explorations to be definitive in advance of furtherfirst-order metaphysical inquiry.
This will hopefully become clearer in what follows.
Regardless, it is fair to ask the proponents of grounding to state how they think
that the relation works. Fortunately, they have been more than happy to oblige. One
split among proponents of ground is over whether talk of grounding is appropriately
cashed out in terms of a grounding predicate or rather in terms of a sentence
operator. Both ways of proceeding are consistent with denying that there is a relation
of grounding. Perhaps not all predicates correspond to properties or relations; Lowe
(2004) discusses what he calls“formal ontological relations,”which despite the name
are not entities in his ontology, and Sider (2009) makes room for metaphysically
fundamental locutions to which no entity corresponds. Both ways of proceeding are
also consistent with affirming that there is a grounding relation. Of course, a
predicate might correspond to an entity; I think they always do unless paradox
threatens, though many of these will be mere beings by courtesy. And a sentence
operator might have as its semantic value a relation between propositions, although
again such a relation might be a mere being by courtesy.^10 (What this discussion
already indicates is that an ontological pluralist will care not merely about whether
grounding is an entity; she will also care about which way grounding is an entity.
More on this in section 8.2.)
Related to thefirst split is the question of the extent of ground. Some proponents of
ground, most notably Schaffer (2009), hold that it is a relation that can relate entities
regardless of ontological category. This position seems to demand the use of a
grounding predicate rather than an operator; if ground talk is regimented via an
operator, then at most grounding is a relation between entities with propositional
structure. A pluralist about ground might accept both relations in her ontology. But
for now let us consider monistic views on which these are in apparent competition.
We’ll begin with a discussion of Schaffer in section 8.2, and then turn to a discussion
of ground as a more restricted relation in section 8.3. We’ll directly compare the two
views in section 8.5.
There are other issues that separate proponents of ground. One concerns the
“internality”of ground: ifxgroundsy, doesxgroundyin every world in which
they both exist? Another concerns the“logic”of ground: is it a transitive, asymmetric
relation, or does it have a more complex logical structure? Neither of these questions
will be extensively discussed in what follows, but when the particular theories that
I will focus on imply answers to these questions, I will note this.
(^10) Two small points. First, many proponents of grounding say that it is a relation between facts rather
than propositions per se, although perhaps facts are just true propositions. By way of contrast, in McDaniel
(2015), I explore a view in which a kind of grounding, which I callinvirtuation, is a relation between
propositions of all truth-values. (This relation is not identical with what Fine (2012a) calls“non-factive
grounding.”) Second, recall Mulligan’s (2010: 583, fn. 24) view, according to which the correlates of
operators are not properties or relations but rather things from a distinct ontological category.