall 2004). This terminology, however, blurs the important distinction between empiricist and modal analyses. As this distinction will be of particular importance for this paper, I subsequently reserve the label “regularity theory” for non-modal analyses.
Often the suitability of factors is also rendered dependent on such context-sensitive conditions as salience (Handfield et al. 2008) or farfetchedness (Hitchcock 2001, 287; Woodward 2003 86–91; Halpern and Pearl 2005, 871). I prefer to first propose a context-independent notion of causation and to postpone all considerations of context-sensitivity to Sect. 4.
For an interesting suggestion as to how to handle instantiations of absences within an event ontology cf. Handfield et al. (2008, sect. 2.2).
Even though locality is relevant for all theories of causation, it is usually sidestepped in the literature. For more details on the problem of suitably interpreting spatiotemporal proximity for a given causal process cf. Baumgartner (2008).
Plainly, the non-redundancy principle does not require relevant difference-making circumstances to exist in the past or the present of a particular causal analysis. These circumstances simply need to exist in a tenseless sense (in the domain of quantification).
Due to the universal (or negative existential) nature of this permanence requirement its satisfaction may be difficult to establish in contexts of epistemic limitations. Plainly though, such uncertainties are a trademark problem encountered in contexts of causal discovery. May (1999, 74) has shown that spurious regularities have certain features that allow for their identification even prior to complete expansions of corresponding factor sets. Halpern and Hitchcock (2010) have recently emphasized that acquiring structural stability across expansions of causal models is of utmost importance for the structural equations framework as well.
One might be inclined to argue that some causes may also have alternative effects and that, in such cases, the direction of determination is reversed. However, note that causes that bring about one effect in one situation and another effect in another situation are not deterministic. In deterministic structures, which constitute the domain of regularity theories, there are no causes with alternative effects.
Similarly, to orient edges in causal Bayes nets at least two alternative paths are required that have a common end node, so-called unshielded colliders (cf. especially Pearl 2000, 51–57).
F is not part of a minimally sufficient condition of E because the firing of the switch \(\mathsf{F}\) can be eliminated from every sufficient condition without sufficiency for E being lost.
Inhibitory signals are represented by ‘
’. They always override stimulatory signals.Keep in mind that (14) is not a propositional expression but a shorthand for a first-order expression that, among other things, imposes spatiotemporal constraints on the instances of the involved factors. In this particular case, these constraints must be taken to imply that \(B\overline{E}\) and E are not proximately instantiated (which would be impossible), when neuron \(\mathsf{E}\) is triggered via \(\mathsf{D}\).
Readers with sympathies for interventionism will deny the equivalence of Fig. 5a and b by arguing that 5a and 5b do not have the same implications on how \(\mathsf{E}\) behaves under possible interventions on \(\mathsf{D}\) or \(\mathsf{B}\) that are independent of \(\mathsf{C}. \) According to Fig. 5a and b, however, \(\mathsf{D}\) and \(\mathsf{B}\) can only be stimulated by \(\mathsf{C}. \) Hence, there are no possibilities to intervene on \(\mathsf{D}\) and \(\mathsf{B}\) independently of \(\mathsf{C}. \) As will be shown below, as soon as 5a and 5b are suitably expanded by further neurons that can stimulate \(\mathsf{D}\) or \(\mathsf{B}\) independently of \(\mathsf{C}\) the equivalence of 5a and 5b breaks down.
Hall (2004) takes an example analogous to the one in Fig. 5 to show that there exists at least one concept of causation, viz. dependence, that does not amount to an intrinsic relation. Menzies (2002) also significantly weakens his intrinsicness thesis (cf. Menzies 1996) in light of an example of this type.
Instead of typicality, Handfield et al. (2008) relativize actual causation to a context-sensitive condition of salience.
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Acknowledgments
I thank Luke Glynn, Wolfgang Spohn, and two anonymous referees of this journal for very helpful comments on earlier drafts. Moreover, I have profited a lot from discussions with audiences at two workshops held at the University of Konstanz in 2009/10. Finally, I am indebted to the Deutsche Forschungsgemeinschaft (DFG) for generous support of this work (project CAUSAPROBA).
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Baumgartner, M. A Regularity Theoretic Approach to Actual Causation. Erkenn 78 (Suppl 1), 85–109 (2013). https://doi.org/10.1007/s10670-013-9438-3
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DOI: https://doi.org/10.1007/s10670-013-9438-3