Abstract
Incorporating normality ascriptions into counterfactual theories of causation was supposed to handle isomorphs. It doesn’t—conjoining isomorphs can produce cases that such ascriptions cannot resolve.
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Notes
For simplicity, I limit the account to atomic effects, whereas Halpern (2016, pp. 25, 81) allows for non-atomic effects.
Some authors see the role of intuitions as much less central for the project of defining causation (Beckers & Vennekens, 2018; Clarke, 2023; Glymour et al., 2010; Woodward, 2021); they, of course, may as well welcome a solution that sacrifices one of the intuitions, if this sacrifice is made for good reasons.
On yet another one (Beckers and Vennekens, 2018), causal models are extended with event timing; causal claims depend on both the casual structure of the case and the timing of the events involved. I’ll leave engaging with that proposal for another occasion; I’ll just flag that this strategy is similar to the one from normality in that on both, causal claims hold in virtue on some properties of events beyond the counterfactual structure.
\(\approx \) is the symmetric part of \(\succcurlyeq \).
Halpern and Hitchcock (2015) call witnesses (ab)normal and events (a)typical. I use a single term for both.
Act-nrm also mistakenly denies that \(N{=}0\) rather than \(N{=}1\) causes \(T{=}1\) rather than \(T{=}0\); this problem has been already pointed out by Rosenberg and Glymour (2018). However, the current counterexample doesn’t piggyback on that previous problem. Say, you could use \({\mathfrak {M}}_{S{=}\text {-}1 \wedge G{=}0 \wedge N{=}0}\) as a witness to vindicate that \(N{=}0\) rather than \(N{=}1\) causes \(T{=}1\) rather than \(T{=}0\). Because \({\mathfrak {M}}_{S{=}\text {-}1 \wedge G{=}0 \wedge N{=}0}\) shares the solution with \({\mathfrak {M}}_{S{=}\text {-}1 \wedge G{=}0}\), they are equally normal, and the latter could be used as a witness to contradict .
I am indebted to Sander Beckers for suggesting this move.
In
and \(\vec {T}'{=}\vec {t}\), I abused the notation; read the expressions as if the assignment on the right side were trimmed to the values of the variables on the left side.The theory still can handle The Patriarch in their current formulation, but not [6], a non-contrastive version of The Patriarch.
The most convincing reason I see for this requirement is that an intervention cannot bring about a state of affairs that cannot exist, and interventions can bring about any combination of values of different variables.
The difference between my strategy and his is that, unlike Clarke, I am ready to admit that if the final case elicits unambiguous intuitions inconsistent with the original case, I may have a reason to treat the changes as altering causal relations.
The cases may but needn’t be each other’s isomorphs.
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Acknowledgements
This paper benefited greatly from the feedback of friends and foes alike: Colin Allen (and the feedback group he organized), Dmitri Gallow, JP Gamboa, Eric Hiddleston, Caitlin Mace, Katie Morrow, Jim Woodward, and the audiences at the 2021 PSA and the 2022 Central APA. Above all, I am grateful to the reviewers for their thorough suggestions. One of the reviewers, who later turned out to be Sander Beckers, proposed how to amend my cases so they work against any normality ordering of solutions, not only standard ones. Amending the cases made the argument much stronger, as it now targets any present or future theory that relies on ordering solutions according to their normality. I wish every author a reviewer like Sander. This work was supported by the Chateaubriand Fellowship of the Office for Science & Technology of the Embassy of France in the United States and a Reinhart Koselleck project (WA 621/25-1), funded by the Deutsche Forschungsgemeinschaft (DFG).
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Wysocki, T. Conjoined cases. Synthese 201, 197 (2023). https://doi.org/10.1007/s11229-023-04101-w
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DOI: https://doi.org/10.1007/s11229-023-04101-w