## 1. Preliminaries



In this section we address five preliminary issues: the distinction
between determination- and explanation-based conceptions of grounding,
the formulation of grounding claims, the distinction between full and
partial grounding, cases that are thought to illustrate the general
concept of grounding, and historical discussions of grounding.


### 1.1 Determination and explanation



An important initial choice point in theorizing about grounding
concerns the theses of *unionism* and *separatism*
(Raven 2015: 326). Proponents of unionism work with an
explanation-based conception of grounding, stipulating that grounding
is a form of explanation, what we will call
*explanation*G** (Dasgupta 2017; Fine 2012a;
Litland 2015; Rosen 2010). For unionists, to say that the bowl's
brittleness is grounded in the ionic bonds of its constituent atoms
is, in the first instance, to say that the bowl is brittle because
these bonds are ionic, that it's brittle in virtue of the ionic
bonding, or that the brittleness is accounted for by the bonding.



Separatists, on the other hand, work with a determination-based
conception of grounding. The guiding idea here is an analogy between
causation and grounding. Causation, while itself a form of
determination rather than explanation, nevertheless backs
explanations. So too separatists claim with grounding: grounding,
rather than being a form of explanation, is a form of
determination--what we will call
*determination*G**--that backs
explanations (Audi 2012a; Schaffer 2009, 2012, 2016a; Trogdon 2013a).
For separatists, to say that the bowl's brittleness is grounded
in the ionic bonds of its constituent atoms is, in the first instance,
to say that these bonds non-causally generate, produce, or bring about
the bowl's brittleness. Just what the intuitive notion of
backing ultimately comes to in the context of causation and grounding
isn't an entirely settled matter--some understand backing
in terms of representation (Trogdon 2018a), while others suggest that
backing itself is to be given a grounding-theoretic treatment (Kovacs
2020; Wirling 2020). (The
"explanation*G*" and
"determination*G*" terminology is
borrowed from Skiles and Trogdon (2021)).



Unionists, as we understand them, are committed to there being
instances of a certain form of explanation and to providing an account
of what it's like; they don't have a corresponding
commitment regarding any form of determination. For separatists, the
reverse is the case. Hence, unionism and separatism are importantly
different theses (cf. Dasgupta 2017: fn. 8; Kovacs 2020). And note
that, even if we agree that there is both
explanation*G* and
determination*G*, there still may be substantive
reasons to go with one view rather than the other. For example, if,
say, explanation*G* is conceptually prior to
determination*G*, then perhaps we should, all other
things being equal, interpret grounding claims as targeting in the
first instance the former rather than the latter. Compare: Strevens
(2008: Ch. 6) claims that we ought to interpret causal claims (e.g.,
"The stone striking the glass caused the window to
shatter") as targeting in the first instance causal explanation
rather than causation understood as a form of determination, as the
former is conceptually prior to the latter.


### 1.2 Regimentation



To regiment grounding discourse is to adopt a formal language in which
we can precisely formulate grounding claims. A regimentation includes
various linguistic policies, including ones specifying which syntactic
forms we should use to express grounding relationships. There are two
general approaches to regimentation. On the first approach,
regimentation is chiefly pragmatic in nature. In this case, we might
regiment in one way rather than another merely because doing so will,
say, make a certain complicated argument or idea easier to follow or
understand. On the second approach, our choices concerning
regimentation are guided by the goal of accurately describing the
structure of reality.



As for the regimentations themselves, two general frameworks have
emerged: *predicationists* formulate grounding claims with a
relational predicate, one corresponding to the English predicate
*grounds* (Audi 2012a; Schaffer 2009; Rosen 2010).
*Connectivists* use a non-truth-functional sentential
connective instead, one corresponding to the English operator
*because* (Fine 2012a; Correia 2010; Schneider 2011). Full
blown connective regimentations will include a logic of grounding,
which on Fine's (2012a, 2012b) development includes structural
rules and properties (e.g., transitivity) and logical rules including
introduction and elimination rules. (See Poggiolesi 2020 for a general
discussion of the logic of grounding.) Note that each of these
approaches to regimentation is compatible with both separatism and
unionism (Kovacs 2018: note 28). For further context, note that there
is corresponding discussion regarding the proper formulation of
truthmaking claims (Melia 2005).



Some claim that a potentially relevant consideration here concerns
ontological commitment (Correia 2010). All other things being equal,
if one way of formulating grounding claims has fewer ontological
commitments than another, then the former is preferable to the latter.
Suppose that the connectivist's connective is understood to be
non-committal, so as not to commit us to a grounding operation. And
suppose that the predicationist's predicate is understood to
commit us to a grounding relation between facts. In this case, it may
be that connectivism has an advantage over predicationism--this
depends on whether there are countervailing considerations (e.g., the
connective treatment may be relatively cumbersome to work with). But
note that the predicationist, of course, might claim that their
predicate is non-committal (nominalists, for example, dispute that
relational terms commit us to properties and relations), and perhaps
there are reasons to think that the connectivist's connective
commits us to a grounding operation. The moral is that we need to
establish which terms are committal before any claims of minimizing
commitment can be made. (Also, note that, with respect to the
potential commitments of predicationism, we may have different
attitudes about relations and facts--you might be happy to
countenance facts but not relations or vice versa.)



While we will introduce some symbols for expressing facts below, we
won't adopt any particular formal language for expressing
grounding relationships, so we needn't adopt either
predicationism or connectivism. For ease of presentation, however, we
will formulate grounding claims with the predicate *grounds*
and speak as if this predicate expresses a relation--the
grounding relation--such that collections of one or more facts
ground particular facts. (See, however, Dasgupta 2014b and Litland
2018a for bicollective conceptions of grounding according to which
collections of facts can be non-distributivity grounded.) Where
*P* is an English sentence, let \([P]\) be a function from
*P* to the fact it corresponds to. So [Gomer is a good dog] is
the fact that Gomer is a good dog. (We will also indicate propositions
in the same manner using angle rather than square brackets.) We assume
that grounding is factive in the following sense: \([P],\) \([P'],\)
... grounds \([Q]\) only if \([P],\) \([P'],\) ... and
\([Q]\) obtain. Much of what we go on to say can be captured without
recourse to relations and facts, but we won't attempt to provide
such translations.



Before proceeding, we should note that some formulate grounding claims
in such a way that all manner of things potentially ground one
another, not just facts (Cameron 2008; Schaffer 2009; Wilhelm 2020).
The theses of separatism and unionism are relevant here (see
 SS1.1).
 Given unionism (grounding is explanation*G*), the
restriction to facts seems quite reasonable. While it makes sense to
say, for example, that [The truck exists] explains something,
it's unclear what it might mean to say that the truck itself
does so (Raven 2015; Trogdon 2013a). But, given separatism (grounding
is determination*G*), the alternative view is a
genuine option. We can coherently maintain that the truck determines
its particular redness (a mode), and this, in turn, backs an
explanation of the existence of the mode in terms of the existence of
the truck.



Moreover, some treat grounding as a quaternary rather than binary
relation. One such view is that the grounding relation includes two
slots for facts and two slots for modes of presentation of those facts
(Jenkins 2011). Another such view is that grounding is contrastive in
nature, so it includes two slots for facts and two slots for contrasts
of those facts (Schaffer 2012). Consider, again, the claim that [The
truckers are picketing] grounds [The truckers are striking]. Depending
on the context, we might read the claim as follows: [The truckers are
picketing] rather than [They're working as normal] grounds [The
truckers are striking] rather than [It's not the case that
they're striking]. Schaffer argues that his version of the
quaternary view is preferable to the binary view insofar as we can
reasonably maintain that grounding is transitive given the former but
not the latter (see
 SS2.3
 for further discussion of transitivity). Schaffer also suggests that
the contrastive treatment of grounding is plausible insofar as it
casts grounding in an apt form to back explanation, which is itself
contrastive in nature.


### 1.3 Full and partial grounding



There is a distinction between full and partial grounding. Suppose
\([P],\) \([P'],\) ... grounds \([Q]\). Speaking in unionist
terms, for a preliminary characterization of the distinction we can
say that \([P],\) \([P'],\) ... partially grounds \([Q]\) when
the former facts contribute to explaining the latter; and \([P],\)
\([P'],\) ... fully grounds \([Q]\) when nothing needs to be
added to the former to get a fully adequate explanation of the latter
fact. Separatists might instead initially characterize the distinction
in terms of partial and full determination.



Sticking with unionism for the moment, we can say that, as any ground
contributes to explaining what it grounds, any ground is a partial
ground. But not all partial grounds provide fully adequate
explanations of what they ground, so not all partial grounds are full
grounds. A merely partial ground is a partial ground that isn't
a full ground. By *grounding* we henceforth mean partial
grounding. The example of the truckers picketing above illustrates the
notion of merely partial grounding--we would need to add facts
about the trucking company and relations between the picketers and the
company (e.g., that the picketers work as drivers for the company) to
get a fully adequate explanation of the fact that they're
striking. As for full grounding, a common view is that conjunctive
facts are fully grounded by their conjuncts--the collection
consisting of [The bowl is brittle] and [The truckers are striking],
for example, is thought to fully ground [The bowl is brittle and the
truckers are striking].



According to the standard definition of partial grounding, \([P],\)
\([P'],\) ... partially grounds \([Q]\) just in case \([P],\)
\([P'],\) ... either on its own or together with other facts
fully grounds \([Q]\) (Audi 2012a; Litland 2015; Loss 2017; Raven
2013; Rosen 2010; Skiles 2015). You might initially view this
definition as being a purely stipulative matter. But it's
actually substantive in nature, as we have a pre-theoretic grip on
both partial and full grounding. In fact, Leuenberger (2020) and
Trogdon & Witmer (2021) argue that the standard definition is
false, proposing cases in which mere partial grounds can't be
supplemented with further facts to yield full grounds. The latter
recommend reversing the direction of the standard definition,
proposing a definition of full grounding in terms of partial grounding
together with other notions.


### 1.4 Illustrative cases



So far, we have considered four grounding claims, namely:


* [The truckers are picketing] grounds [The truckers are
striking].
* [The truck exists] grounds [Thus-and-so particular redness
exists].
* [The bowl's constituent atoms are bonded in thus-and-so way]
grounds [The bowl is brittle].
* [The bowl is brittle], [The truckers are striking] grounds [The
bowl is brittle and the truckers are striking].



Now, you might think there is something to grounding, yet at the same
time, think that these claims aren't true. As for the second and
fourth examples above, perhaps there are no modes or conjunctive
facts. But these are illustrative cases--these claims, whether
true or not, help communicate the relevant notion of grounding and
thus contribute to fixing the topic of discussion. Let's try to
get a better sense of what the range of illustrative cases looks
like.



While there are perhaps different ways of usefully typing illustrative
cases, here we focus on three categories. Importantly, this taxonomy
isn't intended to be exhaustive, and it may be that these
categories aren't exclusive either. First, there are
*metaphysical* cases, cases in which entities that \([P],\)
\([P'],\) ... concern are metaphysically linked with entities
\([Q]\) concerns. Our initial example of the truckers picketing is
such a case. In this case, [The truckers are picketing] concerns the
property of picketing, and the [The truckers are striking] concerns
the property of striking. Plausibly, the property of striking is a
functional property (a property whose nature is exhausted by its
causal role), one functionally realized by the property of picketing
on this occasion (as opposed to, say, the property of engaging in a
work slowdown). The brittleness and mode examples look like
metaphysical cases as well, where mereological realization and mode
determination yoke the relevant entities in these cases, respectively.
For other cases of this type, consider the following sentences, where
"{Beijing}" refers to the set whose sole member is Beijing,
and <The truck is red> refers to the proposition that the truck
is red:


* [Beijing exists] grounds [{Beijing} exists].
* [The grains of sand exist] grounds [The heap of sand exists].
* [The truck is red] grounds [<The truck is red> is
true].



Plausibly, Beijing stands in the set formation relation to {Beijing},
the grains of sand compose the heap, and the truck is a truthmaker for
<The truck is red> (i.e., the former makes the latter true).



Second, there are *logical* cases, grounding claims that
correspond to certain logical inference rules, particularly
introduction rules (cf. McSweeney 2020 and Merlo 2020). Just which
introduction rules are relevant here will depend, in part, upon
whether grounding is worldly in nature (see
 SS2.1
 for discussion). The conjunctive case concerning the bowl being
brittle and the truckers striking above is such a case, which of
course corresponds to conjunction introduction. For other examples,
consider the following two cases, which correspond to disjunction and
existential introduction, respectively:


* [The truck is red] grounds [The truck is red or the bowl is
brittle].
* [The truck is red] grounds [Something is red].



Third, there are *conceptual* cases, grounding claims that
correspond to certain conceptually necessary conditionals (cf.
Smithson 2020). For example, you might think that it's
conceptually necessary that if the truck is burgundy then the truck is
red. The corresponding grounding claim:


* [The truck is burgundy] grounds [The truck is red].



For further examples of this type, consider:


* [Trucks are essentially artifacts] grounds [It's necessary
that any truck is an artifact].
* [The figure is a rectangle with sides of equal length] grounds
[The figure is a square].



The thought is that it's conceptually necessary that if trucks
are essentially artifacts, then it's necessary that any truck is
an artifact; and it's conceptually necessary that if the figure
is a rectangle with sides of equal length, then the figure is a
square.



As mentioned above, these categories are aren't intended to be
exclusive or exhaustive. With respective to exclusivity, the example
of the burgundy truck above is perhaps both conceptual and
metaphysical, as burgundy and red stand in the
determinate-determinable relation, a relation that plausibly
underwrites metaphysical links between properties.



So far, we've focused on specific grounding claims (i.e., claims
to the effect that this collection of facts grounds that fact), but
various generic grounding claims are illustrative cases as well. There
are illustrative generic grounding claims corresponding to the
specific grounding claims discussed above, such as:


* Facts concerning the instantiation of determinate properties
ground facts concerning the instantiation of determinable
properties.



Here's another example, one not connected to any specific
grounding claim we have discussed so far:


* Chemical facts ground biological facts.



This last example speaks to the idea that grounding relations between
different kinds of facts are that in virtue of which the world has a
layered structure (see
 SS3.2
 for related discussion).


### 1.5 Historical connections



There are interesting and difficult questions about grounding, its
history, and what its relationship to the history of philosophy is. On
one view, the notion of grounding is old, perhaps as old as philosophy
itself, with many of its most important thinkers engaging with
questions related to grounding. On another view, the notion of
grounding is decidedly new--it's a recent development in
contemporary analytic metaphysics.



Can we reconcile the grounding-is-old and grounding-is-new views? The
distinction between questions *of* grounding and questions
*about* grounding is helpful here (Raven 2019). To take but one
well-worn example, when Socrates asks in the *Euthyphro* if
someone is pious because they are loved by the gods, or if they are
loved by the gods because they are pious, perhaps Plato is directing
our attention to a question of grounding. When in the contemporary
literature, philosophers are debating about whether grounding is, say,
a strict order (see
 SS2.3),
 this is the result of their asking questions about grounding.
Historically, so the thinking goes, philosophers have been interested
in questions of grounding, whereas the contemporary literature has
been primarily focused on questions about grounding. There is a sense,
then, in which the notion of grounding is as old as the hills, with
the more recent focus in the literature being directed at the notion
itself.



Although this characterization is appealing, it has its limitations.
Clearly, contemporary philosophers are interested in questions of
grounding in addition to questions about grounding. What might be less
clear, however, is that, on the face it, the historical literature is
by no means short of attempts at engaging with questions about
grounding in addition to questions of grounding. Consider, for
example, cosmological arguments. In broad strokes, the thought is that
the totality of contingent entities, the cosmos, stands in need of
explanation, and only considerations involving God understood as a
necessary existent are up to the task. Central to such arguments is an
assumption according to which we can't explain why there are
contingent entities by appealing to the existence of a contingent
entity. Debate has raged for centuries over how exactly we ought to
understand this assumption and whether or not we ought to believe it.
Importantly, this assumption is generally understood as a kind of no
circularity assumption. In debating whether the assumption is correct,
historical figures are, albeit indirectly, debating whether or not the
relation at issue can have reflexive instances. The same goes for
discussions around God's nature as a self-causer. If the
relation at issue is that of grounding, then the history of philosophy
is rich in discussions about grounding.



Ultimately, however, it seems that the "Is grounding old or
new?" question should give way to nuanced and text-based
discussions of structural similarities and causal continuities between
specific thinkers. As this entry will make clear, contemporary figures
don't fully agree on the concept of grounding. Hence, it seems
that there is little to be gained by asking whether thus-and-so
historical figures used the same notion as the contemporary figures,
as the contemporary figures aren't using the same notion
themselves! Beyond tracing out similarities and differences in content
of various notions employed by historical figures and paths of
historical development, the question of whether grounding is old or
new will apparently always be a crude generalization over these
similarities and continuities. And note that there is nothing special
about grounding in this regard--the same could be said for
virtually any philosophically interesting concept, such as causation
or necessity. (For discussions of historical connections to the
ancient period, see, e.g., Corkum 2016 and 2020, Evans 2012, and
Malink 2020; for the early and late modern periods, see, e.g., Amijee
2020, Bliss 2019, Casati 2018, Mulligan 2020, Pearce 2017, Roski 2017,
2020, and Stang 2019.)


## 2. The Nature of Grounding



There are a variety of issues to address related to the nature of
grounding. In this section we focus on objectivity, representation,
hyperintensionality, non-monotonicity, whether grounding is a strict
order, and whether grounding is well-founded. There are other
interesting issues concerning the nature of grounding that we
don't have the space to discuss here. One such issue is that of
*meta-ground*, viz. what if anything grounds the facts about
what grounds what (see Litland 2020 for an overview).


### 2.1 Objectivity and representation



What are the central features of grounding? Grounding theorists
routinely claim that grounding is fully objective. But, given that
objectivity and related notions are used in a variety of ways in
philosophy, it comes as no surprise that there are different ways of
understanding precisely what is being claimed here. On one approach,
the issue chiefly concerns the regimentation of grounding discourse.
If grounding claims are to be formulated with a parameter for facts
concerning human mental activity, then grounding isn't fully
objective (Dasgupta 2017). On a more "metaphysical"
approach, the issue instead chiefly concerns the essence or nature of
grounding, specifically whether grounding is essentially connected to
subjects. Suppose, for example, that part of what it is to be
grounding is that \([P],\) \([P'],\) ... grounds \([Q]\) only if
certain epistemic conditions obtain (e.g., actual subjects are in a
position to understand certain propositions concerning \([P],\)
\([P'],\) ... and \([Q]\)). In this case, grounding isn't
objective.



What might speak in favor of objectivism about grounding? Perhaps our
considered views about causation should guide our theorizing about
grounding (cf. Bernstein 2015). Schaffer (2016a) conceives of
grounding as being broadly analogous to causation and proposes to
extend the familiar structural equation models for causation to
grounding. And A. Wilson (2018) argues that grounding is indeed a type
of causation, proposing an interventionist account of grounding. So,
provided that it's a bad idea to outfit causal claims with a
parameter for facts concerning human mental activity, this is probably
a bad idea for grounding claims as well (cf. Bernstein 2018).
Subjectivism (the claim that, while some facts ground other facts,
grounding isn't fully objective), however, isn't beyond
the pale. One potential route to subjectivism is this: endorse
unionism (grounding is explanation*G*) and argue
that explanation*G* is by its nature subject
involving (Maurin 2019; Thompson 2018).



Roughly speaking, the *representational* approach to grounding
has it that grounding is intimately tied to representation (Fine
2012a; Rosen 2010), while the *worldly* approach denies this
(Audi 2012b; Schaffer 2012). While the representational/worldly
distinction is somewhat hazy, we understand it to be orthogonal to the
objective/subjective distinction. One way to sharpen the distinction
between the representational and worldly approaches is as follows: on
the former, the relata of grounding have concepts among their
constituents; on the latter, this isn't the case (Kramer
& Roski 2015; Correia 2017). So understood, the representational
approach comes in two varieties: either facts are composed entirely of
concepts or they're a mixture of concepts and
non-representational items like objects and properties. On the former
view, facts are akin to Fregean propositions; on the latter view,
they're instead akin to ordered sets of concepts and
non-representational items. (See Correia 2010 for a discussion of the
distinction between the representational and worldly approaches where
it isn't assumed that grounding is a relation.)



What hinges on whether grounding is representational or worldly? This
isn't entirely clear. You might think that grounding being
worldly ensures that the relata of grounding are relatively
coarse-grained, and grounding being representational ensures that the
relata of grounding are relatively fine-grained. Consider the
following two facts: [The liquid is H2O] and [The liquid is
water]. Representationalists, so the thinking goes, might claim that
we have distinct facts here, as they have different concepts as
constituents. And proponents of the worldly approach might claim that
we have only one fact here, as there is no difference in constituents
or manner of combination. And this, of course, is potentially relevant
to theorizing about grounding--if [The liquid is H2O]
and [The liquid is water] are the same fact, then the claim that the
former grounds the latter or vice versa is false provided that
grounding is irreflexive (see
 SS2.3).
 Note, however, that representationalists can coherently maintain that
facts are relatively coarse-grained--perhaps they think that,
while facts are Fregean propositions, concepts are relatively
coarse-grained (Correia 2020). And proponents of the worldly approach
can coherently maintain that facts are relatively
fine-grained--perhaps they think that, while facts are true
Russellian propositions (ordered sets of non-representational items
including properties), properties are relatively fine-grained (Dorsey
2015).



You might also think that if grounding is worldly then unionism is
false. The idea is that, if grounding is worldly, then grounding
can't be a type of explanation, as explanation itself is
representational. There are, however, conceptions of explanation
relative to which explanation is non-representational, and a worldly
unionist is free to appeal to explanation so conceived (Skiles and
Trogdon 2021).


### 2.2 Hyperintensionality and non-monotonicity



Grounding theorists also routinely claim that grounding is
hyperintensional (Bader 2013; Leuenberger 2014; Schaffer 2009). This
issue concerns what linguistic distinctions grounding is sensitive to.
It will be helpful to begin by considering the hyperintensionality of
belief. Consider the following belief attribution:


* Amy believes that Mark Twain was a humorist.



Note that, were we to replace


* Mark Twain was a humorist



as it appears in this belief attribution with a necessarily
co-extensional expression such as


* Samuel Clemens was a humorist



the resulting belief attribution may have a different truth-value than
the original one. This is the sense in which belief is thought to be
hyperintensional.



We can understand the claim that grounding is hyperintensional in a
similar way. Consider again the following grounding claim:


* [Beijing exists] grounds [{Beijing} exists].



Were we to replace


* [Beijing exists]



as it appears in this grounding claim with a necessarily
co-extensional expression such as


* [{Beijing} exists]



the resulting grounding claim may have a different truth-value than
the original one. In this case, it seems that the two grounding claims
do in fact differ in truth-value--while the original grounding
claim is true, the resulting one is presumably false. (See Duncan,
Miller, & Norton 2017 for discussion of the relationship between
grounding and various senses of hyperintensionality.)



Grounding theorists also normally claim that grounding is
non-monotonic (Audi 2012a; Guigon 2018; Rosen 2010). Logical
entailment is monotonic in the following sense: if one sentence
logically entails another, then the first sentence together with any
other sentence logically entails the second. Returning to grounding,
suppose that \([P],\) \([P'],\) ... grounds \([Q]\). And suppose
that \([R],\) \([R'],\) ... obtain. Grounding is non-monotonic
just in case these suppositions are compatible with it not being the
case that \([P],\) \([P'],\) ... together with \([R],\) \([R'],\)
... grounds \([Q]\). To take an example, consider again
[*Beijing exists*] grounds [{*Beijing*}
*exists*]. Rather than replacing [*Beijing exists*] in
this sentence with something else as we did above, let's add
some other nominalized true sentence to it such as [*Gomer is a
good dog*]. The resulting sentence (i.e., [*Beijing
exists*], [*Gomer is a good dog*] grounds
[{*Beijing*} *exists*]) is clearly false, while our
original grounding claim (we're supposing, anyway) is true.


### 2.3 Strict ordering



Some claim that grounding is a strict order--it's
transitive, irreflexive, and asymmetric (Correia 2010; Fine 2012a;
Raven 2013). One way to argue that grounding has some or all of these
features is to embrace separatism (grounding is
determination*G*) and argue that
determination*G* or determination in general has
some or all of them (Audi 2012a). Another option is to embrace
unionism (grounding is explanation*G*), focusing on
the features of explanation*G* or explanation in
general (Raven 2015). Another way, still, is to argue that, given
either separatism or unionism, grounding plays the theoretical roles
normally assigned to it only if it has some or all of these features
(Kovacs 2018). These strategies can be used to argue that grounding
has further properties as well. For example, Litland (2013) and Raven
(2015) claim that explanation in general is non-monotonic, so, given
unionism, grounding is as well; and Audi (2012a) claims that
determination in general is non-monotonic, so, given separatism,
grounding is as well.



While the view that grounding is a strict-order is the prevailing
view, what reasons might there be to think otherwise? (As Bliss &
Priest [2018b] note, there are various possible combinations of formal
properties that we may wish to ultimately consider.) Let's begin
with transitivity. Consider the following case, adapted from one that
Schaffer (2012) proposes. Suppose that the following claims are true,
where *g* is a metal globe:



(1)
[*g* is dented in thus-and-so way] grounds [*g* has
determinate shape *S*].
(2)
[*g* has determinate shape *S*] grounds [*g*
is more-or-less spherical].


If grounding is transitive, then the following is true as well:



(3)
[*g* is dented in thus-and-so way] grounds [*g* is
more-or-less spherical].


You might think, however, that
 (3)
 is false--as Schaffer puts the idea, "The thing is
more-or-less spherical *despite* the minor dent, not because of
it" (2012: 127). Note that
 (1)
 concerns merely partial grounding, while
 (2)
 concerns full grounding. But, as any merely partial ground is a
partial ground, and any full ground is a partial ground, we can read
(1)-(3) as targeting partial grounding, so there is no
equivocation here.



How might proponents of transitivity respond? Litland (2013) proposes
that we can add a fact to the merely partial ground for [*g*
has determinate shape *S*] to get a full ground:



(4)
[*g* is dented in thus-and-so way], [*g* elsewhere
has determinate shape \(S'\)] fully grounds [*g* has
determinate shape *S*].


Given that
 (2)
 also concerns full grounding, the transitive inference from
 (4)
 and
 (2)
 is the following:



(5)
[*g* is dented in thus-and-so way], [*g* elsewhere
has determinate shape \(S'\)] fully grounds [*g* is
more-or-less spherical].


Litland claims that
 (5)
 is plausible, or at least as plausible as
 (1)
 and
 (2).
 And, provided that any collection of facts that is a full ground is
such that any fact among that collection is a partial ground,
 (3)
 follows from
 (5).
 (See Raven 2015 for a similar treatment of this case; see also
Rodriguez-Pereyra 2015 and Tahko 2013 for potential counterexamples to
transitivity involving truth.)



Turning to irreflexivity, Bliss (2018) critically assesses the general
theoretical motivations for thinking that grounding is irreflexive.
Lowe (1998: 145) suggests that self-explanatory states of affairs are
epistemically possible, so perhaps a characterization of grounding
shouldn't rule this out. Historically, certain influential
thinkers have thought that the fact that God exists, for example, is a
self-explanatory state of affairs. Fine (2010) and Kramer (2013)
also discuss various cases that seem to involve violations of
irreflexivity. Here is a case along the lines of those they
discuss--consider the following fact: [Some fact or other
obtains]. Some facts do indeed obtain, so of course [Some fact or
other obtains] itself obtains. And it seems that any fact that obtains
is something that grounds this fact. Since [Some fact or other
obtains] is itself a fact that obtains, it follows that this fact
grounds itself!



In response to cases like this, Woods (2018) distinguishes between
what he calls *vacuous* and *non-vacuous* grounding.
Woods suggests that cases like [Some fact or other obtains] involve
vacuous grounding, and, while vacuous grounding isn't
irreflexive, non-vacuous grounding is. Roughly speaking, \([P],\)
\([P'],\) ... vacuously grounds \([Q]\) when the former grounds
the latter, yet the identity and nature of the constituents of
\([P],\) \([P'],\) ... aren't explanatorily relevant to
\([Q]\) obtaining. Perhaps [The truck is red] is a vacuous ground for
[Some fact or other obtains]--while the former grounds the
latter, it seems that the identity and nature of the truck and the
property of being red don't contribute to explaining why [Some
fact or other] obtains.



Turning to asymmetry, Bliss (2014) and Thompson (2016, 2018)
critically assess the general theoretical motivations for thinking
that grounding is asymmetric and propose potential counterexamples.
Thompson suggests that, given the functional relationship between
mass, volume, and density (the density of a substance is its mass
divided its volume), we should accept that, say, [*g* has
3cm3 volume] grounds [*g* has 2g/cm3
density] and vice versa. It's worth noting, however, that many
reciprocal functional relationships don't involve symmetric
grounding. As Alexander Skiles has suggested to us in conversation,
there is, for example, a reciprocal functional relationship between
how many things are Socrates and how many members Socrates'
singleton has, but it's clear in which direction the grounding
runs in this case.


### 2.4 Well-foundedness



Another issue is whether grounding is *well-founded*. Different
authors mean different things in claiming that grounding is
well-founded. According to Schaffer, grounding is well-founded in the
sense that downwardly non-terminating chains of grounds are
impossible. In conceiving of grounding as a relation between entities
in general and not just facts, Schaffer's rationale concerns the
notion of *reality inheritance*. Schaffer claims that, were
there downwardly non-terminating grounding chains, the being of any
object in such a chain would be "infinitely deferred, never
achieved" (2010: 62). Something "...cannot be real
merely by having a limitless sequence of ancestors, each claiming
reality from its parents"; instead, "There must actually
be a source of reality somewhere" (2016a: 95). This echoes
Leibniz, who claims that in the event that every object is a being of
aggregation, "one never arrives at any real being" (Adams
1994: 333).



Others claim that grounding is well-founded in the sense that any
grounded fact is ultimately grounded by ungrounded facts (Dixon 2016;
Rabin & Rabern 2016). Note that this conception of the
well-foundedness of grounding, in contrast to the one above, allows
for infinitely descending grounding chains. How so? Following Bliss
(2013) and Rabin and Rabern (2016), consider Euclidean space, which is
comprised of points and regions that include those points. Suppose
that regions are gunky in that every region has a region as a proper
part. And suppose that the existence facts concerning regions are
grounded by the existence facts concerning their sub-regions, the
existence facts concerning sub-regions are grounded by the existence
facts concerning their sub-sub-regions, and so on, *ad
infinitum*. Hence, the fact that region *R* exists is a
member of an infinitely descending grounding chain. But suppose that
the existence facts concerning regions are also grounded by the
existence facts concerning points. Suppose, moreover, that the
existence facts concerning points lack grounds. Hence, while the fact
that *R* exists is a member of an infinitely descending
grounding chain, this fact nonetheless is grounded in facts that
themselves lack grounds. The same applies to all the other facts that
are links in the grounding chain in question.



It may be that, if considerations involving reality inheritance are
relevant here, they ultimately support the idea that grounding is
well-founded in the second sense rather than the first. While there
may be something wrong about reality inheritance in the absence of a
source of reality, perhaps there is nothing wrong about endless
reality inheritance *per se*. (See Puryear 2020 for discussion
of the historical context of reality inheritance and Trogdon 2018b for
further discussion of reality inheritance in the contemporary
context.)


## 3. Why Think There is Grounding?


### 3.1 Arguments from theoretical utility



That grounding figures in ordinary and philosophical thinking (and
perhaps other domains as well) and that many grounding claims are
fairly easy to evaluate (e.g., [*Beijing exists*] grounds
[{*Beijing*} *exists*]) gives us defeasible reason to
think that there is grounding (deRosset 2020). What else can be said
on behalf of grounding? Proponents of grounding tend to think that
it's a justified posit on the basis of its theoretical utility.
In this section we set out three theoretical utility arguments for
grounding that involve unity, explanation, and the direction of
priority.



The *unity argument* says that grounding is a justified posit
because of its unifying role (Audi 2012a; Rosen 2010; Schaffer 2009).
On one way of casting the argument, it has three premises. First,
there is substantial unity among the metaphysical relations (relations
familiar from metaphysics such as functional realization and set
formation that resist analysis in purely modal terms). Second, where
there is substantial unity, plausibly there is a unifier, something
that explains why the relations in question resemble one another in
the manner they do. Third, if there is a unifier for the metaphysical
relations, the best candidate is grounding.



The *explanation argument* says that grounding is a justified
posit because of its explanatory role (Audi 2012a; Dasgupta 2014a;
Fine 2012a; Litland 2017; Schaffer 2016a). Recalling the distinction
between unionism and separatism (see
 SS1.1),
 the argument proceeds differently depending on which view is in play
(Kovacs 2017). Given separatism (grounding is
determination*G*), one way to cast the explanation
argument is as follows: there is a form of explanation--what we
can call *ontic* explanation--such that explanations of
this form are backed by worldly relations; and, among the ontic
explanations are ones such that the best candidate for the relation
that plays the backing role is determination*G*.
Given unionism (grounding is explanation*G*), one
way to cast the argument is as follows: there is a form of
explanation, what we can call *metaphysical explanation*, such
that the connections in metaphysical explanations are best expressed
in terms of explanation*G*.



The *priority argument* says that grounding is a justified
posit because of its direction-fixing role--it fixes the
direction of priority between facts, where one fact is prior to
another only if the former is more fundamental than the latter. (See
 SS4.3
 for further discussion of fundamentality; J. Wilson (2014) initially
proposes the priority argument but rejects it--more on this
below.) Let a *priority case* be one in which some fact is
prior to another and entities these facts concern are yoked by
metaphysical relations. One way to cast the priority argument is as
follows: there are priority cases in which the direction of
metaphysical relations doesn't determine which fact is prior to
the other; and the best candidate for that which fixes the direction
of priority in such cases is grounding.



We can cast arguments for grounding in terms of theoretical roles in
addition to those specified by the unity, explanation, and priority
arguments as well. Some, for example, claim that the thesis of
*physicalism* (roughly, the view that the world is ultimately
physical in nature) is usefully formulated in terms of grounding
(Block 2015; Dasgupta 2014a; Schaffer 2017b). With respect to
physicalism *about the mental* in particular (roughly, the view
that mental phenomena are nothing over and above physical phenomena),
a simple grounding-theoretic formulation of the view is this: the
mental facts are grounded by (non-mental) physical facts (perhaps
together with other non-mental facts such as indexical and totality
facts). It's by now a familiar idea that purely modal
formulations of physicalism are inadequate, as there are coherent
versions of dualism that such formulations don't rule out
(Horgan 1993, 2006). Hence, one point in favor of appealing to
grounding in this context is that grounding isn't a purely modal
notion. And Block (2015) argues that even physicalism formulated in
terms of a priori entailment faces the same problem, pointing to a
particular grounding formulation of physicalism as the way to resolve
the issue.



As for further potential theoretical applications, some have proposed
grounding-theoretic accounts of:


* the nature of properties (Audi 2016; Carmichael 2016);
* the distinction between *intrinsic* and *extrinsic*
properties--roughly, properties that something has just in virtue
of how that thing is (e.g., being made of tin) vs. properties
something has because of how it's related to wholly distinct
things (e.g., being next to a tin cup) (Rosen 2010; Witmer et al
2005);
* what it is for an object (e.g., Socrates) in contrast to a word
(e.g., 'Socrates') to have a definition (Rosen 2015);
* what it is for one claim to reduce to another (Fine 2001)
* what it is for the world to be stratified into levels (Rabin 2018;
Schaffer 2012);
* how moral facts (e.g., facts about what we're morally
obligated to do) are related to natural facts (e.g., facts concerning
what maximizes utility) (Rosen 2017);
* the special explanatory gap between the experiential and physical
truths (Rabin 2019; Trogdon forthcoming);
* what it is for the existence of certain entities to depend on the
existence of others (Schnieder 2020);
* what it is for truths to be such that things in the world make
them true (Correia 2014; Rodriguez-Pereyra 2005; Schnieder 2006);
* what it is for one theory to be more parsimonious than another
(Schaffer 2013);
* the nature of free will and moral responsibility (Sartorio
2013);
* what it is for something (e.g., gender) to be a social
construction (Griffith 2018; Schaffer 2017a);
* the historically important view that everything has an explanation
(Amijee 2020a; Dasgupta 2016; K. McDaniel 2019; Schnieder &
Steinberg 2015);
* how multiple objects can exist at the same place and time (Saenz
2015);
* the view that only present things exist (Baron 2014);
* the relation between being *F* (e.g., being blue)
and having the property *F*-ness (e.g., having
blueness) (Dixon 2018);
* how mental events (e.g., pain) can cause physical events (e.g.,
wincing) given that such physical events have physical causes (e.g.,
C-fiber firing) (Clark & Wildman 2018; Kroedel & Schulz 2016);
Stenwall 2021; Tiehen 2015).



This is by no means an exhaustive list--there is something of a
cottage industry of developing grounding-theoretic accounts of items
of philosophical interest.


### 3.2 Skeptical responses



Some are skeptical of grounding. A distinction can be drawn between
what we might call *first-wave* and *second-wave*
grounding skepticism (see Koslicki 2020, though she uses different
terminology). First-wave skepticism is characterized by a general
concern about the intelligibility of the notion. Daly (2012) argues
that the notion of grounding doesn't really make sense. In a
similar spirit, Hofweber (2009) states that grounding theorists are
guilty of engaging in a problematic form of metaphysics--while
they make use of perfectly ordinary terms such as *priority*,
*fundamental* and *ultimately*, they use them in a
distinctively non-ordinary, metaphysical way. (For non-skeptical
rejoinders to first-wave skepticism, see Audi 2012b and Raven 2012.)
Second-wave skeptics, by contrast, generally grant that the notion of
grounding is coherent, but they think that it doesn't belong in
our theoretical toolkit in any case, as the arguments in favor of
positing grounding aren't persuasive. What unites second-wave
skeptics is a shared sense that grounding theorizing is simultaneously
undermotivated and overreaching.



With respect to the unity argument, Koslicki (2015) and J. Wilson
(2016a) challenge the second premise, arguing that, even if the
metaphysical relations (or some sub-collection thereof) are
substantially unified, this on its own wouldn't give us a good
reason to posit a generic relation of grounding as a unifier. J.
Wilson (2014) challenges the first premise as well, arguing that there
is a class of metaphysical relations, what she calls the
*small-g* grounding relations, that are neither
terminologically, formally, nor metaphysically unified. Relatedly,
Turner (2016) describes various differences in the way certain kinds
of grounding claims behave, ultimately distinguishing between two
forms of grounding, *dependence-grounding* and
*realization-grounding.* (For non-skeptical rejoinders to these
challenges, see Raven 2017, and Schaffer 2016b.)



Roughly speaking, *monists* claim that there is ultimately just
one core type of grounding, while *pluralists* claim that there
are different types and no core type. It's important to note
that being a pluralist about grounding doesn't necessarily make
you a grounding skeptic, at least given how we understand the usage of
the terms. It's true that some pluralists, as we've just
seen, are skeptics. But not all of them are. For example, Fine
(2012a), a proponent of grounding if anyone is, stresses the
differences between various forms of grounding, rejecting the idea
that they are unified in a way that might motivate positing a genetic
form of grounding. Just what might make it fitting to call one
pluralist view a version of skepticism about grounding and another
pluralist view non-skeptical instead is perhaps worth further thought.
(For further discussion of monism and pluralism about grounding, see
Berker 2018, Cohen 2020, Griffith 2014, Litland 2018b, Rettler 2017,
and Richardson 2020 and 2021.)



As for the explanation argument, Kovacs (2017) objects to both the
separatist and unionist versions set out above. For example, Kovacs
argues that, with respect to the former version of the argument,
worldly relations such as necessitation taken together with facts
about their relata, rather than determination*G*,
back ontic explanations. Relatedly, Miller and Norton (2017) propose
an explanation of why you might judge, say, that {Beijing} exists
because Beijing exists that doesn't appeal to grounding. And
Norton and Miller (2019) propose an account of the truth conditions
for statements of such explanations that doesn't appeal to
grounding.



Returning to the priority argument, there are two types of priority
cases to consider: cases in which the prior fact is fundamental, and
cases in which neither the prior nor posterior facts are fundamental.
J. Wilson (2014, 2016a) develops a proposal according to which a
primitive notion of fundamentality plays the direction-fixing role in
priority cases of the first type. And this primitive notion and other
grounding-free considerations (e.g., modal considerations) play the
direction-fixing role in cases of the second type. (For non-skeptical
rejoinders, see Cameron 2016 and Raven 2017.)



What about additional theoretical applications of grounding? Returning
to the application to physicalism discussed above, J. Wilson (2014)
points out that, as there are importantly different approaches to
grounding (ones disagreeing about, e.g., how grounding interacts with
reduction, necessitation, and real definition--see
 SS4),
 the bald grounding claim that the physical grounds the mental
doesn't on its own speak to even very basic characteristics of
the mental-physical interface. A natural response, however, is to
simply work in this context with an approach to grounding that is
fleshed out to a degree that such issues aren't left open
(deRosset 2020; cf. J. Wilson 2016a). Still, questions about the
theoretical utility of grounding-theoretic formulations of physicalism
remain, including whether the nothing-over-and-above notion central to
initial characterizations of physicalism is best captured in terms of
grounding (Melnyk 2016; J. Wilson 2016b).



To take another example, Sider (2011: Ch. 8; 2020) questions whether
grounding is apt to play the role of a level connector. Intuitively,
the world has an overarching structure where entities occupy different
levels of reality. One way to formulate the view that grounding is a
level connector is this: different levels of reality are connected to
one another by virtue of grounding relations between facts
characterizing occupants of these levels. With this in mind, consider
the fundamental physical level and a higher level, one occupied by
cities. The grounding theorist might claim that these levels are
connected partly in virtue of the fact that some quantum-mechanical
fact, *Q*, grounds the fact, *N*, that New York is a
city. But Sider asks: what is the grounding profile of this grounding
fact? On the face of it, [*Q* grounds *N*] itself is
ungrounded. Roughly speaking, the worry is this: provided that any
entity that an ungrounded fact concerns is fundamental in nature, it
follows that New York is a fundamental entity. Hence, it may be that
in using grounding to explain how different levels of reality are
connected, we get unacceptable results about which entities are
fundamental. (See
 SS4.3
 for more on fundamentality; for an overview of views according to
which facts like [*Q* grounds *N*] are grounded, see
Litland 2020.)



For a different skeptical take on grounding related to its theoretical
applications, Della Rocca (2014) and Tallant (2018: Ch. 5) argue, very
roughly, that various metaphysical claims (e.g., material objects
persist over time and truths have truthmakers) are false, as these
claims are ultimately about what grounds what but there is no
grounding.


## 4. Interaction with Other Notions



In this section we focus on how grounding might be related to the
notions of necessity, essence, and fundamentality. There are
interesting issues concerning the relationship between grounding and
other phenomena that we don't have the space to discuss here. In
addition to the examples listed at the beginning of this entry (e.g.,
real definition and truthmaking), one such issue concerns the relation
between grounding and *degrees of reality*. Indeed, K. McDaniel
(2017: Ch. 8) sketches an account of the former in terms of the
latter.


### 4.1 Necessity



How do grounding and necessity interact? Let \([P],\) \([P'],\)
... (metaphysically) necessitate \([Q]\) just in case any
(metaphysically) possible world in which the former obtains is a world
in which the latter obtains. The broad consensus is that necessity
isn't sufficient for grounding--it's not the case
that if \([P],\) \([P'],\) ... necessitate \([Q]\), then the
former ground the latter. (B. McDaniel 2019, however, argues that a
restricted form of necessitation is sufficient--as well as
necessary--for grounding.) Consider a necessary fact such as
[\(2+3=5\)]. While this fact might have grounds, facts about, say,
German Expressivist art aren't among them; yet the latter
necessitate the former. Also, there are cases in which the direction
of necessitation and grounding come apart. Plausibly, [{Beijing}
exists] necessitates [Beijing exists], yet presumably the later
grounds the former rather than the other way around.



There are, however, two other issues about the relationship between
grounding and necessity that are less of a settled matter. The first
is whether it's necessary that (full) grounds necessitate what
they ground--according to *necessitarianism*,
necessitation is necessary for grounding. The second is whether
grounding is an internal relation in the following sense: it's
necessary that if \([P],\) \([P'],\) ... (fully) grounds \([Q]\),
then any metaphysically possible world in which \([P],\) \([P'],\)
... and \([Q]\) obtain is a world in which the former (fully)
grounds the latter. According to *internalism*, grounding is
internal in this sense. Internalism entails necessarianism but not
vice versa. Due to limitations of space, we focus on necessitarianism
in what follows. (See Bennett 2011, Litland 2015, Carnino 2017, and
Lovett 2019 for discussion of internalism.)



Following Skiles 2020, there are at least three ways to go about
motivating necessitarianism. One appeals to essences: every instance
of grounding is mediated by essential truths that characterize the
grounds and what they ground or entities these facts concern (see
 SS4.2);
 these essential truths are themselves necessary; and grounds together
with these essential truths suffice for what they ground (Audi 2012a;
O'Conaill 2017; Trogdon 2013b). Another appeals to explanation:
it's necessary that grounds explain what they ground in a
distinctive way; and, for any explanation of this type, its explanans
suffices for its explanandum (deRosset 2010). And another appeals to
laws: every instance of grounding is subsumed by a metaphysical law;
the metaphysical laws are themselves necessary; and grounds together
with the relevant metaphysical laws suffice for what they ground
(Wilsch 2015).



What might a counterexample to necessitarianism look like? Following
Skiles (2015), suppose that the following accidental generalization
obtains:



(1)
[All *F*s are *G*s].


And suppose that exactly *n* things are *F*; let them be
\(a\_1\), \(a\_2,\) ... \(a\_n\). While



(2)
\([a\_1\) is *G*, \(a\_2\) is *G*, ... \(a\_n\) is
*G*]


clearly doesn't necessitate
 (1),
 Skiles proposes that the latter fully grounds the former. Grounding
necessitarians might reply that here we have mere partial
grounding--to get a full ground for
 (1),
 to
 (2)
 we would need to add



(3)
[The only *F* things are \(a\_1\), \(a\_2,\ldots\)
\(a\_n\)].


Skiles considers this reply, noting that
 (3)
 is itself an accidental generalization, one that presumably has full
grounds. Hence, this fact too stands in need a necessitating ground
provided that necessitarianism is true. What then fully grounds
 (3)?
 A natural proposal is that



(4)
\(a\_1\) is *F*, \(a\_2\) is *F*, ... and \(a\_n\)
is *F*.
(5)
\(a\_{n+1}\) is not *F*, \(a\_{n+2}\) is not *F*,
... and \(a\_{n+m}\) is not *F*.
(6)
For any *x*, \(x = a\_1\) or \(x = a\_2\), or
... \(x = a\_{n+m}\).


does so. And note that these facts together necessitate
 (3).
 But what is the grounding profile of
 (6)?
 Intuitively,



(7)
\(a\_1\) exists, \(a\_2\) exists, .... and \(a\_{n+m}\)
exists


grounds
 (6).
 You might claim that
 (7)
 is a non-necessitating full ground of
 (6).
 But one option for necessitarians is to argue that
 (7)
 is instead a special sort of merely partial ground, one that
can't be augmented with further facts to yield a full ground.
This is how Trogdon and Witmer (2021) treat this case and, as a
consequence, reject the standard definition of partial grounding (see
 SS1.3).
 (See Chudnoff 2016; Ch. 6 and Leuenberger 2014 for discussion of
other potential counterexamples to necessitarianism).


### 4.2 Essence



How do grounding and essence interact? On the relevant notion of
essence, essence isn't a purely modal matter--while all
essential truths about some item (truths that characterize what it is
to be that item) are necessary, not all necessary truths about some
item are essential truths about it (Fine 1994). For example, anything
that is identical to Beijing is a city, and this is a candidate
essential truth about Beijing. But, while it's necessary that
Beijing exists only if {Beijing} exists, this isn't a candidate
essential truth about the city (though it's a candidate
essential truth about {Beijing}). Intuitively, you can know everything
there is to know about what it is to be Beijing and not thereby know
anything about sets.



We begin with an essence-to-grounding principle, one specifying a
potential entailment from truths about essence to truths about what
grounds what. According to Rosen (2010), for any *x*, if
it's essential to *x* that *P*, then [It's
essential to *x* that *P*] grounds \([P]\) (see also
Dasgupta 2016 and Kment 2014: Ch. 6). Rosen points out that this
principle, if true, may clarify the grounding profile of certain
universal facts. For example, perhaps [It's essential to
triangularity that all triangles have three sides] grounds [All
triangles have three sides]. (See Glazier 2017 and Zylstra 2019b for
critical discussion.)



Turning to grounding-to-essence principles, some, such as Correia
(2013), O'Conaill (2018), and Trogdon (2013b), focus in this
context on putative essential truths that themselves don't
directly concern grounding (e.g., part of what it is to be the
property of being maroon is that, for any *x*, if *x* is
maroon, then *x* is red). Others, such as Audi (2012a), focus
on corresponding essential truths that encode information about what
grounds what (e.g., part of what it is to be the property of being
maroon is that, for any *x*, if *x* is maroon, then
[*x* is maroon] grounds [*x* is red]). Let's focus
on putative essential truths of the former, grounding-free variety,
where these truths are understood to characterize facts rather than
entities they concern.



You might think that, if \([P]\), \([P'],\) ... grounds \([Q],\)
then part of what it is to \([Q]\) is that if \([P],\) \([P'],\)
... obtains then \([Q]\) obtains. As Fine (2012a) notes, however,
there are potential counterexamples. While [Socrates is a philosopher]
grounds [Someone is a philosopher], on the face of it no essential
truth about the latter encodes information about Socrates in
particular. One possibility is to weaken the proposal so that the
essential truths may characterize either \([P],\) \([P'],\) ...
or \([Q]\). (A further consideration is whether we should understand
this principle as allowing for the relevant essential truths to be
irreducibly collective.) Fine (2012a) takes a different route,
claiming that, whenever some facts ground another fact, there will be
some true generalization of this grounding connection that


1. doesn't mention the grounds;
2. suffices, together with the grounds, for the grounded; and
3. is an essential truth about the grounded.



With respect to the case just mentioned, Fine proposes that this is
the relevant generalization: for any *x*, if *x* is a
philosopher, then [*x* is a philosopher] grounds [Someone is a
philosopher]. Fine notes that this principle, if true, suggests a
top-down approach to establishing what grounds what, one where we
begin with those facts we take to be grounded and then work our way
down to their grounds.



As Rosen notes (2010), however, these principles rule out so-called
Moorean connections, grounding connections that aren't mediated
by essential truths. If, say, non-reductive physicalism about the
mental is best formulated in terms of Moorean connections as Rosen
suggests, then the above grounding-to-essence principle has the
undesirable result of ruling out what is arguably the dominant view
concerning the metaphysics of mind.



While we don't have the space to explore these proposals here,
some have proposed not just essence-to-grounding or
grounding-to-essence principles but full-blown accounts of essence in
terms of grounding or vice versa. deRosset (2013) and Gorman (2014)
propose accounts of essence in terms of grounding. (See Zylstra 2018
for critical discussion.) Correia (2013) and Zylstra (2019a) instead
propose accounts of grounding in terms of essence. Finally, some have
proposed accounts of both essence and grounding in terms of some third
item--Fine (2015) does so in terms of constitutively necessary
and sufficient conditions, and Correia and Skiles (2019) in terms of
generalized identity. (See Zylstra 2020 for critical discussion of
each of the above accounts.)


### 4.3 Fundamentality



How are grounding and fundamentality related? Here we focus on
fundamentality with respect to facts, as opposed to, say, entity or
theory fundamentality. There are two general types of fundamentality,
relative and absolute. As for relative fundamentality, the general
idea is that some facts are more fundamental than others. A simple
grounding-theoretic account of relative fundamentality is this: for
each fact among \([P],\) \([P'],\) ... to be more fundamental
than \([Q]\) is for \([P],\) \([P'],\) ... to ground \([Q]\).
Turning to absolute fundamentality, the idea is that some facts are
fundamental *full stop*. On one familiar conception of absolute
fundamentality, to be absolutely fundamental is to enjoy a distinctive
form of *independence* (Bennett 2017: Ch. 5). One way for a
fact to be independent is for it not to be grounded by other facts.
This suggests a simple grounding-theoretic account of absolute
fundamentality: to be absolutely fundamental it to be ungrounded
(Schaffer 2009).



You might think that the above account of relative fundamentality
fails to identify a necessary condition, especially if you assume
that, for any two facts, one of them is more fundamental than the
other or they're equally fundamental. For example, perhaps
[There are hydrogen atoms in Phoenix] is more fundamental than [There
are H2O molecules in Ithaca] even though the former
doesn't ground the latter (Bennett 2017: Ch. 6). (For more
sophisticated characterizations of relative fundamentality that appeal
to grounding, see Bennett 2017: Ch. 6 and Werner 2021.)



Returning to absolute fundamentality, you might worry that the above
account leaves out an important dimension, specifically the fact that
the absolutely fundamental facts are *complete* in the sense
that, since they are the basic building blocks of reality, to describe
them is in some sense to provide a description of everything (Tahko
2018). Note that absolute fundamentality conceived of as involving
both independence and completeness seems to capture the notion of an
unexplained explainer--the absolutely fundamental facts are
independent and therefore unexplained, and these facts are complete
and therefore explain (Bennett 2017: Ch. 5). Looking to the history of
philosophy, we see that fundamental entities are regularly invoked as
a means of meeting certain kinds of explanatory demands, demands that
perhaps only independent entities could meet. This is typically
evidenced by the arguments from vicious infinite regress that are
commonly wielded in defense of them. It's because we need to
explain, for example, why there are any contingent things whatsoever
that God must exist and, importantly, if God weren't the
terminus point of our regress--because independent--then the
problem that God was invoked to solve wouldn't be solved after
all.



With this in mind, we might revise the simple account of absolute
fundamentality above as follows: to be fundamental is to be a member
of some collection of facts, *F*, such that


1. each fact among *F* is both ungrounded and grounds some
fact; and
2. facts among *F* ground all the grounded facts.



We might wish to add further conditions ensuring that *F* is
*minimal* (there is no proper sub-collection of *F* that
grounds all the grounded facts) and *F* is
*unique*--*F* is the only collection that satisfies
these conditions. Another option is to interpret completeness (or
unique minimal completeness) as being characteristic but not
definitional of absolute fundamentality (Bennett 2017: Ch. 5).
(Whether definitional or not, the grounding role that absolutely
fundamental facts play potentially makes the cost of positing such
facts worth paying--see Bliss 2019 for discussion.) Still another
option for the grounding theorist is to be a pluralist about notions
of absolute fundamentality, characterizing independence, completeness,
and perhaps further notions as well such as *ineliminability*,
granting that they might (in special cases) pull apart. (See Raven
2016 for discussion of ineliminability in this context.)