Metaphysically Opaque Grounding

Abstract

This article explores the concept of metaphysically opaque grounding, a largely neglected form of metaphysical grounding that challenges the commonly held assumptions that grounding is an especially intimate and powerful connection between facts and that it is necessarily connected with the essences of things. I provide a definition of opaque grounding, identify some interesting philosophical views that are committed to it, and explore some consequences for the general theory of grounding. Finally, I briefly address some natural initial doubts about opaque grounding and find them unwarranted. The upshot is that the notion deserves more attention than it has previously received.

1. Introduction

Recent metaphysics has seen much interest in grounding—the relation of noncausal determination whereby a fact obtains in virtue of the obtaining of some other fact or facts. One recurring and largely unquestioned assumption in the discussion is that grounding is, in some important sense, a particularly intimate metaphysical relation. In this vein, for example, Kit Fine calls grounding “the ultimate form of explanation” (2001, 16). Another common and arguably related idea is that grounding is necessarily connected with the core features of things: their essences or natures (Audi 2012, 693–96). In this article, I will be concerned with these ideas about grounding. I believe that certain interesting and widespread philosophical views are committed to there being cases of metaphysically opaque grounding—grounding that constitutes a less than maximally intimate relation, among other things because it does not go together with any essence or nature connections. Thus, for example, a moral nonnaturalist might want to hold that a particular action is morally right in virtue of instantiating certain natural properties, while denying that the essence or nature of moral rightness involves anything natural. I believe that the notion of metaphysically opaque grounding has been largely neglected in the literature, and that it has important and interesting consequences for how to think about grounding. I also believe that a view of grounding which allows for metaphysically opaque cases is defensible.

In this article, I wish to focus on the constructive task of introducing and exploring the idea of metaphysically opaque grounding. To this end, I will try to spell out the notion and motivate interest in it (section 2) as well as demonstrate some ways opaque grounding would impact our understanding of grounding and nearby phenomena (section 3). A thoroughgoing defense of the notion would require much more space and discussion. I will, however, conclude by briefly indicating why some natural initial doubts about opaque grounding are unwarranted (section 4). My hope is thus to be able to draw more attention to this largely neglected idea and its implications, and by doing so stimulate further discussion of whether there are any cases of opaque grounding.

2. Metaphysically opaque grounding

To introduce the notion of metaphysically opaque grounding, I will start by offering a definition before moving on to motivate why the notion is interesting.

To define opaque grounding, we’ll need three conditions. The first one is straightforward:

Grounding: [P] (at least partially) grounds [Q].

Every case of opaque grounding is a case of grounding. I take grounding to be the relation that holds between facts when one fact obtains in virtue of the obtaining of the other(s). ¹ (I take facts to be structured entities built out of objects, properties, relations, and sometimes logical entities. I follow the convention of forming names for facts by using square brackets, thus “[x is F]” denotes the fact of x’s being F.)

Two further, and less self-explanatory, conditions will be needed to define opaque grounding:

Irreducibility: [P] is not part of the metaphysical analysis of [Q].

Essential Isolation: The essence of [Q] does not involve [P].

The ideology involved here takes some unpacking. When employing essentialist terminology, I intend it to be taken in the way rehabilitated by Kit Fine, where a condition φ’s being essential to x goes beyond φ’s merely being metaphysically necessary for x to exist. On that usage, φ’s being essential to x rather amounts to φ’s being part of what it is to be x, φ’s being part of the identity of x, or φ’s being part of the real definition of x (Fine 1994). ²

As for metaphysical analysis, I take it to apply in the first instance to properties and relations and by extension to facts. The metaphysical analysis of a property or relation F states which properties and/or relations F itself consists in. Suppose, e.g., that being a vixen consists in being a fox and being female. The latter two properties then jointly make up the full metaphysical analysis of the property of being a vixen—being a vixen just is being a female fox. This then extends to facts in the obvious way: the facts [Red is female] and [Red is a fox] jointly make up the full metaphysical analysis of [Red is a vixen]. ³

Metaphysical analysis, like essence, goes beyond mere metaphysical modality. I take it that F’s fully consisting in G and H amounts to something more than that being G and H is necessary and sufficient for being F. I suggest we view metaphysical analysis as a structural or constructional notion—when G and H make up the full metaphysical analysis of property F, F is built out of G and H by some appropriate property-forming operation and contains them as constituents (and similarly for relations and facts). ⁴

Equipped with these pieces of ideology, I can now define the notion of metaphysically opaque grounding. Roughly speaking, [P] opaquely grounds [Q] just in case [P] and [Q] jointly satisfy Grounding, Irreducibility, and Essential Isolation. Or, less clunkily: [P] opaquely grounds [Q] just in case [P] grounds [Q] without occurring in the essence or metaphysical analysis of [Q]. But we want to be able to apply the notion of opaque grounding in cases where several facts jointly ground another fact. We thus get the following:

[P₁], … , [P_N] (fully) opaquely ground [Q] = df.

1. (i) [P₁], … , [P_N] fully ground [Q]; and

2. (ii) there is no fact f such that f is among [P₁], … , [P_N] and f is part of the metaphysical analysis or involved in the essence of [Q].

For convenience, I will also introduce a label for nonopaque, “standard” grounding. I will say that [P₁], … , [P_N] (fully) transparently ground [Q] just in case [P₁], … , [P_N] fully ground [Q], but do not fully opaquely ground [Q].

While I believe the notion of opaque grounding is underexplored in the literature, it is not without precedent. Rosen (2010, 310–13) discusses a similar notion under the monicker of ‘Moorean connections’ and considers its implications for the question of what grounds grounding facts. ⁵ In this article, I aim to advance the discussion further by exploring at length the notion of opaque grounding and some of its uncharted repercussions for grounding and related topics.

Why care about opaque grounding? Part of what makes opaque grounding interesting is the nonstandard picture of grounding that emerges if we take the notion seriously—something to be explored in section 3 below. A more straightforward use is that the notion of opaque grounding helps us capture the characteristic commitments of certain interesting metaphysical theories. I will now explain how.

I believe certain important metaphysical theories are implicitly committed to cases of opaque grounding. Explicitly articulating the notion enables us to better recognize what is distinctive about the metaphysical commitments of those theories. The paradigm example I will use is that of classical moral nonnaturalism. Classical moral nonnaturalism (or just ‘nonnaturalism’ for short) is a theory in metaethics that I will take, insofar as its metaphysics is concerned, to be characterized by two commitments. ⁶ The first one is a claim about the natures of certain properties (I will use moral rightness as the example):

Nature-commitment: The property of being morally right is a sui generis nonnatural property whose nature does not involve any natural property. The property of being morally right is not reducible to or built out of any natural properties, and it lacks a real definition in terms of natural properties.

This commitment emphasizes a kind of metaphysical separation or distinctness between the normative property of moral rightness and natural properties. In this vein, Pekka Väyrynen writes:

[T]he non-naturalist thinks that at least some normative properties aren’t identical to any natural or supernatural properties, nor do they have a real definition, metaphysical reduction, or any other such tight metaphysical explanation wholly in terms of natural or supernatural properties. (2018, 171)

But moral nonnaturalists also want to affirm a certain kind of connection between rightness in actions and select natural properties of those actions. More precisely, they are committed to:

Explanation-commitment: Instantiations of the property of being morally right are explained by instantiations of natural properties. Whenever a token action a instantiates moral rightness, it does so because it instantiates some natural property—say, e.g., the property of being happiness-maximizing. When a is morally right, this is in virtue of its being happiness-maximizing; a’s being happiness-maximizing makes it morally right.

When pushed by C. D. Broad to clarify his position, G. E. Moore, the key figure in modern moral nonnaturalism, endorses an analogue of this view applied to moral goodness by affirming that goodness is “‘derivative’ in the sense that, whenever a thing is good […] its goodness (in Mr. Broad’s words) ‘depends on the presence of certain non-ethical characteristics’ possessed by the thing in question […]” (Moore 1942, 588). Thus, something like Explanation-Commitment is assumed already in the paradigm example of moral nonnaturalism in analytic philosophy.

Since logically atomic facts are just instantiations of properties or relations, Explanation-commitment straightforwardly entails an instance of Grounding, namely that [a is happiness-maximizing] grounds [a is morally right]. And since facts are partially built out of properties and relations, Nature-commitment, which is formulated as a claim about properties, strongly supports certain commitments at the level of facts too. If the property of being morally right is not reducible to or built out of any natural properties and lacks a real definition in terms of any natural property, then the same should go for the relation between [a is morally right] and natural facts. A motivating impulse behind moral nonnaturalism is the idea that the nature of moral reality is profoundly different from that of natural reality. Insisting that moral properties are irreducible to natural properties, citing the usual considerations, while somehow taking moral facts (instantiations of moral properties or relations) as consisting fully in natural facts would not do justice to that idea. Thus, any moral nonnaturalist embracing Irreducibility should similarly accept that [a is morally right] neither has a real definition in terms of, nor is reducible to, nor built out of, [a is happiness-maximizing]. In other words: classical moral nonnaturalists are committed to [a is happiness-maximizing] opaquely grounding [a is morally right].

I think moral nonnaturalism is a good example of an interesting metaphysical view that is committed to opaque grounding. You might, of course, think nonnaturalism is false—perhaps because you’re a naturalist who denies that there are any nonnatural properties or facts, or because you’re a moral nihilist who denies that there are any moral facts whatsoever. But, firstly, nonnaturalism is a popular theory in contemporary metaethics. And, secondly, whatever problems that kind of view faces, there does not seem to be anything obviously wrong with its grounding commitments. This gives us reason to take the idea of opaque grounding seriously and explore its consequences. (In section 4 below, I will consider arguments to the effect that the idea of opaque grounding is somehow confused.)

However, I do not think moral nonnaturalism is the only interesting position committed to opaque grounding. Most straightforwardly, there are analogous nonnaturalist views about other kinds of normative properties and facts that seem helpfully explicable in terms of opaque grounding. An aesthetic nonnaturalist may well take beauty to be a sui generis unbuilt property lacking a real definition in terms of natural properties, but still think that instantiations of that property must be grounded in instantiations of natural properties. Such an aesthetician would be taking [o is beautiful] to be opaquely grounded in whatever fact makes o beautiful. But theories committed to opaque grounding do not necessarily have to deal with the normative. For example, a set of metaphysical commitments structurally analogous to those of moral nonnaturalism has some appeal in the philosophy of mind. For on the one hand, it is natural to think that phenomenal properties and physical properties have fundamentally distinct kinds of internal natures and essences. On the other hand, one might want to avoid the view that the mental and the physical are connected only by metaphysically contingent causal laws. Equipped with a notion of opaque grounding, a property dualist can take phenomenal properties to necessarily be instantiated in virtue of instantiations of physical properties, while simultaneously taking the natures of the two kinds of properties to be so radically different that no physical property ever figures in the metaphysical analysis or essence of any phenomenal property. Possessing a developed theory of opaque grounding allows us to articulate what sets this kind of dualism apart both from reductive physicalist grounding views about the phenomenal as well as from more radical Cartesian forms of dualism. ⁷ It should thus be clear that the general idea of metaphysically opaque grounding provides an interesting theoretical option even outside the metaphysics of normativity.

3. Consequences

In this section, I want to draw attention to some ways in which the idea of opaque grounding affects widespread views about grounding and related topics. These consequences further illustrate the importance of the question of whether there is any opaque grounding.

3.a Grounding and constitutive metaphysical explanations

The first consequence concerns how close the relationship between a grounded fact and its grounds needs to be. It is an influential but rarely examined idea that grounding constitutes a maximally strict or intimate explanatory connection between facts. I will call this the idea that grounding is constitutive explanation. ⁸ In the following, I will articulate the core components of the idea and argue that if there is opaque grounding, grounding cannot (always) be constitutive explanation.

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. 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:

We may call an in-virtue claim a statement of ontological or metaphysical ground when the conditional [“Necessarily, if P then Q”] holds of metaphysical necessity and I shall talk, in such cases, of the antecedent fact or facts grounding or being a ground for the consequent fact. […] Just as metaphysical necessity is the strictest form of necessity (at least as compared to natural and normative necessity), so it is natural to suppose that statements of metaphysical ground are the strictest form of in-virtue-of claim. In the other cases, we may sensibly ask for a stricter or fuller account of that in virtue of which a given fact holds. So in the case of the particle [“Necessarily, if the particle is acted upon by some positive force then it is accelerating”], for example, we may agree that the particle is accelerating in virtue of being acted upon by a positive force but think that there is some kind of gap between the explanans and explanandum which could—at least in principle—be filled by a stricter account of that in virtue of which the explanandum holds. But if we were to claim that the particle is accelerating in virtue of increasing its velocity over time (which is presumably a statement of metaphysical ground), then we have the sense that there is—and could be—no stricter account of that in virtue of which the explanandum holds. We have as strict an account of the explanandum as we might hope to have. […] If there is a gap between the grounds and what is grounded, then it is not an explanatory gap. (2012, 38–39)

Elsewhere, Fine writes that grounding is distinguished from other explanatory connections “by being the tightest such connection” (2001, 15). These formulations articulate one crucial part of the idea that grounding is constitutive explanation:

Gaplessness: If [P₁], … , [P_N] (fully) ground [Q], there is no “explanatory gap" between [P₁], … , [P_N] and [Q], and [Q] is thereby given the strictest form of explanation possible.

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:

[T]he relation of ground is distinguished from [other explanatory connections] by being the tightest such connection. Thus when the truth of P causally explains the truth of Q, we may still maintain that the truth of Q consists in something more (or other) than the truth of P. (2001, 15)

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:

Constitution: If [P₁], … [P_N] (fully) ground [Q], [Q] consists in nothing more than [P₁], … [P_N]. ¹⁰

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.” 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:

[Ground] is the ultimate form of explanation; and it is perhaps for this reason that we are not inclined to think of the truth of a grounded proposition as a further fact over and above its grounds […]. (2001, 16)

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. 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. 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. 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:

Necessary Constitution: If [Q] consists in nothing more than [P₁], … [P_N], then necessarily, if [Q] obtains, then [P₁], … [P_N] obtain.

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. 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. 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 Opaque grounding and fundamentality

In this section, I will argue that if there is opaque grounding, this has interesting consequences for how we should think about the relation between grounding and fundamentality.

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 2013; Bennett 2017). (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. 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:

Constituency: Necessarily, if [P₁], … [P_N] fully ground [Q], then there are entities x ₁, … x _N and y such that x ₁, … x _N are constituents of [P₁], … [P_N] and y is a constituent of [Q], and x ₁, … x _N stand in some fundamentality-inducing relation to y.

Various philosophers in the literature have defended positions which commit them to Constituency or something much like it. One example is Tobias Wilsch (2015, 2016), 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 2015, 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 (2018) 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. 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. 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). 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)! 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). 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. 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. 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. 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. 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.

4. Objections

Although in this article I have wanted to focus on the positive contribution of introducing and exploring the concept of opaque grounding, I recognize that there are plenty of questions left to answer to make a fully convincing case for the viability of the concept. While I cannot here hope to do the complexity of the issues full justice, I will briefly outline some natural skeptical reactions to opaque grounding in this section, as well as why I think they are unfounded. I will not deal with objections to the specifics of various substantive theories incorporating opaque grounding claims here (such as, e.g., moral nonnaturalism, opaque property dualism about the mental, etc.). Arguably, there could be reason to believe that the idea of opaque grounding is fruitless and uninteresting if one had good reasons to reject all the theories committed to opaque grounding claims. But many of the objections to the theories in question will have nothing to do with opaque grounding as such. ²⁷ In what follows, I will be considering objections to the very idea of opaque grounding instead.

First, according to some philosophers, normative grounding is distinct from metaphysical grounding. ²⁸ If they are right, moral nonnaturalism would involve normative grounding, and nothing could be concluded about the behavior of metaphysical grounding from consideration of that view. This might lead one to think that the opaque grounding relation I’ve drawn attention to is not of any concern to metaphysics. I reject that. For what it’s worth, I am skeptical that normative grounding is distinct from metaphysical grounding. ²⁹ But even if it is, there are nonnormative cases of opaque grounding one can rely on instead. Recall, e.g., that I mentioned in section 2 the possibility of defending a dualist view about the relation between the physical and the mental which involves an opaque grounding claim. Such a claim would clearly not concern normative grounding. There is more to say on the interesting issue of grounding pluralism, but for present purposes it will have to suffice to note that even grounding pluralists should pay attention to opaque grounding.

A further line of resistance to opaque grounding might stem from the idea that it is part of the very concept of grounding that grounds are always involved in the metaphysical analysis or essence of what they ground. If this is true, whatever explanatory notion is involved in the alleged cases of opaque grounding would have to be distinct from grounding. There are at least two things to say in response. Firstly: even though many philosophers seem to assume that grounding is always transparent, there are also influential treatments of grounding in the literature which question that assumption or simply leave the issue open. ³⁰ While such treatments may yet turn out to be mistaken on substantive grounds, there is no obvious reason to take them to be conceptually incoherent. Secondly: even if the extant concept of grounding did, in fact, turn out to include a requirement that grounding always be transparent, that would not necessarily show anything about which metaphysical relations exist or hold in the world. Perhaps the current concept of grounding should be revised or replaced in order to capture a more theoretically fruitful and interesting relation. Either way, a mere appeal to concepts does not seem to settle any important metaphysical issue here.

A further possible worry is that once we sever any necessary connection between grounding and relations like metaphysical analysis or essential involvement, it is hard to see what distinguishes grounding from mere metaphysical necessitation. The question arises: if the grounds of a fact need not be part of the metaphysical analysis or essence of the fact, can we make sense of how grounding differs from merely modal connections? I think we can. There is no clear reason to accept that the distinction only makes sense if grounding is necessarily transparent. Firstly, we do not need to move beyond the uncontroversial platitudes about grounding to be able to distinguish it from modal phenomena. Grounding is crucially different from mere metaphysical necessitation by being a hyperintensional relation that necessarily connects to explanatory notions expressed by (inter alia) “in virtue of”, “because” and “due to” talk. Secondly, there are already treatments of grounding on the market that distinguish it from necessitation without relying on notions of essence or metaphysical analysis to do so. ³¹ Proponents of opaque grounding are free to help themselves to any of those treatments or to develop entirely new ones. The worry is unfounded.

Thus, none of the objections to opaque grounding discussed here seem forceful. While there is much more to be said on this issue, I hope to have done enough here to show that the proponent of opaque grounding has the resources to respond to the most natural worries about the notion.

5. Conclusion

In this article, I have focused on introducing the notion of metaphysically opaque grounding and exploring some interesting consequences of allowing grounding to be opaque. I have also briefly examined some apparent initial reasons to be skeptical of opaque grounding and found them wanting. Much more work remains to be done, both in understanding the full repercussions opaque grounding would have on our broader metaphysics and in settling whether grounding can, in fact, be opaque. I hope, however, to have convinced the reader that these questions are worth paying closer attention to and that the presumption of grounding’s transparency is more open to question than is assumed by the current orthodoxy.