1 Introduction

This paper is about the so-called meta-grounding question, i.e. the question of what grounds grounding facts of the form ‘ϕ is grounded in Γ’.Footnote 1 An answer to this question is pressing since some plausible assumptions about grounding and fundamentality entail that grounding facts must be grounded. Three different accounts have been proposed to answer the meta-grounding question: Bennett (2011) and deRosset (2013) independently develop accounts according to which grounding claims like ‘ϕ is grounded in Γ’ are themselves grounded in Γ. Call this the “Straight Forward Account” (SFA).Footnote 2 Litland’s (2017) “Zero-Grounding Account” (ZGA) has it that grounding claims are zero-grounded, i.e. grounded in the empty set of facts. And finally, according to a position that I call “Grounding Essentialism” (GE), grounding facts like ‘ϕ is grounded in Γ’ are grounded in essentialist facts, i.e. in facts about the essences of ϕ, or Γ, or both. Versions of (GE) are discussed in Rosen (2010), Fine (2012) and Dasgupta (2014).Footnote 3

I am going to investigate the implications of these accounts concerning the relation between grounding and metaphysical explanation. While some grounding theorists—call them unionists (Raven 2015)—identify grounding with metaphysical explanation, others—call them separatists (Raven 2015)—maintain that grounding and metaphysical explanation come apart. On the latter view, however, grounding is still an explanatory notion in as much as it backs metaphysical explanation, much like causation backs causal explanation (Schaffer 2016). I argue that (ZGA) and (SFA) are incompatible with unionism. I will show that unionist versions of both (ZGA) and (SFA) clash with a crucial intuition about metaphysical explanation. This amounts to a criticism of Litland’s (2017) account, since he endorses both unionism and (ZGA). It can also be taken as a criticism of deRosset (2013), in as much as he endorses a unionist version of (SFA).Footnote 4 The arguments in this paper show that if grounding is metaphysical explanation (i.e. if unionism is true), (GE) has the edge over its competitors (SFA) and (ZGA). The main goal, however, is not to argue for a specific answer to the meta-grounding question, nor to decide the debate between unionism and separatism. The main thesis the paper seeks to establish is that the correct account of what grounds grounding at least partly depends on the answer to the question of whether unionism or separatism is true.

Here is an overview of the paper: I will start with some very brief remarks about unionism and separatism in Sect. 2 and about the relation between grounding and fundamentality in Sect. 3. I then develop the critique of Litland’s unionist version of (ZGA) in Sects. 46. In Sect. 7, I outline the general idea of (GE). I address the relation between (GE) and unionism in Sect. 8. I then sketch (SFA) in Sect. 9 and argue that it is incompatible with unionism in Sect. 10. Finally, Sect. 11 concludes.

2 Grounding and explanation

The notion of grounding is much discussed in contemporary metaphysics. Grounding theorists hold that grounding is intimately tied to two connected notions: metaphysical explanation and fundamentality. I will briefly discuss grounding’s connection to these notions in turn. Grounding is often captured by idioms like “holding in virtue of” or by specific non-causal uses of “because”. There is a widespread agreement amongst grounding theorists that grounding is an explanatory notion. Yet, there are two ways in which this idea can be cashed out. Some theorists take grounding simply to be metaphysical explanation, such that “to say that ϕ1, ϕ2, … ground ϕ just is to say that ϕ1, ϕ2, … explain ϕ in a distinctively metaphysical way” (Litland 2017, p. 281). Raven (2015) calls this position unionism. Other proponents of grounding hold that grounding and metaphysical explanation come apart. On this view, grounding proper is not itself metaphysical explanation but backs metaphysical explanation. Raven (2015) calls this position separatism.

Separatists like Rodriguez-Pereyra (2005), Audi (2012a, b), Schaffer (2012) and Trogdon (2013) have different reasons to argue for separatism. Audi (2012a, p. 119) sees separatism as the best response to the following objection: The attempt to explicate grounding by saying ‘x (at least partly) metaphysically explains y just in case x grounds y’ would amount to mere relabeling if grounding just were metaphysical explanation. Schaffer (2012, p. 124) refers to similarities in the debate about causation and causal explanations and argues that grounding and metaphysical explanation should be kept apart in the same way that causation and causal explanation have to be distinguished. Schaffer also argues for separatism as he wants objects to figure in grounding claims but realizes that they are inapt to figure in explanations.Footnote 5,Footnote 6

Among the unionists we find Rosen (2010), Fine (2012), Raven (2012), deRosset (2013), Dasgupta (2014) and Litland (2017). One motivation for defending unionism can be found in the complexity of the separatist thesis. Note that the separatist (as opposed to the unionist) is left with three tasks instead of just one. She has to give an account of grounding and, as they come apart, of metaphysical explanation, while in addition she has to account for their connection—the backing relation. In this paper I am not going to argue for either of these positions. I will, however, argue that the way we decide this dispute has impact on the way we are able to answer the question of what grounds grounding claims.

3 Grounding, fundamentality, and the ground of ground

Another tight connection that has been pointed out in the literature is that between grounding and fundamentality. Grounding is said to depict the layered structure of reality. By stating what grounds what, we are displaying the world’s layered structure from the fundamental to the increasingly derivative. That is to say grounding is intimately linked to fundamentality, such that the following principle (F) should hold:

(F):

A fact f is fundamental iff it is ungrounded; equivalently, f is non-fundamental or derivative iff it is grounded in some other fact(s).Footnote 7

Against this backdrop, the question of whether or not grounding facts are themselves grounded becomes the question of whether or not grounding facts are fundamental. Given a very plausible assumption, it is easy to see that grounding facts cannot be fundamental. This is Sider’s (2011, p. 106) formulation of the assumption in question:

(Purity):

Fundamental truths involve only fundamental notions.

A fundamental notion is a notion that carves reality at its joints. By this standard, the notion of being a city is not fundamental, according to Sider. Consider the following truth:

  1. (1)

    There exists a city.

By (Purity), (1) is not a fundamental truth, for it involves a non-fundamental notion. Thus, by (F), (1) has to be grounded.

  1. (2)

    That there is a city is grounded in T.

The question of whether or not (2) is itself grounded, according to (F), is tantamount to the question of whether or not (2) is fundamental. If (Purity) is true, however, (2) cannot be fundamental, since (2) contains the non-fundamental notion of being a city. If (F) is true, then this means that grounding facts like (2) are themselves grounded.Footnote 8

This is what makes the so-called meta-grounding question, the question of what grounds grounding facts, so pressing. In the light of (F) and (Purity), grounding facts like (2) must themselves be grounded.Footnote 9,Footnote 10 We now need to ask what it is that grounds grounding facts.

4 Litland’s Zero-Grounding Account (ZGA)

Litland (2017) argues that grounding claims are zero-grounded. This, as we shall see shortly, means that they are grounded in the empty set of facts or statements. Central to Litland’s approach to iterated ground is the distinction between factive and non-factive ground. While most philosophers think that grounding is factive, it is easy to derive from a factive notion of grounding a non-factive version, according to which also falsehoods may flank the grounding connective. Litland, however, takes non-factive ground as the primitive notion from which a factive version of ground can be derived. He uses the already familiar sentential operator ‘<’ for factive grounding statements and the sentential operator ‘⇒’ for non-factive grounding statements.Footnote 11 With the distinction between factive and non-factive ground in hand, we can sketch Litland’s (ZGA):

(ZGA):

If Γ < ϕ, then Γ < ϕ is grounded in (i) Γ and (ii) Γ ⇒ ϕ.

Γ ⇒ ϕ is zero-grounded.

Every true, non-factive grounding claim Γ ⇒ ϕ is (factively) grounded in the empty collection of statements. Borrowing from Fine (2012), Litland expresses this by saying that every true, non-factive grounding claim is zero-grounded. And since every factive grounding claim is partially grounded in the corresponding non-factive grounding claim, every factive grounding claim is partially, mediately grounded in the empty collection of statements. In addition, it follows from (ZGA) that if some truth ϕ is (factively) zero-grounded, then the truth that ϕ is (factively) zero-grounded (0 < ϕ) is itself (factively) zero-grounded (0 < (0 < ϕ)).Footnote 12,Footnote 13

In order for us to be able to evaluate (ZGA), Litland needs to provide answers to the questions of (a) what exactly is meant by zero-grounding and of (b) why we should believe that all true, non-factive grounding claims are zero-grounded.Footnote 14 Litland follows Fine (2012, p. 47) in distinguishing cases in which a statement is ungrounded from cases in which a statement is zero-grounded. In the former case, the statement is not grounded at all—no number of sentences serve as ground for it—whereas in the latter case the fact is grounded, there is a number of sentences in which it is grounded and that number is zero. The distinction between ungrounded and zero-grounded facts is to be understood analogously to the familiar distinction between propositions that are not derivable and propositions that can be derived from the empty collection of premises (Litland 2017, p. 280).

Litland’s official story about zero-grounding is told within the framework of “explanatory arguments”.Footnote 15 This notion is best understood in contrast to what Litland calls “plain arguments”.

(PA):

If there is a plain argument from premises Δ to conclusion ϕ, then if each δ ∈ Δ is true, ϕ, too, is true (Litland 2017, p. 290).

(EA):

If there is an explanatory argument from premises Δ to conclusion ϕ then, if each δ ∈ Δ is the case, then this fully explains its being the case that ϕ (Litland 2017, p. 290).

Put differently, explanatory arguments are solely composed from explanatory inferences. Litland links the notion of explanatory inferences to immediate ground in the following way:

(EI):

If Γ immediately grounds ϕ, the inference from Γ to ϕ is explanatory (Litland 2017, p. 289).Footnote 16

After having further elucidated the notion of explanatory arguments, Litland establishes the following link between grounding and explanatory arguments:

(GEA):

Δ < ϕ iff (i) each δ ∈ Δ is the case and (ii) there is an explanatory argument from Δ to ϕ (Litland 2017, p. 293).

From (GEA) one can derive a link between non-factive grounding and explanatory arguments by dropping the factivity condition (i):

(GEANF):

Δ ⇒ ϕ iff there is an explanatory argument from Δ to ϕ.Footnote 17

With this link in hand, we can now interpret ‘Δ ⇒ ϕ’ as referring to the fact that there is an explanatory argument from Δ to ϕ. How does this help us to elucidate what zero-grounding is? In light of the link between grounding and explanatory arguments a statement is zero-grounded iff there is an explanatory argument to this statement from the empty set of premises.Footnote 18 How do explanatory arguments help us to motivate the claim that all non-factive grounding claims indeed are zero-grounded? Litland develops a pure logic of iterated ground by suggesting introduction- and elimination-rules for grounding operators on the basis of their link to explanatory arguments. This allows him to formally prove that all non-factive grounding claims are zero-grounded. Due to reasons of space I cannot discuss Litland’s logic and his proof. Instead of detailing his formal argument that all true, non-factive grounding claims are zero-grounded for (ZGA), I would like to further examine the consequences of (ZGA). For this purpose it is not necessary to discuss the formal details of Litland’s proof. It will suffice to have clarified what it means that some ϕ is zero-grounded—it means that there is an explanatory argument to ϕ from the empty set of premises.

5 (ZGA) and unionism are incompatible

Litland discusses an objection to his (ZGA) that I take to be very revealing. It is a consequence of his account that every true, non-factive grounding claim has the same ground—the zero-ground. Thus, on Litland’s unionist approach to grounding, this means that every true, non-factive grounding claim has the same explanation. But intuitively, the explanation for why p ⇒ p ∧ p is the case differs from the explanation for why p ⇒ p ∨ p is the case (Litland 2017, pp. 302–303).Footnote 19 The former explanation should have to do with what conjunction is, the latter with what disjunction is. Note that, according to (ZGA), the fact that p ⇒ p ∧ p is zero-grounded amounts to the fact that there is an explanatory argument from the empty set of premises to p ⇒ p ∧ p. According to the objection, however, it is plausible that some fact about conjunction figures in the explanans of p ⇒ p ∧ p and, hence, that it is not the empty set of premises (i.e. not the zero-ground) alone that explains why p ⇒ p ∧ p holds. To further illustrate the plausibility of this, we can look at a different example of an argument from the empty set of premises. The trivial truth that I can’t eat that cake and simultaneously not eat it follows from the empty set of premises by the law of non-contradiction. There is an argument from the empty set of premises to the trivial cake-truth. Whether this argument is explanatory hinges on whether the inferences involved are explanatory. Let’s suppose they are (Litland (2017, p. 290) does not wish to ultimately settle which inferences are and which are not explanatory). If the argument from the empty set of premises to the trivial cake-truth is explanatory, then on (ZGA) we can say that the trivial cake-truth is zero-grounded. Yet, intuitively, it is not the empty set of premises, the zero-ground, by itself that explains why the trivial cake-truth holds. It is plausible that any successful explanation of why the trivial cake-truth holds will include the law of non-contradiction among the explanantia.Footnote 20

This objection casts doubt on a unionist version of (ZGA). If it is plausible that p ⇒ p ∧ p and p ⇒ p ∨ p have different metaphysical explanations, then (ZGA) must hold that grounding and metaphysical explanation come apart, since the central claim of (ZGA) is that all grounding facts have the same ground—namely the zero-ground. But unionism holds that grounding just is metaphysical explanation. Conclusion: if the two grounding claims have different explanations, then (ZGA) must reject unionism. Put differently, the following triad is inconsistent:

(DE):

p ⇒ p ∧ p and p ⇒ p ∨ p have different metaphysical explanations.

(ZGA):

All true, non-factive grounding claims are zero-grounded.

(U):

Grounding is metaphysical explanation.

For Litland to maintain his unionist version of (ZGA) he has to reject (DE). So, what is it that Litland offers as a response to the objection based on (DE)? Litland argues that the objection is misguided, since it falls prey to an ambiguity in what is meant by “explanation”:

In the framework of the explanatory arguments we can see that the objection trades on an ambiguity in what is meant by “explanation”. In this framework there are two things one can mean by an explanation of ϕ: one can mean a collection of propositions ϕ1, ϕ2, … from which ϕ can be derived in an explanatory way; alternatively, one can mean an argument witnessing that ϕ can be derived in an explanatory way. (Litland 2017, p. 303)

While p ⇒ p ∧ p and p ⇒ p ∨ p have the same explanation in the first sense (in both cases there is an explanatory argument to each of these grounding claims from the empty set of premises), p ⇒ p ∧ p and p ⇒ p ∨ p do not have the same explanation in the second sense. This is because the explanatory arguments that witness that these two grounding claims can be derived from the empty set of premises are different in the two cases. What makes them different is that they employ different inference-rules (Litland 2017, p. 303).Footnote 21 It is in virtue of the different inference-rules that the explanations of the two grounding claims differ in the second sense of explanation.

Hence, I take it that in this second sense of explanation the rules by which the explanandum follows from the premise-set have to figure in the explanantia of the grounding facts. So, in the framework of explanatory arguments, the crucial difference between Litland’s two senses of explanation concerns what figures in the explanantia of grounding facts. While in the first sense of explanation it’s only the premise-set that figures in the explanans of the grounding fact, in the second sense it is also the explanatory inference rules on the basis of which the respective grounding claim follows from the empty set of premises.

It is helpful to have some names to refer to these different kinds of explanations. I propose the following terminology: I will speak of the latter kind of explanation as a ‘rule-explanation’, and I will speak of the former kind of explanation as an ‘input-explanation’, since the premise-set can be understood as the input to an explanatory argument in the former kind of explanation. Note that the name ‘rule-explanation’ should not suggest that it’s only the rules that do the explanatory work in the second sense of explanation. Yet, calling it ‘rule-explanation’ signals the distinctive feature that—contrary to input-explanations—the rules also figure in the explanantia of grounding facts.

In this terminology Litland’s response to the objection is that (DE) is only plausible if grounding claims have rule-explanations instead of input-explanations. (ZGA) offers an input-explanation for grounding claims and on this picture it is plain that it is the zero-ground that input-explains all true, non-factive grounding claims. It is also plausible that, on the next iteration, the zero-ground input-explains the existence of an explanatory argument from the empty set of premises to p ⇒ p ∧ p, and so on.

By itself, this response does not appear sufficient. After all, the objector is likely to reply that the plausibility of (DE) renders any type of explanation that assigns the same explanans to p ⇒ p ∧ p and p ⇒ p ∨ p unsatisfactory. Hence, from the objector’s point of view, Litland cannot cast doubt on the plausibility of (DE) merely by assuming or introducing another kind of explanation, input-explanation, for which (DE) is not plausible. However, Litland also tries to explain away the plausibility of (DE) by offering a different picture, according to which (DE) is false but something in the vicinity of (DE) is true. He distinguishes between different ways in which facts can be zero-grounded. “[W]hile every true non-factive grounding claim Δ ⇒ ϕ has the same (immediate) strict full ground—the empty ground—different true non-factive grounding claims are (immediately) zero-grounded in different ways.”Footnote 22 (Litland 2017, p. 303) The ways in which different grounding claims are zero-grounded correspond to the different inference-rules involved in the respective explanatory argument from the empty set of premises to the respective grounding claim. The explanatory argument from the empty set of premises to p ⇒ p ∧ p uses different inference-rules than the argument from the empty set of premises to p ⇒ p ∨ p. According to (ZGA), these two grounding claims, p ⇒ p ∧ p and p ⇒ p ∨ p, are indeed both zero-grounded, yet in a different way. Given unionism, this means that the two grounding claims are indeed both explained by the appeal to the zero-ground, yet each in a different way.

It is doubtful, however, whether Litland’s alternative picture about the different ways in which p ⇒ p ∧ p and p ⇒ p ∨ p are explained by the same explanans suffices to reduce the plausibility of (DE). Note that (DE) is intuitively supported by considering particular examples of grounding claims, namely p ⇒ p ∧ p and p ⇒ p ∨ p. Additionally, the example revolving around the trivial cake-truth provides further reason to think that it is unsatisfactory to only appeal to the zero-ground in metaphysically explaining grounding facts. On the other hand, consider Litland’s picture about grounding facts having the same explanation but differing in the ways in which they are explained. Litland only offers one reason to accept this picture: its consistency with (ZGA). However, consistency with (ZGA) can also be maintained by dropping unionism and keeping (DE). Therefore, Litland is in a dialectically difficult position: (DE) is intuitively supported and can be preserved by abandoning the conjunction of (ZGA) and unionism, while the alternative picture Litland offers does not enjoy comparable intuitive support.

This is not meant to be a knockdown argument against the compatibility of (ZGA) and unionism. The above considerations only show that Litland’s defense leaves him in a dialectically weak position. However, it is also possible to argue directly for the incompatibility of (ZGA) and unionism. I will develop this argument in the rest of this section.

The success of a unionist version of (ZGA) is intimately tied to the question whether appealing to the zero-ground alone can be seen as a satisfactory metaphysical explanation of a grounding claim like, say, p ⇒ p ∧ p. To decide on this question, we have to first think about what constitutes a satisfactory metaphysical explanation of p ⇒ p ∧ p. In light of the framework of explanatory arguments, it is the following question (Q) that a metaphysical explanation of p ⇒ p ∧ p has to answer:

(Q):

Why is there an explanatory argument from p to p ∧ p?

Note that it is of utmost importance to Litland’s framework of explanatory arguments that if an answer to this question is to be a metaphysical explanation of a grounding claim, p ⇒ p ∧ p, the argument from p to p ∧ p needs to be an explanatory one. This is because mere plain (or non-explanatory) arguments do not account for a grounding relation between the premise-set and the conclusion. Hence, answering (Q) requires showing why the argument from p to p ∧ p is explanatory. Another way to put this is that grounding claims express an explanatory connection between the ground and the grounded and not just any connection.Footnote 23 So, what we seek in a metaphysical explanation of a grounding fact is an explanation of why the connection between the ground and the grounded is explanatory. I, thus, conclude that any satisfactory answer to (Q) must tell us why the argument from p to p ∧ p is explanatory.

I will now show that merely appealing to the zero-ground cannot tell us why the argument from p to p ∧ p is explanatory and that, therefore, (ZGA) is ill fitted to answer (Q): Consider the argument from q to p → p.Footnote 24 There surely is some such argument. Yet, q does not ground p → p, factively or otherwise. This is because this argument is not explanatory.Footnote 25 (ZGA) predicts the right results here. Still, the argument from q to p → p is valid. This means that the fact that there is an argument from q to p → p can be derived from the empty set of premises: If we need no additional premise (other than q) to conclude p → p, it is safe to say that we do not need any premises to conclude that we can conclude p → p from q. Analogously, we can derive the fact that there is an argument from p to p ∧ p from the empty set of premises. It seems that both, the fact that there is an argument from q to p → p as well as the fact that there is an argument from p to p ∧ p, can be accounted for (or: input-explained) by appealing to the empty set of premises. This means that the appeal to the empty set of premises does the same explanatory work in both cases. The crucial difference between the two arguments in question, however, is that the latter is explanatory, while the former is not. Yet, since the mere appeal to the empty set of premises, the zero-ground, does the same explanatory work in both cases, merely appealing to the zero-ground cannot explain the crucial difference between those cases. Therefore, (ZGA)’s claim that p ⇒ p ∧ p is zero-grounded does not explain why the argument from p to p ∧ p is explanatory. So, (ZGA) cannot answer (Q). But, as I have argued, an account of the ground of grounding facts should answer (Q), if we assume unionism. I conclude that (ZGA) and unionism are incompatible.

It is important to note that, even though appealing to the empty set of premises does the same explanatory work in the case of the explanatory argument as it does in the case of the non-explanatory argument, this does not entail that the zero-ground bears the same connection to both cases. Quite the opposite is the case: The empty set of premises relates to the fact that there is an argument from p to p ∧ p via explanatory inference rules, while it relates to the fact that there is an argument from q to p → p via non-explanatory inference rules. This indicates that it is really the different inference-rules in play that account for whether the argument in question is an explanatory one. So, it is the appeal to inference-rules rather than to the zero-ground that answers (Q).

Note that this is supported by Litland’s own characterization of explanatory arguments. Litland (2017, p. 289) emphasizes that it’s the inferences that make an argument explanatory. In his examples of explanatory inferences Litland talks about inference rules like conjunction-introduction or disjunction-introduction.Footnote 26 This suggests that arguments are explanatory in virtue of the inference rules they employ. From this perspective it is clear that the mere appeal to the zero-ground does not suffice to explain why the argument in question is explanatory. These considerations much rather motivate the view that the rules involved should be part of the explanantia of grounding facts, i.e. the view that grounding facts should be rule-explained rather than input-explained.

By my lights, the claim that Δ ⇒ ϕ is zero-grounded just amounts to holding the following: We don’t need any premises to derive Δ ⇒ ϕ in an explanatory way because the inferences applied in getting from Δ to ϕ are explanatory. My point is that if it is really the inference rules that make the argument explanatory—which Litland (2017, p. 289) arguably concedes—it is plausible that they figure in the explanans of the grounding fact Δ ⇒ ϕ (i.e. the fact that there is an explanatory argument from Δ to ϕ). If this is true, however, (ZGA) can only maintain that Δ ⇒ ϕ is zero-grounded if grounding and metaphysical explanation come apart. So, (ZGA) and unionism mutually exclude each other, and Litland cannot defend (ZGA) while simultaneously defending unionism.

It is important to note the scope of this objection. It rejects a unionist version of (ZGA) but remains silent about the compatibility of (ZGA) and separatism. For all I have said, there might still be an explanatory connection between the zero-ground and true, non-factive grounding claims. If my arguments are sound, however, this explanatory connection is not identical to metaphysical explanation.Footnote 27

6 Begging the question against (ZGA)?

It is now time to consider an objection to my criticism of a unionist version of (ZGA) and to the claim that the inference-rules involved in an explanatory argument from the ground to the grounded figure in a metaphysical explanation of the existence of the explanatory argument in question.

Objection The above criticism of a unionist version of (ZGA) and the argument according to which the rules play a role in the metaphysical explanation of the zero-grounded grounding fact begs the question against the proponent of (ZGA). According to (ZGA), grounding facts are themselves grounded in the empty set of facts. So, any explanatory argument whose conclusion is a grounding claim has zero premises, i.e. zero explanantia. The whole point of (ZGA) is that there can be explanatory arguments, and therefore explananda that really are explained, without there being any explanans that explains them. So, it is entirely misguided to ask, then, what explains the explananda of explanatory arguments that are zero-grounded (in the sense of being their explanans), and to propose that it’s the rules or the laws that do that. Nothing explains grounding facts in the sense of serving as their explanantia—not other facts, not laws, not principles, etc. Grounding facts nonetheless differ from fundamental facts, since they are explained; there’s an explanation, in the sense of an explanatory argument, that has them as its conclusion. This is not true of fundamental facts.Footnote 28

Response The objection maintains that the whole point of (ZGA) is that there can be explanatory arguments, and therefore explananda that really are explained, without there being any explanans that explains them. I contend that in order for the explananda to really be explained, the argument in question needs to be an explanatory one (as opposed to a mere plain or non-explanatory argument). Since it is the inference-rules that make an argument explanatory (Litland 2017, p. 289), the rules are doing explanatory work.Footnote 29 Maybe grounding facts are zero-grounded, but the zero-ground (alone) does not suffice to metaphysically explain them. The objector’s characterization of (ZGA) has it that nothing explains them, though they are explained. I argue that the objection overlooks that the argument from the ground to the grounded needs to be explanatory (instead of just plain or non-explanatory) (Litland 2017, p. 290). I take it that what makes the argument explanatory, the inference-rules, also does explanatory work.

Another way to make the point is the following: The claim that there is an explanation of grounding claims without there being any explanantia is a large bullet to bite, so much so, I think, that it would greatly decrease the plausibility of (ZGA) itself. Introducing the distinction between input- and rule-explanation, however, provides us with an explanans that does the explanatory work even though there is no input (i.e. no premises) in the explanatory argument from the ground to the grounded. This is because in a rule-explanation the rules at work in an explanatory argument crucially figure in the explanantia of grounding claims. Note that this is consistent with the claim that all true, non-factive grounding claims are zero-grounded, i.e. with (ZGA), yet not with a unionist version of (ZGA).

7 Grounding essentialism (GE)

Dasgupta (2014, p. 566) offers the following example to illustrate how grounding claims work:

(C):

The fact that event e contains people engaged in conference-conducive activities (C-activities) grounds the fact that e is a conference.

The question of what grounds (C) amounts to the question of why the fact that e contains people engaged in C-activities makes it the case that e is a conference. A natural answer seems to involve some facts about what conferences are, i.e. some facts about the essential connection between conferences and C-activities. It lies in the essence of conferences that an event is a conference if it involves people engaged in C-activities. According to Dasgupta (2014, pp. 566–567), this essentialist fact about conferences is also why the fact that e contains people engaged in C-activities makes it the case that e is a conference. Thus, on this essentialist view, (C) is (at least partially) grounded in the essential connection between (some or all constituents of) the grounded fact and (some or all constituents of) its ground. I call this view “grounding essentialism” (GE):

(GE):

If Γ < ϕ, then (Γ < ϕ) is (at least partially) grounded in the essential connection between (some or all constituents of) Γ and ϕ.

This essential connection between (the constituents of) Γ and ϕ can be captured by an essentialist fact about (the constituents of) Γ, or ϕ, or both. Thus, (GE) can also be formulated the following way:

(GE′):

If Γ < ϕ, then (Γ < ϕ) is (at least partially) grounded in some essentialist fact f about (some or all constituents of) Γ, or ϕ, or both (capturing the essential connection between (some or all constituents of) Γ and ϕ).Footnote 30

Rosen (2010), Fine (2012) and Dasgupta (2014) all discuss versions of (GE).Footnote 31 Their versions differ regarding the exact way in which the essential connection between the ground and that which is grounded is to be spelled out. (GE), in general, is the view that grounding facts hold at least partly in virtue of the nature of that which is grounded, or of its ground, or of both.Footnote 32

8 (GE) and unionism

In Sect. 5 I use Litland’s framework of explanatory arguments to argue for the following claim: On a unionist picture, the meta-grounding question, i.e. the question of why there is an explanatory argument from the ground to the grounded, cannot be answered without appealing to the inference-rules that are involved in such an argument. It is now time to determine what this means outside the framework of explanatory arguments.

It is plausible that a grounding claim like Γ < ϕ expresses the fact that Γ and ϕ are in a specific, explanatory sense metaphysically connected. A metaphysical explanation of this very fact should answer the question of why this connection holds. In other words, it should tell us what accounts for this metaphysical explanatory connection.Footnote 33 Schaffer (2017a, p. 3; 2017b, pp. 308–309) argues that explanation has a tripartite structure of source, link, and result. In the case of causal explanation, we have cause, laws of nature, and effect. Logical explanation involves premise, inference rule, and conclusion. Analogously, metaphysical explanation comprises ground, laws of metaphysics, and grounded. Note that grounding, as has been said in Sect. 3, depicts the layered structure of the world. We can understand the explanatory inference-rules in an explanatory argument from the ground to the grounded as the metaphysical laws that govern the layered structure of the world, the laws (or principles) that govern ground.Footnote 34 The explanatory rules in an explanatory argument from the ground to the grounded allow us to explanatorily reason from the former to the latter. That is to say it is those explanatory rules that tie the grounded to the ground. It is plausible to understand these rules as metaphysical laws holding between the ground and the grounded. We can now state what the results of my arguments in Sect. 5 mean outside the framework of explanatory arguments: If unionism is true, a grounding claim Γ < ϕ is itself explained by appeal to the metaphysical laws holding between Γ and ϕ. The grounding claim that the existence of a complex whole is grounded in the existence of its parts, if true, is itself explained by appeal the metaphysical laws applying to wholes and parts.Footnote 35

From this I conclude that the metaphysical laws that govern the layered structure of the world, the metaphysical principles of grounding (in Schaffer’s words) are the obvious candidates to figure in the metaphysical explanation of grounding facts.Footnote 36 Hence, it follows that on a unionist picture, according to which grounding just is metaphysical explanation, the grounds of grounding facts should incorporate the rules or laws that govern the connection between the grounded and the ground.

How does this relate to (GE)? It is plausible that essentialists would want to understand these laws of metaphysics as laws of essence captured by essentialist facts.Footnote 37 Note that according to (GE) grounding facts are themselves grounded in precisely such essentialist facts about the essential connection between (some or all constituents) of the ground and the grounded. We can take Dasgupta’s (2014, p. 566) example from Sect. 7 to illustrate this.

(C):

The fact that event e contains people engaged in conference-conducive activities (C-activities) grounds the fact that e is a conference.

According to Dasgupta’s version of (GE), (C) is itself grounded in the fact that it is essential to conferences to contain people engaged in C-activities. The essentialist fact in which (C) is grounded has it that the metaphysical connection between being a conference and containing people engaged in C-activities holds as a matter of essence. Thus, (GE) explains why the metaphysical explanatory connection between the ground and the grounded holds. It answers the meta-grounding question by citing a law of essence holding between the ground and the grounded. By appealing to some rule or law of essence, (GE) offers a rule-explanation of grounding facts. Thus, in light of my arguments in Sects. 5 and 8, (GE)—contrary to (ZGA)—is still a live option for the unionist.

9 The straight forward account (SFA)

There is still one approach to the meta-grounding question left to discuss. Bennett (2011) and deRosset (2013) independently develop an account which Litland (2017) refers to as the “Straight Forward Account” (SFA). According to (SFA), a fact about grounding, like (Γ  < ϕ) is itself grounded in Γ.

(SFA):

If Γ  < ϕ, then (Γ < ϕ) is itself grounded in Γ.

Due to space limitations, I will confine myself to Bennett’s rationale for this view. Bennett holds that grounding is a “superinternal” relation.

A superinternal relation is one such that the intrinsic nature of only one of the relata—or, better, one side of the relation—guarantees not only that the relation holds, but also that the other relatum(a) exists and has the intrinsic nature it does.” (Bennett 2011, p. 32).

Consider physicalism. The following is a very rough formulation of physicalism in terms of grounding:

(P):

The physical facts ground the mental facts.

Bennett argues, that physicalists are not claiming that the grounding relation between physical and mental facts obtains in virtue of both sides of the relation. The physicalists’ claim rather is that it is in virtue of the intrinsic nature of the physical facts, the more fundamental facts, that (a) the mental facts, the less fundamental facts, obtain and that (b) the grounding relation between the physical and the mental facts obtains (Bennett 2011, p. 33). Bennett concludes from this that grounding is a superinternal relation, that it holds in virtue of only one side of the relation. If physicalism is true, if the mental facts are grounded in the physical facts, then by the superinternality of grounding the fact that the mental facts are grounded in the physical facts is itself grounded in the physical facts.

So, Bennett’s rationale for (SFA) is grounding’s superinternality.Footnote 38 One might wonder, however, whether Bennett’s characterization of superinternality appeals to essences. Bennett puts forth that “[a] superinternal relation is one such that the intrinsic nature of only one of the relata […] guarantees not only that the relation holds, but also that the other relatum(a) exists and has the intrinsic nature it does” (2011, p. 32; emphasis added). Should we thus take Bennett to hold a version of (GE), since this seems to entail that the grounding relation between Γ and ϕ, holds (at least partly) in virtue of the intrinsic nature, the essence, of Γ? No. Bennett is very clear that, on her account, it is not the essences of the physical facts but the physical facts that ground the grounding fact that the mental facts are grounded in the physical facts. So, (SFA) should not be subsumed under (GE).

10 (SFA) and unionism are incompatible

Dasgupta (2014) voices a crucial difficulty for (SFA) that is along the same lines as the objection against (ZGA). Consider the following two grounding claims:

(D):

(p ∨ q) is grounded in p.

(DN):

(¬¬p) is grounded in p.

According to (SFA), both of these grounding facts are themselves grounded in p. From his unionist perspective, Dasgupta (2014, pp. 571–573) claims that this renders (SFA) plainly wrong. Intuitively, we expect (D) and (DN) to have different metaphysical explanations. It is plausible that an explanation of why p makes (p ∨ q) obtain involves some fact concerning disjunction, while an explanation of why p makes (¬¬p) obtain involves something about negation. If grounding just is metaphysical explanation, (D) and (DN) cannot have the same ground—that would entail that they also have the same metaphysical explanation, which appears intuitively incorrect. I think that this criticism has a point. Yet, one has to clearly see that it hinges on the truth of unionism. Thus, while this objection might not show (SFA) to be false, it might still show the account to be incompatible with unionism.Footnote 39 Just like in the case of (ZGA), also here we have an inconsistent triad:

(DE′):

(D) and (DN) have different explanations.

(SFA):

(D) and (DN) are both grounded in p.

(U):

Grounding is metaphysical explanation.

The unionist proponent of (SFA) might try to employ Litland’s strategy of rejecting (DE′). It might be argued that it is only in one sense of “explanation” that (D) and (DN) have different explanations. In another sense of “explanation”, (D) and (DN) have the same explanation. In my discussion of (ZGA), I have identified these two senses of “explanation” as input-explanation on the one side and rule-explanation on the other side.

Note, however, that with regard to (SFA) this strategy runs into the same problem as with regard to (ZGA): Again, merely introducing a sense of “explanation” for which (DE′) does not seem plausible does not suffice as a rejection of (DE′). This is because the point of the objection against a unionist version of (SFA) is that it’s the plausibility of (DE′) that casts doubt on any explanation that assigns the same explanans to (D) and (DN). The dialectic runs parallel to the discussion of (ZGA). The unionist proponent of (SFA) could even make the Litlandian move to try to explain away the plausibility of (DE′) by distinguishing different ways in which a grounding claim like Γ  < ϕ is itself explained by Γ (pertaining to the rules or laws involved). Yet, as long as there is no reason to accept this picture other than its compatibility with (SFA), the conjunction of (SFA) and unionism is in an equally weak dialectical position as the conjunction of (ZGA) and unionism.

It is also possible to argue directly against the conjunction of (SFA) and unionism by applying the same argument used in our discussion of (ZGA). As with (ZGA), the success of a unionist version of (SFA) hinges on whether it is plausible that appealing to Γ can be seen as a satisfactory metaphysical explanation of Γ < ϕ. In Sect. 5 I argue that since grounding claims express an explanatory connection between the ground and the grounded and not just any connection, a satisfactory metaphysical explanation of a grounding fact explains why there is such an explanatory connection between the ground and the grounded. In the framework of explanatory arguments this amounts to the question as to why the argument from the ground (Γ) to the grounded (ϕ) is indeed explanatory. Yet, how should we understand this question outside the framework of explanatory arguments? Given unionism, ‘Γ < ϕ’ amounts to the claim that Γ metaphysically explains ϕ. The unionist meta-grounding question then asks why Γ metaphysically explains ϕ. An answer to this question should tell us why Γ is explanatorily related to ϕ. So, outside the framework of explanatory arguments, the question a satisfactory metaphysical explanation of the grounding claim Γ < ϕ has to answer is best understood in the following way:

(Q′):

Why is Γ explanatorily relevant to ϕ?Footnote 40

Simply referring to Γ does not seem to be an adequate answer to this question.Footnote 41 Take the following example. Suppose the mental fact that I have a headache is grounded in some physical fact f. Now consider the following grounding fact (H):

(H):

f < I have a headache.

The unionist meta-grounding question of why (H) holds, takes the following form: Why is f explanatorily relevant to my having a headache? Intuitively, this question cannot be adequately answered by simply referring to f.Footnote 42 The question of why f is relevant in a metaphysical explanation of my having a headache will much rather be answered by a fact about the relation between f and my having a headache (or by a fact about the relation of the physical and the mental in general).

In conclusion, if grounding is indeed superinternal, f might ground the fact that f grounds my having a headache. Yet, f does not explain why f explains my having a headache. I have argued that it is plausible that a metaphysical explanation of (H) should explain the explanatory relation between f and my having a headache, just as a metaphysical explanation of (D) should explain the explanatory relation between p and (p ∨ q). That is to say on a unionist picture, the meta-grounding question regarding (H) is to be understood along the lines of (Q′). It asks why f is explanatorily relevant to the mental fact that I have a headache. Since (SFA) cannot answer this unionist meta-grounding question, (SFA) and unionism are incompatible. The answer to the unionist meta-grounding question, as argued in Sect. 8, will much rather include some reference to a law holding between the grounded and its ground.

11 Conclusion

I have argued that both (ZGA) and (SFA) are incompatible with unionism (Sects. 5 and 10). The argument for this derives its force from the point that a satisfactory metaphysical explanation of why a grounding fact holds explains why there is an explanatory relation among the ground and the grounded. Assuming unionism, the meta-grounding question concerning some grounding claim Γ < ϕ amounts to asking why Γ is explanatorily relevant to ϕ. Arguably, neither (ZGA) nor (SFA) are fit to answer this question. Further, I have argued that it is plausible that the unionist meta-grounding question is to be answered by appeal to some rules or laws that govern the connection between the ground and the grounded (Sect. 8). Since (GE)’s answer to the meta-grounding question plausibly appeals to essentialist laws holding between the ground and the grounded, (GE)—contrary to its competitors (ZGA) and (SFA)—is still a live option for the unionist. Hence, if unionism is true, then—in light of the arguments in this paper—(GE) has to be preferred over (ZGA) and (SFA).

Note that nothing has been said about whether or not any of the accounts investigated are compatible with separatism. Nothing in the arguments in this paper speaks against a separatist version of (ZGA), (SFA), or (GE). What the arguments in this paper establish, however, is that the answer to the question of what grounds grounding in part depends on how we decide the debate between unionism and separatism.