The Modal Status of Generative Principles

1.

Like most American schoolchildren of my generation, I was raised to believe that the essential properties of an object are the properties it possesses in every possible world (or every world in which the thing exists). But then I read ‘Essence and Modality’ (Fine 1994) and learned that this is not the only way to think of essence, or the best way. It is not the only way because we possess a more fine-grained conception, with a similar Aristotelian pedigree, according to which a thing’s essential properties are the properties it possesses, by its very nature, in virtue of being the thing it is. (It may be a necessary truth, concerning Aristotle, that Aristotle is not the Eiffel Tower; and yet it is no part of Aristotle’s nature to stand in this or any other relation to the Tower.) And it is not the best way because the fine-grained notion is useful in contexts where the modal notion is too blunt a tool. In a paper from around the same time, Fine puts the essentialist account to work in analyzing the concept of ontological dependence (Fine 1995a). But the main application in ‘Essence and Modality’ is the analysis of metaphysical modality itself, and that is what I want to focus on.

The analysis can be put in several ways, but the main idea is straightforward. I’m going to follow Fine’s approach from the 1990s in regimenting claims of essence by means of an indexed sentential operator (Fine 1995b). It lies in the nature of x that p — or better: it lies in the nature of xx that p, where xx can be a plurality. In this format, we say that Socrates is essentially human by saying that it is essential to Socrates that Socrates is human. In symbols, □_s Hs. The analysis of metaphysical necessity is then some version of this:

(1) p is metaphysically necessary iff_df for some xx, it is essential to xx that p.¹

The metaphysically necessary truths are the essential truths: the truths that hold in virtue of the essences of things.

Fine’s early work on essence focused on the essences of individuals and the de re necessities they generate. But any general account will presumably allow essences of entities at every type, including properties and relations (by which I mean, the values of the higher-order variables). It should lie in the nature of bachelor that bachelors are unmarried in the same sense in which it lies in the nature of Socrates that Socrates is human. And once we note this, a certain streamlining is possible, and in fact desirable.

It is a premise of my discussion that ordinary objects like Socrates exist contingently — or at least, that the logic of essence and modality should not say otherwise. But then we face an awkward question from the start. The necessary truths concerning Socrates must have a source: there must be some item x whose nature is responsible for the truth in question. But these truths obtain at worlds at which Socrates does not exist. So what is their source there? Whose nature is responsible for the fact that Socrates is necessarily human (if he exists) when Socrates himself does not exist?

There are ways to answer that retain the idea that Socrates is the source of the truths in question, e.g., by allowing that non-existent objects can have essences that ground the necessities in question. But we can avoid this oddness by taking a leaf from Fine’s more recent work (Fine 2015). On this alternative approach, claims about the essences of individuals are to be construed as claims about the essences of certain properties. Ask not for the essence of Socrates, the man. Ask instead for an account of what it is to be Socrates, i.e., for an account of the essence of a property that Socrates alone instantiates when he exists and which nothing instantiates if he does not. In Fine’s version, the relevant property is an identity property, λx. x = s. But then problems analogous to those raised above will recur. (Can this property exist if Socrates does not?) So I’m going to treat the relevant property as a simple, non-relational property: is-Socrates or Socratizes.² This is a property — a way for things to be — that can happily exist even if Socrates does not. In worlds without Socrates it is simply a property nothing has.³ So my preferred formulation of the claim that Socrates is essentially human is this:

which promises to be altogether neutral with respect to the inventory of objects, as was wanted.⁴ As Fine notes, this reconstrual of claims about individual essences as claims about the essences of properties is not unnatural. When we ask for the essence of Socrates, the question can be put, ‘What is it to be Socrates?’, a question on a par with ‘What is it to be a bachelor?’, both of which are naturally heard as questions about what it is to possess a certain property.

2.

Now that we have shifted focus from claims about the essences of individuals to claims about the essences of certain corresponding properties, we can ask a general question: What can go into the essence of a property F? That is, what sort of proposition can go in for p in true claims of the form □_F p?

The simplest answer would say that p can be anything at all. But this is hopeless for reasons it pays to articulate. Take a run of the mill contingent proposition like Jane is a banker. Grant that it does not lie in the nature of Jane, or banker, or the two together that Jane should be a banker. Still if there are no constraints on what can figure in the essence of a property, we can ask: Could there be a property Z such that it lies in the nature of Z that Jane is a banker? Presumably not, since as we’ve said, it’s a contingent truth that Jane is a banker. Still, if nothing in the framework rules this out, it will be an ‘accident’ from the standpoint of the framework that this proposition is contingent, and that’s clearly hopeless. The proposition is not contingent only because there happens to be no such property as Z. Worse, if the framework allows for Z it presumably also allows for Z*, a property in whose nature it lies Jane is not a banker. But then it will be an accident from the standpoint of the framework that our boring proposition is contingent when the framework would have been happy for it to be necessary (thanks to the existence of Z) or impossible (thanks to the existence of Z*). Since this is clearly hopeless, something in the framework must guarantee that properties with essences of this sort do not exist.

3.

In ‘Essence and Modality’ Fine calls his preferred view of essence the ‘definitional’ conception (as distinct from the ‘modal’ conception), stressing analogies between the essences of objects and the definition of words or concepts. This suggests a much more constrained framework.

According to what might be called the strict definitional conception, the essence of a property F is constrained to consist in a real definition of F: non-circular necessary and sufficient conditions for being F:

where ϕ does not contain F or anything that depends on F for its definition. This would solve the Z problem. If the essence of Z is constrained to include only necessary and sufficient conditions for being Z, it will never lie in the nature of Z that Jane is a banker. Of course it may lie in the nature of Z that that a thing is Z iff Jane is a banker. But then it won’t be essential to this property that the condition for its instantiation is satisfied, so Jane’s profession will remain contingent.

But of course the strict definitional account is too strict. Leaving aside special cases in which we may wish to allow for circular real definitions (Rosen 2015), there will presumably be basic properties that do not admit of reductive definition at all. And yet these properties should presumably have essences. It should lie in the nature of knowledge that if S knows that p then p is true even if knowledge is indefinable. Where x is an individual spatial point indistinguishable from the others, it should lie in the nature of x to be a point — which is to say: it should be essential to being-x that a thing is-x only if it is a point — even if there is no way to complete the definition.

And so we are led to the moderate definitional conception, according to which the essence of a property is constrained to include necessary conditions for its instantiation, or sufficient conditions, or some combination of the two, but nothing else. On this view, the essence of a definable property will be as above, whereas the essence of an indefinable property will contain propositions of the form:

If we wish to retain the biconditional form we can harmlessly admit circular essences to cover these cases.

This would also solve the Z problem. It may lie in the nature of Z that a given thing is Z if (alternatively, only if) Jane is a banker. But from this nothing will follow about whether the relevant condition is satisfied. So the essence of Z will inevitably leave Jane’s profession open, as it must.

4.

This is an improvement on the strict definitional conception. But when we loosen the view up in this way a question arises that will eventually need an answer. Take two unrelated properties like red and round — unrelated in the sense that the essence of the one makes no reference to the essence of the other, direct or indirect. Now ask whether anything in the framework rules out a property Q with the following essence:

The first clause gives a sufficient condition for being Q; the second gives a necessary condition. So far both are formally admissible. But if this is allowed it will be an accident from the standpoint of the framework that there is no Q, and hence that red squares are possible. And that is hopeless.

5.

One response to this problem brings in a new idea. We might say, again following Fine (2015), that when the essence of a property specifies necessary and/or sufficient ‘conditions’ for being F, those conditions must be grounds for being F.⁵ On this view, the admissible essences for monadic properties are built from clauses that look like this:

The last form gives the essence of a fully definable property. When a proposition of this form is true, ϕ(x) constitutes a real definition of F in the strongest sense (Rosen 2015). The second form gives the case in which the essence of a property specifies sufficient grounds for its instantiation, as when it lies in the nature of red that being scarlet grounds being red. The first form is meant to cover cases in which the essence of an indefinable property includes necessary-but-not-sufficient conditions for its instantiation, and for this purpose the relevant notion of ground will have to allow for partial grounds that are not part of strict full grounds. We want to be able to say that it lies in the nature of knowledge that when S knows that p, this fact is partially grounded in (or constituted by) p even if p is not part of a strict full ground for S knows p. So let us help ourselves to some such notion.⁶

The important feature of this proposal is that it constrains the essence of a property to specify only how instances of that property are grounded, not what they ground or otherwise entail. This is clearly the right thing to say in many cases. It lies in the nature of green or blue that x is blue grounds x is green or blue. It lies in the nature of bachelor that being unmarried and male grounds being a bachelor. In other cases, however, the restriction may seem too severe. Might it lie in the nature of scarlet that being scarlet grounds being colored? Possibly, and if so that would violate the principle. But we might also construe determinables like colored as disjunctions of their determinates, in which case it will lie in the nature of colored (and not of scarlet) that being scarlet grounds being colored. So let’s suppose that some such view is right.

If property essences are constrained in this way — to specify grounds for being F — then the putative essence for Q will be inadmissible. It will be fine to say that it is essential to Q that being red grounds being Q. But it will be inadmissible to add that it is essential to Q that being Q grounds being round. A grounding law of this sort would need to be sourced in the essence of round. But we have stipulated that the essence of round makes no reference to red, direct or indirect, as it would if this were so. (If it were essential to round to be grounded in Q, and essential to Q to be grounded in red, then the mediate consequential essence of round would make reference to red, as we have assumed that it does not.) So on this appealing version of the moderate definitional conception, it will be no accident that there is no Q, since its purported essence would be incompatible with an independently motivated constraint on what the essence of a property can include.⁷, ⁸

6.

This is a tempting line of thought, but I will mention a problem for it that will motivate another approach to the Q problem later on. There are cases in which it seems natural to say that B grounds A, or at least that B entails and explains A, where the connection would have to be mediated by the essence of B and not of A. The relevant examples involve what is sometimes called ‘grounding from above’ (Rosen 2017) or ‘explanation by status’ (Kappes 2020). Believers in non-humean laws of nature posit facts of the form law(F, G) — it’s a law that Fs are G — which are meant to entail and explain the corresponding regularities of the form All Fs are G. Believers in modal explanation hold that □p sometimes explains p, or more vividly, that ~◊p explains ~p. (Why are there no round squares? Because there couldn’t be.) Closer to home, we essentialists presumably want to say that when it is essential to Socrates to be human, it follows not only that Socrates is human when he exists, but that Socrates is human when he exists because humanity lies in his nature, and more generally, that □_xp entails and explains p.

There is room for dispute about whether these explanations from above count as grounding explanations, and perhaps about whether they are explanations at all. (In the case of putative essentialist explanations it might be said that what appears to be the explanation of a worldly fact by reference to an essentialist fact is better understood as a way of saying why the worldly fact needs no explanation.) The important point for present purposes is that, be all of that as it may, these cases are clearly cases of entailment. A fact of the form law(F, G) entails the corresponding regularity; the essentialist fact □_xp entails p, etc. Presented with modal facts of this sort, the essentialist is under pressure to find the item or items whose natures yield the modal fact. And in these cases we know exactly where to look. It lies in the nature of law that law (F, G) entails ∀x (Fx → Gx); it lies in the nature of essence that □_xp entails p. And the trouble is that principles like this threaten to violate the constraint that the essence of a property may contain only grounds for its instantiation. It is no part of the non-humean’s story about the laws that the regularity entailed by the law somehow grounds it; it is no part if the essentialist’s view that p somehow grounds □_xp. If anything, the grounding arrows run the other way.

We can put the upshot as a dilemma. Either we constrain the essences of properties to include only necessary and/or sufficient grounds for their instantiation, or we do not. If we don’t we have (as yet) no solution to the Q-problem. If it can lie in the nature of being essentially human to entail being human even though the latter does not ground the former, why can’t it lie in the nature of Q to entail being round? On the other hand, if we do restrict essences in this way, we have (as yet) no account of how being essentially human can entail being human, given that it does not lie in the nature of the former that the latter should somehow ground it. We will come back to this problem in §12.

7.

The discussion so far has been a prelude to what is meant to be the main event. In the example that got this whole business started, Fine (1994) notes that while Socrates is necessarily an element of his singleton set, it does not lie in his nature that this should be so. Rather, it lies in the nature of the singleton that Socrates should belong to it.

Given the essentialist account of modality, this entails and explains a modal claim we take to be true, viz., that as a matter of necessity, the singleton exists iff Socrates exists.

The trouble is that given the definitional view of essence sketched above, it is hard to see how this can work. On the Finean view we have been assuming, the essence of the singleton, like the essence of any individual, is given by the essence of a corresponding property, the property of being singleton Socrates: call it SS. On the moderate definitional view, the essence of a property consists in necessary and/or sufficient conditions for a thing to possesses the property in question. And in this case we know what those conditions are. A given thing is SS iff it is a set with Socrates as its only member:

This will happily ensure that if the singleton exists, so does its member. But it will not guarantee the converse. For all the essence of SS has to say if given as above, there could be a world that contains the philosopher without the set, perhaps because it contains no sets at all.

A more vivid version of the same problem arises when we ask whether the framework can tolerate absolutely necessary beings like the pure sets based on the null set. On the definitional conception, the null set has a predicative essence that tells us what it takes for a given thing to be-the-null-set, a property I’ll call ∅. We know what this account looks like: a thing is ∅ iff it is a set with no members. So understood, the essence of ∅ will guarantee that anything that satisfies this defining condition counts as the null set. But it will not guarantee the existence of a thing that meets this condition, since the definition is consistent with there being no sets of any sort.

And of course the problem has nothing in particular to do with sets. Any metaphysical view beyond the most austere sort of nominalism will contain a theory of generated objects: objects that exist in virtue of the existence and arrangement of things of other sorts. We standardly suppose that as a matter of necessity, whenever some atoms exist they have a mereological fusion. If we have a more interesting theory of parts and wholes, as Fine does (Fine 1999), we may say that whenever we have objects a, b, … standing in some relation R, this generates a new thing — a, b, … qua standing in R, or a,b,…/ R — which exists with a, b, … as parts if and only if Rab …. And so on for every case in which the existence of a state of affairs not involving a certain object is said to give rise to that object as a matter of necessity.

Take the case of these hylomorphic composites. The view implies that necessarily, whenever a bears R to b, there exists a rigid embodiment, a,b/R. For the essentialist, the conditional is necessary only if there is some item (or some plurality) whose essence includes it. The obvious candidate is a,b/R itself. It should lie in the nature of this object to exist whenever a bears R to b. But on the definitional view, the essence of this individual, a,b/R is given as the essence of a certain property, the property of being-a,b/R, which we may call ABR, by means of a formula of the form:

In this case we know what ϕ should be. To be ABR is to be a rigid embodiment with a and b as material parts and R as its ‘form’ or ‘principle of embodiment’. But the content of ϕ is irrelevant to the point at hand. An essence of this sort gives us a condition that a given thing must satisfy in order to qualify as ABR. But it cannot guarantee that anything meets this condition, even on the supposition that a bears R to b. After all, it will always be consistent with the definition that a bears R to b and yet rigid embodiments do not exist (perhaps because composite objects do not exist at all).

8.

What we want to say, of course, is that in all of these cases, the essence of the generated object x includes not just necessary and sufficient conditions for a given thing to qualify as X, but also necessary and sufficient conditions for the existence of such a thing. We would be home free if we could say:

And in the case of a necessary being like the null set, something like:

where T is some utterly minimal tautology or the ‘null fact’ in which so-called zero-grounded facts are grounded (Fine 2012). Principles of this sort are generative principles. As we normally think, such principles are abundant, generating a vast plenum of derivative objects over a base of ungenerated things, and as we normally think, they hold of necessity. For the essentialist they hold of necessity only if there is some item whose essence encodes them. And it is hard to see what this thing could be if not the property that figures in the principle. The problem arises because the definitional conception will not yield essences that encode these principles. So the question is whether the definitional conception can be relaxed to allow for essences of this sort while retaining the spirit of the view.

9.

Some writers have noted the problem and concluded that it cannot be solved, leaving the essentialist about modality with no choice but to regard the generative principles as contingent metaphysical laws, true throughout an inner sphere of worlds that includes the actual world and all of the worlds that are put together according to similar principles, but false in remoter regions of modal space where things like sets and hylomorphic composites do not exist (Rosen 2006).⁹ I now think this may have been too quick.

The idea is to allow the essence of a property to include both defining conditions of the usual sort — necessary and/or sufficient conditions for a thing to be an instance of the property— but also an existence condition. In many cases these will coincide. The definition of bachelor tells us what it is for a thing to be a bachelor, and this in turn tells us everything there is to know what it takes for there to be a bachelor. In the cases of interest, however, the existence condition will not follow from the definition proper. The essence of singleton Socrates, for example, might include two clauses:

Similarly, the essence of the rigid embodiment a,b/R might be given by real definition of the corresponding property ABR together with an existence condition:

Of course, these existence conditions will not need to be penciled in one by one. The existence conditions for ABR presumably follow from the definition of the property together with a general principle, sourced in the nature of rigid embodiment itself, or in the essence of the function denoted by ‘/’ which generates properties like ABR from sequences of objects and suitable relations. The general principle might be:

The existence condition for singleton Socrates presumably follows from the definition of SS together with a general principle, sourced in the nature of set or the set-building operation to the effect that {a, b, …} exists whenever a, b, … all exist (and satisfy some paradox-blocking condition). And yet, even if the existence conditions for the individual generated entities are not basic, they are still there in the essence of the property corresponding to the generated object. To know what it is to be singleton Socrates is to know both that a thing counts as SS iff it is a set satisfying a certain condition, and also that it suffices for the existence of such a thing that Socrates exist.

If this were a coherent position, the existence of this set and every other would be a contingent matter (holding the non-sets fixed). But on the present view it is not coherent. To the nominalist we say:

If this is the correct view, sets and other generated entities will exist automatically, whenever their generating conditions are satisfied, in which case there will be no room for informed coherent doubt about their existence, provided there is no doubt about their essences, or about the states which, according to their essences, suffice to generate them.

10.

When I first considered this possibility in Rosen (2006), I rejected it on the ground that it would overgenerate, rehabilitating a transparently bogus version of the Ontological Argument. (I called essences that include existence conditions of this sort anti-Anselmian.) If it can lie in the nature of singleton Socrates to be a set that exists automatically whenever Socrates exists, can it also lie in the nature of Socrates’ guardian angel to be an angel that exists under just the same conditions? If it can lie in the nature of the null set to be a set that exists no matter what, can it lie in the nature of God to be a god that exists no matter what? If the framework cannot rule out these bogus cases, it is hopeless.

My main purpose in this note is to raise this worry and to suggest a reply on behalf of the essentialist. It would be a disappointment if the essentialist were forced by these considerations to regard generative principles as mere contingent laws. The reality of generated things, necessarily connected to their generators, strikes me as a datum. So the essentialist needs a conception of essence that squares with it, but which does not yield gods and angels along the way.

For it would then be an accident from the standpoint of the framework that these bogus entailments do not hold. What we want is a principled basis for accepting the non-contingent generative principles that yield sets and composite objects and the rest while rejecting these bogus principles, which is to say: We want an account of essence that allows principles of the first sort, but not the second, to figure in the essences of the properties corresponding to generated objects.

11.

Start with the thought, suggested earlier, that the conditions that figure in the essence of a property are not mere conditions for its instantiation; they must be grounds. If there is anything to this restriction it presumably remains in force when we broaden the conception to allow the essence of F to include conditions for the existence of an F. The essences of generated objects will then include clauses like the following:

Claims like these are common in discussions of grounding and generation. Of course, it is also sometimes said that the existence of the generated object is fully grounded, not in the underlying generator by itself, but in the generator together with a principle, e.g., a set existence axiom, whose modal status would then have to be settled independently. But let’s focus on the stripped-down version of the view, which sees the existence of the generated object as fully grounded in its generator.

How might this block the spurious generation of gods and angels? If it can lie in the nature of singleton Socrates that the existence of the set is fully grounded in the existence of its member, why can’t it lie in the nature of Socrates’ guardian angel, or its corresponding property SGA, that its existence is similarly grounded. If it can lie in the nature of the null set to be zero-grounded, why shouldn’t an omnipotent God manage the same feat?

We should of course concede that gods and angels of this sort would not be textbook gods and angels. God is normally taken to be a fundamental being; and that may be incompatible with regarding his existence as zero-grounded. Similarly angels, even guardian angels, are normally conceived as ontologically independent of human beings. So, our question concerns gods and angels of a non-standard sort: intelligent spirits that are not fundamental, but rather grounded in a specific way — guardian angels whose exisence would be grounded in the existence of their human charges; a perfect God whose existence would be zero-grounded, and so on.

But as soon as we say this, we can see why the idea is odd. In the paradigm cases in which B grounds A, there is a sense in which A is barely distinct from B — nothing over and above B, as we sometimes say. Of course, A is always a different fact from B; nothing grounds itself. And yet it is not a genuine further fact but rather always palpably a ‘repackaging’ or ‘unfolding’ of what is already there in B. The fact that Jones is a bachelor is barely anything beyond the fact that he is male together with the fact that is unmarried. The fact that that the ball is red is barely a further fact beyond the fact that it is scarlet, and so on.

If the sort of essence-mediated generation we have been discussing is to be possible then in the very same sense, the existence of the singleton should be nothing over and above the existence of its member; the existence of a,b/R should be nothing over and above Rab, and so on. It is, of course, not obvious that this is so. The singleton is a new object, distinct from and often very different from its member; and when we think of the full universe of sets based on Socrates, a mathematical structure of unfathomable complexity, it may be less than clear that all of this should be reckoned as nothing over and above the philosopher. The same goes for the plenum of hylomorphic composites generated from the base of atoms according to principles of the sort that give us a,b/R from Rab. Still, anyone who is impressed by the metaphysical minimality of these objects relative to their bases, and by the thought that they seem to come ‘for free’ given the coherence of certain ways of talking, will have sympathy for the idea that in these cases, the generated things are ultimately nothing beyond their grounds. All God, the real God, has to do in order to conjure a,b/R into existence is to see to it that Rab. After that, the uncreated essences take over and do the only work they can do: repackaging what is already there.

By contrast, even the most deflationary angelologist will presumably maintain that Socrates’ guardian angel must be something over and above the man himself. A state of affairs in which the angel exists includes Socrates together with another mind with thoughts and powers of its own. A state of affairs in which God exists includes, in addition to the utterly null state that brings zero-grounded items into existence, an omnipotent being. And if that is not ‘something over and above’, God knows what is.

We can put the point a bit less metaphorically. If the existence of an item like singleton Socrates is grounded in the existence of something else according to a principle of generation sourced in its nature, then every material fact about the generated item must be settled by its generator together with the manner of its generation. This is at least part of what it means to say that the generated thing is nothing over and above its grounds. We can say this when it comes to sets and hylomorphic composites and the like; or so we may well hope. But when it comes to gods and angels, it is built into our conception of these things that they must have features, determinate thoughts and actualized powers, that cannot be read off from their humble generators together with their putative principle of generation.

So, that’s a principled way to draw the line. The essences of generated things can include conditions for their existence, understood as conditions for the instantiation of their corresponding properties. But since these conditions are constrained to specify grounds, they can only secure the existence of ‘thin’ objects, the existence of which is intuitively nothing over and above the existence and arrangement of their generators. Since gods and angels could not be thin, there is no worry that the proposal will license principles that conjure them into existence.

12.

This approach to the problem of overgeneration relies on the idea that the essence of a property can only specify its grounds, not what it grounds or otherwise entails. But earlier we saw a problem with this idea. The essentialist about modality should be open to the possibility of entailments and necessitating explanations ‘from above’, as when the non-humean law law(F, G) explains and entails the regularity, ∀x (Fx → Gx). The worry was that if the essence of an item can only specify how facts involving it are grounded, then the essence of law cannot include the connection between a law and the corresponding regularity since the law is not even partly grounded in the regularity. Closer to home, the worry was that the approach threatens the entailment of p by □_xp. It certainly seems to lie in the essence of essence that □_xp entails p, just as it lies in the nature of knowledge that S knows that p entails p. But in the latter case, p is colorably a partial ground for S knows that p, whereas it is no part of the essentialist vision that p is any sort of ground for □_xp. The principle we have been relying on therefore threatens to make a mystery of this entailment.

I think these examples force us to reject this principle. There is no general bar to properties whose natures specify what they ground or otherwise entail. And yet we can still say that in all such cases, the downstream fact must again be ‘barely anything beyond’ the facts that ground or entail it according to the essence of the property in question. p may not ground □_xp; and yet it is intuitively contained within it, or so one might well think.

Return to Q once again. Earlier we suggested that the putative essence for Q is inadmissible because in general, the essence of a property cannot specify what it grounds. But we had another option at that point. Let it be that the essence of a property F can sometimes specify what Fx grounds or otherwise entails. Still, we can tell by inspection that x is round is always a further fact, over and above x is red. If the essence of Q were admissible, then either Qx would have to be a further fact, over and above x is red, or x is round would have to be a further fact, over and above Qx. So for the purposes of excluding Q it would suffice to have a principle to the effect that when the essence of a property mediates an entailment from ϕ to ψ, ψ must be nothing over and above ϕ in the intended sense. This would rule out Q without ruling out an essence for law or □_xp of the desired sort.

13.

Of course, this is still lamentably metaphorical. We are fishing for a principle that requires essentialist principles to be metaphysically conservative or non-ampliative, generating nothing genuinely new that was not already there independently of the principle. But I cannot pretend to know how to state such a principle in less metaphorical terms. It would help somewhat to put the whole thing in terms of ground: to say that the essence of F can only specify how facts involving F are grounded or what they ground, excluding Q for the reasons sketched above. But that would involve taking a stand on the question whether law (F, G) grounds ∀x (Fx → Gx), and on whether □_xp grounds p, an arcane and controverted question.

It is worth stressing one last time that it is not obvious that the essences we have been discussing — the essences of generated objects and the essences that mediate these explanations from above — satisfy the requirement that essentialist principles be non-ampliative in the intended sense. We have already noted one instance of the problem. It sounds fine at first to say that a set is nothing over and above its members, a metaphysical gloss on Cantor’s ‘many thought of as one’. But if this is meant to imply that the hierarchy of sets based on a — a mathematical object of maximal complexity — is nothing over and above a, which might be a speck of dust or even nothing at all, then it is less clear that the set existence principles should be reckoned non-ampliative in the intended sense. A different version of the same problem arises in connection with the explanations from above we were just discussing. In these cases, the essence of law, or of essence itself, seems to mediate a necessary connection between a transcendent fact and a worldly fact. law (F, G), the non-humean law, is an abstract relation between properties which might obtain before the concrete world exists, or at the first moment, before the concrete world is fully real, whereas the regularity that it entails, ∀x (Fx → Gx), is spread out in spacetime. Or consider an essentialist fact, like the fact that it lies in the nature of bachelor that bachelors are unmarried. This essentialist fact can seem even more transcendent than the contingent non-humean law, whereas its prejacent is again a worldly regularity grounded in its instances. The worry is that a worldly fact will always strike us as a further fact, over and above a transcendent fact (though in this case the prepositions are inapt). And insofar as this is so, a general principle that prohibits essentialist bridge principles that would generate ‘new’ things would be overly restrictive.

14.

I’m going to leave this matter unresolved, so let me close by stating what I take to be the upshot of the discussion.

1. Every essentialist needs an answer to the question: What can go into the essence of a property (or relation, or …)? As the Z- and Q-problems show, the answer cannot be ‘anything at all’. So we need a principled constraint on essences.

2. It would suffice for these purposes to say that the essence of property is constrained to specify a definition of F, or grounds for being F. But that is too restrictive.¹⁰ The essences of the properties associated with generated entities like sets and hylomorphic composites must include principles that determine, not just when a given thing counts as F, but also the conditions under which an F exist. E.g., it should lie in the nature of (the property of being) singleton Socrates that singleton Socrates exists iff Socrates exists.

3. If a view of this sort is not to overgenerate (reviving the Ontological Argument), essentialist principles must be restricted so as to ensure that the existential fact generated by the principle is ‘barely anything over and above’ the facts that generate it.

4. It would suffice for this purpose to say that existence principle that figure in the essence of a property must be grounding principles. The essence of Singleton Socrates might be constrained to say: It lies in the nature of singleton Socrates that the existence of Socrates is a necessary and sufficient ground for the existence of the singleton.

5. But we should be leery about requiring that essentialist principles be grounding principles. When it comes to ‘explanations/entailments from above’, and in particular the entailment of p by □_xp, it should lie in the nature of the broadly modal ‘prefixed’ fact to entail its prejacent, even though the prejacent does not ground the prefixed fact and may not be grounded by it.

6. In all of the cases in which the essence of F seems to involve something more than a (full or partial) definition of F — generative principles, entailments from above — the essence is nonetheless constrained to be conservative in an elusive sense. The main unresolved challenge is to formulate this restriction in more explicit terms.¹¹

Competing Interests

The author has no competing interests to declare.