Essence Is Not Modality

The last article closed on a question it could not answer. If full grounds necessitate what they ground, where does the necessity come from? The suggestion was that it comes from essence, from what things are, but only on a conception of essence that does not itself reduce to necessity. This article supplies that conception. It follows Kit Fine's argument in "Essence and Modality" (1994) that essence cannot be defined in modal terms, using the pair the last article used against modal analyses of ground: Socrates and his singleton set.

The beginner article on essence and accident gave Fine's case a paragraph and promised the rest for later. For most of the twentieth century, analytic philosophers took it that to call a property essential to a thing is to say that the thing could not exist without it. Fine argued that this gets the order of explanation backwards. Essence, understood as what a thing is, explains necessity, and if he is right then the possible worlds apparatus of the intermediate tier records the consequences of essence rather than giving an account of it.

The modal account

The beginner tier defined an essential property as one a thing could not have lacked while existing. The intermediate article on possible worlds gave that definition its standard precise form.

The account is a piece of de re modality. It takes an object to the worlds, asks what is true of it at each, and inherits both the clarity and the commitments of that procedure. It is also what the arguments of the last half century about essentialism mostly assumed. When Quine objected that necessity attaches to things only under descriptions, and when Kripke replied that a person could not have had different parents, both were arguing about which de re necessities hold. Neither questioned that settling the necessities would settle the essences.

The existence clause matters. Without it, the account would make Socrates essentially human only if he is human at every world, including the worlds where he does not exist and so is not anything. The account is therefore usually stated conditionally: a property is essential to an object when, necessarily, if the object exists then it has the property. Fine's examples are aimed at this conditional form, and the condition does nothing to block them.

Two directions should be kept apart. The account claims, first, that every essential property is had necessarily, and second, that every property had necessarily is essential. The first direction is accepted by nearly everyone, Fine included: whatever belongs to what a thing is, the thing could not have been without. The case against the modal account is a case against the second direction, the claim that necessity is enough.

Socrates and his singleton

Fine's central example uses elementary set theory. For any object there is a set whose only member is that object, its singleton. Sets are the paradigm abstract objects, and the beginner article on the abstract and the concrete used impure sets, those with concrete members, as a test of where the line between the two categories falls. Singleton Socrates is as impure as a set can be, since everything about which set it is comes from Socrates.

On the standard picture of sets, the singleton exists at exactly the worlds where Socrates exists, and at each of them Socrates belongs to it. So it is necessary that if Socrates exists, he is a member of singleton Socrates. The modal account then delivers a verdict its defenders did not intend.

The argument is valid, and the second premise is a piece of set theory that the modal theorist has no independent reason to deny. Everything rests on the third, and Fine's support for it comes from comparing the case with its converse. It is essential to the singleton that Socrates is its only member, since that is what makes it the set it is: a set has no more to its identity than which members it has. Socrates belonging to the set and the set containing Socrates are, modally, one connection seen from two ends. At every world where either exists, both exist and the membership holds. If the modal account were correct, the two essentialist claims would stand or fall together. They do not. One states what the set is, and the other states a fact about the man that holds because of what the set is.

The case has relatives, and they show that the problem is structural rather than a quirk of set theory.

Take distinctness. Socrates is distinct from the Eiffel Tower, and necessarily so, since what is distinct at one world is not identical at another. So at every world where Socrates exists he is distinct from the Tower, and the modal account makes being distinct from the Eiffel Tower part of his essence. But nothing about being a human being, or about being this human being, concerns a structure that would not be built for more than two thousand years after his death.

Take any necessary truth. Being such that two and two make four is a property Socrates has at every world where he exists, so the modal account counts it essential to him, and equally to the Eiffel Tower and to the number seven. A defender might shrug properties like this off as trivial. The singleton case cannot be shrugged off that way. Being a member of singleton Socrates is specific to Socrates, it is necessary, and it is still no part of what he is.

The general lesson is that necessity is indifferent to the source of a connection. When two things are necessarily connected, the modal profile records that the connection holds wherever they exist. It does not record which of the two the connection flows from, and a claim about essence is a claim about exactly that.

Real definition

If essence is not the collection of necessary properties, something has to be said about what it is. Fine's answer was to return to the older conception that the modal account had displaced, on which the essence of a thing is what its definition gives.

The word "definition" needs care. In its everyday sense it is linguistic: a dictionary defines a word by saying what it means. The older sense is not about words.

The two come apart in both directions. A word can have a nominal definition while there is nothing for it to define, as with "unicorn". A thing can have a real definition that nobody has written down, or that has to be found out rather than stipulated. Nor need every object have a definition that anyone could write out in full. The view requires only that there be a fact about what the object is, and that some truths hold because of it.

Aristotle drew the distinction. In the second book of the Posterior Analytics he separates an account of what a name signifies from an account of what a thing is, and in the Topics he characterises a definition as a phrase signifying the essence. His phrase for essence, to ti ên einai, translates literally as "the what it was to be".

The beginner definition of essence had two halves: the collection of essential properties, taken as an answer to the question of what the thing is. The modal account keeps the first half and reads it modally. The Aristotelian conception keeps the second half and lets it decide the first.

Aristotle also had a category for properties that are not essential and yet go with a kind without exception. In the Topics he calls something a property (idion, traditionally "proprium") of a kind when it belongs to all and only its members without stating what they are, and his example is being capable of learning grammar: every human being has the capacity and nothing else does, but it is not what it is to be human. The later Aristotelian tradition held that propria flow from the essence, so that a thing has them necessarily without their being part of what it is. That is already the gap Fine identified.

Fine's paper "Senses of Essence" (1995) draws the gap more finely. The constitutive essence of a thing is what its real definition states. Its consequential essence adds whatever follows from that by logic alone. Both are narrower than the modal profile. Being a member of singleton Socrates is in neither of Socrates' essences, because it does not follow by logic from what Socrates is; it follows only from what Socrates is together with what the set is.

The asymmetry of the singleton case now has a home. The definition of the singleton mentions Socrates. Whatever the definition of Socrates contains, it does not mention the set. Definitions have a direction where the necessities between their objects do not, and the direction is the one that common sense and set theory agree on. Fine went on to analyse ontological dependence in roughly these terms, as a matter of one thing figuring in what another is ("Ontological Dependence", 1995), and a later article in this tier takes that analysis up.

Reversing the order of explanation

The modal account explained essence by necessity. Fine proposed running the explanation the other way.

The basic locution is "it is true in virtue of the nature of $x$ that $p$", often written as a box with the object as subscript, $\Box_x p$. It is not defined in modal terms. It relates an object to a proposition, the proposition that holds because of what that object is, and unlike plain necessity it is sensitive to which object goes in the subscript. It is true in virtue of the nature of the singleton that Socrates belongs to it. It is not true in virtue of the nature of Socrates. An unrelativised box cannot draw that distinction, which is the singleton argument restated in notation.

The proposal has a model in an older account of analytic truth, on which a conceptual truth holds in virtue of what certain concepts are. Fine's suggestion is that metaphysical necessity stands to objects as conceptual necessity stands to concepts: a claim is metaphysically necessary when it holds because of the nature of the things involved. Different families of necessity then answer to different families of natures, much as the intermediate tier matched different grades of possibility to different domains of worlds.

The reversal buys three things.

The first is an explanation where the modal account offered a description. On the worlds analysis, that Socrates is human at every world where he exists is where the story ends: there is no world where he is a frog, and nothing more to say. The essentialist can say why. Being human belongs to what Socrates is, so any frog standing in his place at a world is not Socrates. Necessity becomes something that holds because of something else.

The second is that the necessities the modal account misclassified are explained without being misclassified. That Socrates belongs to his singleton is necessary because it is true in virtue of the nature of the set. That he is distinct from the Eiffel Tower can be put down to the natures of the two taken together, or to the nature of identity, without being located in Socrates' nature alone. That two and two make four holds in virtue of the nature of the numbers. On this view every necessity has a source, and the source need not be the object the necessity is about.

The third is a connection with the last article. Grounding necessitarianism held that full grounds necessitate what they ground, and left open why they should. If the existence of Socrates grounds the existence of his singleton, the essentialist can say why the first necessitates the second: it lies in the nature of the singleton to exist whenever its member does. On this picture, the natures of things underwrite the necessary connections that grounding relies on. The two notions should not be merged, since grounding relates facts to facts while essence concerns what objects are, and how exactly they connect is still disputed. What they share is the feature that matters here, a direction that bare necessity lacks.

Bob Hale's Necessary Beings (2013) develops a theory of this kind at book length, arguing that metaphysical necessities derive from the essences of things and putting the view to work on questions about which things exist necessarily.

Saving the modal account

The modal theorist has two lines of reply: repair the account so that the counterexamples drop out, or question whether the alternative is intelligible. The repair comes first.

Refinements of the modal account continue to be proposed, and the dispute is not closed. The difficulty they share is the one the reply identifies: a filter strong enough to exclude Fine's cases has to know in advance which side each necessary connection flows from.

The charge of obscurity

The second line of reply accepts the counterexamples and questions the alternative.

A harder objection grants that essence is intelligible and asks whether it can explain necessity at all. Simon Blackburn put it as a dilemma in "Morals and Modals" (1987), aimed at any attempt to say what makes necessary truths necessary.

The essentialist takes the first horn, and Hale, among others, argued that it is not the trap it looks like. Essentialist truths are necessary: if it is true in virtue of the nature of the singleton that Socrates belongs to it, then necessarily it is. But every explanation stops somewhere, and the question is whether it stops in the right place. Explaining the necessity of Socrates' membership by the nature of the set moves from a necessity that is about Socrates and has no account to one that states what the set is. And there is a reason why that kind of truth could not have been otherwise that does not appeal to some further necessity: a set with a different member would be a different set, not the same set with a different nature. What it is for a thing to be the thing it is cannot vary while the thing stays the same.

Whether this ends the regress or merely announces that it ends is the real question, and it remains open. The modal account is not better placed for having no answer. On its non-reductive reading the worlds analysis does not attempt to say why some ways for things to be are not among the possible ones, and on Lewis's reductive reading the answer rests on a plurality of concrete worlds that is costly on its own account.

Next

On Fine's view, essence is one respect in which reality has more shape than the modal facts record: what things are has a direction and a priority that necessity flattens. The next article takes up a second notion of the same sort. Some properties seem to mark genuine divisions in nature and others seem gerrymandered, and David Lewis's account of naturalness, developed by Theodore Sider into a general notion of structure, asks whether reality has a privileged description in whose terms everything else is to be explained.