Abstract
Humean accounts of natural lawhood (such as Lewis’s) have often been criticized as unable to account for the laws’ characteristic explanatory power in science. Loewer (Philos Stud 160:115–137, 2012) has replied that these criticisms fail to distinguish grounding explanations from scientific explanations. Lange (Philos Stud 164:255–261, 2013) has replied by arguing that grounding explanations and scientific explanations are linked by a transitivity principle, which can be used to argue that Humean accounts of natural law violate the prohibition on self-explanation. Lange’s argument has been sharply criticized by Hicks and van Elswyk (Philos Stud 172:433–443, 2015), Marshall (Philos Stud 172:3145–3165, 2015), and Miller (Philos Stud 172:1311–1332, 2015). This paper shows how Lange’s argument can withstand these criticisms once the transitivity principle and the prohibition on self-explanation are properly refined. The transitivity principle should be refined to accommodate contrasts in the explanans and explanandum. The prohibition on self-explanation should be refined so that it precludes a given fact p from helping to explain why some other fact q helps to explain why p. In this way, the transitivity principle avoids having counterintuitive consequences in cases involving macrostates having multiple possible microrealizations. The transitivity principle is perfectly compatible with the irreducibility of macroexplanations to microexplanations and with the diversity of the relations that can underwrite scientific explanations.
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Notes
Perhaps the prohibition on self-explanation is violated in some exotic cases, such as when time-travel occurs. However, following Marshall (2015, pp. 3150–3151, n. 13), let’s grant that it is not violated in routine cases of scientific explanation, even if it is violated in certain pathological cases. Following Miller (2015, p. 1325), Marshall (2015, p. 3152, n. 14) also notes that Lange’s objection to the Humean view of law can be reformulated without appealing to the prohibition on self-explanation; routine scientific self-explanation is just one of the intuitively implausible consequences of the Humean view of law when it is coupled with the transitivity principle.
Marshall (2015, p. 3152) makes exactly this reply to Hicks and van Elswyk. Also note that Hicks and van Elswyk say that in this example, D does not help to scientifically explain F because F would still have obtained had \(\sim \)D, and yet Hicks and van Elswyk say that D helps to metaphysically explain E even though E would still have obtained had \(\sim \)D. Hicks and van Elswyk need some account of why counterfactual dependence is required for scientific explanation but not for metaphysical explanation. (Thanks to Chris Dorst.)
Hicks and van Elswyk (2015, p. 438) acknowledge in a footnote: “Perhaps a dedicated anti-Humean could revive the circularity objection with a contrastive [transitivity] principle. Having not seen such an argument, we are agnostic of its cogency”. They pursue the matter no further. I accept their invitation now. That explanation is contrastive was influentially emphasized by van Fraassen (1980) and Garfinkel (1981).
Lipton (2004, pp. 42–43) makes a very similar proposal. Nothing here will turn on the details.
Schaffer (2005, p. 310) argues that causal relations are contrastive and proposes a principle analogous to transitivity, but exclusively concerning causal relations.
In deeming this premise false, I have presumed that it is not the case that had e been absent, the lion would (or might well) have been absent; the lion would simply have been present without e. But the truth-values of counterfactuals are context-sensitive, so perhaps there are contexts where it is true that had e been outside of region R, then the lion would have been outside of region R. To see that Transitivity yields a plausible conclusion in a context where such a counterfactual holds, let’s change the example to one where it is easier to imagine such a counterfactual holding. Suppose that the presence of a gold bar in room R of the museum helps to scientifically explain why there are so many visitors in R. (The bar attracts a crowd; had the bar been on display in room S of the museum instead of R, the crowd would have been in S and there would have been few people in R.) Consider a particular gold atom g that is in the bar. We can easily imagine a context where it is true that had atom g been in S rather than R, then the entire bar would have been in S rather than R. Accordingly, analogous to premises (i) and (ii) in the lion case, we have the following two premises: The bar’s presence in R rather than S helps to scientifically explain why there are many rather than few people in R, and atom g’s presence in R rather than S helps to metaphysically explain the bar’s presence in R rather than S. Transitivity yields the conclusion that atom g’s presence in R rather than S helps to scientifically explain why there are many rather than few people in R. This seems plausible to me, bearing in mind that the entire bar would have been elsewhere, had g been elsewhere. (However, by singling out atom g for special attention, this counterfactual may give a false impression; to remove this impression, it suffices to add that of course, g makes no greater contribution to attracting a crowd than any other gold atom in the bar does.)
I have adjusted the letters in this passage to match the letters in my earlier statement of the transitivity principle.
For more on this particular explanation (and on non-causal explanations by conservation laws more generally), see Lange (2011).
It is important that the explanandum here is a particular macrolevel outcome rather than a macrolevel regularity. To insist that a particular macrolevel outcome has a microlevel explanation is compatible with accepting the antireductionist idea (e.g., Kitcher 1984, p. 350) that certain macrolevel “patterns” can be explained only by macrolevel, “structural” features—not at the microlevel.
Putnam is often coupled with Fodor as defending anti-reductionism. Putnam says that he does not care whether we call the microdescription a non-explanation or “a terrible explanation” (1975, p. 296). For Putnam, I think, the most important aspect of anti-reductionism is not that a singular occurrence explained by a higher-level science cannot be explained by a lower-level science, but that the higher-level explanation is “autonomous” because it brings great explanatory benefits (such as unification) that cannot be supplied by any lower-level description, no matter how complete (and so the higher-level explanation is far better).
Indeed, casting the explanandum as the fact that all F’s are G, rather than the fact that Ga, may be the cleanest way to put the explanatory circularity argument in the first place. By putting the argument in this way, we side-step questions about what, in addition to Fa and the fact that all F’s are G is a law, is needed to explain Ga, since these are insufficient (as illustrated by the well-known difficulties for the D-N model of scientific explanation).
Compare (Lange 2013, p. 258, n. 3).
Achinstein (1963, p. 126) comes to the same conclusion.
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Lange, M. Transitivity, self-explanation, and the explanatory circularity argument against Humean accounts of natural law. Synthese 195, 1337–1353 (2018). https://doi.org/10.1007/s11229-016-1274-y
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DOI: https://doi.org/10.1007/s11229-016-1274-y