Chapter 2: The Explananda
3.1 Grounding
3.1.1 Relation or Sentential Operator?
There are two putatively competing camps amongst those theorists interested in grounding: those who think of grounding as a sentential operator, and those who think of grounding in an ontologically robust way, as a relation that exists in the world, and that obtains between worldly entities. Here I will argue that there is, in fact, no competition between these views. Those in the former camp are in the business of providing a rigorous formalisation of the notion of metaphysical explanation introduced
50 There are several projects that seek to provide a reductive account of grounding. For instance, Wilson
(forthcoming) seeks to do so in terms of the truth of certain counterpossible claims, while Tallant (2015) seeks to do so in terms of some combination of Lowe’s (2010) relations of Rigid Existential Dependence and Identity Dependence. Grounding, so reduced, is not my target here.
51 Grounding is transitive just in case whenever A grounds B and B grounds C, A grounds C. I have
60 relation which such explanations track. Insofar as there is tension between these two
projects, it is insubstantial tension about which notion should be called ‘grounding’. As the notion of grounding with which I take issue is the relation view, I will use ‘grounding’ to pick out that relation. The sentential operator view is quite compatible with a
grounding-free explanation of the priority intuitions, and I will say little about it beyond this subsection.
To see how the dispute between these camps came about, note that claims about what grounds what, what is prior to what, and indeed, what metaphysically explains what, come in a variety of linguistic forms. While our illustrative examples of priority intuitions were uniformly expressed using ‘because’ to help make clear why some think they are intuitions about explanation, the more extensive list of these intuitions (in footnote 25) includes locutions of ‘grounds’, ‘because’, ‘in virtue of’ and others besides. While on the one hand we can surely translate between these locutions, on the other hand they have different syntactic implications. As Trogdon (2013a:5) points out, “On the syntactical surface level, the verb ‘ground’ is a relational predicate, ‘because’ is a sentential
connective, and ‘in virtue of’ is a sentence-forming operator that requires a sentence as its first argument and a singular term as its second.”
One camp of grounding theorists takes the relational predicate interpretation to be the canonical form of grounding claims. These include Schaffer (2009), Cameron (2008) Audi (2012a), Rodriguez-Pereyra (2005), Raven (2012) and Trogdon (ms-a). The other camp views the sentential operator interpretation as canonical. These include Fine (2012), Correia (2005), Dasgupta (2014) and Litland (2013). Yet, this is not merely a disagreement about how best to formulate the sentences that express grounding claims. It is a disagreement about what we are talking about when we talk of grounding. Those who defend the relation view are ontologically committed to both the relation of grounding and the relata it relates. Those who defend the sentential operator view think of grounding as a non-truth-functional sentential connective, which takes
arguments/sentences on either side. They need take no ontological stand.
Fine, for example, thinks that “the notion of ground should be expressed by means of a sentential operator, connecting the sentences that state the ground to the sentence that states what is grounded” (2012:12). The view is not, as stressed by Trogdon (2013a),
61 on whether there is a grounding relation at all. A putative advantage of the view is its
ontological neutrality. The thought is that one can accept, for example, that ‘{Socrates} exists because Socrates exists’ is true,52 without ontological commitment to philosophers,
sets or the grounding relation. Of course, it remains open to a defender of the operator view to believe in philosophers and sets and some relation obtaining between the two. Indeed, the relation Fine (1994) calls ‘ontological dependence’ very much resembles the relation view of grounding. But, importantly, no such commitment is implied by a commitment to the truth of the grounding claim, and sentential operator theories of grounding are solely focussed on the elucidation of logical relationships between grounding claims.
Trogdon (2013a) notes that there is a parallel dispute in the truthmaking literature. Rodriguez-Pereyra (2005) has argued that the correct form of truthmaking claims is that of a relation between the truth of a proposition and an entity, its truthmaker. Consider ‘<the rose is red> is true in virtue of the redness of the rose’. This expression of
truthmaking implies that there is a thing which is the redness of the rose, which is being reified in order to stand in a relation of truthmaking to the proposition. On the other side, Hornsby (2005) argues that the correct form of truthmaking claims resembles ‘<the rose is red> is true because the rose is red’, where ‘because’ is a sentential operator and there is no implicit commitment to the redness of the rose existing, and standing in a worldly relation to the truth of the proposition. The former understanding seems more in the spirit of Armstrong’s (2004) truthmaker theory, where the existence of things—in his case states of affairs—making propositions true is the name of the game. However, those wary of buying into additional ontology may think that the operator understanding is sufficient to explain the truth of the proposition.53
Returning to grounding, the relation and sentential operator theories connect to metaphysical explanation in very different ways. According to the relation view,
grounding is a candidate determination relation that our metaphysical explanations might (and, if it exists, hopefully do) track, in the sense described in §2.5. I will evaluate the resultant theories in §3.4 and §3.5. In contrast, the sentential operator view resembles the notion of metaphysical explanation itself (§2.3). Thus, a natural view to have is that
52 Sentential operator theorists also express such claims using the phrase ‘in virtue of’ (see Fine, 2012). 53 See Correia (2011) and Schnieder (2006).
62 grounding relations. With this in mind, the supposed tension between the views
evaporates.
Rodriguez-Pereyra (2005) appeals to Ruben’s (1990) ontic view of explanation according to which some worldly relation is required to underwrite metaphysical explanations in order to push those in the operator camp over into the relation camp. On the one hand, this resembles a mere semantic quibble: Rodriguez-Pereyra would prefer to use the term ‘grounding’ to talk about worldly relations. On the other hand, this argument brings us to where I believe the real action is. In other words, the debate should revolve around whether there are grounding relations, in re, that back our metaphysical explanations. The sentential operator view, then, is not the target of my criticism.
In sum, I think it is a mistake to conceive of the sentential operator and relation views as competing theories of the same thing, as this implies that if we go with one, we must scrap the other. I think that both the sentential operator and relation views are good theories of something. Thus I endorse Schaffer’s (2016) proposal of reconciliation. That is, while the relation theorists are trying to give an account of the ontology that
underpins metaphysical explanations, the operator theorists are attempting to formalise the logic of the metaphysical explanations themselves. Thus ‘grounding’, as expressed by the operator theorists, corresponds with ‘metaphysical explanation’ as I am using the term. This sits well with Dasgupta’s claim that in his use, “the term, ‘ground’ is an
explanatory notion: to say that X grounds Y just is to say that X explains Y, in a particular
sense of ‘explains’.” (2014:3).
It should be noted that Schaffer himself rejects reconciliation, as he believes that there are no distinctively metaphysical explanations for the operator theorists to be theorising about—just explanations, backed by different relations (2016). While
Schaffer’s argument may hit home against the sentential operator theory (and against the notion of metaphysical explanation), it does little to impact the dialectic in this thesis. Perhaps the explanations I call metaphysical explanations are not separable from the remaining explanations (most notably, for instance, the scientific explanations). It is still an open question how to account for the priority intuitions. Furthermore, if the goal is to vindicate these intuitions in a way consistent with a general theory of explanation—as
63 preferred views, which are continuous with (indeed, plausibly extensions of) theories
used in the context of scientific explanation.
So, I see the efforts of Fine (2012) and Correia (2005) as attempts to provide a logical system which coherently regiments our intuitions about metaphysical explanations (though one might be sceptical that our priority intuitions exhibit some of the features these authors build into their theories: transitivity, for example. See §3.4). This
regimentation is compatible with a grounding-free explanation of the priority intuitions, and indeed a grounding-free account of metaphysical explanation. That such a
systematisation of these explanations can be developed bodes well for the intelligibility of the notion of metaphysical explanation. As argued by Raven (2012), a successful
regimentation of a theory goes some way towards vindicating the theory itself. Going forward, I will assume there is a well-defined class of metaphysical explanations. When it comes to divvying up the terminology, I will use ‘grounding’ to indicate the worldly relation that, according to some, backs these metaphysical
explanations. With our focus now solely on grounding relations, we now move on to say a little more about these relations.