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What Killed Your Plant? Profligate Omissions and Weak Centering

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This paper is on the problem of profligate omissions. The problem is that counterfactual definitions of causation identify as a cause anything that could have prevented an effect but that did not actually occur, which is a highly counterintuitive result. Many solutions of this problem appeal to normative, epistemic, pragmatic, or metaphysical considerations. These existing solutions are in some sense substantive. In contrast, this paper concentrates on the semantics of counterfactuals. I propose to replace Strong Centering with Weak Centering. This allows that the actual world is not the only world that is closest to the actual world. As a result, some counterfactuals that would otherwise have been true, turn out to be false. When these counterfactuals concern causation, fewer causal claims are true. In addition to describing steps towards solving the problem of profligate omissions, the proposal captures an abstraction that is shared by many of the existing solutions: depending on how the distance ordering underlying the Weak Centering condition is constructed and interpreted, some of these existing solutions can be recovered.

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  1. I follow the literature on the problem of profligate omissions in assuming, at least for the sake of argument, that omissions can be causes. I do not thereby endorse the claim that omissions can be causes (cf. Woodward, 2006, 20–23).

  2. Throughout the paper I assume that the respective c and e are distinct and actually occur. Following Pearl (2000) and Woodward (2003), I interpret causal claims as claims about relationships between variables. That omissions occur should hence be understood as a claim about binary variables, denoting the occurrence of an event, having the value of 0.

  3. Some distinguish between absences and omissions such that the Queen not watering the plant is an absence but Peter not watering it is an omission. This distinction does not bear on the problem of profligate omissions (or absences) and I ignore it for present purposes.

  4. Importantly, the class of normative considerations here includes prescriptive as well as statistical norms.

  5. This taxonomy is not exclusive. The insensitivity condition of Woodward (2006) as well as the proportionality condition of Bontly (2005), or Shapiro and Sober (2012) may be interpreted as working on the level of pragmatics.

  6. In the final stages of preparing this paper for publication in this journal, I came across another paper by Peter Menzies (2011), in which he suggests a proposal that is largely identical to the one proposed here and applies it, among other things, to the problem of profligate omissions.

  7. Menzies (2004, 175) writes that “the absence of any factor that could be regarded as an interferer [such as the presence of nerve gas] can, in the right circumstances, act as a difference-maker for my writing at my computer”. In other words, Menzies proposal would mandate that the absence of nerve gas in your room is a cause of you reading this paper.

  8. The proposal is incomplete in that it leaves open substantive assumptions about the distance ordering of the semantics. The task of interpreting the distance ordering—together with any formal characterization of the notion of “distance”—is notoriously difficult and I do not undertake any such attempt here.

  9. Another option: Instead of denying that causation is a natural relation between events, one could argue that there is a difference between causation and causal explanation, concede that this paper concerns only the latter, and hence maintain that causation proper is a natural relation between events.

  10. Strictly speaking, the assumption is that there is such a system for any possibility. But to ease the exposition I will mostly just talk of the actual world.

  11. The motivation is thus: No world is more similar to the actual world than the actual world is similar to itself. This motivation does not carry over when the ordering is one of closeness instead of similarity.

  12. To be precise, this is but an interpretation of the Weak Centering assumption. The assumption itself says that for all worlds ω, ω is at least as close to itself as every other world.

  13. A more rigorous account of normality is provided by Menzies (2004, 160–69), who defines normality relative to a causal model. See also Menzies (2011, 196–201) for a motivation based in psychological evidence.

  14. Clearly, although Weak Centering is one way, it is not the only way.

  15. It has been investigated elsewhere, however. Menzies (2004) uses a kind of counterfactual dependence but rejects Lewis’ semantics of counterfactuals. Beebee (2004, 298–300) argues against a proposal similar to the present one, yet without situating it rigorously in Lewis’ semantics—I return to her objection later. Menzies (2011, 193–95) argues for Weak Centering in Lewis’ semantics to discuss the problem of profligate omissions, yet among several other problems (I came across this chapter only in the last stages of revising this paper).

  16. I do not take this as a basic assumption, nor do I rely on intuitive judgments that statement 4 is false. In fact, I acknowledge that this reasoning could also be turned against Peter (if statement 2 is denied). I consider this possibility as the objection of “more than one possible preventer” in Sect. 6.2.

  17. Strictly speaking, these assumptions are not necessary to solve the problem of profligate omissions. What matters is not proximal possibility to the actual world of either worlds in which Peter or the Queen waters the plant. Instead, what matters to solve the problem of omissions is the relative proximity of the closest worlds in which Peter waters the plant and worlds in which the Queen waters the plant to each other. I still make these assumptions in this way because they allow an exposition of the framework that is easier to follow and provide a novel taxonomy of objections (see below).

  18. Furthermore, for one detailed account of how to specify the distance ordering see Menzies (2004).

  19. Consider here the intersection of the inner circle and the area left of the finely dotted line.

  20. This case is from Beebee (2004).

  21. This case is from Menzies (2004).

  22. Instead of “proximal possibilities” Menzies (2004, 160) calls this the “field of normal conditions”. But the ideas are largely analogous; except for the fact that I assume that this sphere of possibilities includes the actual world whereas Menzies (2004, 162) explicitly rejects this idea.

  23. In the later paper with List and Menzies (2009), the proximal possibilities contain worlds that different in relevant respects. This is the proposal that I use here.

  24. Although not quite, as we have just seen. To allow that the sphere of proximal possibility includes worlds that differ in relevant respects, Menzies’ (2004) account of the normal evolution of a causal model would have to be amended.

  25. I refer to Lewis (1979) only for illustration. I do not suggest that this is a candidate for the correct distance ordering.

  26. I showed how some interpretations defeat the objection in this way. I do not claim that each interpretation of the distance ordering can defeat this kind of counterexample in this way.

  27. Although the present case of more than one proximal preventer differs from overdetermination cases insofar as neither Anne nor Peter actually waters the plant.

  28. I included the necessary component of Strong Dependence only to show that the Queen and other omissions do not cause the death of the plant. But, strictly speaking, this assumption need not be made, and it need not be show that the Queen is not a cause. It would have been enough to show that the proposed amendment to the sufficient condition of causation is such that the problem of profligate omissions does not arise anymore.

  29. Notation in this quote is adapted.

  30. Using the expression “similarity” for what we called “distance”, Walters (2016) writes that “similarity here is a technical notion”. I prefer to use a neutral term instead of borrowing the term “similarity” and replacing its common meaning with a technical meaning.

  31. The proposal above is not uniquely mandated by such an instrumentalist approach. Yet, given that the proposal is more abstract than existing solutions, it can be seen as a minimal move. Note also that the argument here does not necessarily rely on the instrumentalist approach. The proposal above can also leave the semantics unchanged and instead be interpreted as a theory of pragmatics providing assertibility conditions (cf. Lewis, 2000; McGrath, 2005, 145–46; Walters, 2016).


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I thank Richard Bradley, Ryan Cox, J. Dimitri Gallow, Sebastian Köhler, Christian List, Neil McDonnell, LA Paul, Jesse Saloom, Wolfgang Schwarz, Walter Sinnott-Armstrong, and Orri Stefánsson for helpful comments and discussions. The paper benefitted also from feedback at the meeting of the Gesellschaft für Analytische Philosophie in Osnabrück, the meeting of the Society for the Metaphysics of Science at Rutgers, and a lab meeting of the MADLAB at Duke University. Finally, the paper benefitted from generous comments by two anonymous referees for this journal.

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Correspondence to Johannes Himmelreich.

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Himmelreich, J. What Killed Your Plant? Profligate Omissions and Weak Centering. Erkenn 88, 1683–1703 (2023).

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