The Atlas of Reality

by Robert C. Koons,Timothy Pickavance

  3.3 Relation between Grounding and Ontological Dependence

  Fine (2012a) distinguishes between grounding and ontological dependence. Grounding is an explanatory relation between facts. Ontological dependence is a relation between entities or things: x is dependent on y iff y is contained in the essence of x.

  3.3.1 Two kinds of essence

  Historically, philosophers have talked about the essence of things in at least two different ways. For example, Aristotle insisted that, for each thing, there is a unique answer to the question: What sort of thing is this? This was later translated into the Latin word quidditas, for the what-ness of a thing. For Aristotelians, two things that belong to the same fundamental, natural kinds have the same quiddity or essence. All human beings have the common essence of humanity. All differences between individual human beings are inessential or “accidental” (per accidens, in Latin).

  Other philosophers, like Duns Scotus or Gottfried Leibniz, have spoken in terms of the individual essences of particular things. On this conception of essence, every particular thing has its own unique essence, the what-it-is-to-be that particular thing. Scotus introduced the Latin term haecceitas or “thisness” for such individual essences. Socrates has one haecceity, and Plato necessarily has another, since distinct things must have distinct individual essences (see Section 9.3 for more on haecceities).

  So, we might distinguish between the quiddity of x (x's species, a nature or what-it-is-to-be x that is shared by things with the same form), and the haecceity of x (the thisness of x, what it is to be x in particular). Quiddities are shareable; haecceities are not. If so, we should distinguish between two different kinds of ontological dependence: quidditistic ontological dependence (‘q-dependence’) and haecceitistic ontological dependence (‘h-dependence’). Socrates is q-dependent on his animality and his rationality, and on his soul and body, but not on his parents, while he might be h-dependent on his parents and on the circumstances of his conception, if we assume that these particular parents and the particular event of his conception are in some sense essential to Socrates' particular individuality or identity. In fact, many metaphysicians (following Kripke 1980) subscribe to what is called origins essentialism, meaning that a thing's particular origin is essential to its individual identity (i.e., part of its haecceity).

  So, if we believe in origins essentialism, particular events (like conceptions) might be included in the haecceities of particular things, but not in their quiddities (although the property of having some conception-event or other might be included in the quiddity).

  3.3.2 Circular dependency?

  Fine (1994b) suggests that, while grounding is always asymmetric, two entities might be ontologically dependent on each other. Each of two identical twins might be h-dependent on the other, in the sense that the haecceity or thisness of each includes the other. If Sam and Dan are twins, it might be essential to Sam that he have Dan as a twin, and vice versa. This wouldn't require any vicious circularity, since Sam is a part of the haecceitistic essence of Dan, not of Dan himself. We don't have to suppose that a thing's essence (quiddity or haecceity) is literally a part of it (although we will consider these possibilities in Chapter 9, on particulars).

  Can there be circles of q-dependency? Quite possibly. For example, it seems reasonable to suppose that the properties of being a male member of a species and being a female member of that species are interdependent: to be male is to have some sort of potential to mate with females, and vice versa. Similarly, if two species exist in an essential symbiosis with each other, then it might be that each species is part of the definition of the other.

  Although there can be circles of ontological dependency, grounding is asymmetric. So, we shouldn't say that A ontologically depends on B if and only if A's existence is grounded in B's existence. The existence of A can be fundamental and so not grounded in the existence of B, even if the individual essence of A somehow includes B. To return to our identical twins, Sam's existence is not grounded in Dan's existence, even though Sam's identity essentially involves Dan. Similarly, q-dependency between two species does not entail that the existence of the one species is even partly grounded in the existence of the other. The two species might be causally interdependent over time, but the existence of the members of one species would not be grounded in the existence of members of the other.

  Thus, there must be a real difference between ontological dependence and existential grounding, as Fine assumed.

  3.3.3 Two kinds of fundamental entity

  So, we must distinguish between two kinds of fundamental entities, namely, those whose existence is ungrounded, and those which are not ontologically dependent on any other entity. These are, respectively, G-fundamental and O-fundamental entities.

  Def D3.5 G-Fundamentality. An entity x is G-fundamental if the existence of x is ungrounded.

  Def D3.6 O-Fundamentality. An entity x is O-fundamental if and only if neither the quiddity (generic essence) nor the haecceity (individual essence) of x contains any entity other than x itself.

  Something that isn't G-fundamental will be G-derivative, and, similarly, something that isn't O-fundamental will be O-derivative.

  Can we say that if A ontologically depends on B, then B cannot be wholly entitively grounded in A? Is it impossible for an entitive fundans to be ontologically dependent on its corresponding fundata? It is natural to think, at least at first glance, that if both entitive grounding and ontological dependence exist in a particular case, the two dependency relations must run in the same direction. However, one might think that if B is wholly grounded in A, then A's essence must somehow contain B, as a natural emanation or effluence from A. Otherwise, how could A, all by itself, be a complete explanation of B? If that were so, then whenever A grounds B, A would ontologically depend on B, and not vice versa. If so, then the ground or fundans would depend ontologically on the fundatum, even though the existence and character of the fundatum is wholly grounded in the existence and character of the fundans. The two dependency relations would run in opposite directions!

  But, in fact, this can't be right. Our first intuition was the correct one. The two forms of dependency (grounding and ontological dependency) must run in the same direction. In many cases, it is the nature or essence of the fundatum, not that of the fundans, that explains the grounding relation. After all, p and q need “know nothing of” conjunction in order to ground (p & q), to use Fine's phrase. If this is right, we have found an important relationship between G-fundamental and O-fundamental entities:

  3.3T O-Fundamentality Entails G-Fundamentality. Necessarily, all O-fundamental entities are also G-fundamental.

  O-Fundamentality Entails G-Fundamentality itself entails that all G-derivative entities are O-derivative.

  For another example of this relationship, the existence of a singleton set like {Socrates} seems to be both grounded in the existence of its member, Socrates, and to be ontologically dependent on him.

  But how is this possible? How can the existence of the member all by itself explain the existence of a singleton set, if we must appeal to the essence of the fundatum in justifying the explanation? How can the explanation relation itself depend on the nature of the very thing to be explained? Perhaps we should say instead that singletons are only partly grounded in their members, with the set-hood and membership properties somehow contained implicitly in the other part of the ground. We might need to include some set-making principle in the ground of the existence of the set.

  Let's consider one more time the relation between Socrates and his singleton, {Socrates}. It seems that the existence and character of {Socrates} is at least partially grounded in Socrates himself. It's also true that the individual essence or haecceity of {Socrates} somehow contains or involves Socrates himself, and so we have both kinds of dependency running in the same direction. However, Socrates seems so “know nothing” of the existence of sets. We have to combine Socrates with some kind of singleton-producing principle in order
to have a complete ground of the existence and character of the set {Socrates}. That is, we seem to need something prior in existence to {Socrates} that explains the nature of that set, given the existence of Socrates.

  Let's consider the relations between the counting (or natural) numbers. Suppose we take 1 to be the first number (for present purposes, it wouldn't matter if we counted 0 or 2 to be the first number). It would seem that it is of the very essence of 2 to be the successor of 1 (in this case, it is the individual essence or haecceity of 2 that seems relevant). So, 2 is ontologically dependent on 1. Similarly, it does seem that the existence of 2 is grounded in the existence of 1, and not vice versa. Of course, we might worry that the nature of 1 does not all by itself explain why 1 has a successor at all. But, perhaps we should say that 1's having the generic nature of a counting number does explain its having a successor—it may well be of the very essence of counting numbers to have successors. In any case, it seems that we have a clear case of ontological grounding here.

  In contrast, consider a case of the grounding of a disjunction. Let's suppose that Austin is weird. This fact would seem to ground the disjunctive fact that either Austin is weird or 0 = 1. In other words, the fact corresponding to (3) grounds the fact corresponding to (4):

  (3) Austin is weird.

  (4) Either Austin is weird or 0 = 1.

  However, there is no ontological dependency of any components of (4) on components in (3). In this case, it is the nature of the disjunctive element (the truth-function corresponding to either…or…) in (4) that explains the grounding relation between (3) and (4). However, this disjunctive element is not an entity “in the world”: it is simply part of the proposition whose truth is being explained. Thus, what we are really doing is explaining the truth of a disjunctive proposition in terms of the truth of one of its disjuncts. Such grounding of truth doesn't seem to require any ontological dependence of the fundatum on the fundans. Instead, it is the logical essence of the proposition whose truth is to be explained that provides the motive force for the grounding explanation.

  It seems that we can distinguish two importantly different cases of grounding: (1) those in which we explain the truth of one proposition in terms of the truth of another, appealing to the nature of the constituents of both propositions to explain the connection, and (2) those in which we explain facts about one kind of entity in the world in terms of one or more other entities or facts, appealing to the nature of the grounded entity in explaining its ontological dependence on some element or element in the fundans. The first is conceptual or logical grounding, while the second corresponds to what we will call extra-conceptual grounding. We look at this distinction in more detail in Section 3.4.

  3.3.4 Grounding and essence

  Rosen (2010: 131) has argued that all grounding facts are generalizable. That is, all grounding facts are instances of some general rule or other. We could put this point in terms of formality. Whenever one fact, say, the fact that p, grounds another fact, the fact that q, the two corresponding propositions, p and q, instantiate general forms, Φ and Ψ, respectively, of such a kind that any fact that instantiates Φ grounds a fact that instantiates Ψ. This is Formality of Grounding:

  3.4T.1 Formality of Grounding. Whenever p grounds q, there exist forms Φ and Ψ such that (i) for some x, p = Φ(x) and q = Ψ(x), and (ii) for all true propositions r and s such that for some y, r is Φ(y) and s is Ψ(y), the fact that r grounds the fact that s.

  In addition, Rosen proposes that these general rules are themselves derivable from facts about the essences of the constituents of the two facts.

  3.4T.2 Mediation of Grounding by Essence. Every grounding fact of form (ii) (in Formality of Grounding) is itself grounded in or derivable from some essential truths about the constituents of Φ and Ψ.

  Can we define grounding in terms of essence (Fine 2012a: 75)?

  3.6T.1 Grounding-Essence Correspondence. The fact that p grounds the fact that q if and only if (i) (p & q), and (ii) some generalization of the form For all x, if p(x), then q(x) follows logically from the essences of p and q, together with the essences of things that the facts p and q contain.

  As Fine notes, there are some problems with this suggestion. First, it won't enable us to distinguish between (i) cases where one fact is grounded by a plurality of grounds and (ii) cases where one fact is grounded by a single, conjunctive ground. For example, we might want to say that every conjunctive fact of the form (p & q) is grounded (jointly) by the fact that p and the fact that q. We don't want to say that the fact that (p & q) is grounded in the fact that (p & q), even though it is certainly true that If (p & q), then (p & q) does follow from the essence of the proposition (p & q). Still, one might get around this by adding the condition that the fundatum and fundans can't be exactly the same fact. Then, we could expand the condition to include plural grounds:

  3.5T.2 Plural Grounding-Essence Correspondence. The facts that p1, that p2,…, and that pn jointly ground the fact that q if and only if (i) p1 & p2 &… & pn & q; (ii) some generalization of the form For all x, if p1(x) & p2(x) &…. & pn(x), then q(x) follows logically from the essences of p1, p2,…, pn, and q, together with the essences of things that the facts p and q contain; and (iii) if n = 1, i.e., there is only one grounding fact, then p1 ≠ q.

  Second, Fine argues that Grounding-Essence Correspondence wrongly predicts that (p & p) grounds p. In fact, the problem is more general than this. Grounding-Essence Correspondence predicts that any conjunction of the form (p & q) will ground the fact that p, and that seems wrong. It is rather the case that the conjunctive fact is partly grounded in the facts corresponding to each of its conjuncts. Grounding-Essence Correspondence ignores facts about the relative priority or fundamentality of the two facts.

  However, none of this shows that an essential link might not be a necessary condition of grounding, even if it cannot be a sufficient condition. Thus, we can replace the “if and only if” of Grounding-Essence Correspondence with a simple “only if,” which brings us back to Formality of Grounding and Mediation of Grounding by Essence. It seems that we cannot define grounding in terms of essences, but all grounding relations seem to depend on facts about the essences involved.

  3.4 Conceptual vs. Extra-Conceptual Grounding

  As we saw at the end of Section 3.3.3, we can distinguish between two ways in which grounding can require a link to essences. First, there are those in which it is the truth of one proposition that grounds the truth of a second, due to the essences of the conceptual and logical elements in the two propositions. Second, there are those in which one fact grounds another fact, due to the essences of the (worldly) objects and properties that are constituents of the two facts. Of course, this distinction depends on having some fairly precise notion of both propositions and concepts:

  Def D3.7 Proposition. A proposition is an object or vehicle of thought that represents things as being a certain way and is capable of being true or false.

  Def D3.8 Concept. A concept is a constituent of a proposition or a capacity for thinking propositionally that plays no other role in the world other than as an object or vehicle for thought.

  Philosophers have conceived of propositions in different ways. For example, Bertrand Russell supposed that propositions contain as part the very same properties and objects (like being snowy or Mt. Blanc) that they are about. Gottlob Frege, in contrast, believed that propositions (Gedanke, usually translated ‘thoughts’) contained only modes of presentations (Sinne, or ‘senses’) of such worldly properties and objects. So, on the Fregean view, there are far more concepts in our sense than there are on the Russellian view. Nonetheless, even on the Russellian view there are elemens of propositions (traditionally known as syncategorematic) which are merely conceptual, like the logical connectives corresponding to ‘and’ (conjunction), ‘or’ (disjunction), and ‘not’ (negation), as well as the quantifiers corresponding to ‘all’ or ‘some’.

  We could imagine a hyper-Russellian picture accord
ing to which every element of any proposition is something that also exists in the world beyond the sphere of thought, even disjunction or negation. David Armstrong, for example, believed that the world contains conjunctive facts, corresponding to the ‘and’ operation on propositions. Even so, Armstrong was not a hyper-Russellian, because he thought there were no disjunctive or general facts. For true hyper-Russellians, there might be little or no room for merely conceptual grounding. For the rest, however, the distinction is a significant one.

  Some cases of grounding seem clearly conceptual, like the grounding of the truth of conjunctions, disjunctions, and general propositions. Other cases seem to be cases of extra-conceptual dependence, like the relations between entities and singletons.

  3.6T Conceptual-Grounding to Essence Link. The truth of the proposition p grounds the truth of the proposition q only if p and q are both true, and if p, then q follows logically from the essences of the conceptual elements of the propositions p and q.

  The distinction between conceptual and extra-conceptual grounding turns on a very subtle difference. Compare the following two claims, where ‘[Fa]’ abbreviates the proposition a is F and ‘[Ga]’ abbreviates a is G:

  (5) [Fa]'s truth is grounded in [Ga]'s truth.

  (6) [Fa]'s truth is grounded in a's being F, and a's being F is grounded in a's being G.

  In both cases, the truth of [Ga] is in some sense prior to, more fundamental than the truth of [Fa]. In the first case, the dependency is propositional or conceptual, in the latter case, extra-conceptual. To distinguish between the two, we have to look carefully at what licenses or justifies the explanatory connection between a is F and a is G: is it licensed by the essence of the property designated by ‘___is F’ or the concept the predicate expresses? Is the essence involved in something in the mind-independent world, or is it merely in the mind? We will examine this question in much more detail in Chapters 7 and 8, where we will see that this distinction between properties and concepts is very important for most metaphysicians but is completely absent for others (in particular, for those who adopt the position of Concept Nominalism).