In the recent philosophy of explanation, a growing attention to and discussion of non-causal explanations has emerged, as there seem to be compelling examples of non-causal explanations in the sciences, in pure mathematics, and in metaphysics. I defend the claim that the counterfactual theory of explanation (CTE) captures the explanatory character of both non-causal scientific and metaphysical explanations. According to the CTE, scientific and metaphysical explanations are explanatory by virtue of revealing counterfactual dependencies between the explanandum and the explanans. I support this claim by illustrating that CTE is applicable to Euler’s explanation (an example of a non-causal scientific explanation) and Loewer’s explanation (an example of a non-causal metaphysical explanation).
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See Lange (2009b) for a related account.
One alternative option to monism is causal reductionism, i.e. the view that seemingly non-causal explanations can ultimately be understood as causal explanations. Lewis (1986) and Skow (2014) have presented the most compelling attempt to spell out this strategy. Lewis and Skow rely on the notion of providing information about the causal history of the explanandum. Their notion of ‘causal information’ is significantly broader, and weaker, than the notion of ‘identifying the causes of the explanandum’ figuring in the causal accounts I have referred to earlier. For instance, Lewis and Skow hold that one explains causally by merely excluding a possible causal history of some explanandum E, or by stating that E has no cause at all – while other causal accounts would not classify this sort of information as causally explanatory. I cannot enter an in-depth discussion of the merits of causal reductionism here. I take it as premise – against causal reductionism – that there actually are non-causal explanations including the examples listed above and the two examples I will discuss in Sections 3 and 4.
I adopt Woodward’s (2003) terminology in calling it a counterfactual theory.
It is interesting that Woodward (1979: 45–46) takes the CTE to be a charitable revision of the covering law account.
I assume that a generalization supports counterfactuals only if the generalization is non-accidentally true or lawful. I use a broad notion of laws that includes non-strict ceteris paribus laws, such as Woodward and Hitckcock’s own invariance account. However, my aim here is not to defend a particular view of laws. I want to suggest instead that the CTE is neutral with respect to alternative theories of non-accidental truth or lawhood. I take this to be a strength of the CTE.
One may, of course, also ask whether the proof for Euler’s theorem is an explanatory proof. However, this question changes the topic and, hence, the explanandum, because it concerns an explanation in pure mathematics (as opposed to an applied mathematical explanation). As mentioned in Section 1, I will not address this topic.
Although the veridicality condition is met in the case of Euler’s explanation, one might worry that it does not hold for all scientific explanation, because (a) many scientific explanations involve idealized assumption, and (b) how-possibly explanations play an important epistemic role in the sciences. Both idealized and how-possibly explanations do not meet the veridicality condition. Regarding idealized explanations, it is, however, often possible to (re)interpret the idealizations in a way that is compatible with the veridicality condition by adopting, for instance, dispositionalist and minimalist accounts of idealizations (see Cartwright 1989; Hüttemann 2004; Strevens 2008). Regarding how-possibly explanations, I ultimately agree that the veridicality condition has to be rejected, if the CTE is supposed to be an account of both how-possibly and how-actually explanations. However, many prominent accounts of explanations (including Woodward’s version of the CTE) are (at least, implicitly) presented as accounts of how-actually explanations. In this vein, I also introduce the CTE as an account of how-actually explanations; this account can, of course, be weakened in the case of how-possibly explanations (see Reutlinger, A., Hangleiter, D., Hartmann, S., “Understanding (with) Toy Models”, The British Journal for the Philosophy of Science, “forthcoming” for my approach to how-possibly explanations and toy models).
It is a controversial issue whether the Humean grounding generalization (or a Humean supervenience claim) holds in all possible worlds, or only in a restricted class of worlds (see Hall 2012 for an overview).
See Cohen and Callender (2009) for a version of the BSA that is not committed to fundamental (or natural) predicates.
While Loewer seems to accept the grounding generalization as a key part of the explanans, there might be an alternative version of the Humean metaphysical explanation of laws that does not rely on grounding. This version is inspired by the Canberra plan. According to the Canberra plan version, the explanans consists of the following assumptions: (1) Conceptual analysis: A general statement l is a law in world w iff l is a theorem or axiom of the best system of w. (2) Empirical fact: The mosaic of a world w is such that l is an axiom or theorem of the best system of w. Assumptions (1) and (2) entail the explanandum: (3) Statement l is a law in w. The crucial point here is that the CTE also captures the Canberra plan version of the Humean explanation of laws. Most importantly, the decisive counterfactual is true in Loewer’s version and in the Canberra plan version; see below.
See footnote 11 regarding two qualifications with respect to the veridicality condition in the context of scientific explanations.
At first glance, the same problem appears to arise in the context of dispositional essentialism about laws. According to dispositional essentialism, the nomic essence of some property P grounds the regularities involving instantiation of P in a world (see, for instance, Bird 2007). A proponent of the CTE might be tempted to cash out the explanatory content of this grounding claim in terms of the counterfactual “if P had a non-actual nomic essence, then regularities would be different than they actually are”. According to dispositional essentialism, this antecedent is metaphysically impossible. However, a dispositional essentialist is certainly not committed to this prima facie problematic counterfactual within the CTE framework. A much more plausible and more useful counterfactual is this one: ‘if some non-actual ‘alien’ property P* with a different nomic essence than P’s nomic essence were instantiated (rather than P) in a world w, then the regularities in w would be different than the actual regularities'. The antecedent of this conditional is not impossible and suffices to spell out the explanatory content of the grounding claim that the dispositional essentialist makes.
I believe the very same problem arises in the context of explanations in pure mathematics, where the assumptions in the explanans seem to include necessary truths. It is an open research questions for me whether the CTE applies to explanations in pure mathematics or whether the CTE needs to be supplemented by an alternative theory of explanations in pure mathematics.
One reason for choosing a non-interventionist counterfactual account of causation is that Woodward’s critics have recently argued that interventionist counterfactuals are inherently problematic and ultimately dispensable for understanding causation and causal explanation (see Strevens 2008; Reutlinger 2013).
In Reutlinger 2013, I provide an in-depth discussion of non-interventionist counterfactuals and their semantics.
I would like to thank a referee for urging me to address this point.
This claim is not necessarily at odds with recent attempts to justify the claim that some non-causal explanations do in fact display an asymmetry (see Lange 2011; Jansson forthcoming).
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I would like to thank Hanoch Ben-Yami, Philip Goff, Siegfried Jaag, Lina Jansson, Maria Kronfeldner, Marc Lange, John T. Roberts, Juha Saatsi, and Wolfgang Schwarz as well as audiences in Budapest, Leeds, and Luxemburg for constructive comments. I am particularly grateful to Barry Loewer for many stimulating conversations (about many topics) over the past several years.
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Reutlinger, A. Does the counterfactual theory of explanation apply to non-causal explanations in metaphysics?. Euro Jnl Phil Sci 7, 239–256 (2017). https://doi.org/10.1007/s13194-016-0155-z