Abstract
I present an argument for the view that laws ground their instances. I then outline two important consequences that follow if we accept the conclusion of this argument. First, the claim that laws ground their instances threatens to undermine a prominent recent attempt to make sense of the explanatory power of Humean laws by distinguishing between metaphysical and scientific explanation. And second, the claim that laws ground their instances gives rise to a novel argument against the view that grounding relations are metaphysically necessary.
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Notes
This view is endorsed by, among others, Derosset (2010), Rosen (2010), Audi (2012) and Trogdon (2013a, b), and is called by Bliss and Trogdon (2016), the ‘default view’. Note that Fine (2012) distinguishes different types of ground corresponding to different types of necessity. For instance, he thinks that in addition to metaphysical grounding relations, which are such that the grounds metaphysically necessitate what they ground, there is a distinctive type of nomological grounding relation which is such that the grounds nomologically necessitate what they ground. But even if one adopts Fine’s view, the conclusion I discuss in Sect. 7 will be substantive, since my argument will show that insofar as laws ground their instances, grounds do not even nomologically necessitate what they ground.
In Sect. 6, I will consider indeterministic dynamical laws. I will say more about instances of such laws at that point.
For more on this sort of approach, and on the question of whether such laws can be expressed as universal generalizations, see the opening sections of Maudlin (2007), chapter 1. Insofar as such laws can be expressed as universal generalizations, I assume that they can be expressed as generalizations of the form all sequences of events in which conditions C1, C2, C3… hold satisfy some further condition CN. As an example, on this view f = ma can be expressed as “all sequences of events in which constant net force of f is applied to an object with mass m and in which that the temporal distance between the two events is ∆t, the change in velocity Δv is such that f = m∆v/∆t”.
Indeed even if we restrict our attention to the dynamical case, it may be that laws do not always explain their instances. Here is a potential counterexample. Suppose that I’m not sure whether it is a law that f = ma (in fact it is). But I am sure that you think that f = ma is a law, and I want you to be happy. So I intervene in your experiments in such a way to ensure that in every sequence of events where a net force of f is applied to an object with mass m, that object accelerates at a rate of a = f/m. In each case where I intervene the resulting sequence of events counts as an instance of f = ma (on my definition of ‘instance’). But the fact that it is a law that f = ma does not explain that sequence of events.
For skepticism about grounding in general see Hofweber (2009), Daly (2012) and Sider (2011). (I see the arguments in Wilson (2014) and Koslicki (2015) as versions of particularism (as defined below) as opposed to full blown skepticism about grounding.) Note that philosophers who want to avoid a commitment to relations regiment grounding talk in terms of a non-truth-functional sentential connective. See Fine (2001, 2012) and Correia (2010), and the discussion in Bliss and Trogdon (2016).
When I say that grounding relations are explanatory here I mean to be neutral between the claim that grounding relations themselves are explanatory relations, and the claim that grounding relations merely underwrite (some) explanations. See the discussion of direct versus indirect explanationism below.
Note that this is not the same as claiming that the criteria mentioned in (1)–(3) are themselves wholly uncontroversial (See, for instance, Wilson (Forthcoming) for a recent argument against (2)).
Here is an example of the way in which one of these pseudo-assumptions avoids being a genuine assumption. Suppose one is a factualist. Then one must reject the conclusion of the argument outlined above. After all, I just claimed that instances are sequences of events—and sequences of events are not facts. So according to the factualist, instances cannot be relata of grounding relations. At first glance, then, it seems that ecumenicism is a substantive assumption that is playing a key role in the argument—without that assumption the conclusion of the argument cannot be true. The key thing to notice, however, is that although the factualist cannot accept the conclusion of the argument as I am presenting it here, that argument can be straightforwardly modified in a way that will make it acceptable to the factualist. The simplest way to do this is to maintain premise 1 and 2 as is, and change premise 3 to: “If the Fs explain the Gs and the Fs don’t cause the Gs, then facts about the Fs ground facts about the Gs”. The conclusion of the argument would then be that facts about laws ground facts about their instances. More specifically, given the defense of premises 1 and 3 below, the argument would establish that the fact that it is a dynamical law that events of type E are followed by events of type F grounds the fact that in some particular case an event of type E was followed by an event of type F. This is still a philosophically substantive conclusion, which leads straightforwardly to the two consequences that I discuss in Sects. 6 and 7.
This is a natural but not uncontroversial assumption to make. See Maudlin 2007, chapter 1 for discussion. Again, I am assuming here that insofar as dynamical laws are understood as universal generalizations then they can be understood as ranging over sequences of events as described in footnote 4. Insofar as one understands dynamical laws as universal generalizations but thinks that they take some alternative form, one would need a further step to generate a conflict between my claim that such laws explain their instances and the relevant Finean principle.
Note that I’m not trying to claim that one should endorse the Finean position here. Indeed for my own part, I am moved by the sorts of criticisms of that position found in Marshall (2015). The reason why I think that there is an advantage to claiming that when L is a law what explains instances of L is the fact that L is a law (as opposed to L itself) is that insofar as L is a universal generalization it is the sort of fact that itself ought to have an explanation. For more on this way of thinking see the discussion of pattern explanation in science at the end of Sect. 3 below and in Emery (2017). Note that the claim that L is distinct from the fact that L is a law should be acceptable to both Humeans and non-Humeans.
S1, therefore, is an instance of f = ma, in the sense of ‘instance’ described in Sect. 2: given that at time t1, you applied a net force of 1 N to the rock, f = ma determines, as a matter of nomological necessity, that at time t2 (which is 1 s later) the rock is traveling at a speed of 1 m/s.
Or at least, this is a partial answer to Q-E2. One might think that a full answer to Q-E2 also cites the relevant law. So the reason why the rock was traveling at a speed of 1 m/s at t2 is that you applied a force of 1 N to it at t1 and it is a law that f = ma. That laws explain particular events in this way is wholly compatible with everything I say below about the way in which laws also explain the sequences of events that are their instances.
In terms of the overall philosophical thrust of the argument, the key claim that it is important for me to defend here is just that it is part of standard scientific practice to use laws to explain their instances. In the immediately proceeding section I have defended a specific version of this claim: that scientists use laws to explain their instances by responding to questions like Q-S1 with answers like L1. In my experience this is a very standard way of talking in physics classrooms and in physics labs. But note that those who think that in fact scientists answer questions like Q-S1 by claiming simply that f = ma instead of making the second-order claim that it is a law f = ma, can still accept a version of premise 1 and the rest of my argument. They will just think that what it means to say that laws explain (and ground) their instances is something slightly different than what I mean, and they will need to either (i) claim that dynamical laws like f = ma are not properly regimented as universal generalizations or (ii) reject the Finean claim discussed above, that universal generalizations are always explained by (and grounded in) their instances. For more on (i) see Maudlin (2007), chapter 1. For more on (ii) see Marshall (2015).
An anonymous reviewer points out that one might combine (i) the view that when scientists are really doing when they seem to be using L1 to answer Q-S1 is really using L1 to answer Q-S1* and (ii) the view that Q-S1 is explained by something distinct from L1, say facts about mechanisms or facts about the causal relations between the individual events in the sequence. This would avoid leaving Q-S1 unexplained, but it raises several further worries. First it is unclear why scientists would use laws to answer Q-S1* if they take something entirely different to answer Q-S1. Second, these alternative accounts suggest answers to Q-S1 which themselves presumably should have explanations Why is it, for instance, that the event of applying a force of 1 N to the rock at t1 causes the rock to be traveling at 1 m/s at t2? A natural answer to this is again: because it is a law that f = ma. So what first appears to be an alternative answer to Q-S1 may nonetheless end up committing us to the view that laws explain their instances—they just do so in a somewhat more indirect way by explaining the causal relations that in turn explain their instances, or by explaining the mechanisms that in turn explain their instances.
I am here assuming that the most plausible way to answer Q-P1 will involve answering Q-S1 in the way I have suggested above. But I’m open to the idea that you might try to answer questions like Q-P1 by appealing directly to the relevant law, and either using the fact that it is a law to answer Q-S1 or leaving questions like Q-S1 unanswered. (In particular, I think it is at least somewhat plausible to think that indeterministic laws don’t explain particular sequences of events even though they do explain patterns in large numbers of such sequences.) Insofar as one wants to leave Q-S1 unexplained, what the argument in this section establishes will not be that ‘laws explain their instances’ but rather that ‘laws explain patterns of events involving many of their instances’, and the conclusion of the argument will need to be adjusted accordingly. But the consequences that I discuss in Sects. 6 and 7 will remain unchanged.
I discuss this norm in more detail in Emery (2017). It is of course open to the person who wishes to reject premise 1 to argue that this norm gets trumped in the relevant sorts of cases. But given the examples provided of the sorts of weird and novel entities and relations that scientists are willing to introduce in order to satisfy the relevant norm, this will take some substantive philosophical work.
Note that this claim is wholly compatible with the thought that there are very few paradigm examples of explanation in science in which the explanans does not cause the explanandum. But I take it that, at a minimum there are explanatory relations between scientific “levels”, e.g. between chemistry and biology or between statistical mechanics and thermodynamics that are naturally understood as straightforward grounding explanations. Note also that the claim I am defending here is entirely compatible with the fact that non-causal explanations were at least occasionally discussed in philosophy of science long before the grounding literature began to develop in metaphysics (cf the discussion in Achinstein (1983) or Lewis (1986)). For one thing, although they were not put in terms of grounding, we might interpret such discussions as in fact being discussions of explanations in which the explanans grounds the explanandum. (This is especially plausible insofar as metaphysicians working on grounding often tell us that they are not describing a wholly novel and technical concept, but rather one that is relatively natural and has made appearances in the literature throughout the history of philosophy.) But also, the existence of some cases that do not fit neatly into the two categories of interest here—and that perhaps generate philosophical interest for precisely that reason—does not threaten the claim that paradigm cases of explanation tend to fit into those categories.
Here and throughout I am interested in a metaphysically robust notion of explanation wherein there are objective facts of the matter about what explains what, and whether something is a genuine explanation is determined by something over and above the extent to which it provides a sense of satisfaction or understanding. I’m not sure whether those who take the latter view of explanation should think that there is any pressure to keep one’s theory of explanation simple, but in any case those who take the former view should accept that there is at least some such pressure, so only those who reject any metaphysically robust notion of explanation at all can avoid the point being made here.
An even simpler account than the one that I am proposing here is one on which all cases of genuine explanation are cases in which the explanans causes the explanandum. I am assuming here and throughout that the costs of rejecting paradigm cases of explanation in which the explanans grounds the explanandum (or reinterpreting those as cases in which the explanans causes the explanandum) are too high to take this option seriously. (Note that even Skow (2014, 2016), who is often described as endorsing the view that all explanation is causal explanation, explicitly allows that there are grounding explanations in addition to causal explanations).
These are the sorts of cases listed in Schaffer (2009). Note that the point I am making here stands even if we wish to be factualists instead of ecumenicists in the sense described in Sect. 2. On the factualist view, the point is that grounding relations are usually taken to form an heterogenous group because they are usually taken to relate facts of many different types: e.g. facts about Socrates and facts about his singleton set, facts about truths and facts about their truthmakers, facts about wholes and facts about parts, and so on.
Note that particularists like Wilson (2014) will be especially willing to accept that grounding relations form a heterogenous group and that there are few substantive constraints on what counts as a grounding relation, but they don’t think that there are no constraints whatsoever. Perhaps most notably, they think that grounding relations are distinct from causal relations. A particularist, then, will think that the conclusion of the argument in Sect. 2 is most perspicuously understood as the claim that laws non-causally explain their instances. This is perhaps less exciting than the claim that laws ground their instances as understood by a unificationist. But it is still substantive and still has interesting consequences that correspond to the consequences discussed in Sects. 6 and 7 below. See, e.g., footnote 45 below.
My goal here is to defend premise 3 in general, but it is of course also worth emphasizing that the relation between laws and their instances plausibly satisfies all of the uncontroversial hallmarks of a grounding relation: I have already argued that laws explain their instances but don’t cause their instances, and note that it does not sound odd at all to claim that the event of applying a net force of 1 N to the rock at t1 was followed by the rock traveling at a speed of 1 m/s at t2 in virtue of the fact that it is a law that f = ma. In Sect. 7 below I will claim that the relation between a law and its instances is not even nomologically necessary. I say more about whether and to what extent this might in fact disqualify laws from grounding their instances at the end of that section.
A similar point will apply to other cases of purely mathematical explanation that are distinct from the types of mathematical explanation discussed in Lange (2017).
This is a natural way of reading the discussion in Achinstein (1983), chapter 7.
Of course, in many cases, scientists are not willing to accept the simpler theory because it violates some other principle or criteria that they have reason to endorse. Similarly, philosophers who are committed to views that conflict with the two consequences discussed in Sects. 6 and 7 may insist on rejecting premise 3 and taking the law-instance relation to be a sui generis type of explanation. I say more about this sort of strategy at the end of Sect. 6 and in footnote 65 below.
Or at least it would still follow in the sense that facts about laws would ground facts about instances. As I discussed in Sect. 2, insofar as the conclusion of my argument is reinterpreted as a conclusion about facts about laws grounding facts about instances, the interesting consequences discussed in Sects. 6 and 7 still follow.
Lange says that for ordinary dynamical laws like f = ma, an explanation of p by appeal to the fact that p is a law is a causal explanation, but he explicitly allows that some causal explanations may be such that the explanans grounds the explanandum (2017, p. xvii). This is because he has a highly permissive notion of causal explanation on which any explanation that provides information about the world’s causal network is a causal explanation. This is a variation of the explanation by causal relevance proposal discussed below. Lange also goes on to say that “the power of p’s lawhood to explain why p is the case arises from the connection between lawhood and necessity: it it is a law that p, then p holds because p must hold” (xviv). Those who think that chancy laws can explain their instances in the way I describe in Sect. 7 will need to think that they derive that explanatory power not from the fact that the explanandum in question must hold, but from the fact that the explanandum in question is very likely to hold. But this seems a relatively natural extension of Lange’s view—or at least of the more lenient version of Lange’s view that I have been considering here.
The main difference between this case and the meteor case (which again is explicitly endorsed by Skow) is that EM is a individual event and S1 is a sequence of events. It is of course open to someone who is putting forward this account of causal relevance to claim that it only applies to explanations in which the explanandum is an individual event. But insofar as they do so, explanation by causal relevance is no longer a plausible candidate for capturing the relation between laws and their instances—at least not for the kinds of laws and the kinds of instances that I am interested in in this paper (and recall that I’m happy if the account here does not generalize to all kinds of laws and instances). So on this view, explanation by causal relevance while perhaps a counterexample to premise 3, does nothing to undermine the conclusion of the argument.
It is of course open to the advocate of explanation by causal relevance to claim that there is some important difference between the meteor example and the comet example that makes it such that only the former is a plausible candidate for explanation by causal relevance. But it is unclear what this difference would be. Just as an example, note that one commonly cited difference between causation and grounding is that causation is usually diachronic whereas grounding is usually synchronic. Perhaps, then, the explanans in any causal explanation must occur before the explanandum. That may rule out LC as a causal explanation of EC. But if it does so it also rules out LM as a causal explanation of EM, which is precisely the sort of example that advocates of explanation by causal relevance (like Skow 2014) are hoping to capture. And this criterion on causal explanation would also mean that explanation by causal relevance, while perhaps a source of counterexamples to premise 3, is not a plausible candidate for capturing the relation between laws and their instances. It would thus leave the conclusion of the argument unscathed.
I mean here just that it is pre-theoretically surprising. Presumably it would not be surprising to those who advocate for the causal relevance account.
Two other accounts of explanation that would plausibly give rise to a type of explanation in which the Fs explain the Gs, while neither causing nor grounding the Gs, are Hempel and Oppenheim’s (1948) deductive-nomological account of explanation and Kitcher’s (1989) unificationist model. There are serious worries about both of these models and I won’t discuss them in any real detail here, although I do say a bit more about this in part VI. It is also worth noting, however, that the unificationist may also be happy to accept the claim that laws ground their instances. Perhaps the way in which laws ground their instances provides some form of unification of them. So it is not obvious that unificationism about explanation is in conflict with either premise 3 or the conclusion of the argument. Thanks to an anonymous referee for this suggestion.
Maudlin (2007) is a contemporary advocate of this challenge.
It is not entirely clear what Loewer takes to be an instance of a law and what sorts of laws he is interested in but in the literature that follows his paper (Lange 2013; Hicks and van Elswyk 2014; Marshall 2015; Roski 2017), most authors seem to be interested in laws as universal generalizations and instances of laws as instances of the corresponding quantificational formulas. Note that this is compatible with my usage of the word ‘instance’ if one is willing to assume that dynamical laws can be expressed as universal generalizations that range over sequences of events as described in footnote 4.
See Loewer (2012, pp. 130–131).
A bit of nuance here: it is unclear from Loewer (2012) whether he thinks that (i) the instances of f = ma metaphysically explain f = ma, (ii) the instances of f = ma metaphysically explain the fact that it is law that f = ma, or both. Insofar as he only endorses (i), we will need an extra step to get a conflict between Loewer’s view and the conclusion of the argument in Sect. 2, which is that the fact that f = ma is a law grounds instances of f = ma. There are several ways to make this additional step. Perhaps the most straightforward is to claim that Humeans who accept (i) should also accept (iii): f = ma plays a role in metaphysically explaining the fact that f = ma is a law. Combined with the claim that partial explanation is transitive, this results in the instances of f = ma both playing a role in explaining the fact that it is a law that f = ma and being explained by that fact. One could also claim that the fact that it is a law that f = ma grounds instances of f = ma by grounding f = ma, which in turn grounds instances of f = ma. Assuming that f = ma is properly regimented as a universal generalization in the way described in footnote 4, this latter proposal would involve giving up the Finean principle that universal generalizations are always explained by their instances. See the discussion at the end of Sect. 2. Thanks to an anonymous referee for pushing me on this point.
This is a place where the debate between unificationism and particularism about grounding is relevant. Those who are particularists will likely be far less troubled by circles of explanation involving grounding, since they think that there is little of importance that unifies grounding relations. Two things to note however: first, it would be a surprising and interesting result if Humeans had to be particularists about grounding in order to adopt Loewer’s solution to the explanatory challenge; and second, those who do adopt particularism here still need to argue that the sense in which laws ground their instances is an importantly different sense from the sense in which those instances ground the laws.
Unless one is a particularist. See the preceding footnote.
Loewer has not endorsed this strategy in print, but has suggested it in personal correspondence.
I don’t have space here to go into these worries in detail. But in brief, entailment is clearly neither sufficient nor necessary for explanation in paradigm cases (see Bromberger 1966). And it is unclear whether unification really tracks the distinctively mind-independent type of explanation at issue throughout this paper, as opposed to explaining in the sense of increasing understanding. Note also that, as mentioned in footnote 38 above, unificationists about explanation might be happy to accept the conclusion of the argument anyway.
It is worth noting that the conclusion of the argument in Sect. 2 also undermines a recent alternative defense of Humean theories of laws in light of the explanatory challenge. On this proposal, which is due to Marshall (2015), we first distinguish between L and the fact that it is a law that L and then claim that (i) instances of L explain the fact that it is a law that L, while (ii) L explains instances of L, thus avoiding any straightforward explanatory circularity. But insofar as one accepts the conclusion of the argument in Sect. 2 one must also accept that (at least sometimes) the fact that it is a law that L explains instances of L.
See for instance Audi (2012), Derosset (2010), Rosen (2010) and Trogdon (2013a, b). Bliss and Trogdon (2016). Dissenters include Dancy (2004), Schnieder (2006), Chudnoff (2011), Leuenberger (2014) and Skiles (2015). See footnote 2 for a discussion of Fine’s (2012), distinction between metaphysical and nomological grounding.
I say “small” here because I am at least open to the view that if there were widespread violations of the supposed law, then it would not in fact be a law. Insofar as you think that it is not metaphysically possible for a law to have exceptions, read on for further reasons for thinking that the argument of Sect. 2 leads to the view that grounding relations are not always metaphysically necessary.
For the particularist, the interesting claim here will be that not all non-causal dependence relations are metaphysically necessary; indeed some are not even nomologically necessary. The particularist likely felt less pressure to think that all non-causal dependence relations were metaphysically necessary, since they didn’t think that such relations formed a uniform class. But given that many of the paradigm cases of non-causal dependence discussed in the literature are metaphysically necessary, the consequence noted here is still a substantive result.
My own view is that many of the laws may be chancy even if the fundamental laws turn out to be deterministic (see Emery 2015). But in any case it is an open question whether the fundamental laws are deterministic or indeterministic, and the defender of grounding necessitariansim will presumably not want to hang her hat on the hope that the former will turn out to be true.
Nothing much turns on this terminology, though, and the reader is welcome to replace each use of ‘instance’ below with ‘sequence of events such that, given the first event, it follows from the law that the later events are very likely to occur.’
Note that the question of why S2 occurred is distinct from the question of why S2 was likely to occur. Although I take it that physicists would also answer the latter question by appealing to L2, my focus here is on the fact that they answer the former question by pointing to L2.
Notice that I am staying entirely neutral here on whether L2 also explains sequences of events in which the relative frequency diverges significantly from the chance.
Interestingly this argument may also call into question the very distinction between grounding and causation on the structural equation account set out in Schaffer (2016a). According to Schaffer, on that account, one of the key differences between grounding and causation is that causation may be indeterministic, while grounding is not.
Readers who are worried about the assumptions that I am making about partial grounding here should read on—I say more about them below.
Or at least it is a natural assumption that there are such nomologically possible worlds, given the plausible candidates for what could be added to L2 in order to get the full grounds of S2.
So in Fine’s (2012) terminology, I was assuming that partial grounds are partial strict grounds.
Thanks to Al Wilson for helpful dsicussion on this section.
Thanks to both David Kovacs and Jonathan Schaffer for suggesting this line of thinking.
Perhaps this sort of view would be amenable to those propensity theorists who say that chances are causal dispositions (see Gillies 2000). But note that even such theorists rarely say explicitly that chances enter into causal relations.
Here’s a particular line of thought that deserves attention: Suppose the grounding necessitarian rejects premise 3 and instead posits a sui generis type of explanatory relation which holds between laws and their instances. True, the paradigm cases of explanation tend to be ones in which the explanans either causes or grounds the explanandum, so the simplest plausible theory of explanation conforms with premise 3. But the paradigm cases of grounding tend to be those in which the ground metaphysically necessitate what they ground, so the simplest plausible theory of grounding is one on which grounds metaphysically necessitate what they ground! Here I think that it is important to note that while we surely have some pre-theoretic grip on the notion of grounding (at least under the kinds of minimal assumptions that I have been making about that notion here), it seems highly plausible that we have a firmer pre-theoretic grip on the notion of explanation. Indeed, I would suggest that our pre-theoretic grip on explanation is prior to any pre-theoretic grip we have on grounding: paradigm cases of grounding are precisely those cases in which we are committed to explanatory relations that are not obviously causal. Second, while I am willing to allow that grounding has a rich and interesting philosophical history, I think explanation has seen more sustained recent philosophical investigation—thus our diagnosis of what counts as a paradigm instance of explanation is relatively secure, while we are still in the process of understanding grounding, and with it what counts as a paradigm case of a grounding relation. Similar points apply to the philosopher who wants to avoid the consequence discussed in this section by rejecting premise 2 of the argument, and who claims that although rejecting premise 2 involves giving up a default assumption that follows from paradigm cases of causation, so too does accepting the argument and the consequences that follow—in particular the consequence that grounds do not always metaphysically necessitate what they ground.
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Acknowledgements
Thanks to Tom Donaldson, Matt Duncan, Mike Hicks, Tyler Hildebrand, David Kovacs, Marc Lange, Barry Loewer, Casey McCoy, Michaela McSweeney (and her Fall 2017 graduate seminar at Boston University), Daniel Nolan, Mike Raven, Jonathan Schaffer, Josh Schechter, Amy Seymour, Alex Skiles, Brad Skow, Alberto Tassoni, Kelly Trogdon, and Al Wilson for helpful discussion and to audiences at University of Colorado Boulder, University of North Carolina Chapel Hill, the Metaphysics on the Mountain II Conference, and the Ground in Philosophy of Science conference at the University of Geneva.
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Emery, N. Laws and their instances. Philos Stud 176, 1535–1561 (2019). https://doi.org/10.1007/s11098-018-1077-8
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DOI: https://doi.org/10.1007/s11098-018-1077-8