Abstract
Humean accounts of natural law have long been charged with being unable to account for the laws’ explanatory power in science. One form of this objection is to charge Humean accounts with explanatory circularity: a fact in the Humean mosaic helps to explain why some regularity is a law (first premise), but that law, in turn, helps to explain why that mosaic fact holds (second premise). To this objection, Humeans have replied that the explanation in the first premise is metaphysical whereas the explanation in the second premise is scientific, so (since these two varieties of explanation operate very differently) the two explanations cannot be chained together to yield explanatory circularity. This paper presents a new circularity argument that avoids this objection because both explanations in the premises are metaphysical. The new circularity argument also avoids the objection that the contrasts at the point where the two explanations are chained together fail to line up properly. The upshot is to leave the Humean account of law with two unattractive options: to regard scientific explanation under natural law as not constituting genuine explanation at all or to regard the Humean account as involving a vicious explanatory circularity.
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Notes
Since the Humean facts in the mosaic are that various perfectly natural, non-modal, non-dispositional, non-haecceistic, intrinsic properties are instantiated at spacetime points (or by occupants thereof), I will sometimes refer to the mosaic’s “events” rather than the “facts” in the mosaic. This should cause no confusion. (Laws, of course, are not events.) See note 8.
Later I will also discuss the reply from Hicks 2021. These papers cite some of the other replies.
Hicks says that the contrasts’ failure to align explains why the argument leads from true premises to a false conclusion: that Ga (rather than ~ Ga) holds helps to explain why E has (rather than lacks) the power to explain why Fa scientifically explains Ga. Here is why the conclusion is false. The contrast in the conclusion’s explanandum is that E lacks this explanatory power although Fa&Ga is true. But had this contrasting condition been true, it could not have been explained by ~Ga (the contrast in the conclusion’s explanans). So the conclusion cannot be a genuine explanation since when A rather than A’ explains why B rather than B’, it must be that if B' had been true, then it would have been explained by A’.
Of course, that a single particular flame burns yellow may not be (on the Humean account) a “difference-maker” regarding E’s lawhood; there may well be sufficiently many other sodium-salted flames burning yellow that even in the absence of the particular flame with which D is concerned, E would still add enough strength to earn its way into the BS. (D’s flame isn’t special in this regard; perhaps no single particular sodium-salted flame burning yellow is a difference-maker.) Nevertheless, it remains the case that D (and each other particular flame) helps to make E strong enough to qualify for the BS. Premise (4) does not say that D alone suffices to metaphysically explain the fact that E is a law rather than an accident; premise (4) requires only that D help to metaphysically explain why E is a law rather than accidentally true. D (and each other particular flame) can do that even without being a difference-maker regarding E’s lawhood.
The dialectical situation is more complicated than I have described since, as Salmon (1967:16–17) notes, Black recognizes that his “self-supporting” argument cannot address Hume’s classic problem of induction. Black may well be correct that without depending on some other inductive argument (that could be called into question later, but is not being called into question now), no inductive argument can be given a justification.
Hicks (2021:539–40) interprets laws precisely as I have just described (as rules of inference) in suggesting that a law does not itself explain a mosaic fact, but instead explains why one mosaic fact has the power to explain another.
Of course, the Humean does not herself characterize Humeanism as taking “scientific explanations” to lack explanatory power. My point (in the rest of this section) is that the Humean has not succeeded in showing that “scientific explanations” under the Humean’s thin conception deserve to be regarded as possessing explanatory power.
Duguid (2021:6049) pursues exactly the Humean strategy that I have just described: “it is open to Humeans to rescue the explanatory role of laws by appealing to a ‘thinner’ form of explanation”, namely, where “scientific explanations that involve laws should be treated as cases of subsumption under a pattern.” Duguid aims to motivate this “thin” notion of explanation by arguing that explanations involving such subsumption are “commonplace”; Duguid gives examples such as “I sit at the back of the lecture theatre because all of the cool kids sit at the back of the class.” I applaud Duguid for aiming to give this sort of independent motivation for the thin notion of explanation. But Diguid’s examples seem to me to provide little motivation for the thin notion. Although the generalization that all the cool kids sit at the back of the class is appropriate to give in reply to the question “Why do you sit at the back of the lecture theatre?”, the generalization may not actually help to explain why I sit there. The generalization may merely describe the explanation without figuring in it: the reason why I sit there is the same as the reason why all of the other cool kids sit there. There is also another way for the generalization to gesture toward an explanation that does not work by subsuming the fact being explained under that generalization: I sit at the back because although I am not a cool kid myself, I want to appear cool and I know that all of the cool kids sit at the back.
Admittedly, the Hempel passage begins by announcing its subject to be scientific explanation generally. But the passage then immediately says that unification is “especially” central to theoretical explanation (the subject of Hempel’s chapter). Furthermore, the passage characterizes the sort of unification relevant to explanation as involving “common structures and processes” that lie behind diverse empirical phenomena. These “common structures and processes” (the passage continues) all conform to “specific, testable, basic principles”—that is, to natural laws. Explanatory unification is thus achieved not by various empirical phenomena all falling under the same theoretical regularities that thereby become laws (as the Humeans portray that unification), but rather by various empirical phenomena all depending on the same theoretical structures and processes that are governed by independently-constituted laws. For these reasons (along with its focus on the explanation of a given empirical pattern rather than a given particular event), this passage does little to suggest the Humean conception of laws as explaining events by virtue of unifying them.
I have argued that it is viciously circular for a fact D in the mosaic to metaphysically explain another fact E’s power to scientifically explain D. However, Hicks and Wilson (forthcoming: Sect. 4.2) seem to suggest that this arrangement is not viciously circular, but rather routine:
“[I]t seems quite natural for facts about X to figure in explanations of what can explain X. In order to show that some Y explains that X, we will need to bring up features of both X and Y. To explain why your stepping on my tomato plant explains its stunted growth, I will need to point out features of its stunted growth – for example the fact that the branches that died are the ones you stepped on. Rather than being circular, this is straightforwardly good practice in higher-order explanation.”
(Thanks to a referee for suggesting that I address Hicks’s and Wilson’s remark).
To construe Hicks’s and Wilson’s remark as relevant to the purported vicious circularity that I have discussed, we must ensure that Hicks and Wilson are talking about how something is explained rather than how we know how something is explained. Hicks and Wilson say that “[i]n order to show that some Y explains that X, we will need to bring up features of both X and Y.” This remark seems to concern how we know that some Y explains X, whereas our topic is what makes Y explain X. (That the branches that died are the ones you stepped on is a good reason to believe that your stepping on the plant explains its stunted growth).
Furthermore, to construe Hicks’s and Wilson’s remark as relevant, we must bear in mind that the circularity argument is concerned with the way that a law explains a fact in the mosaic (recall note 1). Hicks and Wilson begin their remark by referring to “facts about X”, so X seems to be a particular (e.g., an event or object). But then Hicks and Wilson say that facts about X “feature in explanations of what can explain X”, as if X is now itself a fact being explained. Throughout the following example, I distinguish facts from what they are facts about.
Suppose that the fact that the rock possessed energy T at time t helps to explain why the window shattered. I agree with Hicks and Wilson that facts about the window’s shattering can help to explain why this energy fact about the rock can help to explain why the window shattered. For instance, the fact that the window came into contact with the rock at t helps to explain why the fact about the rock’s energy at t is explanatorily relevant to the fact that the window shattered (i.e., helps to explain why the energy-at-t fact is explanatorily relevant rather than the energy-at-t fact still holding and the fact that the window shattered still holding, but the former not being explanatorily relevant to the latter). But this contact-at-t fact, though a fact about the window (just like the fact that the window shattered), is not the fact about the window that is being explained by the energy-at-t fact (namely, that the window shattered). So we do not end up here with some fact X helping to explain why some other fact Y helps to explain X. Instead, we have one fact about the window helping to explain why Y helps to explain another fact about the window. Presumably, the fact that the window shattered does not help to explain why the energy-at-t fact helps to explain why the window shattered (rather than the energy-at-t fact still holding and the fact that the window shattered still holding, but the former not helping to explain the latter).
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Lange, M. A new circularity in explanations by Humean laws of nature. Philos Stud 180, 1001–1016 (2023). https://doi.org/10.1007/s11098-023-01925-7
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DOI: https://doi.org/10.1007/s11098-023-01925-7