In Defence of Hybrid Contingentism

2.1 The haecceities objection against hybrid contingentism

Haecceitistic properties, in the sense relevant for the haecceities objection to be investigated, are properties that single out a unique individual in a modally robust way. The property of being a philosopher is thus not a haecceity since it fails to single out a unique individual even in the weak sense of applying, in fact, only to one individual. Neither is the property of being the most famous proponent of the theory of forms, which while singling out Plato in this weak sense, fails to do so with any modal robustness: while it applies, in fact, to Plato (and only to him), it could have applied to someone else instead. The property of being identical to Plato, in contrast, is a haecceity of Plato in the intended sense: necessarily, anything has that property just in case it is identical to Plato. We can regiment the relevant notion of a property X being a haecceity of an individual y as follows:

The hybrid contingentist position that we are interested in accepts that there is a modally stable plenitude of haecceities, in the sense that necessarily everything necessarily has a haecceity:¹⁰

Now, the first step in Williamson’s haecceities objection to this form of contingentism is to introduce a further notion, that of a property tracking an individual (2013: 269). X tracks y just in case X is a haecceity of y and X cannot be a haecceity of anything other than y. We can abbreviate the second conjunct, which makes explicit that the haecceity has, in a modally robust sense, a unique target, as follows:

Williamson’s notion of tracking then amounts to the following:

With the notion of tracking at hand, he proceeds to argue as follows:

[G]iven the background logic, Plato’s haecceity necessarily tracks Plato. Even if Plato had never been, by [(Haec Plenitude)] there would still have been a property tracking him (and only him). But how can it lock onto him in his absence? In those circumstances, what makes him rather than something else its target? (2013: 269)¹¹

In the remainder of this section, we aim to get a better understanding of the nature and import of this objection. We start with a couple of clarifications. First, note that Williamson is presupposing not only that Plato has a haecceity, as is guaranteed by (Haec Plenitude), but also that he has exactly one (as witnessed by the uniqueness-implying expression ‘Plato’s haecceity’). Williamson is justified in making this presupposition, because he has opted to identify higher-order entities intensionally (2013: Ch. 6, §1): in particular, he treats properties as identical just in case they necessarily apply to the same individuals, which, when combined with (D-Haec), ensures that no individual can have more than one haecceity. This intensional setting in which Williamson prefers to evaluate hybrid contingentism is, however, not essential to the haecceities objection he takes the position to face. The objection gets going as soon as we have at least one contingently existing individual and at least one necessarily existing haecceity of that individual. By drawing hyperintensional distinctions among properties, our hybrid contingentists can only increase, not decrease, the number of problematic haecceities, e.g. by regarding the intensionally equivalent properties of being identical to Plato and either Greek or not Greek and being identical to Plato and either a philosopher or not a philosopher as distinct haecceities of Plato. There is thus nothing inherently intensional about the haecceities objection (later on, in §3.3, we will see that there are, on the contrary, good reasons to think that a hyperintensional setting is a more natural environment for it).

Second, the relevant fact about the background logic, to which Williamson is appealing in the first sentence of the quote, is that its propositional modal logic is S5. Tracking claims are of the form □A ∧ ¬♢B which are never contingent in S5. So, given that our hybrid contingentists want to preserve S5 (as we will presuppose throughout the paper they do), they have to accept that any true tracking claim is necessarily true. Since they accept that e.g. the property of being identical to Plato in fact tracks Plato, they have to accept that it does so necessarily and thus would have still tracked Plato, even if Plato had been absent. This, Williamson thinks, puts them in a bad position. What the badness is supposed to consist in exactly is best understood by taking into account the discussion immediately following the passage quoted above. There, Williamson considers and rejects three ‘explanations of tracking’ (2013: 269) which hybrid contingentists might be tempted to put forward.

His first victim is the constitutional explanation: contingentists cannot maintain that haecceities track their targets in virtue of containing the target as a constituent. For this would precisely fail to explain how a haecceity of Plato can still track him when he is absent and thus not available to be a constituent of anything.

Next, he rejects the relational explanation: contingentists cannot maintain that haecceities succeed in tracking their absent targets via actual entities which are distinct from the target but uniquely determine the target. This might work in some cases, as when a merely possible knife is singled out via its actual blade and handle. But there is no reason to think that this strategy is successful in general.

Third, he rules out the qualitative explanation: contingentists cannot maintain that haecceities track their absent targets in virtue of somehow encoding the target’s qualitative character, among other things, because that threatens to commit them to an implausible version of the identity of indiscernibles which rules out numerically distinct but qualitatively identical individuals.

What this discussion makes clear is that the badness of the hybrid contingentists’ position is supposed to consist in their inability to provide certain explanations. But even if this is appreciated, our understanding of the haecceities objection remains, as yet, imperfect. For we also need to get clearer on what exactly is taken to be the explanandum. Of course, we saw Williamson pinpointing tracking as the phenomenon to be explained. Given (D-Track), the objection is thus most straightforwardly understood as challenging contingentists to provide an explanation, applicable in the absence of Plato, of the following fact, where p stands for Plato and P for a haecceity of Plato (e.g. the property of being identical to Plato):

(1)

On closer inspection, however, putting claims of this form at the centre of the objection is somewhat surprising (see Goodman 2016: 618). For that P is a haecceity of p (the first conjunct) uncontroversially entails that P cannot be anything else’s haecceity (the second conjunct). In fact, Williamson (2013: 268) himself points out that necessarily if X is a haecceity of some individual y, then necessarily X is a haecceity of z only if y and z are identical. This strongly suggests that the task of providing an explanation of (1) boils down to that of providing an explanation of:

(2)

Williamson seems to agree. In a response to Goodman, he still identifies the challenge to contingentists as that of explaining how a haecceity can ‘lock onto’ its absent target (Williamson 2016: 642). But he now uses claims of the form ‘X locks onto y’ interchangeably with the simple haecceity claim, Haec(X, y), not with the more complex and partially redundant tracking claim. In the following, we will follow Williamson (2016) both in this usage of the ‘locks-onto’-construction as well as in taking the challenge for the contingentists to be that of explaining how simple haecceity claims can be true in the problematic circumstances. (We will revisit this choice in §4.5 as part of an attempt to show, more generally, that the contingentist response to the haecceities objection to be proposed is robust with respect to a number of variations on how exactly the challenge is formulated.)

2.2 What the haecceities objection is not

It is easy to misunderstand the haecceities objection as aiming to reveal a more fatal flaw in the contingentists’ position than an explanatory embarrassment. This impression can arise because Williamson had argued before (2013: Ch. 4) that contingentists should accept the Being Constraint as a principle of modal logic. Put loosely, the Being Constraint dictates that an individual can only have properties if it exists. And now one might think that the point of the haecceities objection is to show that hybrid contingentists are committed to an inconsistent trio comprising (i) the Being Constraint; (ii) the claim that, necessarily, Plato is locked onto by a haecceity; and (iii) the claim that, possibly, Plato fails to exist. In particular, it might be thought that if Plato is necessarily locked onto by a haecceity, then he necessarily has a (relational) property in a way that entails, via the Being Constraint, his necessary existence.

But this is not what the haecceities argument is getting at, and appreciating this will allow us to draw a lesson that will be important later on. To see why the objection should not be taken to trade on the Being Constraint, we need to get clearer on what Williamson takes that constraint to amount to. We start by considering one of its crucial instances:

(3)

According to (3), self-identity requires existence. Since Williamson (2013: 154) thinks that even contingentists should accept (3), he advises them, reasonably, to deny that Plato is necessarily self-identical

(4)

since this would entail the necessary existence of Plato when combined with (3).

Now, if the haecceities objection were to trade on the Being Constraint, the following would have to be an instance of this constraint:

(5)

According to (5), being locked onto by the haecceity P requires existence. The point of the haecceities objection would then be that just like (3) and (4) entail the necessary existence of Plato, so do (5) and the following claim, which hybrid contingentists must accept (see §2.1):

(6)

However, this construal of the objection misunderstands the scope of Williamson’s Being Constraint. To see this consider:

(7)

This entails Plato’s necessary existence together with:

(8)

Even contingentists who deny (4) cannot easily deny that necessarily either Plato is self-identical or he is not, so they had better not regard (7) as instantiating the Being Constraint. And, Williamson agrees, they don’t have to (2013: 156 ff.). Rather, he advises them to stress that the necessitated formula in (4), but not that in (8), is a predication (the direct result of applying an n-place predicate to n individual constants or variables). He further advises them to insist that only predications ascribe properties to things. Accordingly, formulas of the form (3), (5), and (7) only instantiate the Being Constraint if the antecedent of the embedded conditional is a predication. But then (5) doesn’t instantiate the Being Constraint any more than (7). For recall that Haec(P, p) abbreviates □∀x(Px ↔ x = p), which isn’t a predication.

This contingentist take on the Being Constraint has a consequence which will be important later. Let us say that a term t occurs in an existence-demanding position in A(t) just in case A(t) logically entails ∃x t = x. By accepting the Being Constraint as a principle of modal logic, contingentists have to regard term positions in predications, but only in predications, as existence-demanding. The haecceities objection can then be seen as putting pressure on contingentists to also regard the term position in a haecceity claim, Haec(F, t), as existence-demanding. But this pressure is not to stem from the Being Constraint, but from the explanatory embarrassment that contingentists are alleged to face otherwise.

2.3 The importance of the haecceities objection

The haecceities objection is not the only consideration which Williamson invokes against hybrid contingentism. In fact, he takes his case to be overdetermined: even with the haecceities objection taken out of the equation, uniform necessitism would still surpass hybrid contingentism when compared by ‘the normal standards of theory choice’ (2013: 277), which he takes to include the theoretical virtues of uniformity and strength.

The case for uniformity is obvious. Uniform necessitism is uniform in that it is necessitist on the first-order level and on all higher-order levels, while hybrid contingentism mixes contingentism on the first-order level with necessitism on all higher-order levels. The case for strength is less obvious. Uniform necessitism and hybrid contingentism are individually consistent but mutually inconsistent, so neither theory is stronger than the other in the sense of entailing it without being entailed by it. What Williamson has in mind is a less formal sense of strength as informativeness, according to which universal generalisations such as scientific laws typically count as stronger than their negations (2013: 276). In this sense, Williamson takes uniform necessitism to be stronger than hybrid contingentism, for it asserts a necessitated universal generalisation, (Nec), where hybrid contingentism asserts its negation, ¬(Nec).

Are these considerations really persuasive enough to warrant, by themselves, a dismissal of hybrid contingentism? With respect to uniformity, Goodman (2016: 614–5) argues that, when concerned with a type-hierarchy like that exhibited by the formal higher-order language in which hybrid contingentism and uniform necessitism are formulated, asymmetries among the very first level, on the one hand, and all higher-order levels, on the other hand, are relatively unproblematic. Williamson (2016: 640–1) agrees at least insofar as he accepts that the asymmetry exhibited by hybrid contingentism is much less problematic than the asymmetry of a theory which was contingentist about, say, 14th order properties but necessitist on all other levels.

With respect to strength, let us take Williamson’s specific criterion for informativeness—necessitated universal generalisations are more informative than their negations—for granted. This is applicable to the lone claims (Nec) and ¬(Nec), but Williamson points out himself that these are, respectively, merely the bare bones of first-order necessitist and contingentist theories, which their proponents are likely to flesh out with additional claims. In fact, in the context of his major argument against uniform contingentism, it is such ‘enriched’ necessitist and contingentist theories which he compares (2013: Ch. 7, §§2,3). But then it is not obvious that it is the isolated claims (Nec) and ¬(Nec) which should be evaluated in terms of informativeness rather than the enriched theories incorporating them. Williamson’s specific criterion for informativeness, however, will not in general be applicable to such enriched theories, and it is not clear how it should be generalised.

Naturally, these comments are in no way intended to approach anything like a definite appraisal of the force of these additional arguments against hybrid contingentism. Rather, their point is just to indicate that, at least as long as the verdict on these additional arguments is still out, the success or otherwise of the haecceities objection seems to have a substantial impact on the contest between uniform necessitism and hybrid contingentism. This is sufficient reason to study the objection more closely.

3.1 The haecceities objection as a grounding challenge

The haecceities objection turns on the idea that contingentists are unable to explain the fact that haecceities continue to lock onto their targets even in circumstances in which the targets don’t exist. What notion of explanation is the objection operating with? What kind of explanation can contingentists reasonably be expected to give of the problematic haecceity facts?

It is clear that contingentists cannot be expected to provide a causal explanation. Plato’s being locked onto by a haecceity is not the sort of thing to be explained causally. So, the challenge must be concerned with some type of non-causal explanation. What might appear, at least on first sight, as a genuine candidate is an explanation by derivation (a type of explanation explicitly acknowledged by Williamson (2013: 425–6)). In a modest sense, a theorist can be said to explain certain facts by proposing a theory from which the facts can be derived. But the haecceities objection cannot be concerned with this notion of explanation. For recall that the objection only got off the ground because the problematic haecceity facts follow from the hybrid contingentists’ theory: the problem is supposed to be precisely that they cannot adequately explain some facts to which their theory commits them.

So, contingentists are challenged to provide a non-causal explanation of the problematic haecceity facts which does more than to merely point at some principles from which they can be logically derived. Rather than a causal or logical basis, then, it seems that what they are challenged to provide is a metaphysical basis. The central point of the objection seems to be that because hybrid contingentists (i) accept that haecceities necessarily lock onto their targets but (ii) simultaneously allow some of the targets to exist contingently, they allow for the haecceity facts to obtain in some circumstances in which it is no longer clear in virtue of what, metaphysically speaking, they are supposed to obtain.

Put like this, it is extremely natural to take the haecceities objection to consist in a challenge to provide a grounding explanation. For it is the express aim of grounding explanations to not merely specify some fact(s) entailing the explanandum, but to specify the explanandum’s metaphysical basis: to tell us in virtue of what it obtains, where this phrase is given a distinctly metaphysical reading (see e.g. Fine 2012: §1.1). On this construal, then, contingentists are challenged to specify metaphysical grounds for the fact that, say, the property of being identical to Plato locks onto Plato, grounds which are available in the absence of Plato.

Note that this way of construing the haecceities objection coheres well with the specific explanatory locutions in terms of which it has been put. Thus, we saw that contingentists are challenged to specify what makes Plato the target of this haecceity (see §2.1). Such constructions are widely regarded as a paradigmatic device to convey propositions about grounding: a question of the form ‘What makes a so-and-so?’ would be regarded a typical way to ask for grounds e.g. by Rosen (2010: 110), Audi (2012: 104), and Correia and Schnieder (2012: 1).¹² That the challenge also contains a contrastive element—contingentists are asked to explain what makes Plato rather than something else the target of the haecceity—does not make it any less suited for a grounding reading, since it is a familiar fact that grounding explanations are frequently put in contrastive terms (see Schaffer 2012).

In the quote, contingentists are also asked to explain how the haecceity locks onto Plato. Now, alongside questions of the form ‘What makes a so-and-so?’, grounding claims are typically taken to be connected to why-questions (see e.g. Rosen 2010: 117; Audi 2012: 104; Schaffer 2012: 122). How-questions, in contrast, aren’t usually singled out as paradig matic examples of questions aiming at grounding explanations.¹³ Nev ertheless, such questions are still often used by philosophers to ask for grounding explanations. For instance, many recent discussions of Bradley’s Regress center on how-questions, such as ‘How do relations relate?’. In these discussions, the relevant questions are typically taken to be interchangeable with questions formulated in more paradigmatic grounding vocabulary, such as ‘In virtue of what do relations relate?’.¹⁴ Since it seems that the present how-question can similarly be read as interchangeable with the question ‘In virtue of what does the haecceity lock onto Plato in his absence?’, its presence doesn’t distract from the plausibility of the grounding construal.

The present construal also coheres well with the response strategies we saw considered on behalf of the contingentists (see §2.1). For these seem to be just the sort of strategies one would consider, if one were looking for the metaphysical grounds of haecceity facts. Thus, recall the constitutional strategy, which tried to explain the fact that a given haecceity of Plato locks onto him by pointing to the (alleged) fact that it has Plato as a constituent. This is just the sort of thing we would expect a grounding theorist to consider, since it is a prominent idea among grounding theorists that facts about complex entities can be grounded in facts about their constituents or parts (see e.g. Cameron 2014). Similarly, consider the qualitative strategy which tried to explain the fact that a given haecceity locks onto Plato in terms of the qualitative character of Plato which the haecceity is somehow meant to encode. Again, this looks like just the sort of thing a grounding theorist would consider, since attempts to ground non-qualitative facts in terms of purely qualitative facts are equally familiar (see e.g. Dasgupta 2009, 2017).

Now, of course, we also saw Williamson rejecting these explanatory strategies. But the fact that they are considered as candidates in the first place can still illuminate the notion of explanation at play. For, importantly, Williamson rejects them because they fail to apply in the relevant cases (in case of the constitutional strategy) or because they have implausible consequences (in case of the qualitative strategy). He does not reject them because they fail to appropriately engage with the challenge and, in particular, not because they somehow aim at the wrong kind of explanation.

3.2 Grounding and hyperintensionality

We have seen good reasons to conceive of the haecceities objection as a challenge to provide metaphysical grounds for the problematic haecceity facts. Since theories of ground require the drawing of hyperintensional distinctions, a fruitful engagement with the haecceities objection, when understood in the way proposed, will also require the drawing of such distinctions. Since the most natural way to draw the required hyperintensional distinctions involves the hyperintensional individuation of properties and propositions, the most natural setting in which to engage with the haecceities objection is one which allows for such hyperintensional individuations.

Let us unpack this reasoning and consider how it fits into the more general dialectic. By saying that grounding requires the drawing of hyperintensional distinctions, I mean that we need to allow intensionally equivalent expressions to differ in the semantic contributions they make to grounding claims in which they occur (see e.g. Bliss and Trogdon 2016: §4): substituting a sentence S for either Q or R in ‘Q because R’ (where ‘because’ is used to express a connection of ground) can change the truth-value of the grounding claim even if S is intensionally equivalent to the sentence for which it is substituted. For example, while ‘grass is green’ and ‘grass is green or grass is green’ are intensionally equivalent, ‘(grass is green or grass is green) because grass is green’ is typically considered a true grounding claim (since true disjunctions are taken to be grounded in their true disjuncts), while ‘grass is green because grass is green’ is not (since grounding is taken to be irreflexive). The most straightforward way to draw the required hyperintensional distinctions is by regarding the grounding connective as operating on the propositions expressed by the sentences flanking it while allowing intensionally equivalent sentences to express distinct propositions.

On the present construal of the haecceities objection, hybrid contingentists are, in effect, challenged to provide a sentence S which when plugged into

(9)

yields a grounding claim that can plausibly be regarded as true even in circumstances in which the target of the haecceity is absent. Since such grounding claims require the drawing of hyperintensional distinctions in the way described, and since the most natural way to do so involves distinguishing the propositions expressed by intensionally equivalent sentences, the most natural environment for a fruitful engagement with the haecceities objection is one that allows for such a fine-grained individuation of propositions.

It may be possible to draw the required hyperintensional distinctions while still individuating propositions intensionally. This could be done by regarding the ‘because’ of grounding claims as sensitive not only to the propositions expressed by the sentences flanking it but also to the way in which they are expressed. This option seems, however, less desirable: by treating grounding locutions as creating such intrans-parent contexts, it would threaten to unduly assimilate grounding to more paradigmatic intransparent context creating phenomena (notably cognitive attitudes), thereby belying the intended status of grounding as an objective and worldly explanatory relation whose obtaining is independent of anything such as a cognitive perspective (see Dorr 2016: 43–6 for more detailed considerations along these lines). In the following, we will therefore assume that the hyperintensional distinctions required for a sensible engagement with issues of ground are to be drawn on the level of properties and propositions.

It it is important to avoid the impression that by proceeding with our investigation in such a hyperintensional setting, we are somehow rigging the deck against necessitists who launch the haecceities objection against hybrid contingentism. This impression might arise because we saw Williamson launch it in an intensional setting. But the impression is mistaken. To see this, let us momentarily stand back from the grounding interpretation of the explanatory challenge posed by the haecceities objection which led us to adopt the hyperintensional setting. Whatever the notion of explanation involved, the gist of the haecceities objection is this: necessitists are in a better explanatory position than contingentists because they can, while contingentists cannot, appeal to the fact that Plato exists with respect to all circumstances in which the fact that Haec(P, p) needs to be explained. But this means necessitists must be assuming that the following is a true explanatory statement:

(10)

If Plato’s existence didn’t even partly explain the haecceity fact, why would the contingentists’ inability to appeal to Plato’s existence ever put them in a worse explanatory position? But now recall that, according to necessitists, the proposition expressed by Haec(P, p) as well as that expressed by ∃x p = x holds necessarily. Since necessitists will hardly be prepared to accept that any necessity whatsoever partly explains any necessity whatsoever, they must take the explanatory connective in (10) to be hyperintensional. So, in propounding the haecceities objection, necessitists must themselves acknowledge the need for drawing hyper-intensional distinctions. If they were then to deny to the contingentists the most natural way of doing so (i.e. by individuating properties and propositions hyperintensionally), the contingentists could rightly object that the deck is being rigged against them: they are confronted with a challenge that can only be posed in hyperintensional terms but denied the proper means to implement said hyperintensionality.

3.3 Moving on

The grounding construal of the haecceities objection strikes me as sufficiently natural to merit further investigation. In particular, I submit that if hybrid contingentists can address the objection on this construal, as I argue in §4 they can, then this is good news for them: they’re confronted with a challenge, and, on a plausible way of spelling out what exactly the challenge consists in, they can meet it.

Note that I’m not making the psychological claim that the grounding construal was at the forefront (or even in the backseat) of Williamson’s mind when he articulated the objection. Rather, my point is that, absent any explicit account of what notion of explanation the objection is operating with, contingentists can only sensibly engage with it by making some assumption as to what kind of explanation they’re challenged to provide, and, given how the challenge is in fact posed to them, the grounding interpretation seems reasonable.

It is, of course, open to necessitists to respond by specifying an alternative notion of explanation and to provide reasons for why the objection is better understood as operating with this alternative notion. (For instance, they might try to specify a hyperintensional but non-metaphysical notion of explanation with which the objection can plausibly be taken to be concerned, in the hope that, on that understanding, nothing analogous to the grounding principles to be defended in the next section will be available to the contingentists.) In fact I hope that even those not ultimately convinced by the present construal of the challenge might find it useful as a foil against which to contrast their preferred alternative. The task for them would then be to say exactly in what respects their construal differs from the grounding construal and why the contingentists’ response to be developed in §4 does not carry over to their construal of the challenge.

4.1 Essential haecceities

The property of being identical to Plato locks onto Plato. Does it do so essentially or accidentally? Note that this question presupposes that it makes sense to speak not only of the essences of individuals but also of the essences of properties when these are conceived of as higher-order entities. But given that it is legitimate to inquire into the essence of first-order entities, and given that there are higher-order entities in addition to first-order entities, why should it be illegitimate to inquire into the essences of those too? A growing number of philosophers finds no objection to this (see e.g. Correia 2006; Hale 2013: Chs. 5, 6; Dasgupta 2016: 415, n. 44), and I will follow them here both in assuming the legitimacy of the general enterprise as well as in extending Fine’s box-subscript notation to formulate claims about the essences of higher-order entities. Thus, just like we can formulate the claim that it is part of the essence of the individual Plato (p) that Plato is human (Hp) as

(11)

we can formulate, for example, the claim that it is part of the essence of the property of being human (H) that it is concreteness demanding, i.e. can be instantiated only by concrete things (□∀x(Hx → Cx)), as

(12)

And, in the same way, we can formulate the claim that it is part of the essence of the property of being identical to Plato (P) that it locks onto Plato (Haec(P, p)) as

(13)

I will take such essence claims to be interchangeable with claims about the nature of the respective entity. Accordingly, (11) can be put as the claim that being human belongs to the nature of Plato and (13) as the claim that locking onto Plato belongs to the nature of the haecceity in question.

Sometimes philosophers understand essence claims in purely modal terms. For instance, (11) is understood as the claim that Plato cannot exist without being human. On an analogous construal, all it would take for (13) to be true is that P cannot exist without locking onto Plato. In this sense, it is trivial that the haecceity essentially locks onto Plato, for we noted early on (§2.1) that haecceity claims are necessarily true if true at all.

Often, however, more is meant by an essence claim such as (11) than that Plato cannot exist without being human. Thus, Fine (1994) famously pointed out that Plato cannot exist without there being infinitely many primes either, and yet there seems to be a good sense in which Plato’s humanity does, but the infinity of primes does not, belong to Plato’s essence. Someone seeking to understand Plato’s nature should know about his being human but need not know anything about the cardinality of prime numbers. While the former fact seems to go right to the heart of Plato’s nature, the latter seems entirely unconnected and irrelevant to him.¹⁵

In this more demanding sense of ‘essence’, the question whether the property of being identical to Plato essentially locks onto Plato is not trivial. Neither are questions concerning the essences of first-order entities, understood in this more demanding sense. Intuitions often divide over which necessary features of an individual are essential to it. Still, there are better and worse candidates, as witnessed by Fine’s examples. And this is the same for higher-order entities: the fact that there are infinitely many primes is as irrelevant to the property of being identical to Plato as it is to Plato. It is thus no more plausible that it should belong to the essence of this property than that it should belong to the essence of Plato. In contrast, locking onto Plato is an excellent candidate for an essential feature of the property. Unlike being such that there are infinitely many primes, locking onto Plato doesn’t seem irrelevant to the property of being identical to Plato at all. Someone seeking to understand the nature of this property need not know anything about prime numbers. But she should know that it is a property that locks onto some individual (in contrast to, say, the property of being human), and she should know that it is Plato who the property locks onto (in contrast to a haecceity of, say, Aristotle).

This consideration immediately supports the claim that locking onto Plato is part of the (Finean) essence of the haecceitistic property of being identical to Plato. But the consideration also supports a more general and strengthened principle.

First, there’s nothing contingent about the connection under consideration: it seems implausible that P should lock onto p essentially in some possible circumstances but only accidentally in others. Rather, given that P’s locking onto p is, in fact, sufficient for P to do so essentially, it should be necessarily sufficient: □(Haec(P, p) → □P(Haec(P, p))).

Second, there is nothing special about the given haecceity of Plato. In our hyperintensional setting, we may distinguish the present haecceity from, say, the property of being identical to Plato and either a philosopher or not a philosopher. The latter is still a haecceity of Plato, and it is equally plausible that it cannot lock onto Plato without doing so essentially. The same goes for all of his other haecceities, so our consideration motivates the general principle: ∀X□(Haec(X, p) → □_X(Haec(X, p))).

Third, there is nothing special about the haecceities of Plato. If Plato’s haecceities can’t lock onto their target without doing so essentially, the same holds for Aristotle’s haecceities and their target. This is ensured by strengthening the principle to: ∀X∀y□(Haec(X, y) → □_X(Haec(X, y))).

Fourth, there is nothing special about the haecceities of entities that actually exist. If Plato and Aristotle cannot be locked onto by their haecceities without those doing so essentially, then Wittgenstein’s merely possible daughter (who by contingentist lights doesn’t actually exist but could have existed) cannot be locked onto by her haecceities without those doing so essentially. This is ensured by further strengthening the principle to: ∀X□∀y□(Haec(X, y) → □_X(Haec(X, y))).

Fifth, and finally, prefixing a formula such as the above with a necessity operator doesn’t require additional justification, since our hybrid contingentists take the existence of all higher-order entities to be non-contingent. In responding to the haecceities objection, contingentists are thus entitled to rely on the following principle:

We noted that the notion of essence at play in this principle is to be understood in the demanding Finean sense. We can be even more specific. Fine (1995: 276ff.) distinguishes between constitutive and consequential essence, where the latter is the logical closure of the former: that Plato is human is plausibly part of his constitutive essence, in which case it is part of his consequential essence that he is human or a mollusk.

Furthermore, Fine (1995: 281ff.) distinguishes between immediate and mediate essence, where only the latter is subject to a certain type of ‘chaining’: that {Plato} contains Plato is plausibly part of its immediate essence, and that Plato is human is plausibly part of his immediate essence. In this case, it is part of the mediate essence of {Plato}, but not part of its immediate essence, that it contains something human.

In an important sense, it is the immediate constitutive essence of an entity that characterises what the entity is in its most core respects, and it is this notion of essence with which (Essential Haecceities) is concerned: the principle ensures, for instance, that for each haecceity of Plato, locking onto Plato is a core feature of the haecceity, in the sense of belonging to the haecceity’s immediate constitutive essence (rather than merely to its consequential or mediate essence).

When understood in the way described, (Essential Haecceities) will afford a response to the haecceities challenge once it is combined with plausible views about the connection between essences and grounds.¹⁶

4.2 Essences as grounds

Suppose someone asks you why it is that a given sample of water is composed of H₂O. And let us stipulate, as done by Dasgupta in a very similar context (2016: 386), that the inquirer is interested neither in semantics nor in epistemology. She doesn’t want to know why it is that ‘water’ refers to a substance composed of H₂O. Nor does she want to know what reason we have to believe that water is composed of H₂O. Rather, she is interested in metaphysics. She is asking why (in a metaphysical sense) the sample of water is composed of H₂O. Once her question is understood in the intended metaphysical sense, it is very tempting to answer it by pointing out that it is part of the nature of the sample of water that it is a substance composed of H₂O. Being composed of H₂O is part of what it is to be water, and that is why the sample of water is composed of H₂O.

Motivated by considerations like these, Rosen (2010: 119), Kment (2014: 163), and Dasgupta (2014: 591, 2016: 386–7) have suggested that whenever it is part of the essence of x that S, then this very fact about the essence of x serves as a full ground for the fact that S.¹⁷ Following Fine (2012: §1.4) in using the connective < (which connects a sentence S, stating the grounded, and a sentence Q, stating its full grounds, so that Q < S can be read as ‘S because Q’), and making the full modal force of the principle explicit, we can spell it out as follows:

Put like this, the principle applies not only to all actual individuals but also to those which the contingentists regard as merely possible. It further ensures that the role of essence facts as grounds is non-contingent: if the fact that it is part of the essence of a water sample to be composed of H₂O grounds the fact that it is so composed, it shouldn’t be possible for the fact that it is part of the essence of the water sample to be composed of H₂O to obtain, without it grounding the fact that the water sample is so composed.

Again, it is vital that the notion of essence at work here is understood in the Finean sense. Otherwise, the principle would render the fact that there are infinitely many primes (and any other necessity) grounded in the essence of Plato (and that of any other individual). And, again, it is immediate constitutive essence that the principle is concerned with (see Dasgupta 2014: §XI). If it were to apply to consequential essence, for instance, it would render any logical truth fully grounded in the essence of any individual.

As stated, (Essences as Grounds) concerns only the essences of individuals. Given that claims concerning the essences of individuals can serve as grounds in the way captured by the principle, one would expect the same to hold for essences of properties. Why would higher-order essences not give rise to the same grounding patterns as their first-order cousins? In any case, the motivation for the first-order principle carries over to the corresponding higher-order principle. If someone were to ask why it is that the property of being human is concreteness requiring, we would find it adequate to respond that that is simply part of the nature of this property. Higher-orderising the principle thus doesn’t distract from its plausibility:

4.3 Fundamental essences

Let’s go back to the imagined conversation regarding the composition of the water sample. In particular, suppose that your interlocutor reacted to your initial response that the sample is composed of H₂O because it is part of its nature to be composed of H₂O as follows: ‘I get that the sample of water is composed of H₂O because that is part of its nature. But why is that? Why is being composed of H₂O part of what it is to be a sample of water?’ As Dasgupta (2016: 386) observes, one is tempted to dismiss the question as illegitimate or else tempted to say something along the lines of ‘that is just what water is …’. But, he goes on to point out, in doing the latter one would of course just be restating the very fact one was asked to explain, so that this response too is most naturally heard as trying to resist the request for further explanation. And this seems like just the right thing to do, for it seems that at this point the interlocutor is simply asking for an explanation where no explanation is to be had. This suggests that essence facts are explanatorily fundamental in the sense of not having any grounds themselves. Using Fund(S) to abbreviate ∀Q¬(Q < S) and making, again, the principle’s intended modal force explicit, we can capture this idea with the following principle:

It is, once more, important that we are concerned with immediate constitutive essence (see Dasgupta 2014: §XI; Glazier 2017: 2879). Otherwise (Fundamental Essences) would conflict with certain (not implausible) views, such as that (i) it is part of the essence of {Plato} that it has some member while (ii) this essence fact is grounded in the further essence fact that it is part of the essence of {Plato} that it has Plato as a member. In fact there is no conflict, for plausibly only the latter essence fact concerns the immediate constitutive essence of {Plato}; that the former essence fact has a ground thus doesn’t constitute a counterexample to (Fundamental Essences).

Some additional comments may help to further clarify (Fundamental Essences). First, note that Dasgupta (2014: §§VII, XI; 2016: §3) in fact subscribes to the principle that all essence facts are autonomous, by which he means that they lack grounds (i.e. are fundamental in our sense) and, furthermore, are not even apt for being grounded. Dasgupta thus subscribes to a principle strictly stronger than ours. Our contingentist response to the haecceities objection, while being compatible with Dasgupta’s position, requires only accepting (Fundamental Essences) and doesn’t require accepting Dasgupta’s stronger principle nor its underlying distinction between ungrounded facts apt for being grounded and ungrounded facts unapt for being grounded.

Second, it may appear that (Fundamental Essences) conflicts with an argument by Tillman (2016) to the effect that ‘at least some essence facts […] do have a [grounding] explanation’ (191). The appearance is misleading and results from a varying use of the expression ‘essence fact’. Suppose it is part of the essence of table t to be wooden (□_t(Wt)). What I mean by an ‘essence fact’ is the fact that □_t(Wt), while Tillman means the fact that Wt. He is arguing, for instance, that the fact that Wt is grounded in the fact that t is composed of particular cellulose fibres arranged in a particular way. Since his argument is thus silent on the grounds of □_t(Wt), it doesn’t conflict with (Fundamental Essences).¹⁸

Just like (Essences as Grounds), (Fundamental Essences) only concerns the essences of individuals. But, again, the motivation for it carries over to the higher-order case. We already noted that if someone were to ask why it is that the property of being human is concreteness requiring, we would find it adequate to respond that that is simply part of the nature of the property of being human. If our interlocutor was to ask why this is so, we would feel that a point has been reached where no further explanation is to be had. (Fundamental Essences) thus doesn’t lose any of its plausibility if it is made to concern essences of higher-order entities:

4.4 Addressing the haecceities objection

The account developed in §§4.1–4.3 allows hybrid contingentists to address the haecceities objection on the grounding construal. The challenge is to find grounds for the fact that a given haecceity of Plato locks onto Plato, grounds which remain available in the absence of Plato. The trio of (Essential Haecceities), (Essences as Grounds_HO), and (Fundamental Essences_HO) affords an answer to this challenge: rather than regarding haecceity facts as partly grounded in contingent facts concerning the existence of the individual being locked onto, the principles render haecceity facts fully grounded in necessary facts about the essence of the property that does the locking, facts which are themselves necessarily fundamental.

Let’s go through the reasoning in detail. Consider the property of being identical to Plato (P) which, as our contingentists accept, locks onto Plato (p) in all possible circumstances: □Haec(P, p). The challenge for the contingentists is now to say what grounds the fact that P locks onto p, i.e. the fact that Haec(P, p), in those possible circumstances in which p is absent. To meet the challenge, we first note that the following is an instance of (Essential Haecceities):

(14)

So, in all possible circumstances, if P locks onto p, then it is part of the essence of P to lock onto p. Together with □Haec(P, p) this entails, by uncontroversial modal reasoning, that, in all possible circumstances, it is part of the essence of P to lock onto p:

(15)

Next, we note that (Essences as Grounds) ensures that, in all possible circumstances, if it is part of the essence of P to lock onto p, then this essence fact fully grounds the fact that P locks onto p. That is, we have:

(16)

From (15) and (16) it follows, by uncontroversial modal reasoning, that, in all possible circumstances, the fact that P locks onto p is fully grounded in the fact that it is part of the essence of P to lock onto p:

(17)

We now note that (Fundamental Essences) ensures that, in all possible circumstances, if it is part of the essence of P to lock onto p, then this essence fact is fundamental. That is, we have:

(18)

From (15) and (18) it follows, by uncontroversial modal reasoning, that, in all possible circumstances, the fact that it is part of the essence of P to lock onto p is fundamental:

(19)

In tandem, (17) and (19) provide our contingentists with an answer to the haecceities challenge: in all possible circumstances, including any in which p is absent, the fact that P locks onto p is grounded in the fact that it is part of the essence of the haecceity P to do so, a fact which in all possible circumstances, including any in which p is absent, is a fundamental fact, a fact itself not in need of further grounds.

The reasoning is not threatened by the fact that our hybrid contingentists, qua first-order contingentists, will adopt, with respect to their first-order quantificational apparatus, a free logic with its characteristically weakened rules of existential generalization and universal instantiation (see Williamson 2013: 39–43 for discussion). While, in such a setting, (Essential Haecceities) does not entail (14) by itself, it still does so in tandem with the unproblematic additional assumption that the individual in question possibly exists (♢∃x p = x).

In general, given the non-contingency of haecceity facts, i.e. given

(20)

(Essential Haecceities) and (Essences as Grounds) together entail, even given free first-order quantifiers, that it is impossible for any possible haecceity to lock onto any possible target, without this fact being necessarily grounded in the fact that the haecceity essentially locks onto the target:

(21)

And, again given (20), (Essential Haecceities) and (Fundamental Essences) together entail, even given free first-order quantifiers, that it is impossible for any possible haecceity to lock onto any possible target, without it being a necessarily fundamental fact that the haecceity does so essentially:

(22)

Together, (21) and (22) ensure that it is impossible for any possible haecceity to lock onto any possible target without this fact being necessarily grounded in the necessarily fundamental fact that the haecceity does so essentially.

A potential worry about this response to the haecceities challenge is that one of its central claims about the essences of haecceities might come back to bite our hybrid contingentists via an essence-based account of ontological dependence (for which, see Fine 1995). When extended to higher-order entities, such an account will have it that X ontologically depends on y just in case y features in X’s essence. Plausibly, the present response, via entailing □_P(Haec(P, p)), renders Plato featuring in the essence of his haecceity P. When combined with an essence-based account of dependence, it thus entails that the haecceity ontologically depends on Plato. And this may seem problematic, since ontological dependence is often taken to entail necessitation: if X ontologically depends on y, then X cannot exist without y existing too. But, of course, our hybrid contingentists cannot accept that any of Plato’s haecceities necessitates him, since they take all haecceities (like any other higher-order entities) to exist necessarily, but Plato to exist contingently. I will address this objection in detail in §5. Before that, though, §§4.5–4.8 illustrate that the present response strategy is robust with regard to a variety of alternative choices in formulating the haecceities challenge. While I discuss each variation in isolation, they could also be combined. But the same is true for the respective modifications of the contingentist response which I trust will become apparent without explicit discussion.

4.5 Varying the explanandum: tracking facts

So far we’ve followed Williamson (2016) in construing the haecceities challenge as concerned with simple haecceity facts

(2)

rather than with tracking facts which contain an extra conjunct making explicit that the target of the haecceity is unique in the sense that nothing other than it could have been locked onto by the haecceity (see §2.1):

(1)

We justified this simplification with the observation that the haecceity conjunct uncontroversially entails the uniqueness conjunct. Now it may be objected that while this simplification is clearly acceptable in the intensional setting in which Williamson develops the haecceities objection, it is less clear that it is acceptable once we move to a hyperintensional setting that we identified as a more natural habitat for the objection in §3.2. The point is not that the question of whether the haecceity conjunct entails the uniqueness conjunct depends on this choice (it doesn’t) but that only in an intensional setting the entailment ensures that the proposition expressed by (2) is identical to that expressed by (1). So, a necessitist might object to the account proposed in §4.4 by granting that the haecceities objection is best understood as a request for a grounding explanation but insisting that it is the whole of (1) that contingentists should provide a grounding explanation for, not just (2).

It is not obvious that our contingentists have to agree with this. Rather, they may insist that it is (2) whose obtaining in the relevant circumstances is in direct need of an explanation and that, for the reasons discussed in §3.1, the explanation needed is a grounding explanation. Insofar as an additional explanation for the obtaining of (1) in the relevant circumstances is needed, they may go on to maintain, this need is met by the mixed explanation that results from combining the grounding explanation for (2) with the observation that (2) uncontroversially entails (1).

Still, it is useful to see that, if our contingentists were to accept the need for a pure grounding explanation of (1), they could extend the account from §4.4 to meet that need too. For it doesn’t seem unreasonable for them to maintain that P’s locking onto p not only entails the fact that P can’t lock onto anything else, but also serves as a full ground for that fact. In general they may plausibly endorse:

Armed with this, a pure grounding explanation for a simple haecceity fact of the form (2) can be easily extended to a pure grounding explanation for the corresponding tracking fact of the form (1).

It may be worried that there is a conflict lurking between this strategy and (Fundamental Essences). For it may be felt, firstly, that it is not only part of the essence of P that P locks onto p, □_p(Haec(P, p)), but also that P can’t lock onto anything but p, □_p(Unique(P, p)). And it may seem, secondly, that, given Haec(P, p) < Unique(P, p), the first essence fact should ground the second, □_p(Haec(P, p)) < □_p(Unique(P, p)), contradicting the fundamentality of essence facts.

This worry can be dispelled by recalling from the discussion in §§4.1–4.3 that the claim □_p(S) states that it is part of the immediate constitutive essence of P that S and that our principles concerning essence, including (Fundamental Essences), are exclusively concerned with this narrow notion of essence. We can thus reject □_p(Unique(P, p)) but still allow, without incurring any conflict with (Fundamental Essences), that it is part of the consequential essence of P that Unique(P, p) (which is, after all, a consequence of Haec(P, p)) and that this fact about P’s consequential essence is grounded in □_p(Haec(P, p)), a fact about its immediate constitutive essence.

4.6 Varying the explanandum: existential haecceity facts

Another interesting variation of the challenge has been floated by Goodman (2016: 619). He suggests that, rather than focussing on simple haecceity facts of the form (2), the objection should be construed as focussing on the corresponding existential facts, such as:

(23)

In support of this construal, Goodman reminds us that the haecceities objection is meant to target hybrid contingentists, not uniform contingentists. And he notes that what distinguishes the hybrid contingentists considered by Williamson (2013: Ch. 6, §4) from their uniform counterparts is not the claim that (2) would have still been true if Plato had been absent, but the claim that (23) would have still been true. Goodman therefore suggests that (23) is the more natural target for the objection. Williamson (2016: 643) disagrees and still prefers to construe the objection as focussing on (2).

Without taking a stance on this dispute, we may note that it can only strengthen the contingentists’ position if their response to Williamson’s challenge can be extended to additionally address Goodman’s. And it seems that it can. For it is a popular idea among grounding theorists that existential quantifications are fully grounded in each of their true instances. Focussing on higher-order quantifications, the idea can be captured by the following typically ambiguous schematic principle (where F is to be uniformly replaced by an arbitrary predicate, X by a predicate variable of the corresponding syntactic type, and A( ) by a suitable predicate context):¹⁹

Assuming, as is plausible, that the grounding pattern (Existential Grounding_HO) seeks to capture is non-contingent, its instances may be prefixed with a necessity operator, thus licensing the inference of:

(24)

Given □Haec(P, p), this entails

(25)

With (Existential Grounding_HO) in place, the response to Williamson’s challenge provided in §4.4 can thus straightforwardly be turned into a response to Goodman’s challenge: in all possible circumstances, including any in which Plato is absent, ∃X Haec(X, p) is fully grounded in Haec(P, p). As before, in all possible circumstances, this fact is in turn fully grounded in □_p(Haec(P, p)), which, in all possible circumstances, is fundamental.

There is a well-known reason to be wary of principles such as (Existential Grounding_HO) for anyone who is a contingentist about the entities in the range of the quantifier at issue.²⁰ Since our hybrid contingentists are necessitists about all higher-order entities, this is not a reason for them to be wary of (Existential Grounding_HO). The principle does, however, face an entirely general difficulty (see Krämer 2013). For it has the following problematic instance (which results from letting F be the zero-place predicate ∃X X, letting A( ) be the null context, and letting X be a sentential variable):

(26)

This instance is problematic since its antecedent is true but its consequent conflicts with the widely accepted irreflexivity of grounding.

It is a matter of controversy what the right reaction to this problem of existential ground is, but the contingentists’ response to Goodman’s challenge just outlined remains intact on some of the main promising strategies suggested by (or on behalf of) grounding theorists: First, Correia (2014b) and Woods (2018) propose to allow for isolated cases of reflexive grounding, a concession which throws up no specific problems for the present response. Second, blaming the problem on the impredicativity of instances such as (26), Krämer (2013) suggests restricting (Existential Grounding_HO) to instances in which F is itself free of higher-order quantifiers. Since the instance needed by our contingentists to address Goodman’s challenge is not ruled out by such a restriction, this strategy does not conflict with the present response either. Third, developing an idea due to Fine (2010), Fritz (2021: §3.3.1) suggests allowing a truth S in one capacity (e.g. as an example of an arbitrary truth) to ground S in another capacity (e.g. as an existential quantification), a proposal he makes precise in a way consistent with the irreflexivity of ground. In the resulting setting, the task of grounding ∃X Haec(X, p) in its capacity as an existential quantification consists in grounding a specific ‘t-complex’ associated with that formula. And, in that setting, Haec(P, p) will be ensured to ground this t-complex via a property-analogue of Fritz’s principle (∃S*) with which he captures, in the propositional case, the idea that higher-order quantifications are grounded in their instances.²¹

4.7 Varying the form of explanation: contrastive explanation

We noted in §3.1 that the original formulation of the haecceities objection contains a contrastive element: contingentists are asked to explain what makes Plato rather than something else the target of his haecceities in circumstances where Plato is absent. We noted also that this contrastive element doesn’t render the proposed grounding interpretation of the objection any less plausible. Now, one may grant this but object that the grounding-based response to the haecceities objection from §4.4 doesn’t do justice to the objection’s contrastive nature.

The response from §4.4 can be extended to allay such worries. A natural way to make the contrastive nature of grounding explanations explicit is due to Schaffer (2012, 2016). His contrastive treatment of grounding involves viewing grounding claims as having the following form (2012: 130):

(27)

We don’t have to follow Schaffer in taking all grounding claims to exhibit this form but may simply acknowledge that some do. Or rather we may take some grounding claims to have the form that results from transposing (27) into our setting, which takes the canonical way of formulating grounding claims to involve the sentential connective < rather than a relational predicate ‘grounds’ in combination with talk of facts. A natural way to do so is to allow the grounding connective to be flanked by pairs of sentences:

(28)

For a statement of the form (27) to be true, Schaffer requires that the fact that Q* (the fact that S*) be a non-obtaining fact constituting an alternative to the obtaining fact that Q (the fact that S). In our setting, this corresponds to the requirement that for a statement of the form (28) to be true, Q* (S*) be a false sentence stating an alternative to what is stated by the true sentence Q (S).

Now, the account from §4.4 delivered the result (17) that P’s locking onto Plato is necessarily grounded in the fact that it is essential to P to lock onto Plato. In combination with the observation that, necessarily, P doesn’t lock onto Aristotle and that, necessarily, it is not essential to P to lock onto Aristotle, we may naturally take this to support the contrastive grounding claim that, necessarily, P’s locking onto Plato, rather than onto Aristotle, is grounded in P’s essentially locking onto Plato rather than P’s essentially locking onto Aristotle:

(29)

Next, following Schaffer’s usage, but adjusting it to our setting, we may call a pair of sentence S and its contrast S* a difference. The account from §4.4 delivered the result (19) that it is necessarily fundamental that it is essential to P to lock onto Plato. Combining this with the observation that, necessarily, it is not essential to P to lock onto Aristotle, we may naturally take this to support the claim that it being essential to P to lock onto Plato, rather than it being essential to P to lock onto Aristotle, is a fundamental difference (in a sense of fundamentality, Fund*(S, S*), appropriately extended to cover differences (see Schaffer 2012: 133)):

(30)

In tandem, claims such as (29) and (30) allow us to take seriously the contrastive element of the haecceities challenge and still account for it.

4.8 Varying the notion of explanation: essentialist explanation

Glazier (2017) has argued that (Fundamental Essences) remains problematic even when understood to concern immediate constitutive essence. He observes that it will have implausible consequences when combined with the view that an entity is fundamental as soon as it features in some fact that is fundamental. For consider the claim that a philosophy conference is, as a matter of immediate constitutive essence, a social event. The claim is not implausible but entails, together with (Fundamental Essences) and the present conception of fundamental entities, that philosophy conferences are fundamentalia, which seems implausible.

A possible response here is to reject the account of fundamentality and e.g. maintain instead that an entity is fundamental just in case the fact that it exists is a fundamental fact. But this is not the response I want to focus on. Rather, I’d like to point out that even a much more concessive reaction to the present criticism of (Fundamental Essences) leaves the general response strategy to the haecceities objection largely intact. The conclusion which Glazier draws himself from the above observation is that metaphysical explanations should be seen as a genus of which grounding explanations constitute but one species. Essentialist explanations are to be regarded as a distinct species of metaphysical explanations. Contingentists sympathetic to this conclusion can still respond to the haecceities objection without much need for adaptation. For, importantly, Glazier agrees that (i) the fact that it is essential to x that S serves to explain that S and that (ii) by providing an essentialist explanation we have reached, in an important sense, explanatory bedrock. He just thinks that the explanation mentioned in (i) is not a case of grounding, but an essentialist explanation in its own right and, accordingly, that (ii) should not be understood as the claim that essence facts lack grounding explanations but as the claim that they lack essentialist explanations. Contingentists sympathetic to this account will take the considerations from §3 to motivate the idea that the haecceities objection is a challenge to provide a metaphysical explanation (which, by their lights needn’t be a grounding explanation). And they will take the considerations from §§4.1–4.4 to point to such a metaphysical explanation, although they will interpret it as an essentialist explanation, not as a grounding explanation.

5.1 The dependence objection

The essence-based response to the haecceities objection developed in §4 crucially involves the claim that locking onto Plato is part of the essence of each of his haecceities, such as P:

(31)

We noted that this essence claim might appear to lead to trouble when combined with an essence-based analysis of ontological dependence as developed in Fine 1995. On that analysis, x’s depending on y is taken to be a matter of y’s occurring in a proposition that belongs to x’s essence. (Here and in the following, any talk of dependence is short for talk of ontological dependence.) Treating quantification over propositions as quantification into the position of sentences and letting Occurs(x, S) stand for the relation of an individual occurring in a proposition (which we follow Fine in regarding as primitive), such an account entails the following principle:²²

Fine’s account is attractive because it allows (in combination with plausible background assumptions) for the correct classification of certain paradigmatic instances (and counter-instances) of dependence which competing accounts fail to accommodate. Thus, modal accounts of dependence cannot allow for asymmetric dependence relations between entities with the same modal-existential profile, such as the singleton {Plato} and its only member Plato. The essence-based (Dependence), in contrast, delivers the intended result that {Plato} depends on Plato (but not vice versa) when combined with the assumptions that Plato occurs in the proposition expressed by ‘Plato ∈ {Plato}’ and that it is true that □_{Plato}(Plato ∈ {Plato}) but false that □_Plato(Plato ∈ {Plato}).

We can now formulate the present dependence objection to our contingentists more precisely. First, to the extent that Fine’s analysis of what it means for a first-order entity to depend on another first-order entity is plausible, it is natural to endorse, in the present setting, an analogous analysis of what it means for a higher-order entity to depend on a first-order entity. Such an account will entail the following principle:

Second, given that Plato counts as occurring in the proposition expressed by ‘Plato ∈ {Plato}’, he should presumably also count as occurring in the proposition expressed by Haec(P, p), the proposition that the property of being identical to Plato locks onto Plato. But then the combination of (Dependence_HO) and the crucial essence claim (31) renders Plato’s haecceity P dependent on Plato. Third, the objection continues, x’s depending on y is often taken to imply that x necessitates y (in the sense that, necessarily, x exists only if y does):

For instance, {Plato} uncontroversially necessitates Plato. And Fine seems to subscribe to the general principle (Dep to Nec) when he says in the opening paragraphs of his 1995 paper that ‘if something is taken to exist, then so must anything upon which it depends’ (269). To the extent that (Dep to Nec) is plausible, we should again accept the following higher-order version:

But then the fact that Plato’s haecceity P depends on Plato entails that Plato’s haecceity P necessitates Plato. This, however, hybrid contingentists cannot accept, since they take the haecceity to exist necessarily but Plato to exist contingently. The objection concludes that the contingentists’ response to the haecceities challenge is inconsistent with (a higher-orderisation of) Fine’s essence-based account of dependence. And this is bad, not only because an attractive account of dependence is thereby placed beyond their reach but also because, dissatisfyingly, it is precisely the contingentists’ reliance on a Finean notion of essence in response to the haecceities challenge which forces them to reject this account.²³

In the following my aim is to address the dependence objection by showing that, first appearance to the contrary, the essence-based response to the haecceities challenge coheres well with Fine’s essence-based account of dependence. We will see, in §5.2, that Fine in fact takes it to be an advantage of his analysis of dependence that it avoids a commitment to (Dep to Nec). Indeed, he does so precisely to allow that haecceities, which he conceives of as first-order entities, depend on their targets but do not necessitate them. A higher-orderisation of Fine’s analysis will thus not contain (Dep to Nec_HO) either, so the immediate problem is avoided. There is, however, a follow-up worry: if haecceities constitute the only exception to the dependence to necessitation link, the hybrid contingentists’ position may still appear to involve some kind of special pleading. To dispel the follow-up worry, I develop Fine’s account in two dimensions. In §5.3, I provide an independent case in which dependence does not result in necessitation. In §5.4, I explain what distinguishes those cases in which dependence results in necessitation from those in which it doesn’t.

5.2 A closer look at Finean ontological dependence

In spite of Fine’s remarks mentioned in §5.1, his considered view is that dependence should not be taken to entail necessitation and that it is an advantage of his analysis of dependence that it avoids commitment to (Dep to Nec). Thus, before endorsing (Dependence), Fine considers an alternative, according to which x’s depending on y boils down to x being essentially such that it exists only if y does (1995: 272–4). This alternative analysis entails:

Like (Dependence), (Dependence*) allows for asymmetric dependencies between entities with the same modal-existential profile, such as {Plato} and Plato. But Fine is not satisfied with (Dependence*), and an important reason for his dissatisfaction is that he thinks that an account of dependence should be compatible with contingentists maintaining that (necessarily existing) haecceities, which Fine, unlike us, treats as first-order entities, depend on their (contingently existing) targets (274). (Dependence*), however, is not compatible with this position since it uncontroversially entails (Dep to Nec). In contrast, Fine points out, (Dependence) is compatible with the contingentist position and should therefore be preferred over (Dependence*).²⁴

In its current form, the dependence objection can thus be rejected: Fine did not in fact incorporate (Dep to Nec) into his official account of dependence. A higher-orderisation of his account therefore shouldn’t incorporate (Dep to Nec_HO) either. So, the essence-based response to the haecceities challenge doesn’t conflict with (a higher-orderisation of) Fine’s actual account.

This certainly is a welcome observation for our hybrid contingentists, but some doubts may linger on. For it is striking that compatibility with necessary haecceities depending on contingent targets is the only reason Fine ever gives for doubting that dependence always leads to necessitation.²⁵ In light of this, the dependence objection may be refined: granted, Fine’s actual account does not incorporate an entirely general dependence to necessitation link. But consider a variant of Fine’s account that does. There is a good case to be made that this variant is preferable to Fine’s actual account. For if the contingentists’ haecceities constitute the only would-be exception to an otherwise entirely general and undisputed principle connecting dependence to necessitation, it might well be better to stick with the general principle. In particular, since the would-be exception seems, at least so far, entirely unprincipled: if dependence results in necessitation in all other cases, why is this supposed to be different when it comes to haecceities depending on their targets? So, it might well be better to hold onto the dependence to necessitation link in full generality and to simply deny contingentists their extravagant dependence claim. That the essence-based response to the haecceities objection forces our hybrid contingentists to make that dependence claim is simply a reason to reject that response.

For all that has been said, this version of the dependence objection is in good standing. But, fortunately, more can be said. Specifically, contingentists can show that the connection between dependence and necessitation is not as general as the objection makes out, but subject to further, independent counterexamples (§5.3). What is more, they can give a precise account of the principle determining whether or not dependent entities necessitate what they depend on (§5.4).

5.3 Finean ontological dependence without necessitation

Contingentists can provide an independent reason (independent from the case of haecceities, that is) for why a Finean account of dependence should not take dependence to always result in necessitation. The reason is that the account otherwise threatens to become incompatible with flexible essentialism, the view that some individuals have flexible essences. The essence of an individual is flexible with respect to a certain feature if the individual can survive slight but not arbitrarily large variation of the feature. Plausible examples include the essences of concrete artefacts which are often taken to be flexible with respect to their material origins. For instance, it is often thought that a given chair could have been made from a slightly different matter than it actually is (e.g. from matter that differs from the original only in a single molecule) but could not have been made from an entirely different hunk of matter (e.g. from matter that doesn’t share any molecules with the original).

Arguably, flexible essentialism is a majority position.²⁶ But, to echo a methodological point frequently stressed by Fine (1994: 5, 1995: 274), the strength of the argument to be developed against (Dep to Nec) does not rest on flexible essentialism being correct: the legitimacy of an account of dependence should not be made to rest on the falsity of a respectable modal view such as flexible essentialism.

Before bringing out the conflict between (Dep to Nec) and flexible essentialism, it is perhaps worth emphasising that the aim of the present section is not to develop a comprehensive account of flexible essences from the perspective of a contingentist operating with Finean notions of essence and dependence (a worthwhile project which, however, goes beyond the scope of this paper). Rather, the aim is merely to make plausible that, from said perspective, a natural way to account for some flexible essences conflicts with a fully general dependence to necessitation link.

To bring out the conflict, let us contrast the view of Flexi, a contingentist who believes that chair c₀’s essence is flexible vis-á-vis its material origin m₀, with that of Stricto, a contingentist who believes that chair c₀’s essence is inflexible vis-á-vis its material origin m₀. Characterising Stricto’s position is easy enough. He thinks that c₀ is essentially made from m₀. Accordingly, he accepts the following, where Mxy stands for ‘x is made from y’:

(32)

By (Ess to Dep), the Finean account of dependence then renders the chair depending on its actual matter, a result which Stricto will happily accept. What is more, from Stricto’s perspective, there is no reason to object to (Dep to Nec) either, for he takes the chair to necessitate its actual matter anyway.

In contrast to Stricto, Flexi does not think that c₀ is essentially made from m₀, and accordingly she does not accept (32). Just how she is to characterise c₀’s essence in more positive terms has been the subject of some controversy. What is uncontroversial is that she takes c₀’s essence to allow for a range of possible origins, each member of which sufficiently overlaps c₀’s original matter m₀. To have a simple model, let us stipulate that c₀’s range of possible origins is {m₋₁, m₀, m₁}. It now turns out there are two importantly different ways to flesh out this idea.

Suppose, for the sake of definiteness, that sufficient overlap amounts to overlap by 99%. Uncontroversially, then, Flexi will allow that there is a possible world w₁ at which c₀ is made from m₁ instead of m₀, where m₁ shares 99% of m₀’s parts. Now, a well-known style of argument (see e.g. Chisholm 1973; Chandler 1976; Salmon 1981) has it that Flexi must also allow for a world w₂ at which c₀ is made from m₂, where m₂ shares 99% of m₁’s parts but only 98% of m₀’s parts. After all, the reasoning goes, c₀ is supposed to survive slight changes in material origin, and the change from w₁ to w₂ is as slight as that from w₀ to w₁.

To reason this way is to take c₀’s essence to be not only flexible but also shifting. For it involves the assumption that c₀’s range of possible origins shifts from one possible world to another: at w₀, c₀ is made from m₀, and m₀ is at the centre of c₀’s range of possible origins, a range which includes m₁ but does not include m₂. At w₁, however, where c₀ is made from m₁, it is m₁ which is at the centre of c₀’s range of possible origins. As a result, the range of possible origins shifts (in comparison to w₀) and now includes m₂ (but no longer includes m₋₁, which overlaps by 99% with m₀ but only by 98% with m₁).

If flexible essences are taken to be shifting, they come with enormous costs. For we simply cannot allow that w₂ is possible with respect to the actual world w₀ on pain of contradicting our explicit assumption that it is, in fact, impossible that c₀ be made from material that overlaps m₀ by less than 99%. The most promising attempt to avoid this is to maintain that the argument only shows that w₁ is possible with respect to w₀, that w₂ is possible with respect to w₁, and that this doesn’t mean that w₂ is possible with respect to w₀ (see e.g. Salmon 1981: §28.3). But this is a very high price to pay: it is to give up the principle that what is possibly possible is possible (ruling out S5, and even S4, as the background logic for metaphysical modality).²⁷

In light of these enormous costs, it is often found preferable to conceive of c₀’s flexible essence as fixed rather than shifting (see Williamson 1990; Leslie 2011; Roca-Royes 2016). Understood this way, m₀ is taken to be at the centre of c₀’s range of possible origins with respect to any world. Matter m₀ is thus not only at the centre of c₀’s range of possible origins with respect to w₀, where c₀ is made from m₀, but also at w₁, where c₀ is made from m₁. As a result, c₀’s range of possible origins remains fixed across all worlds.

This way of characterising flexible essences is compatible with S5. For while w₁ is still deemed possible (simpliciter), w₂ is now deemed impossible (simpliciter): c₀’s essence allows for the same origins at each world, and m₂ is not among them. A potential drawback of this account is that it may seem to unduly privilege the actual world w₀. To see this, contrast it with the shifting conception, according to which c₀’s actual origin is on par with all other possible origins: at each world w at which c₀ exists, we have whatever matter c₀ is made from at w at the centre of c₀’s shifting range of possible origins at w. On the fixed conception, in contrast, m₀ is assigned a privileged status vis-á-vis c₀: it is placed firmly at the centre of c₀’s fixed range of possible origins which it continues to occupy even at worlds where c₀ is made from different matter. This gives rise to an awkward question: Isn’t it a cosmic coincidence that we happen to find ourselves in world w₀ where c₀ is made from matter located right at the centre of its range of possible origins rather than in a world, such as w₁, where it is made from matter more peripherally located?

Proponents of the fixed conception have a response: Yes, c₀ is at the center of its range of possible origins at w₀, but this doesn’t result in privileging w₀ over w₁. For they claim that where we take to be one object c₀ at w₁ and w₂, there are in fact many distinct but spatially coincident objects: in particular, in addition to c₀ there is c₁ which spatiotemporally coincides with c₀ at all worlds at which they both exist. Like c₀, c₁ has a fixed flexible essence and thus a fixed range of possible origins. But the ranges are distinct: where c₀’s possible origins centre around m₀, c₁’s possible origins centre around m₁. Thus, c₁ is at the centre of its range of possible origins at w₁, and it is peripherally located at w₀, thereby compensating any privilege w₀ may have otherwise had over w₁.

While not without costs of its own, the fixed conception of flexible essences seems preferable to the shifting alternative. A Finean account of dependence had better be compatible with it. But it is hard to see how the Finean account could be compatible with this fixed conception of flexible essences, if the Finean account includes the principle (Dep to Nec). For a natural way for Flexi to characterise c₀’s fixed flexible essence is by endorsing the following:

(33)

To illustrate, the fixed flexible essence of c₁ is, in contrast, characterised as follows:

(34)

Focussing on the case of c₀, the hunks of matter m₋₁, m₀, m₁ presumably count as occurring in the proposition that Mc₀m₋₁ ∨ Mc₀m₀ ∨ Mc₀m₁, in which case (33) and (Ess to Dep) render c₀ dependent on these hunks of matter. In and of itself this dependence seems unproblematic and perhaps even desirable, given the special status these hunks of matter have, on the fixed conception of flexible essences, in determining c₀’s unalterable modal profile. But if Fine’s account also includes the principle (Dep to Nec), then it additionally renders c₀ necessitating each hunk of matter in its range of possible origins. And this would clearly be unacceptable to Flexi: while a strict essentialist will accept that c₀ can only exist in worlds where its actual matter exists, the whole point of flexible essentialism is that c₀ can be made from matter other than its actual matter, in which case c₀’s existence should not be taken to be constrained by that of its actual matter.²⁸ If the Finean account of dependence is to be compatible with the natural idea of capturing c₀’s flexible essence with a claim such as (33), it thus cannot incorporate the principle (Dep to Nec). This means the putative, entirely general connection between dependence and necessitation is to be rejected for reasons independent of the case of haecceities depending on their targets.

5.4 When does ontological dependence result in necessitation?

We’ve already gone a long way towards addressing the dependence objection in its refined form from §5.2. Contrary to it, there are independent reasons for contingentists to resist a general dependence to necessitation link. Our rebuttal of the dependence objection will be complete if we can additionally dispel the impression that, in rejecting that link, our contingentists have to make an unprincipled distinction between cases where dependence comes with necessitation (such as {Plato} depending on Plato, or a chair depending on its matter if its essence is taken to be inflexible) and cases where it doesn’t (such as Plato’s haecceities depending on Plato, or a chair depending on the hunks of matter in its range of possible origins if its essence is taken to be flexible).

The impression can be dispelled as follows. First, contrast essence claims that give rise to necessitating dependence with essence claims that give rise to non-necessitating dependence.

Necessitating Dependence: {Plato} necessitates Plato, and the singleton is rendered dependent on its member Plato as a result of the following essence claim:

(35)

On Stricto’s view, c₀ necessitates m₀, and the chair is rendered dependent on its matter m₀ as a result of the following essence claim:

(32)

Non-Necessitating Dependence: On Flexi’s view, c₀ does not necessitate m₋₁, m₀, m₁, and it is rendered dependent on these hunks of matter as a result of the following essence claim:

(33)

According to our hybrid contingentists, Plato’s haecceity P does not necessitate Plato, and it is rendered dependent on Plato as a result of the following essence claim:

(31)

Second, recall the notion of a term position being existence-demanding from §2.3: The position in which term t occurs in sentence A(t) is existence-demanding just in case A(t) logically entails ∃x t = x. And remember that we are following Williamson’s lead in taking contingentists to endorse the Being Constraint, which means that they must accept term positions in predications, but only in predications, as existence-demanding (where a predication was defined as the direct result of applying an n-place predicate to n individual constants or variables).

Now a striking difference between those essence claims resulting in necessitating dependence and those resulting in non-necessitating dependence is this: in the former cases, the sentences in the scope of the essence-operator are best formalised as predications: the direct result of applying a two-place relational predicate (the predicate ∈ and M, respectively) to two individual constants. Accordingly, these sentences are subject to the Being Constraint, and our contingentists will regard their term positions as existence-demanding.

In the latter cases, this is different: neither Mc₀m₋₁ ∨ Mc₀m₀ ∨ Mc₀m₁ nor Haec(P, p), which, recall, abbreviates □∀x(Px ↔ x = p), is a predication, and our contingentists will neither take Haec(P, p) to entail ∃x p = x nor take Mc₀m₋₁ ∨ Mc₀m₀ ∨ Mc₀m₁ to entail a claim of the form ∃x m_i = x. In other words, even given the Being Constraint, our contingentists will neither take the term p to occur in an existence-demanding position in Haec(P, p) nor take any term of the form m_i to occur in an existence-demanding position in Mc₀m₋₁ ∨ Mc₀m₀ ∨ Mc₀m₁.

This, however, suggests that our contingentists have a principled way of distinguishing between those cases where dependence comes with necessitation and those where it doesn’t. The principle is this: While the truth of an essence claim of the form □_a(A(b)) (or, respectively, of the form □_F(A(b))) is sufficient for the individual a (the property F) to depend on the individual b, it is not sufficient for the individual a (the property F) to necessitate b. Rather, whether or not the dependence comes with necessitation hinges on the further question of whether or not the position occupied by the term b in the sentence A(b) is existence-demanding. If the answer is ‘yes’, then the truth of □_a(A(b)) (the truth of □_F(A(b))) not only guarantees that the individual a (the property F) depends on the individual b but also that a (F) necessitates b. If the answer is ‘no’, then the truth of □_a(A(b)) (the truth of □_F(A(b))) only guarantees that the individual a (the property F) depends on the individual b but not that a (F) necessitates b.

Our contingentists can thus comprehensively reject the dependence objection, even in its most sophisticated form from §5.2. First appearance to the contrary, the essence-based response to the haecceities challenge from §4 fits in seamlessly with a Finean essence-based account of dependence. While it requires the rejection of a general connection between dependence and necessitation, such a connection was never meant to be part of that account anyway, and there are good, independent reasons for why it shouldn’t be. What is more, rejecting the connection does not commit contingentists to an unprincipled distinction between necessitating and non-necessitating dependence, since they can give a precise account of the principle underlying this distinction.