Metaphysical Grounds and Essence

Metaphysical Grounds and Essence

Fabrice Correia

Is it possible to provide an account of metaphysical grounding in terms of essence? E. J. Lowe (2009) addresses a similar question about truth-making and essence, and makes a suggestion which points towards a positive answer. Kit Fine (2012) addresses the origi-nal question and answers negatively. I argue that the prospects for an account of metaphysical grounding in terms of essence are not as bad as one might have thought.

1. IntroductionPhilosophers traditionally distinguish between the essential and the accidental. A feature is said to be essential to a thing if it pertains to what the thing is, in a specifically metaphysical sense; and a feature is said to be accidental if it is a feature the thing has, but which merely characterises how the thing is, without telling us anything about what it is.

The concept of metaphysical grounding (hereafter, simply ‘ground-ing’) has perhaps been less visible than the concept of essence in the history of philosophy, but it has constantly been used. A fact is grounded in other facts provided that the former obtains in virtue of the latter, where ‘in virtue of ’ is understood as having metaphysical force. The concept of grounding is involved in many important phil-osophical theses, like for instance the following:1

Mental facts obtain in virtue of neurophysiological facts;

Dispositional properties are grounded in categorical proper-ties;

1 See e.g. Fine 2001, Correia 2005, Schnieder 2006a and 2006b, Correia 2010 and Rosen 2010.

Metaphysical Grounds and Essence, in M. Hoeltje, B. Schnieder and A. Steinberg (eds.), Varieties of Dependence. Ontological Dependence, Grounding, Supervenience, Response-Dependence, Basic Philosophical Concepts Series, München, Philosophia, 2013, 271—96.

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Legal facts are grounded in non-legal, e.g. social, facts;

Morally wrong acts are wrong in virtue of non-moral facts;

Determinables are exemplified in virtue of corresponding de-terminates being exemplified;

Universals exist in virtue of their having exemplifiers;

A whole exists in virtue of the fact that its parts exist and are arranged in such and such a way;

Every truth is made true, i.e. given any truth, there is an entity x such that this truth is true in virtue of the existence of x.

According to many, the concept of essence is central to metaphysics, insofar as one of the main tasks of the metaphysician is to identify the essential features of all things. Some also take the concept of grounding to be equally central, and hold that one of the main tasks of the metaphysician is to determine what grounds what. Along this line of thought is the venerable tradition which holds that one of the general aims of metaphysics is to unveil the layered structure of reali-ty, which consists of a level of basic, i.e. ungrounded, facts, and a (perhaps itself structured) level of facts grounded in the former facts.2

Granted that both essence and grounding are legitimate concepts, there arises the question how each is to be understood, and how they are related. Each concept has sometimes been characterised in terms of modality (and truth-functions). Thus, for instance, it has been suggested that for a feature to be essential to a given thing is for it to be the case that as a matter of metaphysical necessity, the thing has that feature if it exists. And a natural thought is that for a fact to be grounded in other facts is for it to be the case (i) that all the latter facts obtain, and (ii) that as a matter of metaphysical necessity, the former fact obtains if the latter facts do.

2 See e.g. Fine 2001, and also Schaffer 2009 (although Schaffer takes enti-ties of any kind, not just facts, to be capable of being tied by the relation of grounding).

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In recent years, many have voiced scepticism about the availability of such accounts of essence and grounding.3 Consider for instance the accounts just mentioned. Holding both accounts at once yields trou-ble. For if we take both of them to be correct, we will have to say that whenever a feature F is essential to a given existing thing x, the fact that x has F is grounded in the fact that x exists. Yet, it may be doubted that the fact that Socrates is human obtains in virtue of the fact that he exists, even on the assumption that Socrates is essentially human. Each account is also problematic in isolation. As Kit Fine (1994) argues, although it is plausible to say that as a matter of meta-physical necessity, Socrates belongs to {Socrates} if Socrates exists, we don’t want to say that it is essential to Socrates that he belongs to {Socrates}. And although it is plausible to say that as a matter of metaphysical necessity, the fact that Socrates exists obtains if the fact that {Socrates} exists does, we don’t want to say that the former fact obtains in virtue of the latter fact. These are objections to particular modal accounts of essence and grounding. But other such accounts are subject to similar objections, and it is reasonable to think that all accounts of that sort are bound to fail.

Granted that no satisfactory modal account of essence or grounding can be found, what are the available options? A fairly liberal move, which we may dub ‘double primitivism’, is to take both notions to be primitive. The view is forcefully expounded in Fine 2012 (§11 on es-sence and ground):

I think it should be recognized that there are two fundamental-ly different types of explanation. One is of identity, or of what something is; and the other is of truth, or of how things are. It is natural to want to reduce them to a common denominator – to see explanations of identity as a special kind of explanation of truth or to see explanations of truth as a special kind of explanation of identity or to see them in some other way as in-stances of a single form of explanation. But this strikes me as a mistake.

3 On essence, see e.g. Dunn 1990 and Fine 1994, and on grounding e.g. Correia 2005 and Rosen 2010.

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And it seems to me that [it is an error to attempt] to assimilate or unify the concepts of essence and ground. The two con-cepts work together in holding up the edifice of metaphysics; and it is only by keeping them separate that we can properly appreciate what each is on its own and what they are capable of doing together.

Obviously, any ‘common denominator’ view would be better than double primitivism insofar as ideological economy is concerned. In this paper I want to argue that the prospects for an account of grounding in terms of essence – one of the ‘common denominator’ views mentioned by Fine – are not as bad as one might have thought.

2. Grammatical and Semantical Points The concept of truth is sometimes expressed by means of a predi-cate (in English, typically ‘is true’) and sometimes by means of a sen-tential operator (in English, typically ‘it is true that’). The same goes for the concept of grounding. A widely used predicate for grounding is (without surprise) ‘is grounded in’, and quite often people use the sentential operator ‘because’ in order to express the concept.

Simple claims of ground formulated with the help of ‘is grounded in’ typically take the form:4

Pred f is grounded in f1, f2, …,

where ‘f1, f2, …’ is a list of one or more singular terms for facts. This is the mode of expression I previously used in the informal presenta-tion of the concept. The reason why it is allowed to fill in the second position of the predicate with a list of several terms is that it is thought – correctly in my opinion – that room should be left for the view that there are cases where several facts together ground a fur-ther fact, without there being a fact doing the job alone. Thus, it is plausible to hold that the conjunctive fact that Geneva is in Switzer-land and Rubí is in Catalonia is grounded in two facts, namely the fact that Geneva is in Switzerland and the fact that Rubí is in Catalonia,

4 What follows in this section substantially overlaps section 1.1 of Correia 2010, which contains further material. Also relevant is section 1.2 of the same paper.


while one may deny that there is a single fact which, alone, grounds the conjunctive fact.

Correspondingly, simple claims of ground formulated with the help of the operator typically take the following form:

OP p because p1, p2, …,

where ‘p1, p2, …’ is a list of one or more sentences. Notice that ‘be-cause’ here is used in a way which diverges from its common use in English, insofar as (i) its second position can be filled in with a list of several sentences, and (ii) it is intended to express a notion of com-plete explanation in all cases – i.e. ‘p because p1, p2, …’ is taken to entail ‘its being the case that p is fully explained by its being the case that p1, its being the case that p2, …’.

An alternative predicational view is that the relata of the grounding relation are propositions rather than facts. In the mouth of some phi-losophers ‘fact’ and ‘true proposition’ mean the same, but here I think of propositions as entities which are conceptual in nature (like e.g. Fregean thoughts) and of facts as worldly entities (like e.g. Arm-strongian states of affairs).5 The difference between the two views about the nature of the relata of the grounding relation will not be important in the present context, and I will accordingly leave it aside. For the sake of definiteness, I will exclusively speak of grounding ties between facts. Following a standard notational convention, I will use ‘[p]’ as short for ‘the fact that p’.

For those who do not countenance facts or other entities capable of being the relata of a predicate for grounding, only the operational mode of formulation will be available as a mode of expression to be taken at face value. In contrast, if one countenances such entities, say facts, one will have both modes of expression at hand. For starting with a predicate for grounding over facts, one can define a sentential operator as follows:

p because p1, p2, … iffdf [p] is grounded in [p1], [p2], …,

5 On this account, ‘Russellian propositions’ like the one composed of Socrates and the property of being human do not count as propositions; they (or at least, those which are deemed ‘true’ by Russellians) may indeed be viewed as facts in my sense.

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and starting with a sentential operator one can define a predicate in the following way:

[p] is grounded in [p1], [p2], … iffdf p because p1, p2, ….

In this case, there arises the question which mode of formulation is more basic. I will leave this question aside, as well as the question whether facts or other suitable entities should be countenanced. As we shall see, unlike the difference between taking facts and taking propositions to be the relata of the grounding relation, the difference between the two modes of expression matters in the present context. I will call those who reject facts ‘anti-factualists’ and their opponents ‘factualists’. And I will call those factualists who take the basic mode of formulation to be predicational ‘predicationalists’ and those who take it to be operational ‘operationalists’.

3. The Simple Accounts Let a be my laptop, b be a red ball, a+b be the mereological fusion of a and b, and {a, b} be the set whose sole members are a and b.

Consider first the following list of putative cases of grounding ties:

(1) [a+b exists] is grounded in [a exists], [b exists];

(2) [{a, b} exists] is grounded in [a exists], [b exists];

(3) [b is a red ball] is grounded in [b is red], [b is a ball];

(4) [The proposition that b is red is true] is grounded in [b is red].

Then consider the following list of essentialist claims:

It is part of the nature of [a+b exists] that it obtains if both [a exists] and [b exists] do;

It is part of the nature of [{a, b} exists] that it obtains if both [a exists] and [b exists] do;

It is part of the nature of [b is a red ball] that it obtains if both [b is red] and [b is a ball] do;

It is part of the nature of [the proposition that b is red is true] that it obtains if [b is red] does.


It seems to me that many of those who would take items from the first list to be true would also take the corresponding items from the second list to be true (barring a negative attitude regarding the con-cept of essence). And I suspect that some among them would take the following account of grounding in terms of essence to be partic-ularly attractive (here and throughout the rest of the paper I use ‘--- → ...’ for ‘if ---, then ...’):

SPRED f is grounded in f1, f2, … ↔df. (i) f1 obtains ∧ f2 obtains ∧ …, and (ii) It is part of the nature of f that: f1 obtains ∧ f2 obtains ∧ … → f obtains.

I myself toyed with this account in the past before getting convinced that it is problematic.

A similar account can be formulated if the target concept is ex-pressed by means of a sentential operator rather than by means of a predicate:

SOP p because p1, p2, … ↔df. (i) p1 ∧ p2 ∧ …, and (ii) It is part of what it is for it to be the case that p that: p1 ∧ p2 ∧ … → p.

In contrast with (SPRED), (SOP) is formulated with the help of an un-common essentialist notion. The most common notion of essence is the notion of what a given thing – e.g. Mont Blanc, Socrates, or the number 7 – is. This is the notion alluded to in the introduction to this paper. A less common notion is the notion of what it is to be such and such – e.g. a mountain, human, or prime. An even less common notion is the one at work in (SOP), i.e. the notion of what it is for it to be the case that blah – e.g. what it is for it to be the case that Mont Blanc is a mountain, what it is for it to be the case that Socrates is human, or what it is for it to be the case that 7 is prime. I have argued elsewhere (2006) that the second notion (which I dubbed ‘generic’) cannot be reduced to the first (which I dubbed ‘objectual’), in par-ticular that ‘what it is to F’ cannot be understood as ‘what the proper-ty of being F is’ and the likes. Likewise, I think that the third notion – which we may dub ‘alethic’ – cannot be reduced to the first, and in particular that ‘what it is for it to be the case that p’ cannot be under-

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stood as ‘what the proposition that p is’. I am aware that some will be sceptical about the third notion (and probably most of them also about the second), but I will not here enter into a debate. 6

(SPRED) and (SOP) are intended to be accounts of the most basic con-cept of grounding. One can think of other such accounts, similar to (SPRED) and (SOP), namely:

S′OP p because p1, p2, … ↔df. (i) p1 ∧ p2 ∧ …, and (ii) It is part of the nature of [p] that: p1 ∧ p2 ∧ … → p.

S′′OP p because p1, p2, … ↔df. (i) p1 ∧ p2 ∧ …, and (ii) It is part of the nature of [p] that: [p1] obtains ∧ [p2] ob-tains ∧ … → [p] obtains.

Only (SOP) can be available to an anti-factualist. In the case of factual-ists, we must distinguish between the predicationalists and the opera-tionalists. Only (SPRED) is available to a predicationalist. In contrast, in principle an operationalist can adopt either of (SOP), (S′OP) and (S′′OP). But notice that going for (S′′OP) would be a bit odd. For by accepting the account, one would have the required resources for defining a predicate for grounding, along the lines of (SPRED), and it is not clear how one could then justify the claim that the most basic concept of grounding should be expressed by means of an operator rather than by means of a predicate so defined. Similar considerations may be raised against (S′OP). For the sake of simplicity I will leave both (S′OP) and (S′′OP) aside, but it will nevertheless be clear how the discussion could be extended to these accounts.

Let me turn now to some objections to the proposed accounts. E. J. Lowe (2009) examines an account of truth-making which bears a certain resemblance to the proposed accounts of grounding, and raises an objection against the former which can be raised, mutatis mutandis, against the latter. The account of truth-making runs as fol-lows:

6 In the context of discussing the connections between essence and grounding, Fine (2012, n23) stresses that ‘there is something to be said’ in favour of the concept of alethic essence.


TM The proposition that p is made true by x ↔df. (i) x exists, and (ii) It is part of the nature of the proposition that p that: x exists → the proposition that p is true.

Lowe’s objection to (TM) consists in proposing a counterexample to the left-to-right direction of the bi-conditional (pp. 213–4). Consider red ball b and the redness trope t which inheres in b. It is plausible to say – and many friends of truth-making would be willing to say – that the proposition that b is red is made true by t.7 If this is taken for granted, then by (TM) we should conclude that it is part of the na-ture of that proposition that it is true if t exists. But according to Lowe, this conclusion is problematic. For the proposition could exist without the trope, while – Lowe argues – nothing can be essentially dependent on (i.e. have as part of its essence a relation to) something without which it could exist.

The objection can be turned in an obvious way into an objection to (SPRED). It is perhaps plausible to say that:

(a) [b is red] is grounded in [t exists].

Taking this and (SPRED) for granted, we must say that it is part of the nature of [b is red] that it obtains if [t exists] obtains, and therefore that the former fact is essentially dependent upon the latter. But granted that [t exists] could not exist without t while [b is red] could, [b is red] could exist without [t exists], and we face the same problem as above.

One can also indirectly extract from Fine (2012) two further candi-date counterexamples to the left-to-right direction of (SPRED). The following two claims are plausible:

(b) [Someone is a philosopher] is grounded in [Socrates is a philos-opher];

(c) [b is coloured] is grounded in [b is red].

By (SPRED), the first claim entails that [someone is a philosopher] is essentially dependent upon [Socrates is a philosopher], and the sec-ond claim that [b is coloured] is essentially dependent upon [b is red].

7 See Mulligan, Simons and Smith 1984.

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But [Socrates is a philosopher] is essentially dependent upon Socrates and [b is red] upon the colour red, and so by (SPRED) and the transitivi-ty of essential dependence, [someone is a philosopher] is essentially dependent upon Socrates and [b is coloured] upon the colour red. Yet, the objection goes, there are no such dependencies. Fine puts it in a colourful way by saying that [someone is a philosopher] ‘knows nothing’ of Socrates, and likewise that [b is coloured] ‘knows nothing of ’ specific colours.

Unlike (a)–(c), claims (1)–(4) above cannot be used to provide coun-terexamples to (SPRED) – at any rate, using them to this effect would be much less effective. For in each case, the derived dependencies are quite plausible.

Let us turn to (SOP). Consider the operational statement of ground corresponding to (b):

(b′) Someone is a philosopher because Socrates is a philosopher.

By (SOP), the statement entails that it is part of what it is for it to be the case that someone is a philosopher that someone is a philosopher if Socrates is. Here, no reference is made to [someone is a philoso-pher]. In fact, the expression ‘what it is for it to be the case that someone is a philosopher’ does not contain any sub-expression which has a reference, and accordingly no statement of type ‘x essentially depends upon y’ is entailed. As a consequence, one cannot object to (SOP) as in the previous case via a denial of essential dependency. Yet I guess that a similar kind of objection can be put forward: instead of denying that a given entity is essentially dependent upon Socrates, one will deny that what it is for it to be the case that someone is a philosopher has anything to do with Socrates.

Similar objections to (SOP) can be raised starting from the operational versions of (a) and (c). In contrast, like in the case of (SPRED) the op-erational versions of (1)–(4) cannot be used to provide counterexam-ples to the account.

4. Generalisation Consider again the second objection against (SPRED). Granted that [someone is a philosopher] is grounded in [Socrates is a philosopher],


the account entails that the grounded fact is essentially dependent upon the grounding fact, and this is taken to be problematic. Now, if we grant that there is such a link of grounding, then we will likewise grant that the following generalisation holds as well: [someone is a philosopher] is grounded in any fact of type [so and so is a philoso-pher]. This remark naturally leads one to modify (SPRED) as follows:

GPRED f is grounded in f1, f2, … ↔df. (i) f1 obtains ∧ f2 obtains ∧ …, and (ii) There is a condition Φ such that Φ(f1, f2, …) and it is part of the nature of f that: for all g1, g2, … such that Φ(g1, g2, …), g1 obtains ∧ g2 obtains ∧ … → f obtains.8

An important difference between (GPRED) and (SPRED) is that while in the latter what follows the essentialist operator ‘it is part of the na-ture of f that’ is a singular sentence about f1, f2, …, in the former it is a general sentence which makes no reference to any of these facts (unless condition Φ does make reference to some of them, of course). Lowe’s final suggestion for an essentialist account of truth-making results from such a generalisation move (2009, 215), as well as the essentialist account of grounding presented and criticised by Fine (2012, §11) I will introduce later.

(GPRED) nicely escapes the objections raised against (SPRED). For sup-pose we assume again that (a) holds. Then by the new account we must take the following to hold as well:

There is a condition Φ such that Φ([t exists]) and it is part of the nature of [b is red] that: for all g such that Φ(g), g obtains → [b is red] obtains.

This existential statement follows from the sentence which results from replacing both occurrences of the variable in the embedded open sentence by the condition ‘is the fact [x exists], for some x which is a redness trope inhering in b’, namely the conjunction:

[t exists] is the fact [x exists], for some x which is a redness trope inhering in b

8 Here and below, ‘there is a condition Φ’ is to be understood as a non-objectual quantifier into predicate position.

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∧

It is part of the nature of [b is red] that: for all g such that (g is the fact [x exists], for some x which is a redness trope inhering in b), g obtains → [b is red] obtains.

We can certainly accept this sentence as true without being commit-ted to accepting unwanted dependencies, since the condition in ques-tion does not make reference to objects that would yield such de-pendencies. Examples (b) and (c) can be handled in a similar way.

The new account also fares well with respect to cases (1)-(4), which were not problematic. Consider for instance:

(1) [a+b exists] is grounded in [a exists], [b exists].

By (GPRED), accepting (1) requires accepting:

There is a condition Φ such that Φ([a exists], [b exists]) and it is part of the nature of [a+b exists] that: for all g1, g2 such that Φ(g1, g2), g1 and g2 obtain → [a+b exists] obtains.

This statement follows from the sentence which results from replac-ing both occurrences of the variable in the embedded open sentence by the condition ‘are two facts, one identical with [a exists] and the other one with [b exists]’. Accepting this sentence is once again not problematic given that the condition does not refer to problematic entities: as previously stressed, it is quite plausible to hold that [a+b exists] is essentially dependent upon both [a exists] and [b exists]. Cases (2)–(4) are similar.

Let us turn to (SOP). Since here we do not have facts to generalise from, the account cannot be modified in exactly the same way. But a similar manoeuvre suggests itself, yielding an account I will call ‘(GOP)’. Consider a statement of type ‘p because p1, p2, …’. There are two cases two distinguish. The first is the case where none of ‘p1’, ‘p2’, … makes reference to any object. Then there is no need to modify (SOP). The account must be modified only in the second case, i.e. the case where some of ‘p1’, ‘p2’, … makes reference to some object(s). For the sake of simplicity, I illustrate how the modification must be made in the simple case where each of ‘p1’, ‘p2’, … either makes no


reference to any object, or makes reference to (a finite number of) objects only by means of singular terms it contains:

GOP Case 1: None of ‘p1’, ‘p2’, … makes reference to any object. Then (GOP) runs just like (SOP).

Case 2: Some of ‘p1’, ‘p2’, … makes reference to some object(s). Thus each ‘pi’ which makes reference to some object(s) can be rewritten as ‘pi(ai1, ai2, ...)’ so that reference is made completely explicit. The account goes as follows (where ‘pi’ makes refer-ence to nothing, the sequences ‘ai1, ai2, …’ and ‘xi1, xi2, …’ should be read as empty, and ‘pi(xi1, xi2, …)’ as ‘pi’):

p because p1, p2, … ↔df.

(i) p1 ∧ p2 ∧ …, and

(ii) There is a condition Φ such that Φ(a11, a12, …, a21, a22, …, ...) and it is part of what it is for it to be the case that p that: for all x11, x12, …, x21, x22, …, ... such that Φ(x11, x12, …, x21, x22, …, ...), p1(x11, x12, …) ∧ p2(x21, x22, …) ∧ … → p.

Thus, for instance, on this account the statement:

b is red because t exists

should be understood as:

(i) t exists, and

(ii) There is a condition Φ such that Φ(t) and it is part of what it is for it to be the case that b is red that: for all x such that Φ(x), x

exists → b is red.

One may then take the truth of (ii) to be witnessed by the condition of being a redness trope inhering in b, and doing so one will not be committed to accepting unwanted dependencies. More generally, giv-en the previous discussion it should be clear that (GOP) escapes the difficulties met by (SOP).

(GOP) is an account Fine (2012, §11) examines and rejects on the basis of three objections.9 The first objection, which actually also affects

9 It is perhaps worth stressing that in that section of the paper, as well as in other parts, Fine uses talk of facts and of facts being grounded in other

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(SOP), is that the account does not do justice to the distinction be-tween plural grounds and conjunctive grounds: on the account, ‘p because p1, p2, …’ is always equivalent to ‘p because p1 ∧ p2 ∧ …’. That such a failure to discriminate between plural and conjunctive grounds is problematic can be illustrated by considering the grounds of conjunctive truths. It is plausible to hold that true conjunctions are grounded in their conjuncts, i.e. that if ‘p1 ∧ p2’ is true, then ‘p1 ∧ p2 because p1, p2’ is true as well. But since grounding is irreflexive, ‘p1 ∧ p2 because p1 ∧ p2’ cannot be true.10

The second objection presupposes a distinction between constitutive and consequential concepts of essence I will discuss below. In a nut-shell, the objection runs as follows. Let ‘p’ be a true statement, which for the sake of simplicity we suppose not to contain referring expres-sions. If the concept of essence expressed by the essentialist operator in (GOP) is consequential, then the account will make the false predic-tion that ‘p because p ∧ p’ is true. Hence, for (GOP) to be correct the concept of essence involved cannot be consequential. But it cannot be constitutive either, since constitutive essence is itself to be under-stood in terms of consequential essence and grounding: ‘The constitu-tive claims of essence can [...] be taken to be those consequentialist statements of essence that are not partly grounded in other such claims’.

Finally, the third objection runs as follows. It may be thought that for every object x which exists in time, it is part of the nature of x that x exists simpliciter iff x exists at a time. On this assumption, (GOP) will predict that if object x exists in time, then both x exists simpliciter because x exists at a time, and x exists at a time because x exists sim-pliciter. But this is impossible, since grounding is asymmetric.

I take the first objection to (GOP) – the indiscrimination objection, as we may call it – to be very serious, but I am not impressed by the other ones.

facts only for convenience; what he has in mind is really a notion of ground expressed by means of a sentential operator. 10 Bernard Bolzano (1837, II, §205) already made this point.


Let me start with the third objection. Let x be something which exists in time, and suppose that:

(α) It is part of the nature of x that x exists simpliciter iff x exists at a time.

In order for (GOP) to predict what Fine says it does, we should be able to derive from (α) certain truths which hold in virtue of what it is for it to be the case that x exists simpliciter and of what it is for it to be the case that x exists at a time. Presumably, the essentialist statements that should be derivable are:

(β) It is part of what it is for it to be the case that x exists simplicit-er that: x exists at a time → x exists simpliciter

and

(γ) It is part of what it is for it to be the case that x exists at a time that: x exists simpliciter → x exists at a time.

But (α) is an objectual essentialist statement which tell us something about what x is, whereas (β) and (γ) are alethic essentialist statements which tell us something about what it is for it to be the case that x exists simpliciter, and something about what it is for it to be the case that x exists at a time, respectively, and accordingly I do not see that (β) or (γ) follows from (α). Consider the principle that one can always correctly infer ‘it is part of what it is for it to be the case that F(x) that F(x) if G(x)’ and ‘it is part of what it is for it to be the case that G(x) that G(x) if F(x)’ from ‘it is part of the nature of x that F(x) iff G(x)’. I take it to be subject to counterexamples. For instance, con-sider an Aristotelian view of universals according to which it is part of the nature of humanity that it exists iff something exemplifies it. I take it that, consistently with this view, it can be maintained that it is not part of what it is for it to be the case that something exemplifies humanity that something exemplifies humanity if humanity exists. I thus take the general principle to fail, and I do not see that the partic-ular instance of the principle concerning (α), (β) and (γ) is in any bet-ter position.

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Now for the second objection. The distinction between constitutive and consequential essence was first made in Fine 1995a, §3, which discusses exclusively the objectual notion of essence:

An essential property of an object is a constitutive part of the essence of that object if it is not had in virtue of being a con-sequence of some more basic essential properties of the ob-ject; and otherwise it is a consequential part of the essence. [...] The constitutive essence is directly definitive of the object, but the consequential essence is only definitive through its connec-tion with other properties.

This characterisation is not altogether clear (to me, at least), but an important point to retain is that the consequential essence of an ob-ject is closed under a certain consequence relation.11 Clearly, if there is such a distinction for objectual essence, it (or a very similar distinc-tion) will also apply to alethic essence. If this is conceded, then we may grant that on a consequential conception of alethic essence it will be correct to say that it is true in virtue of what it is to be the case that p that p if (p ∧ p) (on the grounds that ‘p if (p ∧ p)’ is a con-sequence, in the appropriate sense, of anything whatsoever), and in so doing we will agree with Fine that if the concept of essence ex-pressed by the essentialist operator in (GOP) is consequential, then the account will predict that ‘p because (p ∧ p)’ is true.

If all this is conceded, then why not take the concept of essence in-volved in (GOP) to be constitutive? Fine tells us that on his view about the relationships between constitutive and consequential essence, the former is to be defined in terms of the latter and of the concept of grounding, and clearly on this view (GOP) cannot be understood in the proposed way. But why should one accept Fine’s view, rather than the more natural view, mentioned and flatly rejected by him (2012, §11), that consequential essence is the closure of constitutive essence un-der (an appropriate relation of) logical consequence?

I believe that the Finean distinction between constitutive and conse-quential essence is sound, both in the objectual and in the alethic case

11 Fine elaborates a bit on the kind of consequence relation he has in mind in his 1995a, §4. See also Fine 1995c and 2000.


(and also in the generic case, for that matter).12 I construe constitu-tive objectual essence in such a way that a proposition belongs to the constitutive essence of an object just in case it correctly tells us some-thing which pertains to what the object is, and similarly I take a prop-osition to be constitutive of what it is for it to be true that blah just in case it correctly tells us something which pertains to what it is for it to be true that blah. And I take it that consequential concepts of es-sence are, in both the objectual and the alethic case, to be defined as closures of the constitutive concepts under appropriate consequence relations. This being said, in response to Fine’s second objection I recommend to understand (GOP) as involving constitutive alethic es-sence – more generally, I recommend to understand the essentialist concepts in the four accounts of grounding we met so far as being constitutive rather than consequential.

Before moving to the next section, let me mention a further objec-tion to (GOP). In a nutshell, the objection is that by (GOP), partial grounds must be full grounds. Consider a statement of ground of type:

12 I should perhaps mention that I have not always been of that opinion (see Correia 2007, fn. 14). Fine (1995a, 58) stresses that it is difficult to see where and how to draw the line between constitutive and consequential es-sence, and that before we get clear on these issues ‘it seems advisable to work as far as possible with the consequentialist notion’. I agree that the question of where and how to draw the line is difficult. In particular, consti-tutive essences are certainly not ‘logically inert’, to use Fine’s (1995a, 57) expression, and it is not clear which closure principles for constitutive es-sence should be accepted (see the end of this section for some thoughts). But even if it is granted that it is ‘advisable to work as far as possible with the consequentialist notion’, we should not refrain from working with the constitutive notion if we believe that this is what is needed. I should perhaps mention here that in my 2012, I present a theory of essence in the spirit of Fine (the ‘rule-based’ account), which distinguishes between basic essential truths – which would correspond, at least extensionally, to the Finean consti-tutive truths – and derivative essential truths, which result from the interaction of basic essential truths and the nature of logical concepts. The derivative truths are not obtained by closure under a consequence relation, though, the derivations involving, so to speak, more fine-grained mechanisms. In that paper I do not give a recipe for identifying constitutive essences, nor do I try to theorise on the closure principles for constitutive essences.

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(I) p because F(a), G(a).

By (Gop), it follows that F(a) ∧ G(a), and that

(II) There is a condition Φ such that Φ(a) and it is part of what it is for it to be the case that p that: for all x such that Φ(x), F(x) ∧ G(x) → p.

Let Φ0 witness the truth of (II). We then have:

(III) Φ0(a) and it is part of what it is for it to be the case that p that: for all x such that Φ0(x), F(x) ∧ G(x) → p.

Now define condition H(x) as Φ0(x) ∧ F(x). The first conjunct of (III) and the fact that F(a) allow us to infer that H(a). In addition, by the second conjunct of (III), it is part of what it is for it to be the case that p that for all x such that H(x), G(x) → p. So we have:

(IV) There is a condition Ψ such that Ψ(a) and it is part of what it is for it to be the case that p that: for all x such that Ψ(x), G(x) → p.

But then by (GOP) again, it follows that

(V) p because G(a).

But there are many statements of type (I) which we may take to be true while rejecting the corresponding statement of type (V).

At a crucial point, this objection – call it the reduction objection – in-volved the transition from the second conjunct of (III),

(t1) It is part of what it is for it to be the case that p that: for all x, Φ0(x) → (F(x) ∧ G(x) → p),

to

(t2) It is part of what it is for it to be the case that p that: for all x, Φ0(x) ∧ F(x) → (G(x) → p).

Clearly, if the conditional involved in (t1) and (t2) is the material con-ditional, then the transition from the embedded universal statement in (t1) to the embedded universal statement in (t2) is classically logi-cally valid. And even without this assumption about the conditional, it is plausible to hold that the transition is in an intuitive sense logical-


ly valid. Now, it might be stressed, once it is granted that the essen-tialist operator in (t1) and (t2) expresses a constitutive concept of es-sence, it is not obvious that the transition from (t1) to (t2) is legitimate.

At this point some might wish to simply deny that the transition is legitimate, on the grounds that constitutive essences are ‘logically in-ert’. But this view about constitutive essences is too extreme to be plausible. For although constitutive essences are not closed under arbitrary consequence relations – in particular, they are certainly not closed under classical logical consequence – they are arguably closed under certain non-trivial consequence relations which are ‘more tight’ than classical logical consequence. For instance, it seems that we can legitimately infer ‘it is part of the constitutive nature of Socrates that he is both G and F’ from ‘it is part of the constitutive nature of Soc-rates that he is both F and G’. My impression is that the inference from (t1) to (t2) is just as legitimate as the one just mentioned.

Here is an argument to the effect that the inference is legitimate if ‘→’ stands for the material conditional. Contexts of type ‘it is part of what it is for it to be the case that p that ---’, even understood as ex-pressing constitutive essence, must be closed under some equivalence relation ≈ of ‘meaning the same’. Plausibly, this relation should satisfy the following general principles:

¬(α ∧ β) ≈ ¬α ∨ ¬β;

(α ∨ β) ∨ γ ≈ α ∨ (β ∨ γ);

If α ≈ β, then α ∨ γ ≈ β ∨ γ;

If α ≈ β, then γ ∨ α ≈ γ ∨ β;

If α ≈ β, then ∀xα ≈ ∀xβ.

Once this is granted, it can be proved that the transition from (t1) to (t2) is truth-preserving.

It is perhaps possible to agree on the previous argument, and at the same time defend the view that if ‘→’ is understood as expressing something else than the material conditional (say, a ‘relevant’ condi-tional), we get an account of grounding which is both plausible and immune from the previous objection. Perhaps. I leave it up to those

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who wish to put forward such a view to come up with an appropriate conditional, and argue that the resulting account does escape the re-duction objection.

To conclude this section, let me stress that (GPRED) is immune from the indiscrimination objection, but not from the reduction objection if the latter is effective at all against (GOP). The details are straight-forward.

5. Escaping the Unwanted Dependencies and the Indis-crimination Objections

As previously stressed, the indiscrimination objection affects (SOP) as well as (GOP). But it affects neither (SPRED) nor (GPRED). Also, the simple accounts are immune from the reduction objection. The whole situa-tion can be summed up in the following table, where ‘√’ signifies that the objection applies, ‘×’ that it does not, and ‘√?’ that the objection applies if the conditional expressed by ‘→’ is the material conditional, and perhaps does not apply otherwise:

(SPRED) (SOP) (GPRED) (GOP)

Unwanted dependencies √ √ × ×

Indiscrimination × √ × √

Reduction × × √? √?

In this last section I wish to suggest a modification of the two opera-tor accounts and give a final verdict on the viability of these and the other two accounts.

Let us first focus on the indiscrimination objection to (SOP). The ob-jection states that the account cannot do justice to the distinction between plural grounds and conjunctive grounds. The account, as well as each of the other accounts we have met so far, involves in condition (ii) of its analysans the standard dyadic conditional ‘if …, then …’. The source of the indiscrimination problem is that the list ‘p1, p2, …’ in (Sop)’s analysandum is represented in the antecedent of


the conditional by the conjunction ‘p1 ∧ p2 ∧ …’. In order to escape the problem I suggest that the account be modified by replacing the standard conditional by a new conditional, ‘IF …, THEN …’, whose first position can be filled in with a list of one or more sentential ex-pressions, and which is defined as follows:

IF p1, p2, …, THEN p iffdf if it is the case that p1 ∧ it is the case that p2 ∧ …, then it is the case that p.

Of course, it is crucial for this proposal that ‘it is the case that ---’ should not be taken to be a mere notational variant of ‘---’, for oth-erwise ‘IF p1, p2, …, THEN p’ would just be a notational variant of ‘if p1 ∧ p2, …, then p’ and thus nothing would be gained. For the pro-posal to be of any help, I must not only insist that ‘it is the case that ---’ and ‘---’ are not mere notational variants; I must also argue that the presence of ‘it is the case that’ in the definition of the new condi-tional makes the difference I want it to make.

Now, it will be asked, how could ‘it is the case that ---’ and ‘---’ fail to be mere notational variants? I simply reply that they are not. I agree that all the (truth-evaluable) instances of ‘it is the case that p iff p’ are (perhaps logically) necessarily true. Accordingly, I agree that in exten-sional contexts and many intensional contexts, occurrences of ‘it is the case that’ can be eliminated without affecting truth-value. But this is compatible with the view that the use of ‘it is the case that’ is sometimes non-redundant. For instance, the use of the phrase ‘it is the case that’ allows one to make informative claims about pieces of logical vocabulary, whereas dropping the occurrences of the phrase removes (some of) the informative aspect of what is said. This can actually be seen by comparing the following two principles:

∀p1∀p2 (if it is the case that p1 ∧ it is the case that p2, then it is the case that p1 ∧ p2).

∀p1∀p2 (if p1 ∧ p2, then p1 ∧ p2).

Both can be argued to be true, perhaps even logically necessary. But while the first principle records an important feature of conjunction (it is a version of the inference rule of conjunction introduction for-mulated as a statement rather than a rule), the second merely reflects a general property of the conditional and tells us nothing about con-

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junction. What is more, there are arguably true statements involving ‘it is the case that’ which become falsehoods if the occurrences of the expression are eliminated. For instance, it is plausible to hold that this is the case for

It is a fundamental fact about conjunction that: ∀p1∀p2 (if it is the case that p1 ∧ it is the case that p2, then it is the case that p1 ∧ p2),

and

It is part of the nature of conjunction13 that: ∀p1∀p2 (if it is the case that p1 ∧ it is the case that p2, then it is the case that p1 ∧ p2),

which is closer to the focus of this paper.14

What I suggest in place of (SOP) is thus the following account:

ΣOP p because p1, p2, … ↔df. (i) p1 ∧ p2 ∧ …, and (ii) It is part of what it is for it to be the case that p that: IF p1, p2, …, THEN p.

The previous considerations make it plausible to hold that the transi-tion from

It is part of what it is for it to be the case that p that: IF p1, p2, …, THEN p

to

It is part of what it is for it to be the case that p that: if p1 ∧ p2 ∧ …, then p

is not legitimate, and accordingly that a case can be made for the view that (ΣOP) escapes the indiscrimination objection. (GOP) was also sub-

13 Or perhaps of conjunction and other items, among them e.g. the condi-tional. 14 Kevin Mulligan (2010, 568) defends the view that ‘it is the case that p because p’ must hold in case ‘p’ is true. This view, if correct, provides a fur-ther example, granted that no instance of ‘p because p’ can be true.


ject to the objection, and I recommend that it be modified in the same way. The resulting account will be labelled ‘(ΓOP)’. Since (SPRED) and (GPRED) were not affected by the objection, there is no need to modify them.

Let me now turn to the unwanted dependencies objection to the simple accounts (SPRED) and (SOP). Of course, if the objection is effec-tive at all against (SOP), it will affect equally well (ΣOP). But I think that the objection can be resisted.

Recall the form of the objection as stated against (SPRED): from a plau-sible claim of ground, one derives, using the account, the conclusion that a certain fact is essentially dependent upon another fact, and one rejects the conclusion – the rejection being just flat (Finean rejection) or based on the assumption that essential dependence entails existen-tial dependence (Lowean rejection).

As stressed en passant in section 3, the notion of essential dependence which is at work here can be defined as follows:

DEP x essentially depends upon y ↔df. for some condition Φ, it is part of the nature of x that Φ(y),

where the essentialist operator is the operator involved in the account and so, given my previous recommendation, should be understood as expressing constitutive objectual essence. Now for one thing, pace Lowe, I do not think essential dependence so defined entails existen-tial dependence – where to say that an object existentially depends on another object is to say that the former (metaphysically) cannot exist without the latter. For instance, suppose there is such a thing as the property of being identical to Socrates.15 It is then plausible to say that the property is essentially dependent, in the sense of (DEP), up-on Socrates, on the grounds, say, that it is part of the nature of the property that Socrates exemplifies it if he exists. Yet one can consist-ently maintain that the property necessarily exists, while Socrates ex-ists only contingently. Thus, in my view, if the inferred dependencies in the objection against (SPRED) are to be rejected, the rejection should not be of the Lowean sort.

15 See Fine 1995b, 274, and Correia 2005, 52.

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Taking this for granted, is it so clear that these dependencies should be rejected? Consider for instance the case of [someone is a philoso-pher] and [Socrates is a philosopher]. We reached the conclusion that the former is essentially dependent upon the latter on the basis of the assumption that:

(#) It is part of the nature of [someone is a philosopher] that it ob-tains if [Socrates is a philosopher] does,

which itself was derived from the assumption that [someone is a phi-losopher] is grounded in [Socrates is a philosopher]. It does not strike me as intuitively incorrect to accept (#), and accordingly it does not strike me as intuitively incorrect to hold that the existential fact essen-tially depends, in the sense of (DEP), upon the singular fact. To the contrary, I find (#) quite plausible, and I am therefore happy to hold that there is this dependency link between the two facts.

The other proposed counterexamples to (SPRED) do not impress me more than the one just discussed, and, likewise, I am not impressed by the unwanted dependencies objection against (SOP) / (ΣOP).

6. Concluding Remarks We ended up with four essentialist accounts of grounding, (SPRED), (ΣOP), (GPRED) and (ΓOP), and if the arguments I proposed in this paper are correct, their behaviour with respect to the unwanted dependen-cies, the indiscrimination and the reduction objections can be repre-sented by modifying the table from section 5 as follows:


That is to say: the simple accounts (SPRED) and (ΣOP) escape all three objections; (GPRED) and (ΓOP) escape the first two objections but not the third if they are understood as formulated in terms of the mate-rial conditional; they may escape this objection if another conditional is taken to be at work, but this needs to be argued for.

I favour the simple accounts over any versions of (GPRED) and (ΓOP), and among the simple accounts I favour (ΣOP). I prefer the simple accounts because they are simpler than any versions of (GPRED) and (ΓOP). And I favour (ΣOP) over (SPRED) because the latter, but not the former, requires accepting an ontology of facts, whereas I believe that an account of grounding should be as far as possible neutral on the question whether there are such entities. Whether (ΣOP) – or any other account presented in this paper, for that matter – can stand further examination is something I do not want to bet on at the pre-sent time. Yet I hope to have shown that some accounts of ground-ing in terms of essence have some plausibility.16

16 I wish to thank Benjamin Schnieder and Alex Steinberg for their very extensive and valuable comments on an earlier draft of this paper, and also to Kathrin Koslicki and the audiences at the Goethe Universität Frankfurt Research Colloquium in philosophy (February 2011), the Ontological Dependence Workshop at the University of Bristol (February 2011) and the Grounding and Modality Workshop at the University of Glasgow (April 2011) for helpful dis-cussion. This work was carried out while I was a Swiss National Science Foundation professor (projects PP001-114758 and PP00P1-135262), and in charge of the Swiss National Science Foundation sinergia project ‘Intention-ality as the Mark of the Mental’ (project CRSI11-127488). The research lead-ing to these results has also received funding from the European Communi-ty’s Seventh Framework Programme FP7/2007-2013 under grant agreement no. FP7-238128.

(SPRED) (ΣOP) (GPRED) (ΓOP)

Unwanted dependencies × × × ×

Indiscrimination × × × ×

Reduction × × √? √?

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