Abstract
This paper examines some recent attempts that use counterfactuals to understand the asymmetry of non-causal scientific explanations. These attempts recognize that even when there is explanatory asymmetry, there may be symmetry in counterfactual dependence. Therefore, something more than mere counterfactual dependence is needed to account for explanatory asymmetry. Whether that further ingredient, even if applicable to causal explanation, can fit non-causal explanation is the challenge that explanatory asymmetry poses for counterfactual accounts of non-causal explanation. This paper argues that several recent accounts (Woodward, in: Reutlinger and Saatsi (eds) Explanation beyond causation: philosophical perspectives on non-causal explanations, Oxford University Press, Oxford, pp 117–140, 2018; Jansson and Saatsi in Br J Philos Sci, forthcoming; Jansson in J Philos 112:7–599, 2015; Saatsi and Pexton in Philos Sci 80: 613–624, 2013; French and Saatsi, in: Reutlinger and Saatsi (eds) Explanation beyond causation: philosophical perspectives on non-causal explanations, Oxford University Press, Oxford, pp 185–205, 2018) fail to meet this challenge. The paper then sketches a more positive proposal for dealing with explanatory asymmetry in non-causal explanations.
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Notes
This approach is taken by Reutlinger (2017, pp. 253): “I think there are good reasons to hold that some non-causal explanations are not asymmetric…I believe that some (for instance, Euler’s explanation [in the bridge example discussed below in Sect. 2]) … lack such an asymmetry because the counterfactual dependence in question is symmetric.”
Woodward (2018, p. 128) says that the bridges’ arrangement “has perfectly ordinary causes rooted in human decisions to construct one or another particular configuration. Because these decisions cause the configuration, it is clear that [N] is not somehow part of an explanation of the configuration.” Of course, I grant that the bridges’ arrangement (and hence ~ E, let’s suppose) is causally explained by earlier human decisions. But I do not see how it follows, from the interventionist account’s entailing that human decisions causally explain ~ E, that the account entails that “the direction [of explanation] must run from the configuration to the impossibility of traversing.” Whether the account says that N non-causally explains ~ E depends on what the account says a non-causal explanation consists in; nothing in the account, as far as I can tell, ensures that if ~ E has a causal explanation, then nothing can satisfy the requirements for being a non-causal explanation of ~ E. (Furthermore, some philosophers (e.g., Salmon 1989, p. 183; Lange 2017, pp. 58–64) have maintained that a given fact can have both causal and (at least partly) non-causal explanations.) As we have seen, that N is unsuitable to be a target of intervention does not entail, on Woodward’s account, that N cannot be the explanans in a non-causal explanation of a singular fact since (Woodward 2018, p. 122) “one possible form of non-causal explanation answers w-questions … but does not do so by providing answers to questions about what happens under interventions.”
I do not know whether in some cases a token knot’s tricolorability in fact explains why it cannot be untied; see Sect. 2.4. But some knot invariants presumably do explain why some knots can(not) be untied, and I would not want to preclude tricolorability’s doing so.
Woodward (2003, pp. 220–221) mentions this explanation, which is also discussed originally by Ehrenfest 1917 and more recently by Callender 2005. Although an explanation of the possibility of stable planetary orbits is not an explanation of a singular fact, I mention it in this section (devoted to proposals regarding explanations of singular facts) in order to examine whether Woodward’s strategy in this case can be used to account for the asymmetry in the explanations of various singular facts (regarding token bridge arrangements.
Woodward does not endorse D’s explaining P (or vice versa); he sees little empirical basis for maintaining that A would still have held, had D (or had P) been different. He is not prepared to endorse (or to deny) substantivalism. But this demurral makes no difference to his point, which is that his account of non-causal explanation correctly identifies what it would take for D to explain P or vice versa—e.g., correctly identifies where substantivalists see the explanatory asymmetry as coming from.
Lange (2013, p. 488) introduced this example as a non-causal explanation.
Presumably, J&S would allow this principle to be loosened to permit statistical explanations of outcomes governed by indeterministic laws.
Baron et al. (2017) argue for an account of counterfactuals that would permit the nontrivial truth of countermathematicals such as “Had 23 been divisible into a whole number by 3, then Mother would have been able to divide her 23 strawberries evenly among her 3 children without cutting any.” They see such countermathematicals as underwriting “extra-mathematical” scientific explanations, thereby “extend[ing] the counterfactual theory of explanation to non-causal cases” (p. 1). But it seems to me that their approach to these counterfactuals inevitably also endorses “Had Mother been able to divide her 23 strawberries evenly among her 3 children without cutting any, then 23 would have been divisible into a whole number by 3.” With that symmetry in counterfactual dependence, there would be explanatory symmetry on their account. They do not raise this issue; they (p. 28) defer to Woodward to defend using counterfactual dependence to understand explanatory dependence.
My thanks to a referee for suggesting that I consider such a possible reply on Jansson’s behalf.
It might be suggested that the counterfactual-dependence arrow would be one-way if ~ E grounded N. For instance, Socrates’s existence grounds the existence of singleton {Socrates}. Had Socrates not existed, {Socrates} would not have existed. But had {Socrates} not existed (because nominalism about sets held), Socrates would still have existed. Could the asymmetry of non-causal scientific explanation of singular facts (where explanations supply information about counterfactual dependence) arise in this way?
Whether in the bridge example ~ E (partially) grounds N depends on what “grounding” consists in—which is not a topic that I can address here. But whatever we may ultimately say about grounding, the counterfactuals in the strawberries example are not parallel to those in the Socrates case. Had Socrates not existed, {Socrates} would not have existed, but had nominalism about numbers held so that it is not the case that 3 fails to divide 23 evenly, Mother would still have been unable to divide her 23 strawberries evenly among her 3 children without cutting any.
Some knot invariants give necessary and sufficient conditions for the knot’s being capable of being untied. For instance, a knot on the surface of a torus is specified by a pair of coprime integers where it can be untied if and only if either integer is 1 or − 1.
An analogy: Let C be that a given bishop currently on a black square (in a chess game) cannot ever occupy a given (white) square, let R be that bishops move only diagonally, and let R’ be that “blackness” must be conserved in a bishop’s moves. R’ identifies a “bishop invariant” that entails C (and had R’ not obtained, C would not have obtained). But R’ does not explain C.
S&P term some regularity explanations “causal” on p. 621, for example.
For these derivations, see Lange 2017, pp. 96–112, 145–149. The symmetry principles sustaining these counterfactuals, such as the principle of relativity, are taken to be invariant under these counterfactual antecedents. Caution: we have two senses of “invariance” operating here! Invariance under counterfactual antecedents, which the principle of relativity possesses, is distinct from invariance across reference frames, which the speed c possesses.
Admittedly, any test case (even one where there is overwhelming scientific agreement about the direction of explanation) might be questioned by an otherwise well-supported philosophical account of explanation. At a minimum, though, we would like an account of explanation to be able to explain away any places where scientific practice departs greatly from the account’s verdicts—and, in a case where there is significant disagreement among scientists about the order of explanatory priority, we would like an account of explanation to illuminate the source of that disagreement. (For an example of a philosophical account of non-causal explanation identifying in one historical case the source of scientific disagreement about the direction of explanation, see Lange 2017, pp. 150–186).
Here “constraint” is being used in the sense familiar from Lagrangian mechanics—e.g., that the rolling marble must remain in contact with the inclined plane, that the plane is rigid.
Perhaps F&S think that the explanatory asymmetry arises from the way in which facts about the system’s symmetries and conserved quantities can be deduced from facts about the system’s manipulable properties. From the latter facts, we can derive the system’s Lagrangian, then identify its symmetries, and from them infer that certain quantities are conserved. By contrast (F&S may be arguing), we cannot take the properties of (including the relations among) the system’s components and infer directly that certain quantities are conserved, and from there infer the Lagrangian’s symmetries. Rather, in Lagrangian mechanics, we can infer the conservation of certain quantities only by the intermediate step of first identifying the Lagrangian along with its symmetries.
To this strategy for saving explanatory asymmetry, I would reply that a different derivation would allow us to use the conserved quantities to arrive at the symmetries. We could begin by taking the components’ properties and using Newtonian (rather than Lagrangian) mechanics to derive the system’s time-evolution and thus that certain quantities are conserved. We could then use their conservation to deduce the Lagrangian’s symmetries. Thus, explanatory asymmetry cannot be rescued in this way.
This is not the notion of “constraint” in note 18.
I cannot do more here than sketch the following positive views. I elaborate and defend them more fully in Lange (2017).
These ideas are often expressed. For instance: “In physics, the frame-dependent quantities…are taken to be non-fundamental. … Frame-independent quantities, on the other hand, do correspond to fundamental, objective features of the world. The space–time interval is a fundamental, objective feature of the world, according to the theory of special relativity. … Reality is observer-independent. It does not depend on our arbitrary descriptions or conventions.” (North 2009, pp. 63, 67) For many similar passages, see Lange (2017, pp. 141–145).
My thanks to Chris Dorst, Alex Reutlinger, and two referees for helpful comments on earlier drafts.
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Lange, M. Asymmetry as a challenge to counterfactual accounts of non-causal explanation. Synthese 198, 3893–3918 (2021). https://doi.org/10.1007/s11229-019-02317-3
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DOI: https://doi.org/10.1007/s11229-019-02317-3