2.1 Causation

What, then, is the notion at work in (1)? An initial possibility might be to understand it as a causal relation. That is, to interpret (1) as:

1. (1c) [Esther has the right to vote in US elections] is caused by [Esther is an eighteen-year-old US citizen].

Causation is one of a handful of explanatory relations that encode the idea of one or more things accounting for, or giving rise to, something else. For this reason, it can be expressed by phrases such as ‘making,’ ‘because,’ ‘in virtue of,’ and ‘explain,’ as in ‘The blossoming of the cherry tree made him joyful that day,’ ‘The gathering took place because we wanted to celebrate,’ ‘The fact that Jude helped Amy explains the fact that she was grateful to him,’ and similar examples. Due to its explanatory nature, causation has several formal features that are commonly associated with explanation: controversial cases aside, it is thought to be irreflexive (nothing causes itself), asymmetric (if c causes e, then e does not cause c), and transitive (if c causes e, and e causes f, then c causes f).

Nevertheless, the idea that causation is our target relation faces various problems. First, according to some prominent accounts, the holding of a causal relation between cause and effect either consists in or at least requires energy transfer between them (see, e.g., Castañeda Reference Castañeda1984; Fair Reference Fair1979), which is obviously absent in the case of the relation between legal facts and base facts.

Second, causation is a diachronic relation, with causes (typically) preceding their effects in time: the blossoming of the tree precedes the joy it causes, the desire to celebrate precedes the gathering taking place, Jude’s helping Amy precedes Amy’s gratitude toward him, and so on.Footnote ¹¹ But now consider the instant t at which Esther, a US citizen, turns eighteen. It is not as if Esther needs to wait until after t in order to acquire the right to vote in elections. Rather, the time at which she becomes an eighteen-year-old US citizen is the very time at which she acquires the right to vote. To dramatize the point, if the polling station were to remain open just until t, she should still be able to cast her vote. Similarly, at each later time, t′, it is the fact that Esther is at least eighteen years old and a US citizen at t′ that determines that she has the right to vote at t′. So the relation we’re looking for should at least be able to hold synchronically.Footnote ¹²

This temporal discrepancy is a symptom of a deeper divergence between ways in which things can be “brought about,” or “determined,” by other things. Causal determination is one way in which some facts or events can bring about or give rise to others. Yet when Esther’s age and citizenship together combine to make it the case that she has the right to vote, her right is generated by these other properties in a different way: it is constitutively determined by them.

To see the contrast between constitutive and causal determination, consider two phenomena that are both generated by human affairs, but in very different ways. On the one hand, consider climate change. Climate change is clearly partly a product of human activities, in the sense that it is caused by them. However, climate change is not determined by humans in the sense of being constituted by them. This becomes evident when we ask what climate change is. For, albeit caused by humans, climate change is nevertheless a natural phenomenon as it consists of natural processes and events describable in purely physical terms, without reference to humans.

On the other hand, consider the property of being popular. This property is also, in a sense, the product of human affairs: it is the way that people regard other people (or things) that determines whether someone (or something) is popular. But the sense in which someone’s being popular is a function of facts about us is quite different. For it is not as if people’s attitudes and responses caused someone to be popular, as if by dressing them up somehow. Rather, for someone to be popular just is for them to be regarded in certain ways by other people: this is what being popular is or consists in. As before, there is a temporal component to this. Once the (extrinsic) conditions for being popular have been met, it is not as if one needs to wait in order to instantiate the property of being popular. Rather, at each time t when someone satisfies the conditions for being popular, that determines that they are popular at t.

For a case that manifests the contrast between constitutive and causal determination in relation to the same explanandum, consider the question of what makes a certain wall white.Footnote ¹³ If we were asking the causal question, the answer would presumably appeal to past facts about the wall, leading up to it being painted white, and the explanation would thereby be diachronic. If we were asking the constitutive question, the answer, by contrast, would appeal to things such as the reflectance profile of the surface, the surface’s disposition to appear in certain ways to perceivers under normal conditions and the like (depending on one’s metaphysics of color), and the explanation would be synchronic.

These examples should serve to highlight the distinction between constitutive and causal determination, and serve as a comparison with the legal case that interests us here. Just as Esther’s being popular is constitutively determined by underlying facts about collective mental states, and the surface’s color is determined by its categorical or dispositional features, Esther’s right to vote constitutively depends, given US law on the matter, on her age and citizenship. Naturally, these cases are different in many other respects since they involve different relata, but they are similar in how they are determined by the underlying facts.

2.2 Supervenience and Necessitation

Granting that the ‘in virtue of’ relation expressed by (1) is not causation, another possibility might be to understand it in modal terms. One option here would be to cash out (1) as a necessitation claim to the effect that the fact that Esther is an eighteen-year-old US citizen necessitates the fact that she has the right to vote:Footnote ¹⁴

1. (1n) Necessarily, if [Esther is an eighteen-year-old US citizen] obtains, then [Esther has the right to vote in US elections] obtains.

Likewise, another possible modal interpretation would be to cash out (1) as a supervenience claim, to the effect that [Esther has the right to vote in US elections] supervenes on [Esther is an eighteen-year-old US citizen]:Footnote ¹⁵

1. (1s) For any two possible worlds w, w′: if w, w′ agree on whether [Esther is an eighteen-year-old US citizen] obtains, then w, w′ agree on whether [Esther has the right to vote in US elections] obtains,

where two worlds agree on whether [p] obtains iff either [p] obtains at both worlds or it obtains at neither.

Supervenience and necessitation have been used to formulate a wide range of determination theses in the philosophy of mind, language, and epistemology, including physicalism, dualism, and a variety of internalist and externalist theses.Footnote ¹⁶ Yet the project of interpreting ‘in virtue of’ claims as supervenience or necessitation claims faces serious challenges, some inherent to their use in the legal case, and others more general in character.

Let us start with the specific challenges inherent to the legal case. One problem is that, on the usual interpretation that supervenience and necessitation claims are given, claims such as (1n) and (1s) are false. Since the modality within them is typically understood as metaphysical modality, (1n) implies that it is absolutely impossible for Esther to be an eighteen-year-old US citizen without having the right to vote, and (1s) implies that it is impossible for Esther’s voting rights to change without a change in her age or citizenship. But this seems clearly false. Since the laws governing voting rights are contingentFootnote ¹⁷ – they could be, and could have been, different – there are situations (say, the actual world) where Esther is both an eighteen-year-old US citizen and can vote in elections, and there are also possible situations where she’s an eighteen-year-old US citizen and yet she can’t vote – say, because the minimum voting age is set at twenty-one.

One way to fix this problem would be to restrict the modality in (1n) and (1s). In this vein, the scope of (1n) and (1s) could be interpreted as limited to worlds where US voting laws are as they actually are. If we only look at worlds where US law is such that all and only eighteen-year-old US citizens have the right to vote, any two people who have the same age and citizenship will be alike as to whether they can vote, and so in particular [Esther has the right to vote] will supervene on, and be necessitated by, [Esther is an eighteen-year-old US citizen] within this set of worlds.

Even this amended version, however, is liable to serious objections. One problem is that the truth of (1n) and (1s) is compatible with their converses also being true. In general, necessitation and supervenience are not asymmetric relations, and so they can run in both directions. Explanation, by contrast, is asymmetric: if x explains y, in the relevant sense, then y cannot explain x, since circular explanations are vicious.

But the problem here runs even deeper. For it’s not just that (1n) and (1s) leave open that their converses might be true. Rather, their converses are true: all worlds (with the same laws as actuality) where Esther has the right to vote in US elections are worlds where she is at least eighteen years old and a US citizen: she couldn’t have that right without having that age and citizenship; and any two worlds (with the same laws as actuality) that agree on whether Esther has the right to vote must also agree on whether she is at least eighteen years old and a US citizen. Therefore this is a case in which supervenience and necessitation run in both directions. But then, if the restricted version of supervenience or necessitation yielded apt regimentations of ‘in virtue of’ claims, we should also say that Esther is at least eighteen years old and a US citizen in virtue of having the right to vote, which is clearly false.

More generally, it is by now widely accepted that supervenience and necessitation do not adequately capture the notion of determination or dependence that is at work in claims such as (1), for two sorts of reasons.Footnote ¹⁸ One problem is that supervenience and necessitation have different formal properties than those that are generally thought to be possessed by the target notion of determination or dependence.Footnote ¹⁹ First, supervenience and necessitation are reflexive relations, meaning that they hold between anything and itself: for any x, x is necessitated by and supervenes on x. Second, as witnessed by the case involving Esther, they are not asymmetric: x being necessitated by or supervening on y does not rule out y likewise being necessitated by or supervening on x.Footnote ²⁰ Third, they are monotonic relations, meaning that supervenience and necessitation bases can be arbitrarily expanded salva veritate: if x is necessitated by or supervenes on y, then, similarly, x is necessitated by or supervenes on y together with anything else.

Determination and dependence, by contrast, are often thought to have different logical features. They are irreflexive: nothing depends on or is determined by itself. They are asymmetric: if x depends on and is determined by y, then y does not depend on and is not determined by x. And they are nonmonotonic, so that it is not the case that if x depends on and is determined by y, then x depends on and is determined by y together with anything else.

That said, for two main reasons it is unclear whether this argument is ultimately compelling. First, it is not entirely clear that determination and dependence really do have the formal properties that the argument ascribes to them. One way of establishing that they do would be by showing that determination and dependence inherit these properties from other relations to which they are closely connected, and especially from explanation and relative fundamentality, both of which are irreflexive, asymmetric, and nonmonotonic.Footnote ²¹ However, it is an open question how determination and dependence are related to these other notions, and so it is an open question whether it shares such properties with them.Footnote ²²

The second reason why the argument is not conclusive is that, even if determination and dependence do have these properties, it might still be possible to define them in terms of supervenience (or necessitation), by appealing to one-way supervenience (see Berker Reference Berker2018: 736; Kovacs Reference Kovacs2019). To illustrate, say that a set Γ one-way supervenes on a set ∆ iff (i) Γ supervenes on ∆; (ii) ∆ does not supervene on Γ; and (iii) Γ does not supervene on any proper subset of ∆. Then we would have introduced a supervenience relation that is both asymmetric (and hence irreflexive) and nonmonotonic, thus possessing the desired formal features.

However, a second line of argument has proven more resilient. The central problem is that one of the key features of determination is that, unlike intensional notions such as supervenience and necessitation, it is hyperintensional. This means that it can fail to hold between cointensional (i.e., necessarily coextensive) entities, and that it can fail to hold under substitution of necessary equivalents.

This key difference underlies the fact that modal accounts of constitutive determination systematically overgenerate by producing many false positives. That is, cases of entities that are related by supervenience or necessitation but where no determination relation holds.

First, necessary entities one-way supervene on many things they do not depend on. For a trivial example, [2 + 2 = 4] one-way supervenes on the fact that I’m sitting: any two worlds that agree on whether I’m sitting also agree on [2 + 2 = 4] (and not vice versa), simply because they must agree that [2 + 2 = 4] obtains.

Second, following Fine’s (Reference Fine1994, Reference Fine1995) popular example, consider Socrates and {Socrates}, the set whose sole member is Socrates.Footnote ²³ Given standard assumptions in set theory, [Socrates exist] and [{Socrates} exists] are cointensional: any world where Socrates exists is a world where {Socrates} does, and vice versa. So [Socrates exists] and [{Socrates} exists] supervene on, and necessitate, each other. Yet it is plausible that while {Socrates} exists because Socrates does, the converse is not true. Therefore, while the determination and the dependence each run in one direction, with the existence of {Socrates} determined by and depending on the existence of Socrates, the necessitation and the supervenience run in both directions. And this gives rise to another false positive: [Socrates exists] supervenes on and is necessitated by [{Socrates} exists], without being determined by it. At the same time, trying to solve this problem by using the notion of one-way supervenience would yield a false negative. For, by hypothesis, [{Socrates} exists] is determined by [Socrates exists], yet the former fails to one-way supervene on the latter, since the supervenience runs in both directions.Footnote ²⁴ So, in general, cases of determination between cointensional entities generate false positives for supervenience, and false negatives for one-way supervenience.

Other cases of this sort are not hard to find. For one, consider truths and their truthmakers. For example, [grass is green] and [<grass is green> is true]Footnote ²⁵ are cointensional: wherever grass is green, the proposition that grass is green is true, and vice versa. Yet it is grass being green that makes the proposition <grass is green> true, not the other way round. And one-way supervenience fails to hold.

For another, some cases involving legal particulars and base facts are also of this kind. As we noticed, [Esther has the right to vote in US elections] and [Esther is an eighteen-year-old US citizen] are cointensional relative to worlds that share the same voting laws as the present-day United States. Yet it is the former fact that holds in virtue of the latter, not vice versa. And one-way supervenience fails to hold.

What the foregoing points suggest is that analyzing the target notion of determination in causal or modal terms won’t work. For this and related reasons, in recent years an increasing number of philosophers have started to theorize about determination directly, rather than trying to replace it with surrogate notions. The underlying idea behind this turn was not to introduce or engineer a novel technical concept but rather to take seriously a notion that is already present in ordinary discourse, and that has been at the core of philosophy for a long time.Footnote ²⁶ The result has been a growing body of work dealing with the nature and logic of determination in its own right, developed under the heading of “grounding theory.”Footnote ²⁷

2.3 Metaphysical Grounding

The notion of ground has become the locus around which the study of constitutive determination has settled. It promises to capture and regiment the idea of some things giving rise to, or accounting for, some others, where this generative link holds, typically at least, not across time, as in the case of causation, but rather across different “levels of reality” at a time. In this spirit, one may suppose that physical facts about particles ground chemical facts about molecules, which in turn determine the existence of biological organisms and (perhaps) their mental states, whose interactions generate societies and legal systems. By providing an interlevel connector, the notion of ground underwrites a conception of reality on which not everything is metaphysically on a par. Only a restricted class of entities – if any – is regarded as absolutely ungrounded and therefore fundamental,Footnote ²⁸ whereas all others are derivative, arising from the more fundamental ones on which they depend.

Now let’s go back to particular legal facts. As we noticed at the beginning, legal particulars are a clear example of derivative entities. When we wonder why someone’s action has the legal status it does, it is not as if there were no answer to be had. Such facts cannot just be brute, inexplicable elements of reality. Rather, such facts must be explainable by some array of other facts. Taking grounding as our relation of choice then leads us to understand (1) as:

1. (1g) [Esther has the right to vote in US elections] is grounded in [Esther is an eighteen-year-old US citizen].

This reading of (1), however, is only as helpful and illuminating as the underlying notion of grounding it appeals to. In what follows, I set out some of the core features of grounding and outline some of the debates concerning them, placing particular emphasis on those of special relevance to the arguments to follow. In particular, it will be especially important to be aware of: (i) the relation among grounding, determination, and explanation; (ii) some key distinctions in the theory of ground (full vs. partial, mediate vs. immediate, etc.); (iii) ground’s structural features (asymmetry, transitivity, etc.); and (iv) the relation between grounding and metaphysical necessity. At the end of Section 2.3.4, I’ll flag the assumptions I make regarding these issues and how they bear on subsequent arguments.

3.1 Explanatory Norms

We begin with models that invoke laws as partial explanantia of legal facts. Consider again the fact that Esther has the right to vote in US elections. If asked why that is the case, in most contexts it would suffice to point out that she has the appropriate age and citizenship to be able to vote. Yet, crucially, the fact that this response would be felicitous in many contexts is compatible with thinking that the explanation thereby given is no more than a convenient shorthand. If someone wanted the whole story, one may think, we should mention not only Esther’s age and citizenship but also the fact that it is the law in the US that eighteen-year-old US citizens have the right to vote in elections. Legal norms, in this view, are crucial – if often tacit – ingredients in legal explanations (see Enoch Reference Enoch2011, Reference Enoch2019; Rosen Reference Rosen2017a, Reference Rosen2017b).

After all, it seems obvious that particular legal facts counterfactually depend on legal norms: if the norms had been suitably different, different legal facts would have obtained. If, say, the law had been that only citizens who are at least twenty-one years old have the right to vote, then eighteen-year-old Esther would not have had that right. And although counterfactual dependence is not the same as metaphysical dependence,Footnote ⁴⁶ it does suggest the presence of an underlying relation of dependence that would explain it.Footnote ⁴⁷ Just as the fact that changing one’s age can make a difference to whether one can vote is due to the fact that one’s age explains whether one can vote, the fact that changing the voting laws can make a difference to whether one can vote might be similarly due to the fact that the laws also help to explain this.

The view that norms feature in explanations is also reflected in the role that we routinely assign to them in legal reasoning. When a lawyer wants to know what legal features a particular has, they usually look for two elements: the facts of the case and the laws that apply to them. Only then can they establish the conclusion, which they reach by performing an inference from the facts and the laws. A straightforward explanation of this aspect of legal epistemology is that laws are essential premises in arguments for conclusions about legal particulars because facts about legal particulars are metaphysically explained by laws.

In short, what motivates the idea that legal norms must be part of the explanation of legal facts is that without them, legal explanations look objectionably incomplete, both modally and epistemically. Let us call this the motivation from norms’ apparent role in explanation. I take it that it is a desideratum for any view of the matter that it should make good on this idea, or at least find a convincing way of explaining it away. Yet, crucially, there are different ways of trying to satisfy this desideratum and, as we shall see, none of them is immune from problems.

3.2 Legal Norms as Partial Grounds: Models 1–2

A clear way of vindicating the role of legal norms in explanation is to posit them as additional partial grounds of legal facts. Since any ground is an explanans of what it grounds, the appearance that legal norms are explanatory is obviously vindicated by assigning this role to them. On this model, let us call it Model 1 (M1), each particular legal fact is grounded in two sorts of ingredients (see Figure 1): (i) some legal norm(s) connecting the legal property (or relation) involved in the target legal fact to some underlying properties (or relations), and (ii) some base facts involving the instantiation of the properties (or relations) singled out by the correlative legal norm.Footnote ⁴⁸

Figure 1

Model 1: General and applied to a case.

Figure 1 Long description

The first section consists of the text Legal fact at the top, with two arrows labelled Partial ground pointing to it from the lower left text Base facts and the lower right text Legal norms. The second section consists of the text Esther has the right to vote in the U S elections at the top, with two arrows labelled Partial ground pointing to it from the lower left text Esther is an 18-year-old U S citizen and the lower right text U S voting rights laws.

A short but compelling argument appears to provide substantial support in favor of M1. Suppose, for reductio, that [Esther has the right to vote in US elections] is fully grounded in [Esther is an eighteen-year-old US citizen]. By Grounding Necessitarianism,Footnote ⁴⁹ it follows that every world where Esther is an eighteen-year-old US citizen is a world where she has the right to vote in US elections. But that seems false. For surely the law that sets out voting requirements is metaphysically contingent, and so there are worlds with different laws where Esther is an eighteen-year-old US citizen but doesn’t have the right to vote. If so, then [Esther is an eighteen-year-old US citizen] is at best a mere partial ground of [Esther has the right to vote in US elections], from which it follows that something needs to be added to ground the latter fact. And the legal norms connecting the target legal properties with the underlying conditions seem ideally placed to fill this gap. For not only is it intuitive that legal norms are part of the reason why legal facts obtain, but adding them to the grounding base is also the key to preserving Grounding Necessitarianism: every world where Esther is an eighteen-year-old US citizen and where it is the law that eighteen-year-old citizens have the right to vote is a world where Esther has the right to vote. In Section 3.8, we will see how this line of argument might be resisted (besides merely rejecting Grounding Necessitarianism). For now, it suffices to note that it provides a powerful reason in favor of taking legal norms as partial grounds of legal facts.

An interesting extension of Model 1 may be provided to account for an additional explanatory role that legal norms might be thought to play. It may seem plausible that legal norms explain not only legal facts but also the fact that legal facts depend on the base facts that they do. You may ask: why is having a certain age and citizenship the fact in virtue of which one has the voting rights that one does? Because the law says so, the answer goes.

As before, this is reflected in the existence of a counterfactual connection, this time holding between the fact about the grounding connection linking legal facts and base facts on the one hand, and the relevant legal norm on the other. Not only would the fact that one has the right to vote fail to obtain if the relevant legal norms were different; the fact that one’s right to vote depends on one’s age and citizenship would also fail to obtain. Therefore one might suppose that legal norms also explain why legal facts are grounded in the base facts that they are. If we again treat this kind of explanation as a grounding explanation, then this leads to an extension of Model 1 that conjoins it with the claim that the fact that a legal fact is grounded in the base facts that it is is, in turn, grounded in the relevant legal norm(s). On this model – let us call it Model 2 (M2) – legal norms play two explanatory roles (see Figure 2): they ground both (i) the target legal facts and (ii) the grounding connection between them and the base facts that ground them.

Figure 2

Model 2: General and applied to a case.

Figure 2 Long description

The first section, Legal fact, is placed at the centre, Base facts at the bottom right, and Legal norms at the bottom left. Two arrows labelled Partial ground originate from Legal norms, one pointing to Base facts and the other pointing to Legal facts. In the second section, Esther has right to vote in the U S elections is placed at the centre, Esther is an 18-year-old U S citizen at the bottom right, and U S voting rights laws at the bottom left. Two arrows labelled Partial ground originate from U S voting rights laws, one pointing to Esther is an 18-year-old U S citizen, and the other pointing to Esther has the right to vote in the U S elections.

Notice that the grounding relation that holds between legal norms and the grounding facts in question should be regarded as a relation of partial grounding. For the existence of a legal norm is clearly compatible with the absence of the legal fact and the base fact whose grounding connection it actually grounds. So given the factivity of ground, the existence of the legal norm is compatible with the absence of the grounding fact that it actually grounds.

As an example, consider again the norm that eighteen-year-old US citizens can vote in elections. At the world-time pair {@, t}, Esther is an eighteen-year-old US citizen, and the voting law grounds [[Esther is an eighteen-year-old US citizen] grounds [Esther has the right to vote]]. Yet Esther could have failed to be a US citizen (if, say, she had been born outside the US to noncitizen parents, and was never naturalized), in which case she wouldn’t have had the right to vote in the US (keeping the voting laws fixed). So it is possible for the actual voting laws to exist without it being the case that Esther’s being an eighteen-year-old US citizen grounds her having the right to vote. So again, assuming Grounding Necessitarianism, the voting law cannot be a full ground for [[Esther is an eighteen-year-old US citizen] grounds [Esther has the right to vote]].

This naturally raises the question of what should be added to complete the explanation of this grounding fact. On a conservative account, appealing also to [Esther is an eighteen-year-old US citizen] as an additional ground may be thought to provide an adequate basis. For worlds where the norm that eighteen-year-old US citizens have the right to vote exists and where Esther is an eighteen-year-old US citizen are worlds where [Esther is an eighteen-year-old US citizen] grounds [Esther has the right to vote]. Thus the legal norms, combined with the satisfaction of their “antecedent” conditions, necessitate both the target legal facts and the grounding connection between them and their base facts. Perhaps there are better ways of completing Model 2, but we won’t pursue this matter further. The key element of M2 that interests us here is simply that legal norms play this double role of first-order grounds and meta-grounds.Footnote ⁵⁰

3.3 Problems of Logical Form

What form, then, do legal norms have? When, in the preceding sections, we gave a rough gloss of the law that putatively figures in explanations of facts about people’s right to vote, we described it as the norm that US citizens who are at least eighteen years old have the right to vote in general elections. Taking this surface form as a faithful guide to logical form leads to viewing legal norms as having the form of generalizations:

with the specific norm in question taking the form:

This proposal, however, is deeply problematic (see Rosen Reference Rosen2017a: 287). For accidental generalizations – that is, facts with the form of unprefixed universally quantified claims – are plausibly grounded in their instances,Footnote ⁵¹ which in this case are facts about material conditionals of the form [ $\phi$ (a) $\to$ Fa].Footnote ⁵² And conditional facts with true consequents are plausibly grounded in their consequents, [Fa], just as disjunctions are grounded in their true disjuncts.Footnote ⁵³ Yet on the models we are considering (M1 and M2), legal norms are taken to be grounds of such facts, and so construing them as generalizations leads to violating the asymmetry (and, via transitivity, the irreflexivity) of grounding (see Figure 3).

Figure 3

Violations of asymmetry and irreflexivity.

Figure 3 Long description

The first section consists of the text F a at the top centre, with two arrows labelled Partial ground pointing to it, one from phi a at the lower left and one from for all x (phi of x) implies F of x at the lower right. A third arrow labelled Partial ground originates from F a at the top centre and curves back to point to F a at the lower right. The second section mirrors this arrangement using the case example. Esther has the right to vote in the U S elections is at the top centre, with two arrows labelled Partial ground pointing to it, one from Esther is an eighteen-year-old U S citizen at the lower left and one from for all x (x is at least eighteen years old and x is a U S citizen) implies x has the right to vote in the U S elections at the lower right. A third arrow labelled Partial ground originates from the top text Esther has the right to vote in the U S elections, and curves back to point to the same text repeated at the bottom.

A natural response might be to construe legal norms as prefixed generalizations, that is, as general facts involving some kind of intensional or hyperintensional operator, such as ‘according to the law of s,’ along the following lines:

If laws are understood in this way, then this problem should not arise. First, prefixed facts of this kind, like modalized facts more generally, are plausibly not grounded in their instances (Rosen Reference Rosen, Hale and Hoffmann2010).Footnote ⁵⁴ Second, in the legal case specifically, it is especially implausible to think that facts of the form of [Law] might be grounded in this way. As Rosen (Reference Rosen2017b: 143) usefully remarks: “Despite the wide diversity of views, no one thinks that what makes it the case that it’s illegal to drive down Main Street at 80 mph is the fact that particular token acts of speeding down Main Street, past, present, and future, happen to be illegal.”

In addition to this, the view that laws’ internal structure has this form comports well with the pretheoretical observation that when we routinely make claims about the content of valid legal norms, we do so in various more or less interchangeable ways that involve the use of such operators: ‘according to the law of system s, p,’ ‘under the law of s, p,’ ‘it is the law in s that p,’ ‘the norm that p is legally valid in s,’ and the like. Further, the fact that legal norms should be viewed as prefixed, rather than naked, generalizations is also independently clear from the fact that when we appeal to them in legal explanations, we appeal to what the law says, and no law is law simpliciter, but rather only relative to a particular system.Footnote ⁵⁵

Construing the general facts that supposedly ground legal facts in this way, however, only tells us this much about the form of laws. In particular, it doesn’t tell us anything about the internal structure of the prefixed content that norms have.Footnote ⁵⁶ And, broadly speaking, two paths ahead seem to be the most promising at this point. The first elaborates on the refinements above and regards laws as mere prefixed generalizations, while the second views them as endowed not only with an explanatory role but also with explanatory content.

3.4 Explanatory Norms with Nonexplanatory Content

If we conservatively apply the revisions outlined earlier, we get a conception of laws’ structure as prefixed universally quantified conditionals or biconditionals, derived from the addition of the prefix to [Gen], as in:

On this elaboration of models M1–2, legal facts of the form [Fa] are always fully grounded in general norms of the form [Gen-Law] together with base facts of the form [ $\phi ($ a)]. For instance, [Esther has the right to vote in US elections] will be grounded in [According to US law, all eighteen-year-old US citizens have the right to vote in US elections] together with [Esther is an eighteen-year-old US citizen].

This sort of account, however, faces a serious problem, highlighted by Rosen (Reference Rosen2017a: 293). The problem is that if the operator ‘according to the law (of s)’ is closed under logical consequence, then it will threaten to generate countless bogus explanations. For instance, given closure and antecedent strengthening, from

it will follow that

And while this also has the form of [Gen-Law], it is plausible that neither it nor facts about the satisfaction of its antecedent are grounds for particular legal facts concerning voting rights. First, Esther’s being wealthy plays no role in grounding her right to vote, even if she is in fact wealthy, since any ground must be relevant to the explanation of what it grounds,Footnote ⁵⁸ and Esther’s being wealthy is irrelevant to her having the right to vote. Second, even if one takes it to be true that, according to US law, wealthy US citizens of age have the right to vote, it is doubtful that this fact would be responsible for explaining anyone’s right to vote. For, again, it seems irrelevant to Esther’s (or anyone else’s) right to vote that under US law, wealthy US citizens have the right to vote in elections.

One solution to this problem might be to drop closure and deny that, in general, the logical consequences of what the law says are law.Footnote ⁵⁹ This would then allow one to say, for instance, that it does not follow from its being the law in the US that eighteen-year-old US citizens can vote that it is the law in the US that wealthy eighteen-year-old citizens can vote, and to thereby deny that this latter fact obtains.

This strategy, however, may sound too drastic: after all, wealthy US citizens do have the right to vote under US law, even though no particular citizen has that right in virtue of being wealthy. What should be opposed, in other words, is not that the law says this (i.e., that [Gen-Law-V*] obtains), but rather that this law, or facts about the instantiation of its conditions, participate in the explanation of particular legal facts.

This last observation motivates a different solution that preserves closure but discriminates, among facts of the form [Gen-Law], between those that do and those that do not play an explanatory role. The starting point is that even if closure holds, M1–2 are not committed to regarding facts such as [Gen-Law-V*], or facts about the satisfaction of their antecedents, as grounds for legal facts. These models say that every legal fact is grounded in a combination of base facts together with legal norms of the form given by [Gen-Law], but they do not say that every fact of the form [Gen-Law] is a ground of a particular legal fact. So it is open to the advocate of M1–2 to think of the form of legal norms along the lines of [Gen-Law], and keep closure (thereby allowing for facts such as [Gen-Law-V*]), while denying that legal facts are grounded in facts such as [Gen-Law-V*].

To emphasize: the view we are considering denies that whenever facts of the form [According to the law of s, $\forall$ x ( $\phi ($ x) $\to$ Fx)] and [ $\phi$ (a)] obtain, they will ground a fact of the form [Fa]. For, given a genuine law with that form, closure generates countless facts that share the same form but play no role in grounding [Fa]. Yet, crucially, this is compatible with endorsing M1–2. For these views merely hold that each legal fact of the form [Fa] must be grounded in some plurality of facts of the form [According to the law of s, $\forall$ x ( $\phi ($ x) $\to$ Fx)], [ $\phi ($ a)]. If one wishes to reserve the label “legal norm” or “law” just for facts that do play this grounding role, then the current reply strategy can be expressed by saying that not all facts of the form [According to the law of s, $\forall$ x ( $\phi ($ x) $\to$ Fx)] correspond to genuine laws or legal norms.

Although this seems a viable solution, it does raise a difficult question. If not all facts of the form [Gen-Law] are genuine laws, then logical form alone won’t allow us to distinguish real laws from bogus ones (Rosen Reference Rosen2017a: 293). This poses the challenge of providing a criterion for distinguishing, among facts of the form [According to the law of s, $\forall$ x ( $\phi ($ x) $\to$ Fx)], between those that do and those that do not play a role in grounding explanations of legal facts – between those that do and those that do not express genuine laws. It is an open question whether this challenge can ultimately be met.Footnote ⁶⁰

3.5 Explanatory Norms with Explanatory Content

A different sort of strategy to deal with the problem of bogus laws seeks to block the problematic result by exploring the hypothesis that on top of playing an explanatory role, laws also have explanatory content. The problem was that facts of the form of [Gen-Law], which merely establish sufficient conditions for the instantiation of the target legal property or relation, are not necessarily explanatory. So one possible way out could be to modify one’s conception of legal norms’ internal structure to prevent the generation of pseudo-laws via closure.

One promising way of doing this, pursued by Rosen (Reference Rosen2017a), is to conceive of legal norms as having explanatory content. The rough idea is that when a law connects the instantiation of a legal property F to the satisfaction of some underlying conditions $\phi$ , it does not merely say that anything that is $\phi$ is also F. Rather, it says that anything that is $\phi$ is thereby F, that is, that $\phi$ -things are F because they are $\phi$ (Rosen Reference Rosen2017a: 293–4):

Armed with this conception of laws, M1–2 could maintain that legal facts of the form [Fa] are always fully grounded in some base fact [ $\phi$ (a)] together with a law to the effect that anything that is $\phi$ is such that its being $\phi$ explains its being F.

Notice how this solves the earlier problem (Rosen Reference Rosen2017a: 294). To work with the specific case we’ve been using, the relevant norm would be:

And from this, it won’t follow that

For [Ex-Law-V*] involves not merely a strengthening of the antecedent but also a modification of the consequent. Notice, further, that while [Ex-Law-V] does classically entail

this is not a problem (Rosen Reference Rosen2017a: 295). For one thing is for it to be the case that under US law, wealthy US citizens of age have the right to vote because they are US citizens of age, and another, quite different thing is for it to be the case that according to US law, wealthy US citizens of age have the right to vote because they are wealthy US citizens of age. The former norm follows from the fact that under US law, US citizens of age have the right to vote because they are US citizens of age, but it is unproblematic. And the latter would be problematic, but it doesn’t follow from that fact.

Rosen’s proposal solves the problem of bogus laws while retaining closure, but it raises the question of what kind of explanation figures in the laws thus conceived. Since we’ve seen that neither causation nor modal relations capture the relation between legal facts and base facts, it is implausible that either would give us the notion we need.

One possibility mentioned by Rosen (Reference Rosen2017a: 296), is to take this to be a generic form of explanation. The hope would be to find some core notion of explanation that is shared by all explanatory relations (grounding, causation, etc.), and which could be used for the purpose in question. Specifically, the idea would be that grounding, causation, and other relations belong to the class of explanatory relations in virtue of pertaining to a common genus of which they are species, and in terms of which they are to be defined. If this is true, then there might be an interesting, general notion of explanation in the background that could figure in the content of laws.

That said, as things stand, it is fair to say that the prospects of this strategy look uncertain. For one thing, it is far from clear that such a generic notion of explanation exists. In particular, granting that grounding, causation, and so on all belong to a common class of explanation, it is unclear what the relationship between them and that class is. Perhaps there is nothing significant that these relations share, and they are mere determinates of a determinable notion of explanation with no interesting set of common features. Furthermore, even if an interesting common genus does exist, it is unclear what it would be like, and whether it could be used for the specific task of filling in [Ex-Law]. So although this may be a research path worth pursuing, it is safer to explore some alternative responses.

An obvious suggestion would be to take ‘explain’ in [Ex-Law] to mean metaphysically grounds, yielding laws with the following structure:

This immediately raises the question of whether the notion of grounding invoked by the law is that of full or partial ground. Precisifying [G-Law] as involving a relation of full grounding will give us:

Now, this formulation of legal norms need not be objectionable in itself.Footnote ⁶¹ What is objectionable, however, is to combine it with M1 or M2. For if the actual norms have the form of [FG-Law], then it seems to follow that base facts are full grounds of the legal facts they ground.Footnote ⁶² Yet according to M1–2, base facts are mere partial grounds. So norms that take the form [FG-Law] contradict M1–2 (see also Epstein Reference Epstein2015).Footnote ⁶³ Relatedly, while, strictly speaking, legal norms’ having this form does not rule out their being additional partial grounds of legal facts, they could only play this role by overdetermining them. Yet the spirit of M1–2 is that legal norms should play a significant role in legal explanations, and the redundant role they’d be left with violates this spirit. So it seems that legal norms cannot both have this explanatory content and also play an explanatory role (compare with Berker Reference Berker2019).Footnote ⁶⁴

An alternative proposal would be to take legal norms to make a claim of partial grounding:Footnote ⁶⁵

Unlike the previous proposal, this formulation fits well with the view, expressed by M1–2, that base facts are partial grounds of legal facts. Because of this, it also allows for the possibility that legal norms themselves play a nonredundant grounding role, thereby enabling a faithful implementation of these models. Are there any reasons to resist it?Footnote ⁶⁶

One possible worry is that this conception of the form of legal norms sits uncomfortably with the role that they are meant to play. The function of a legal norm is to regulate or constitute a certain property or relation, to tell us what needs to be the case in order for someone or something to instantiate it. Legal norms address questions (“Under what conditions is one a citizen?,” “What is legally prohibited?”) and give us guidance by providing authoritative answers to them. But how could they fulfill this role, unless they specified the full grounds of the property or relation in question? To leave out part of the explanation might seem objectionably incomplete.Footnote ⁶⁷

If legal norms are meant to specify the complete set of conditions that lead to the instantiation of the legal property they regulate, yet they cannot make a claim of full metaphysical ground, then a possible solution may come from appealing to a sort of grounding pluralism, that is, to the idea that there’s a plurality of grounding relations. In a moderate form, grounding pluralism has been advocated by Fine (Reference Fine, Correia and Schnieder2012), who has argued that there are three fundamentally distinct notions of grounding: metaphysical, natural, and normative grounding, exemplified by claims such as the following (Fine Reference Fine, Correia and Schnieder2012: 37):

These three kinds of grounding are fundamentally distinct, according to Fine, in the sense that none of them is reducible to any of the others, or definable in terms of a common generic notion. Further, each of them is related to its own primitive modality: metaphysical grounds metaphysically necessitate what they ground, natural grounds naturally necessitate what they ground, and normative grounds normatively necessitate what they ground.

In this spirit, Enoch (Reference Enoch2019) proposes that we should also countenance a relation of legal grounding. Legal grounding is meant to be the explanatory relation that holds within the framework set up by the law. Within the legal story, as it were, the fact that Esther is an eighteen-year-old US citizen fully explains why she has the right to vote in US elections. More generally, legal norms create a narrative within which base facts are the full legal grounds of particular legal facts, and nothing else is needed to explain them. Interestingly, moreover, notice that this being so is compatible with holding that in the global metaphysical hierarchy, the full explanation of legal facts will involve both the underlying base facts and the legal norms themselves.

Insofar as one is happy to countenance a plurality of grounding relations, the notion of legal grounding – of “grounding within the law” – may be used to characterize legal norms in the obvious way:

Now, the key question is whether this notion of legal grounding is definable in terms of a more basic grounding relation or is rather primitive. Taking it as primitive may seem objectionable, for it would threaten to give us a recipe for the proliferation of primitive grounding relations across the board. Within the game of chess, checkmating one’s opponent grounds winning the game. So checkmating chessly grounds winning a game of chess. Within the rules of English, spelling the first-person pronoun with a lower-case “i” makes it the case that one made a grammatical mistake. So writing “i” to refer to oneself orthographically grounds misspelling the word. And so on. This seems clearly absurd (see Rosen Reference Rosen2017a: 286; although see Enoch Reference Enoch2019 for an attempt to vindicate this strategy).

On the other hand, if legal grounding is not primitive, then the obvious way of defining it would be in terms of metaphysical grounding and legal norms, along the following lines:

That is, to be legally grounded in some fact is to be metaphysically grounded in it, together with the relevant norm. Legal grounds are just metaphysical grounds that combine with laws.

The main problem with this proposal, as noticed by Rosen (Reference Rosen2017b: 156) in the parallel moral case, is that this definition is circular. For the definiens of the legal grounding relation involves [LG-Law], which in turn involves the definiendum, that is, the very notion of legal grounding that it seeks to define. Since it is unclear how else the notion of legal grounding may be defined, it is unclear how promising it would be to rely on this idea.

3.6 Legal Norms as Meta-Grounds and Linking Principles: Models 3–4

The only account of legal norms’ logical form, among those considered here, that was apparently exempt from problems is [FG-Law]. On this account, legal norms relate target legal properties with some underlying conditions by stating that facts about the former are fully metaphysically grounded in facts about the latter. The problem arising in connection with this account did not concern the account per se, but rather the untenability of combining it with M1 or M2. According to M1–2, legal norms are partial grounds of legal facts; and yet how can this be true, if legal norms’ content is that base facts on their own fully ground legal facts? This suggests that perhaps the best response to the challenges we’ve met is to reject these models.

Now, one may think that if we accept [FG-Law] as the correct account of norms’ logical form, and reject M1–2, then we’re necessarily left with a Humean conception of legal norms that rejects their apparent role in explanations.Footnote ⁶⁸ But this would be a mistake, since [FG-Law] is compatible with views that do assign an explanatory role to laws, if only a role that is different from that of being partial grounds of particular legal facts.

One such view – let us call it Model 3 (M3) – can be extracted from M2 by dropping the claim that legal norms are partial metaphysical grounds of legal facts. Then, M3 is the view that whenever some particular legal fact is (fully) grounded in some base facts, a connecting norm grounds this grounding fact. This model vindicates at least one sense in which norms are often held to be explanatory, as we’ve seen. Why is the right to vote explained by one’s age and citizenship, one may ask? Because there is a law that regulates voting rights, which establishes that anyone with a certain age and citizenship (thereby) has the right to vote (see Figure 4).

Figure 4

Model 3: In general and applied to a case.

Figure 4 Long description

The first section consists of Legal facts at the top, enclosed in a large brace with Base facts at the bottom. An upward arrow labelled Full ground points from Base facts to Legal fact. To the right, the text Legal norm has a left-pointing arrow labelled Partial ground pointing toward the large brace containing Legal fact and Base facts. The second section has the text Esther has the right to vote in the U S elections at the top, enclosed in a large brace, with Esther is an 18-year-old U S citizen at the bottom. An upward arrow labelled Full ground points from Esther is an 18-year-old U S citizen to Esther has the right to vote in the U S elections. To the right, U S voting rights laws have a left-pointing arrow labelled Partial ground pointing toward the large brace.

Two clarifications are in order. First, M3 takes legal norms to ground facts about grounding. But are they full or partial grounds? For reasons discussed earlier (see Section 3.2), to regard them as full grounds would violate Grounding Necessitarianism. So they must be partial grounds. What, then, are their partners in ground? As we saw in Section 3.2, one option would be for legal norms to ground grounding facts in combination with base facts. But this is strictly optional to M3, and there may be better options.

Second, while M3 may in principle be combined with a number of different views regarding the form of the relevant laws (including [Gen-Law]), given the problems we’ve discussed, the most natural proposal is to couple it with [FG-Law]. We then get the result that, according to this version of M3, (i) every particular legal fact of the form [Fa] is fully grounded in some base facts of the form [ $\phi$ (a)]; and (ii) whenever [ $\phi$ (a)] fully grounds [Fa], this fact is in turn fully grounded in a fact of the form [According to the law of s, $\forall$ x ( $\phi ($ x) $\to$ [ $\phi$ (x)] fully metaphysically grounds [Fx])], together with [ $\phi ($ a)].

There are two main difficulties with M3, one for each of the claims it makes.Footnote ⁶⁹ The first is that it holds that legal facts are fully grounded in base facts and, as we’ve seen, this seems to lead to an absurd conclusion via Grounding Necessitarianism. Since this problem is shared by all the models we’ll consider from now on – as they all take base facts to be full grounds – we shall deal with this at the end.

The second difficulty, which affects M3 specifically, concerns its second claim. Model 3 makes a claim about the grounds of a kind of grounding fact: it holds that whenever some base facts ground a legal fact, this fact is grounded in some legal norms (possibly together with facts about the fulfillment of underlying conditions). Now, this claim may or may not be true, but it is worth highlighting that it clashes with the main views on the question of what grounds facts about grounding.

Three main answers to this question have been offered in the literature. On the “collapse” view advocated by Bennett (Reference Bennett2011) and deRosset (Reference deRosset2013), facts of the form [Γ fully grounds [p]] are always fully grounded in Γ. On the essentialist view held by Dasgupta (Reference Dasgupta2014a), Fine (Reference Fine, Correia and Schnieder2012), and Rosen (Reference Rosen, Hale and Hoffmann2010, Reference Rosen2017a), whenever Γ grounds [p], there is always some item or items x₁ … x_n drawn from Γ or [p] such that it lies in their nature that whenever the facts Γ obtain, they ground the fact that p. On this basis, the account then says that [Γ fully grounds [p]] is grounded in Γ, together with this fact about the essence of x₁ … x_n. Finally, on the zero-grounding view put forward by Litland (Reference Litland2017), all grounding facts are zero-grounded, that is, grounded in the empty set. Since M3 is incompatible with any of these views, there are reasons to doubt its truth.

This takes us to our last hypothesis concerning the explanatory role of laws. So far, we’ve been assuming that if legal norms play an explanatory role, they do so by grounding some thing or another, in one way or another. This, however, leaves out one important option that we haven’t considered thus far. On a unionist conception of grounding, grounding is identical to metaphysical explanation. To say that Γ metaphysically explains [p] is just to say that Γ grounds [p], and vice versa. Thus, on this conception, each explanans of a grounded fact must be one of its grounds, and grounding explanations have only two parts: what is grounded and what grounds it. Accordingly, within this conception the only explanatory role left for legal norms is that of being partial grounds.

However, as we saw in Section 2.3.1, this is not the only available conception of grounding. On a competing separatist view, grounding backs metaphysical explanation without being identical to it, and although every ground is an explanans of what it grounds, the converse need not be true. In particular, on one way of developing separatism (see Schaffer Reference Schaffer2016, Reference Schaffer2017a, Reference Schaffer2017b), grounding explanations are built from three irreducible elements: grounds, grounded, and grounding principles connecting them. This way of modeling metaphysical explanation is conceived by its proponents as just a particular instantiation of the structure of explanation more generally. Explanation is thought of as having a tripartite structure that always involves sources, links, and results: sources generate results via linking principles (Schaffer Reference Schaffer2016, Reference Schaffer2017a). Sources on their own generate nothing, since links are also needed in order to produce them. And to regard links as additional sources would be to commit a category mistake.

This general structure is realized by different types of explanation in similar ways. In causal explanation, there are causes (e.g., the rock striking the window), laws (laws of nature), and effects (e.g., the shattering of the window). No effect follows from its causes absent a suitable law of nature; and to regard laws as causes would be a category mistake. In logical explanation, there are premises, inference rules, and conclusions. No conclusion follows from its premises absent a suitable inference rule; and to regard inference rules as premises would be to commit a category mistake. In metaphysical explanation, there are grounds, groundeds, and grounding principles, which Schaffer (Reference Schaffer2016, Reference Schaffer2017a, Reference Schaffer2017b) calls “laws of metaphysics.” No derivative entity can arise from its grounds absent a grounding principle connecting them. And to regard grounding principles as further grounds would again be a mistake.

To take a simple example, the existence of a singleton – say, {Socrates} – can only be generated from the existence of its member, Socrates, together with the operation of set formation. Given Socrates as its input, set formation delivers {Socrates} as the output. To take another example, one might think that moral facts can only be generated from nonmoral facts in combination with some moral law connecting moral properties with nonmoral properties. In the same vein, legal norms would function as grounding principles that connect target legal properties with underlying conditions, and give rise to legal facts in combination with facts about the satisfaction of those conditions. No legal fact may be produced merely on the basis of the underlying base facts: legal norms are also needed. Yet one shouldn’t conflate these norms with grounds, since they play a fundamentally different role. The resulting model – let us call it Model 4 (M4) – can be represented in the following way (see Figure 5).

Figure 5

Model 4: In general and applied to a case.

Figure 5 Long description

The first section consists of Legal fact at the top, with Base facts at the bottom, and an upward arrow labelled Full ground pointing from Base facts to Legal fact. To the right, Legal norm has a curved left-pointing arrow labelled explains pointing to Legal fact. The second section mirrors this arrangement with the case example. Esther has the right to vote in the U S elections is at the top, with Esther is an 18-year-old U S citizen at the bottom, and an upward arrow labelled Full ground pointing from Esther is an 18-year-old U S citizen to Esther has the right to vote in the U S elections. To the right, U S voting rights laws have a curved left-pointing arrow labelled explain pointing to Esther has the right to vote in the U S elections.

According to M4, legal facts are fully metaphysically grounded in base facts, but are also metaphysically explained by legal norms, without being grounded in them. Legal norms are explanantia, but not grounds.

This model raises a number of difficult questions regarding what form legal norms, conceived as grounding principles, should have, as well as whether they are suitable to play this role. It is an open and interesting question, for instance, whether [FG-Law] would be the right form for legal grounding laws to have. It certainly speaks in its favor that [FG-Law] can be used within M4 without undermining its key tenets, as it did with M1–2. But, apart from this, it should be noted that none of the main accounts of metaphysical laws that are currently on offer takes this form. On Schaffer’s (Reference Schaffer2016) view, grounding principles are taken to be dependence functions modeled through structural equations. On Glazier’s (Reference Glazier and Jago2016) view, they are expressed through a distinctive two-place sentential operator introduced for this particular purpose. And on Wilsch’s (Reference Wilsch2016) deductive-nomological model, which follows Hempel and Oppenheim’s (Reference Hempel and Oppenheim1948) famous account of scientific explanation, they take the form of quantified conditionals.

Another source of skepticism is that metaphysical laws are usually taken to be metaphysically necessary, whereas legal norms are clearly not. Relatedly, by virtue of being a “third” element in explanations, distinct from grounds and groundeds, they are often conceived as ungrounded or not apt for being grounded, while legal norms surely cannot be fundamental and have to be grounded in some underlying facts. Correlatively, they should also be much more general in their scope of application. Going back to the case of singleton sets, there is a unique function, set formation, that takes in certain inputs and returns certain outputs. It is not as if there is one grounding principle for the construction of {Socrates}, another quite different law for the construction of {Plato}, and so on. Yet since each legal norm is different, and different laws are involved in the explanation of different legal facts, to regard them as metaphysical laws would be to do precisely this.

Therefore, if there are any metaphysical laws at work in the legal case, they would probably operate at a much higher level of abstraction, rather than the level at which specific legal norms operate. Perhaps, for instance, there could be a “law of jurisprudence” to the effect that whenever some norm is in place connecting $\phi ($ x) and Fx, and [ $\phi ($ a)] obtains, those two things together give rise to [Fa]. This could be a metaphysical law – applying to, and thereby explaining, all legal facts – as in fact it might even have the modal strength of metaphysical necessity. But it would not itself be a legal norm, and in fact it would suggest that legal norms are further partial grounds of legal facts, as M1 and M2, but not M4, have it.

Perhaps this is not a knock-down objection. Perhaps, for instance, we could draw a distinction between derivative and fundamental grounding principles, treat legal norms as derivative and contingent laws, and thereby preserve a sparse basis of fundamental and necessary “laws of jurisprudence” in the face of an abundance of higher-level principles at the derivative level. But whether or not this problem can be solved is a difficult issue, and one that must be grappled with.

In this section, I have outlined four different models of how particular legal facts might be explained, and of the place of legal norms within such explanations. These models differ on the role they assign to base facts, as to whether these are partial or full grounds. They also differ on the specific explanatory role they assign to norms, as to whether these are the grounds of legal facts, the grounds of grounding facts, or grounding principles. But these models all try to accommodate the motivation we started with, that legal norms should be explanatory, and they all assume that they are explanatory. Now, we turn to a final set of objections seeking to show that the preceding models are all false.

3.7 Problems of Modal and Temporal Profile

In this section, I present a pair of structurally analogous arguments against explanatory norms. Both arguments are inspired by, and closely related to, an influential line of argument developed by Epstein (Reference Epstein2015, Reference Epstein2019a, Reference Epstein2019b) against the view that particular social (and legal) facts are grounded in the metaphysical determinants of social (and legal) rules. However, the arguments I present do not entirely follow Epstein’s, and make subtly different points (for reasons that will emerge in due course).Footnote ⁷⁰ Nevertheless, they are based on the same raw material, which involves a combination of assumptions regarding the modal and temporal profile of legal facts, and structural features of grounding.

The same line of reasoning on which the arguments are based can be redirected, in slightly different ways, toward any of M1–4. However, for the sake of brevity, I will fully outline and discuss only the version that targets M1–2 specifically. Still, I will indicate how some minimal adjustments lead to rejecting the view that legal norms are partial grounds of grounding facts (as per M3), and that they are metaphysical explanantia of legal facts (as per M4). The overall conclusion is that, if these arguments are successful, some legal facts are not explained by any norms. This will then pave the way for the introduction of Model 5 (M5), which conceives of legal norms as inert generalizations.

3.8 Nonexplanatory Norms: Model 5

If all the preceding accounts are inadequate, then perhaps we ought to reject the view that legal norms are explanatory. Even though it seems as though legal norms contribute to the metaphysical explanation of legal facts (or of grounding facts about them), they are in fact explanatorily inert generalizations. The resulting view, M5, holds, like M3–4, that legal facts are fully grounded in base facts. The fact that Esther has the right to vote in elections, for instance, is fully grounded in the fact that she is an eighteen-year-old US citizen. But, unlike M3–4, M5 maintains that legal norms are mere summaries of grounding patterns involving legal properties and base conditions.Footnote ⁹⁰ Legal norms, on this view, don’t govern the explanatory connections that tie legal properties together with the underlying properties that ground them. Rather, they merely report grounding conditions for the instantiation of legal properties and relations. Because of this, they can unproblematically take the form of [FG-Law], stating that if anything meets certain conditions, then this fully grounds the instantiation of a legal property or relation (see Figure 6).

Figure 6

Model 5: In general and applied to a case.

Figure 6 Long description

In the left section, Legal fact is at the top, Base facts is at the bottom, and an upward arrow labelled Full ground points from Base facts to Legal fact. A large brace encloses both Legal fact and Base facts, with the label Legal norm placed at the midpoint of the brace on the right side. In the right section, Esther has the right to vote in the U S elections is at the top, Esther is an 18-year-old U S citizen is at the bottom, and an upward arrow labelled Full ground points from Esther is an 18-year-old U S citizen to Esther has the right to vote in the U S elections. A large brace encloses both statements, with the label U S voting rights laws placed at the midpoint of the brace on the left side.

It is worth noting that legal norms, thus understood, can still play a valuable epistemic role in explaining – that is, in knowing or figuring out – what legal facts obtain. For instance, knowing that anyone with a certain age and citizenship thereby has the right to vote will allow one to infer whether someone is legally entitled to vote from their age and citizenship. In fact, it is hard to see how knowledge of legal facts could be acquired at all in the absence of knowledge of the relevant norms. So they would not only be useful for gaining knowledge of legal facts, but would be indispensable for it. For this reason, although M5 explains away the appearance that legal norms metaphysically explain legal facts, it still assigns a meaningful epistemic explanatory role to them. To this extent, there may still be a sense in which M5 fulfills the desideratum of vindicating norms’ apparent role in explanation, though this remains to be seen.

To illustrate M5 in more detail, let me present its most elaborate implementation in the literature, namely Epstein’s (Reference Epstein2015, Reference Epstein2019a, Reference Epstein2019b) account of social (legal) facts. Epstein’s view is constructed around two main building blocks. First, lawmaking facts, such as facts about the enactment of statutes, judicial decisions, and the like metaphysically determine legal norms, which Epstein calls “frame principles.”Footnote ⁹¹ Frame principles do not govern the production of legal facts or the grounding relations between legal facts and base facts. Rather, they summarize the grounding conditions of instantiation for legal properties and relations, and thereby express ways in which legal facts are grounded. Formally, frame principles can be modeled as functions from worlds to worlds. The frame principle that sets out conditions for voting rights, for instance, is the function that, given as input a world where Esther is an eighteen-year-old US citizen, returns a world where this fact grounds the fact that Esther has the right to vote in US elections. The set of all frame principles is what Epstein calls a “frame.”Footnote ⁹²

Second, relations of full ground between legal facts and base facts unfold in the ways codified in the frame principles set up by lawmaking facts. One way of thinking about this is to imagine lawmaking facts as constructing a scaffold within which legal facts arise from base facts. Once lawmaking facts set up conditions for the instantiation of a legal property, facts about the satisfaction of these conditions give rise to legal facts. In a sense, frame principles are like lenses we use to “see” what legal facts there are at a world, given the base facts that obtain there. If, say, we look at a world w through the lenses of present-day US law, then if Esther is an eighteen-year-old US citizen at w, we should also see that Esther has the right to vote at w. If the frame through which we look at w is different, then, even given the same set of base facts, we might see different legal facts to be generated at it.

It could be doubted whether the epistemic role assigned to norms by M5 adequately vindicates norms’ apparent role in explanation. But whatever one thinks about this issue, there is also another challenge the account faces: a challenge that it shares with any view on which base facts are the full grounds of legal facts (including M3–4). We noticed at the beginning that there is a powerful argument against these views (and, correlatively, in favor of accounts that are premised on their denial, i.e., M1–2). The problem is that the claim that base facts are full grounds of legal facts appears to lead to a failure of Grounding Necessitarianism. For recall that given Grounding Necessitarianism, it follows that if some base facts fully ground a legal fact at @, then any world where the former facts obtain is a world where the latter fact does, and this seems clearly false. For instance, in a world in which US voting laws set the minimum age at twenty-one, eighteen-year-old Esther intuitively does not have the right to vote, even though she would have that right at @. How can views that take base facts as full grounds of legal facts address this challenge?

One possibility is to preserve Grounding Necessitarianism by claiming that, despite appearances, legal facts that are actually fully grounded in some base facts obtain at any world where those base facts are present. What needs to be acknowledged is that the lawmaking facts are contingent. In the actual world, lawmaking facts set up the conditions for having the right to vote (being a first-degree murder, being a war criminal, etc.) as they do, but they could easily have been different, and could easily be superseded by new ones. Yet, crucially, this does not mean that in worlds where the lawmaking facts are different, the particular legal facts that obtain in the actual world fail to obtain.

On the way of developing this strategy pursued by Epstein (Reference Epstein2015), this is so because legal norms are modal principles endowed with unrestricted necessity, quantifying over all possible worlds irrespective of whether the lawmaking facts that set them up in the actual world exist there.Footnote ⁹³ If this is the scope that legal norms have, then they guarantee that base facts ground legal facts even at worlds where such lawmaking facts fail to obtain (unless their presence is required by the instantiation conditions included in the legal norms themselves). For instance, laws of war criminality might say that, necessarily, if someone commits certain atrocities during a war, that grounds the fact that they are a war criminal, where the necessity operator is unrestricted (see Epstein Reference Epstein2019b: 234). If so, then Khan would be a war criminal in every world where he commits the relevant atrocities, no matter whether the Geneva Conventions are enacted there.

One objection to this view is that while it might be defensible to assign this modal strength to some legal norms (such as the laws of war), it will be less plausible for others. For instance, it is odd to think that eighteen-year-old Esther has the right to vote in worlds where the voting laws set the minimum age at twenty-one just because in the actual world the voting laws grant her that right.Footnote ⁹⁴ In other words, the problem is that at least some legal facts appear to be modally sensitive not only to their base facts but also to lawmaking facts, such that had those been different, different legal facts would have obtained.

In response, one might secure a sense in which legal facts are modally sensitive to lawmaking facts, by drawing on the distinction, familiar from two-dimensional semantics, between worlds considered as actual and worlds considered as counterfactual (Epstein Reference Epstein2015: 119). In particular, although on this view Esther has the right to vote even at worlds where the lawmaking facts are different, it is still true that if the actual world had been different (if different legal norms had been actual), then she may not have had that right (at this or other worlds). More generally, given what lawmaking facts there actually are, the frame principles associated with them apply universally across modal space. But if the actual laws had been different, or if they were to change, then different frames would have been, or will be, (unrestrictedly) applicable.

If this response seems too actuality-centric, one could allow for a different kind of frame-dependence that eliminates the apparent bias in favor of (frames set up at) the actual world. In this vein, one could hold that different frames can be set up at different worlds, and that the question of what legal facts obtain is a matter that can be settled only relative to a frame of choice, without this having to be the actual frame. Given a frame f set up at a “pinned” world w_p, the legal facts that obtain at any world w are those that arise, given the base facts that obtain at w, in accordance with the conditions set out by f at w_p. Yet given a different choice of frame, different legal facts can be “seen” to obtain at every world.Footnote ⁹⁵

A different way of making plausible the idea that actual base facts ground the corresponding legal facts even at worlds with different laws is to appeal to a form of relationalism about legal facts and properties. In this vein, as we saw, Schaffer (Reference Schaffer2019) has argued that social features are relative to rules. For instance, the apparent monadic property of being a war criminal is really a two-place relation that holds between certain individual people and the Geneva Convention of 1949. More generally, given an apparent n-place social feature F, F is really an n+1-place feature, F relative to N, where N is a slot to be filled by a set of norms that provide grounding conditions for its instantiation.Footnote ⁹⁶ If legal features involve relations to rules, then it is less counterintuitive to think that they can be instantiated at worlds where the actual laws are absent. At worlds where the age requirements are set at twenty-one, for instance, eighteen-year-old Esther still possesses the right to vote relative to actual present-day US law. (Of course, she won’t be able to exercise that right, but that is a different issue.) In general, given a law that sets conditions for the instantiation of a legal feature, it is not so implausible that one can possess that feature relative to the law in question at contexts where the laws are different.

Finally, the last reply available to the advocate of M5 (and M3–4) is to reject Grounding Necessitarianism and claim that grounding is a contingent relation.Footnote ⁹⁷ At the actual world, Esther has the right to vote wholly in virtue of the fact that she’s an eighteen-year-old US citizen, yet at worlds where the voting laws are different, she lacks that right despite having the same age and citizenship she has here. The modal scope of legal norms is accordingly viewed as restricted, though there are different options as to how the restriction can be modeled. A legal norm N may be taken to apply only to worlds in which N is set up (or only in worlds where N exists); or N could apply to some worlds beyond those in which it exists, without it extending to all worlds; and so on. One could even be a pluralist about the modal scope of legal norms, and think that some norms “export” to worlds beyond those where they exist, while others do not, so that the question of modal scope will need to be settled on a case-by-case basis.

Whichever choice is made here, it is worth emphasizing that on this view, grounding will not in general necessitate. Legal facts that are fully grounded at the actual world in some base facts can fail to obtain at worlds where the same base facts obtain yet the norms are different, if those norms’ modal scope is restricted. However, proponents of this view can still hold on to a restricted version of necessitation, namely that base facts necessitate legal facts within the relevant frame (Schaffer Reference Schaffer2019: 757). That is, if the norms’ scope, while not completely unrestricted, extends beyond the actual world, then base facts will necessitate the corresponding legal facts within the frame projected by those norms. Whether this kind of connection between grounding and necessity is strong enough is a matter that needs further exploration.

3.9 No Legal Norms: Model 0

All the models that we have discussed presuppose the existence of laws or legal norms, understood as general standards that connect legal relations with the underlying features responsible for explaining them. This is a natural assumption to make. On a widespread view, legal norms make up the law of a legal system, and play a critical role for laypeople, lawyers, and legal philosophers alike. To the layperson, they provide action guidance and serve as grounds of praise, and for criticizing (non)compliance. To lawyers, they constitute one object of discovery in courtroom disputes, the target of legal interpretation, and a key premise in inferences to conclusions about the legal properties of individuals.Footnote ⁹⁸ To legal philosophers working in general jurisprudence, they constitute the target inquiry, with positivists and nonpositivists making competing claims about their nature and grounds.

Yet their existence can be challenged in various ways. First, one might be skeptical of their existence on the basis of a general opposition to abstract objects. Legal norms are not identical to concrete acts of lawmaking or to legal texts. They are determined by such things, to be sure, but they can survive changes that the latter cannot, and cannot be perceived. Rather, one plausible way to think of them is as “created” or “dependent” abstracta.Footnote ⁹⁹ Legal norms are complex abstract objects, composed of normative contents bearing the relation of legal validity to legal systems. Since they come to stand in the validity relation in virtue of contingent social facts, they exhibit temporal duration, unlike ordinary abstract objects. And since they bear this relation to legal systems, they can be thought of as having some sort of spatial location. Still, their abstract nature makes their ontological status open to the worries that apply to abstract objects in general.Footnote ¹⁰⁰

Second, one could harbor particularist scruples. Legal norms are supposed to provide general, exceptionless connections between base conditions and legal facts, such that if the former are satisfied, the latter obtain. One, however, could be skeptical that any such connections exist that are not hopelessly gerrymandered or tediously long. Alleged truths of that sort, the particularist claims, always, or nearly always, admit of exceptions, and so the most we can get are rough approximations that never truly hold in full generality.

Third, one might have reservations on account of parsimony, arguing for the elimination of legal norms from the fact that they don’t do any important work in our theories. As we saw when dealing with M5, it could be disputed whether legal norms play any role in metaphysical explanations. Moreover, while this is consistent with legal norms playing an epistemic role in reasoning to legal facts, this too can be challenged. A different option is to suggest that we can derive the legal facts from the base facts in combination with the things – let us call them the ‘legal determinants’ – that are normally thought to determine the legal norms, without passing through those norms. Rather than thinking that statutory provisions, judicial decisions, and the like determine something called “the law,” which then determines the legal facts, another possibility is to cut out this middle level entirely. Perhaps we don’t need to first determine the content of the law, in order to then infer the legal properties of individuals, but could instead establish those properties on the basis of the legal determinants directly.Footnote ¹⁰¹ If legal norms are explanatorily inert both metaphysically and epistemically, then why not eliminate them altogether? To posit unnecessary entities of this sort would be a clear violation of Ockham’s injunction not to multiply entities beyond necessity.

Notice the subtle difference between this view and others we have discussed. If, as is often assumed, grounding is a transitive relation,Footnote ¹⁰² then there is a sense in which even models on which legal facts are explained by norms can ultimately dispense with those norms, for any explanation of legal facts by norms could be replaced by one that is just as complete, yet appeals to the grounds of the legal norms instead. Here, by contrast, legal norms are not thought to play even a mediate role in (metaphysical or epistemic) explanation, and this is regarded as a reason to eliminate them.

A picture of this sort, which does away with law and focuses on legal relations instead, has been recently advocated by several authors.Footnote ¹⁰³ It also appears to have been adumbrated in parts of Dworkin’s work, especially in passages such as the following:

The view – M0 – that results from this eliminativist position explains legal facts without any appeal to norms. Unlike in M5, according to this model, base facts aren’t the full grounds of legal facts. Rather, legal facts are grounded also in the sorts of facts that, according to all other views, are responsible for determining legal norms (see Figure 7).

Figure 7

Model 0: General and applied to a case.

Figure 7 Long description

The illustration is split into two sections, with the general form on the left and a U S voting rights case on the right. In the left section, Legal fact is at the top centre, with two upward arrows labelled Partial ground pointing to it, one from Base facts at the lower left and one from Legal determinants at the lower right. In the right section, Esther has right to vote in the U S elections is at the top centre, with two upward arrows labelled Partial ground pointing to it, one from Esther is an 18-year-old U S citizen at the lower left and one from Social and/or moral facts at the lower right.

The exact nature of the legal determinants is one of the central questions in general jurisprudence, and it needn’t concern us here. These uncontroversially include things like legal texts, statutory enactments, judicial decisions, and the actions and mental states of lawmakers. They might also (more controversially) include social rules and conventions, or moral facts and principles. Legal positivists and nonpositivists disagree on what the legal determinants are, for example on whether they are wholly social or partly moral in character. And although this issue is usually framed as concerning the grounds of law, notice that for someone who opts for M0 and eliminativism about law, the same dividing lines and theoretical options with regard to the determination of law can be reframed as having to do with the determination of legal facts instead. The key point for our purposes is that, according to M0, the legal determinants determine the legal facts directly, acting as immediate partial grounds of those facts, without going through law as an intermediary.