3.a.1. Constitutive explanation

It is a recurring theme in the grounding literature that one (or indeed the) characteristic feature of grounding is how strict or close a connection it is. Due to this, a correct grounding explanation is supposed to provide a form of understanding and illumination which is simply not attainable in other kinds of explanations.Footnote ⁹ This renders grounding explanations particularly satisfactory and desirable in our theorizing about the world. This idea is articulated in the following way by Kit Fine:

Elsewhere, Fine writes that grounding is distinguished from other explanatory connections “by being the tightest such connection” (Reference Fine2001, 15). These formulations articulate one crucial part of the idea that grounding is constitutive explanation:

Since the full ground of a fact need not logically or analytically entail the grounded fact, the talk of explanatory gaps in this context should not be understood merely in terms of logical or conceptual notions. What’s in question here is rather (the absence of) some metaphysical explanatory gap. But how are we to understand this?

The supposed power of grounding to bridge metaphysical explanatory gaps, I suggest, is closely connected with another aspect of constitutive explanation. It is here helpful to focus on how Fine, in the passage quoted above, contrasts the strictness of grounding explanation with that of causal explanation. The particle’s being acted upon by some positive force causally (or naturally) explains the particle’s accelerating, but this explanation is not maximally strict, and leaves the relevant kind of explanatory gap open. The (grounding) explanation of the particle’s accelerating in terms of its increasing its velocity over time, however, is maximally strict, and closes the explanatory gap. The key to this difference seems to be that in a constitutive explanation, the explanandum fact consists in nothing more than the explanans. Hence Fine writes:

Even though being acted upon by some positive force makes the particle accelerate, the former is not what the particle’s accelerating consists in, or what it is. So even though we can successfully explain, and thus come to understand, why the particle accelerates by citing its being acted upon by some positive force, this explanation still leaves an important gap in our understanding of the relevant fact. We can know what causes the fact to obtain without knowing its deeper inner nature—what it consists in and really is. When we have a successful grounding explanation of the particle’s accelerating in terms of its increasing its velocity over time, by contrast, we possess an explanation that proceeds by specifying wherein the fact consists. In such a case, understanding why the fact obtains goes hand in hand with understanding what the fact is, wherein it consists. This, I take it, is the basic idea that underlies both the label ‘constitutive explanation’ and the thesis that grounding is the strictest and most intimate explanatory connection possible (i.e., Gaplessness). The idea is captured by the following principle:

An important corollary to Gaplessness and Constitution is that there is a straightforward connection between grounding and the highly coveted status of one fact’s being “nothing over and above” some other facts. It is a popular idea that when [P] (fully) grounds [Q], [Q] is nothing over and above [P], and therefore constitutes a theoretical “free lunch.”Footnote ¹¹ On the face of it, it’s unclear why this should be so. By the irreflexivity of grounding, [P] and [Q] are nonidentical whenever one grounds the other, so a grounded fact is always something numerically additional to its grounds. Furthermore, explanation in general does not seem to secure “nothing over and above”-ness. Even if the window’s shattering has a full (causal) explanation in terms of Cicero’s throwing a rock against it (plus the necessary background conditions), the explanandum fact is clearly something “over and above” its explanantia. The key would seem to lie precisely in the supposed strictness of grounding, qua constitutive explanation. Thus, Fine writes:

As we have seen, constitutive explanation—by contrast with, e.g., causal explanation—proceeds by identifying wherein the explanandum fact consists. Since this relation between explanandum and explanans is supposed to close any metaphysical explanatory gap, it would seem appropriate to think of it as the tightest and most intimate connection short of numerical identity. If anything other than strict identity can secure the status of “nothing over and above”-ness, constitutive explanation would seem to be it.

Taking a step back to consider the larger picture, the idea of grounding as constitutive explanation is undeniably attractive. On this picture, a grounded fact always consists in its grounds. This highly intimate relation of consisting in guarantees that the grounded and its grounds are so closely linked that the grounding connection between them constitutes the “ultimate form of explanation,” where no stricter explanation is even possible. The maximal closeness between the grounded and its grounds finally allows us to treat the former as “nothing over and above” the latter, thus securing various theoretical benefits.

3.a.2 Opaque grounding vs. constitutive explanation

I will now argue that if there is opaque grounding, this alluring picture of grounding cannot be right—it depicts a mere part of the landscape. If there are opaque grounding cases, none of the principles outlined above hold in full generality and, consequently, not all cases of grounding are cases of constitutive explanation.

Let us start with Constitution. Suppose that [a is happiness-maximizing] opaquely grounds [a is morally right], as on our now familiar form of moral nonnaturalism. It then seems that the latter fact does consist in something more than the former. Clearly, [a is morally right]’s obtaining is explained by the obtaining of [a is happiness-maximizing] on the view in question. But as we have already seen, not just any explanatory relationship between facts suffices for one fact to consist in nothing more than another. For instance, a caused fact does not consist in its causal explanantia taken together. One relation that clearly does suffice is metaphysical analysis: since being a vixen simply consists in being female and being a fox, [Red is a vixen] consists in nothing more than [Red is female] and [Red is a fox] jointly. It also seems plausible that certain relations (though it is hard to say precisely which) of essential involvement between facts would suffice for consisting in: if [Q] has the right kind of real definition in terms of [P₁] … [P_N], then [Q] consists in nothing more than [P₁] … [P_N]. But both these kinds of relations are ruled out by the nonnaturalist. According to her view, the natural property instantiated in the ground is neither part of the metaphysical analysis nor part of the essence of the moral property instantiated in the grounded fact. Perhaps there are further relations that would suffice for one fact to consist in nothing more than another, but it is hard to see any natural sense in which the moral nonnaturalist could take the opaquely grounded fact [a is morally right] to consist in nothing more than [a is happiness-maximizing]. Thus, Constitution is false if there is opaque grounding.

Gaplessness is equally hard to square with opaque grounding. When [a is happiness-maximizing] opaquely grounds [a is morally right], the explanatory situation is much the same as in causal cases. The nonnaturalist can rightly claim to have provided an explanation of why [a is morally right] obtains—on her view, it obtains because [a is happiness-maximizing] obtains. But she is not offering that explanation as an account of wherein [a is morally right] consists. Indeed, she is explicitly refusing to give any account of wherein the moral fact consists, since she takes the property of being morally right to be an absolutely fundamental property. On her view, there is nothing further in which the property of moral rightness consists, and correspondingly, there is nothing further in which the fact [a is morally right] consists either. Thus, her grounding explanation of [a is morally right] in terms of [a is happiness-maximizing] is not of the strictest form possible.Footnote ¹² An account which proceeded by identifying grounds wherein [a is morally right] consisted would be stricter. But just like in a causal explanation, the opaque grounding explanation provides us with an account of why the explanandum fact obtains without illuminating the deeper inner nature of that fact, wherein it consists, or what it is. The metaphysical explanatory gap that constitutive explanation would close remains open despite our access to the full grounds of the fact. This shows that if there are cases of opaque grounding, Gaplessness cannot be true.

As one would expect in light of the preceding, the alleged connection between grounding and the notion of being “nothing over and above” some facts is also severed in opaque grounding cases. In such a case, the ground features neither in the essence nor in the metaphysical analysis of the grounded fact. As we have seen, this means that [Q] consists in something more than [P], and that there is an explanatory gap between the two, since [Q] has not been given the strictest possible kind of explanation. It is then exceedingly hard to see how committing to [Q] could carry no further theoretical cost than merely committing to [P] does. This is made vivid by considering the go-to example of opaque grounding. If moral rightness really is a fundamental property, the metaphysical analysis and essence of which do not involve happiness-maximization in any way, then [a is morally right] must be something over and above [a is happiness-maximizing]. Committing to the relevant opaque grounding claim involves committing to the existence and instantiation of a further property than merely committing to [a is happiness-maximizing] does—a moral property whose nature and essence do not involve happiness-maximization. This nonnaturalist metaphysics is supposed to be a paradigm example of an ontologically inflationary view on which moral facts are something “over and above” natural facts. If such a view could be combined with the idea that [a is morally right] is a “free lunch” relative to [a is happiness-maximizing], then clearly anything goes when theory-constructing with the help of grounding. So, plausibly, opaque grounding does not give us cases of one fact being “nothing over and above” its grounds.Footnote ¹³

3.a.3 Upshots

I have argued that opaque grounding clashes with the two principles that characterize the idea that grounding is constitutive explanation. If there is opaque grounding, Constitution and Gaplessness both fail as universal claims about grounding. The attractive picture of grounding outlined above then cannot do full justice to the facts. A different picture emerges instead. On this picture, grounding does not guarantee the most intimate connection imaginable between facts, a connection which would flow through their inner natures, rendering the grounded fact ontologically innocent. In some cases, grounding instead looks more like the looser connection of causation. Much like causation, opaque grounding does not illuminate the identity of the explanandum (what that fact is and wherein it consists), nor does it make for any “ontological free lunch.” In such cases, grounding simply backs an explanation of why one fact obtains in terms of the obtaining of another, just like causation.Footnote ¹⁴

A further consequence concerns how grounding interacts with modality. If grounding were without exception constitutive explanation, a given fact could not differ in its grounds between different possible worlds. This is a consequence of the following plausible principle:

Consider, e.g., [Red is a vixen], and suppose it consists in nothing more than [Red is a fox] and [Red is female] jointly. A fact cannot obtain unless everything wherein it consists also obtains. So [Red is a vixen] simply couldn’t obtain unless [Red is a fox] and [Red is female] both obtain.Footnote ¹⁵ Given the common assumption that only obtaining facts exist, this amounts to a form of ontological dependence where it is metaphysically impossible for the fact to exist without its grounds.Footnote ¹⁶

However, since an opaquely grounded fact’s obtaining does not consist in the obtaining of its grounds, a case of opaque grounding need not be accompanied by any such relation of ontological dependence. In such a case, there may yet be ontological dependence. For example, a moral nonnaturalist may hold that being happiness-maximizing is the only possible right-making property of actions. She will then be committed to the view that [a is morally right] cannot exist unless [a is happiness-maximizing] exists (given the assumption that only obtaining facts exist). But in that case, the commitment stems from her normative theory rather than from the metaphysics of grounding. On other moral theories incorporating opaque grounding claims, [a is morally right] does not depend ontologically on any of its grounds. A moral nonnaturalist may, e.g., believe that there are distinct and independent properties F₁, … F_N, instantiations of which each suffice to make an action morally right. In that case, [a is morally right] may actually be grounded in [a is F₁] while being possibly grounded in any one of [a is F₁] … [a is F_N]. On this scenario, [a is morally right] does not ontologically depend on any of the facts [a is F₁], … , [a is F_N] individually. This constitutes a further similarity between opaque grounding and causation. Even if [a is G] causes [a is H], the latter fact typically could have had a different cause, since the effect does not consist in the cause (even together with the relevant background conditions). In cases of nonconstitutive grounding explanations, we can get the same kind of modal behavior. Thus, by severing the supposed link between grounding and constitutive explanation, we allow more theoretical options for philosophers who employ a notion of grounding.

3.b.1 Opaque grounding, constituency, and fundamentality-inducing relations

Philosophers have long made appeal to a notion of relative metaphysical fundamentality. But it is an increasingly popular view in recent metaphysics that patterns of fundamentality are never brute but are explained by facts involving grounding and other relations of metaphysical explanation, building, or “construction” (Jenkins Reference Jenkins, Hoeltje, Schnieder and Steinberg2013; Bennett Reference Bennett2017). (Let us call such relations, whichever they may be, fundamentality-inducing relations, and the views invoking them to explain fundamentality explanation-based accounts. Possible candidates beyond grounding include, e.g., relations like composition and constitution.). Thus, e.g., all friends of grounding accept that if [P] grounds [Q], then [P] is more fundamental than [Q], and it is natural to think that in such a case, [P] is more fundamental than [Q] because the former grounds the latter. Strikingly, however, there is one way in which grounding and relative fundamentality differ: whereas grounding is most commonly taken to be a relation exclusively between facts, relative fundamentality often holds cross-categorically.Footnote ¹⁷ One might think, e.g., that the concrete individual Caesar is more fundamental than his singleton set {Caesar}, or that the numbers 3 and 4 and the successor relation are all more fundamental than the fact [4 is the successor of 3]. This raises the question of how grounding connects not only to fundamentality itself, but also to the other fundamentality-inducing relations.

A natural thought is that grounding is constrained by other fundamentality-inducing relations. For when we consider various cases of grounding, there seems to be a systematic pattern at work: grounding only holds between facts when other fundamentality-inducing relations hold between constituents of those facts. Thus, e.g., [Caesar exists] grounds [{Caesar} exists], and there is also an object-level connection: Caesar forms {Caesar}, whereby the man is more fundamental than the set. [Red is a fox] and [Red is female] together ground [Red is a vixen], and there is a corresponding relation between the properties involved in the facts. Being a fox and being female jointly make up the full metaphysical analysis of being a vixen, whereby the former two properties are more fundamental than the latter. For a final example, consider the way in which some appropriate combination of facts about the existence and arrangements of particles a ₁–a _N ground [Bo exists] (where Bo is the badger outside). This grounding relation between facts too correlates with a metaphysical connection between constituents of the facts, for a ₁–a _N are more fundamental than Bo by composing him.

Cases like these make the following principle seem compelling:

Various philosophers in the literature have defended positions which commit them to Constituency or something much like it. One example is Tobias Wilsch (Reference Wilsch2015, Reference Wilsch2016), who defends a deductive-nomological analysis of grounding, and a constructional conception of metaphysical laws. On the former, grounding just is determination in accordance with metaphysical laws. On the latter, all metaphysical laws involved in grounding govern the behavior of construction relations—relations whereby “the constructing entities are more basic than the constructed entity, and the constructed entities exist in virtue of the constructing entities” (Wilsch Reference Wilsch2015, 3300). Wilsch’s notion of a construction relation can thus plausibly be taken as equivalent to my notion of a fundamentality-inducing relation. The deductive-nomological analysis and the constructional conception of metaphysical laws together entail that whenever [P₁], … [P_N] ground [Q], there is some construction relation holding between some constituent(s) of the grounds and some constituent(s) of the grounded fact—i.e., they entail Constituency.

For another example, consider Kelly Trogdon’s (Reference Trogdon2018) attempt at illuminating grounding by connecting it to the idea of grounding mechanisms. Trogdon informally characterizes grounding mechanisms as “determination relations of a certain sort holding between constituents of grounding facts and constituents of the facts they ground,” and cites set formation, constitution, the determinate-determinable relation, and functional realization as examples of such determination relations (1290). Given the plausible assumption that Trogdon’s determination relations render determined entities less fundamental, those relations are all fundamentality-inducing relations. (He does not explicitly discuss the connection between determination relations and fundamentality.) The idea is then that many metaphysical explanations provide understanding of their target phenomenon by appealing to a specific grounding mechanism and thereby demonstrating “how the grounding connection runs.” Trogdon stops short of asserting that every case of grounding involves some grounding mechanism, and leaves open the possibility of so-called “bare grounding” unmediated by any determination relation. However, he seems to believe that the plausible examples of bare grounding would be cases of grounding within the logical or conceptual domain (1295) and expresses sympathy for the idea that in such cases, we are not really dealing with metaphysical grounding (1301–2). Trogdon’s view, at least when restricted to nonlogical cases, consequently seems very close to Constituency.

Thus, Constituency enjoys both prima facie intuitive appeal and support in the literature. However, if there are the right kind of opaque grounding cases, Constituency cannot be correct. To see why, return to our go-to example of opaque grounding. On the moral nonnaturalist view, the fact [a is morally right] is fully grounded in [a is happiness-maximizing]. At the same time, the nonnaturalist holds that the property of moral rightness is itself not reducible to or built out of any natural property or properties, including the property of being happiness-maximizing. Rather, she will think that the property of being morally right is an absolutely fundamental property, not metaphysically constructed out of anything else. Consequently, her grounding claim will be inconsistent with Constituency. [a is happiness-maximizing] fully grounds [a is morally right], but there are no fundamentality-inducing relations connecting the constituents of the two facts. Those constituents are the token action a, the property of being happiness-maximizing, the action a (again), and the property of being morally right. On pain of violating the irreflexivity of relative fundamentality, a clearly cannot stand in a fundamentality-inducing relation to itself. And since moral rightness is supposed to be an absolutely fundamental property, it cannot be that the action a and/or the property of being happiness-maximizing (either singly or jointly) stand in any fundamentality-inducing relation to moral rightness. Thus, if an opaque grounding claim of this sort is correct, Constituency is false.

3.b.2 Upshots

Whether Constituency holds might seem like a narrow technical issue, but the preceding discussion has a number of noteworthy consequences. The first one is that if there are opaque grounding cases of the relevant kind, this means that there can be nonfundamental instantiations of fundamental properties. As we have seen, the nonnaturalist takes the property of being morally right to be absolutely fundamental but holds that [a is happiness-maximizing] fully grounds [a is morally right]. Since grounding induces relative fundamentality (and logically atomic facts are simply instantiations of properties or relations), this amounts to recognizing a nonfundamental instantiation (namely the grounded fact [a is morally right]) of the fundamental property of moral rightness. Though recent metaphysics has been more concerned with the possibility of nonfundamental entities being involved in fundamental facts, it is an interesting question too whether there can be nonfundamental instantiations of fundamental properties.Footnote ¹⁸ If my argument is correct and opaque grounding is possible, we cannot infer from a property or relation’s being fundamental to every instantiation of it being similarly fundamental.

Secondly, the preceding has consequences downstream for the relation between fundamentality and modality. It is a popular idea in metaphysics that fundamental entities are freely modally recombinable: since all fundamental entities are wholly independent of each other in an important metaphysical sense, any possible way for one fundamental entity to be should be compossible with all the ways every other fundamental entity could be.Footnote ¹⁹ But if there are opaque grounding cases of the sort described above, they provide striking counterexamples to this idea. Suppose that any fact of the form [x is morally right] must be opaquely grounded in a fact of the form [x is happiness-maximizing] (i.e., being happiness-maximizing is the one and only possible right-making property).Footnote ²⁰ Then, despite being an absolutely fundamental property, moral rightness is not modally free relative to other absolutely fundamental properties. For it is not free to be instantiated in an action without being co-instantiated with whatever fundamental properties ultimately ground an action’s being happiness-maximizing—it simply cannot come apart from those properties. Indeed, if—as seems plausible—being happiness-maximizing (or whatever property turns out to play the right-making role) is not a fundamental natural property, the fundamental property of moral rightness will even be modally constrained by a less fundamental property (in addition to being constrained by the fundamental natural properties the instantiations of which ultimately ground instantiations of being happiness-maximizing)!Footnote ²¹

A possible reaction to this is to question an implicit presupposition of mine, namely that opaque grounding is itself a fundamentality-inducing relation. It might be thought mysterious how [a is happiness-maximizing]’s grounding [a is morally right] can render the latter fact less fundamental than the former when there is no constituent of the grounded fact that is any less fundamental than any constituent of the ground. But while it is certainly possible to hold that the typical connection between grounding and relative fundamentality breaks down in opaque cases, I prefer to resist this conclusion. The connections between metaphysical explanation and relative fundamentality are pervasive, and an explanation-based account of fundamentality offers the best hope of making sense of this phenomenon. And even opaque grounding connections support metaphysical explanations of facts. My preferred route is rather to draw some further distinctions within our theory of fundamentality to dissolve the supposed mystery. On an explanation-based account of fundamentality, patterns of relative fundamentality are explained by relations of metaphysical explanation. But explanation is a very fine-grained phenomenon, and it is important to attend to precisely what the explanandum of the relevant metaphysical explanation is. When particles a₁–a_N compose the badger Bo, this licenses an explanation of Bo’s existence, why he is an entity at all (rather than nonexistent). But when [a is happiness-maximizing] opaquely grounds [a is morally right], what gets explained is why the fact obtains (as opposed to not obtaining).Footnote ²² We can recognize this difference in the explanatory target at the level of fundamentality, by saying that the particles a₁–a_N are ontically more fundamental than Bo the badger, while [a is happiness-maximizing] is alethically more fundamental than [a is morally right] (on the opaque account), but not ontically more fundamental.Footnote ²³ Having drawn this distinction, we can reconcile the view that grounding is always fundamentality-inducing with the feeling that there is something quite different about [a is happiness-maximizing]’s being more fundamental than [a is morally right] as compared to the particles a ₁–a _N’s being more fundamental than the badger Bo that they compose.Footnote ²⁴

Another objection questions a different assumption of mine, namely that the fundamentality status of a property is determined by fundamentality-inducing relations distinct from grounding. I have assumed that the nonnaturalist’s view entails that moral rightness is an absolutely fundamental property since she takes rightness not to be built out of any other properties (for example, by having a metaphysical analysis in terms of those properties). On this approach, it is the holding (or absence) of property-to-property building or construction relations that determine whether a property is fundamental or not, as opposed to the holding (or absence) of the grounding relation between facts involving that property (i.e., instantiations of the property). There is a possible alternative approach to determining the fundamentality status of properties which we can call ‘grounding-first.’ According to a rough characterization of this approach, for a property F to be nonfundamental is for its instantiations to be grounded.Footnote ²⁵ On the grounding-first view, the nonnaturalist’s view of moral rightness does not count as one where moral rightness is absolutely fundamental, despite her taking rightness not to be built out of any other properties, since she takes every instantiation of moral rightness to be grounded in some instantiation of a natural property. Thus, given the grounding-first view of fundamentality, we do not get the result that opaque grounding allows for nonfundamental instantiations of fundamental properties.

However, I believe this grounding-first approach to fundamentality is unsatisfactory, and that its limitations come to the fore precisely in opaque grounding cases. Among friends of grounding, it is standardly assumed that the kind of ontological simplicity to strive for is simplicity among the fundamentalia—postulating fundamental entities contributes to the “cost” of a theory, whereas nonfundamental entities can be multiplied without affecting the parsimony of the theory.Footnote ²⁶ But combining this assumption with the grounding-first approach leads to unsuitable results, for that approach will not be able to capture the way in which, e.g., nonnaturalist theories in metaethics are less parsimonious than their naturalist competitors. Both nonnaturalists and naturalists will hold, e.g., that every fact of the form [x is morally right] is fully grounded in some natural fact or facts, thus rendering moral rightness nonfundamental on both views by the lights of the grounding-first approach. But then there will be nothing to distinguish nonnaturalism and naturalism from the perspective of parsimony—on both views, every fact of the form [x is morally right] is fully grounded and thus a nonfundamental fact, consequently rendering the property of moral rightness similarly nonfundamental. This illustrates the inadequacy of the grounding-first approach to fundamentality for properties and relations. It is perfectly clear that moral naturalism should come out as more ontologically parsimonious than moral nonnaturalism. The grounding-first approach, however, fails to deliver this. In order to determine whether, e.g., moral rightness is fundamental or not according to a theory, we need to go beyond the mere facts about which facts ground which and look into whether moral rightness is constructed out of other properties and relations according to the theory. This objection to the argument of the current section thus fails.