As it was noted in Chapter 2, Fine concluded on the grounds of the analysis of chosen examples that the modal account is too broad to express the intended concept of essence. The diagnosis was that it lumps together the conditions of the object’s identity and the consequences of its identity. Furthermore, the consequences of the object’s identity cannot be excluded from the account without invoking the nature of the object in question. However, the nature of objects is what we were supposed to explain, thus cannot be used in the explanation.
For Fine, the main problem of the modal account is the fact that the metaphysically necessary truths are insensitive to the source of their necessity (i.e. the subjects of underlying essentialist truths). Logical form of de re modal statements is symmetric in its terms and de re necessary claim is taken to be true only if an object in the subject position necessarily fulfils the given condition, regardless whether this or some other object is the ground of it necessarily fulfilling the condition. On the other hand, an essential truth has its source in specific objects, for example, Socrates is essentially a human being is true in virtue of Socrates’ essence; and this has to be somehow preserved in its explanation. In other words, the concept of essence is too refined to be captured with the concept of metaphysical necessity.
The most persuasive example that Fine provides against the modal account is the one concerning Socrates and singleton Socrates. We tend to accept ‘Singleton Socrates essentially
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contains Socrates’ as true since it is part of the singleton’s essence to have the member that it has. On the other hand, ‘Socrates is essentially a member of singleton Socrates’ is intuitively false since it is not part of Socrates’ essence to be a member of the singleton. Indeed, it is implausible to claim that in order to understand the essence of a person one should know to which sets he belongs. However, on the modal account both statements come out true since Socrates is necessarily a member of singleton Socrates as well as singleton Socrates necessarily contains Socrates, if they exist.
On the definitional account, the essentialist asymmetry is preserved. Singleton Socrates is defined as a set whose sole member is Socrates, and thus singleton Socrates essentially contains Socrates. Socrates’ definition, on the other hand, does not mention his membership in singleton Socrates; therefore, it is not the case that Socrates is essentially a member of singleton Socrates. Hence, the relationship between the singleton and Socrates is essential to the singleton only.
The corresponding essentialist claims are formulated in the logic of essence by attaching the essentialist operator ‘it is true in virtue of the identity of x that’ – x – to the sentence, A.74 Take the sentence A to be ‘Socrates is a member of singleton Socrates’, then
{s}A means that A is true in virtue of the identity of singleton Socrates, and conveys that singleton Socrates has essentially Socrates as a member. Conversely, sA means that A is true in virtue of the identity of Socrates and conveys that Socrates is essentially a member of singleton Socrates.
The proposed formalization of essentialist statements succeeds in tracking the source of their truths because the essentialist operator picks out the subjects of essentialist claims.
74 Given that the understanding of the basic elements suffices for my purposes, I will not provide a detailed summary of the logic of essence, developed in Fine 1995b and 2000. Let me just mention that the language, besides an essentialist operator symbol and formulae expressing the idea that A is true in virtue of the identity of x, contains special 1-place rigid predicates and a 2-place dependence predicate. The logic is an extension of first-order logic (including the abstraction operator ) with new axioms and rules for new predicates and formulae, and the possible worlds semantics.
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Fine sometimes calls it relativized or indexed operator. An intended meaning of the statement of the form xA is that A is true in virtue of the identity of x, and it is only taken to be true when each of the objects mentioned in A is involved in the nature of x.75 For example, it is not taken to be true in virtue of the number 2 that Socrates = Socrates. Similarly, {s}A is true since Socrates’ membership is part of the singleton’s essence, while it is not part of the Socrates’ essence, thus falsifying sA (Fine 1995b: 241-2 and 2000: 543).
It should be noted that the notion of a proposition’s being true in virtue of the identity of x is not signifying a property of propositions, but a relativized property. Given any proposition and any objects (which may or may not be subjects of the proposition), we ask whether it is true in virtue of the identity of those objects (Fine 1994: 15, fn. 2). Moreover, the relation between an object and a proposition is not analyzable and this is reflected in the essentialist operator. That is to say, although the notation ‘it is true in virtue of the identity of x that’ might suggests ‘an analysis of the operator into the notions of the identity of an object and of a proposition being true in virtue of the identity of an object’, Fine insists that the operator is a primitive and is not to be further analysed. Fine’s insistence on the primitiveness of the essentialist operator corresponds with his view that essence cannot be explained in any fundamentally different terms, only understood better through the analysis of its workings, and here he relies on the propositional construal of essence. In Fine’s words, ‘we should understand the identity or being of the object in terms of the propositions rendered true by its identity’ (Fine 1994/95: 273). Thus, the identity or essence of an object is given by a privileged collection of true propositions, namely, a collection of propositions that are true in virtue of the object’s identity.
75 In terms of possible worlds semantics, a statement is true in virtue of the nature of certain objects if it is true in any world compatible with the nature of those objects. Under the assumption that a world is compatible with the nature of all and only those objects that it contains, then the condition is that it should be true in all those worlds that contain those objects. The presence of an object in a world guarantees its possibility, not existence (Fine
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In conclusion, let us take a look at the other two examples causing troubles to the modal account. One is the problem of the necessary truths that come out as essential to every object. For example, it is necessary that Socrates is such that there are infinitely many prime numbers, if he exists. Thus, it is essential to Socrates that there are infinitely many prime numbers. This is not a problem for the definitional account since it is not part of Socrates’
essence that there are infinitely many prime numbers. Alternatively, this proposition is not a member of the collection of properties that are true in virtue of Socrates’s identity. The other problem was plaguing only the existence-conditioned version, according to which a property F is an essential property of an object x if and only if it is necessary that the object x has the property F if x exists. Given that no object could exist but lack existence, on this account, existence is an essential property of every object. Since on the definitional account, existence is essential to an object only if it is part of the object’s essence, not every object is essentially existent. Again, no problem arises.