in any other properties and relations from those that are. Call the former properties
and relationsultimate. Is grounding ultimate regardless of whether it is metaphys-
ically primitive 1?
We get different answers depending on whether grounding is a universal or there
are tropes of grounding.
Suppose grounding is a universal. Then there are two important questions about
how grounding relates to itself. First, there is the question about whether the
universal of grounding is itself ultimate. Second, there is the question about the
grounds of groundingfacts. Many proponents of universals includefactsin their
ontology; such entities are conceived as structural complexes whose constituents are
universals and particulars.^17 Consider a given physical fact P that grounds a given
mental fact M. There is also the fact that P grounds M; call this fact G. What grounds
G? Perhaps P alone.^18 Perhaps P and M collectively ground G.^19 Perhaps the essence
of M grounds G.^20 (If we are thinking about grounding as a relation between entities,
what sort of entity is an essence? Fortunately, that question will be discussed in
section 9.4.)
All of these answers have some plausibility, but none of them is clearly relevant to
the question of what grounds the grounding relation itself.Ifall relations are
grounded in facts in which that relation is a constituent, then it is plausible that
what grounds grounding includes what grounds facts about grounding. But if the
constituents of facts are not grounded in facts, then one of the answers to the
question of what grounds grounding facts might be right, while grounding might
nonetheless be an ultimate relation.
Suppose grounding is best treated trope-theoretically. Then strictly speaking there
is no single relation of grounding, but rather there are many tropes of grounding. The
closest approximation to a single relation of grounding is a maximal class of
grounding tropes. And plausibly this maximal class of tropes is grounded in its
elements.^21 What about the tropes of grounding themselves? First, note that most
(^17) Armstrong (1997) is one of the leading proponents of facts construed in this way. See also McDaniel
(2009a). 18
19 This is the view defended by Bennett (2011a) and deRosset (2013).
Schaffer has suggested to me in personal communication that it is plausible that ground is an internal
relation in the Lewisian sense: that is, grounding never differs between duplicate pairs; this suggests that it
is not merely P and M that collectively ground G, but rather P and M along with their intrinsic natures.
However, as Alex Skiles has pointed out to me, in Schaffer’s (2009) system partial grounding is understood
as a binary relation that takes single entities rather than pluralities as its relata, and hence we could not say
that P and M are collectively partial grounds of G. That said, I take it that Schaffer’s statement of the logical
form of partial grounding is highly negotiable. 20
With respect to fact grounding, a version of this view is defended by Dasgupta (2015); see also Rosen
(2010), Fine (2012a), and Correia (2013) for discussions of several formulations of this kind of view (for
fact grounding). 21
Many proponents of grounding think that sets are grounded in their elements; see, e.g., Schaffer
(2009: 375). For a potentially contrasting view, see Ehring (2011), who holds that tropes get their character
from the natural classes of which they are members. This suggests that, for tropes, the class is prior to the
member.