First, let us consider the modal definitions of ‘essential property’ regarding ordinary objects and the analysis of Fine’s counterexamples involving ordinary objects.
In this system, the truth that Socrates is essentially human is interpreted as the assertion that Socrates exemplifies the property of being human in every possible world in which he is concrete, where ‘exemplifies’ is the formal substitute for the ordinary predicative copula ‘is’ or ‘has’. On the other hand, in those possible worlds in which Socrates is not concrete, he does not exemplify the property of being human or any other property that humans typically exemplify. In fact, he exemplifies the negations of those properties as well as the so-called logical properties, such as being one or being distinct from everything else, which any ordinary object exemplifies in every possible world (Zalta 2006: 679).
CEUeTDCollection
Based on these considerations, three distinct notions of ‘essential property’ as applying to the ordinary objects can be defined. (We use the variables u and v to range over only ordinary objects.) These three notions can be formulated as follows:
(3) Necessary(F, u) =df Fu
(4) WeaklyEssential(F, u) =df ( E!u Fu)
(5) StronglyEssential(F, u) =dfWeaklyEssential(F, u) & Necessary(F, u)
The notion defined in (3) – Necessary(F, u) – corresponds to the necessary or trivially essential properties, such as the property of being self-identicalE ([ z z =E z]), which every ordinary object exemplifies in every possible world. However, if an object u exemplifies the property F in every possible world, then u also exemplifies F in those worlds in which it is concrete. Thus, the property of being self-identicalE is also a weakly essential property of u, defined in (4). On the other hand, it is not a strongly essential property of u, which is defined as a conjunction of WeaklyEssential and the negation of Necessary (ibid: 679-80).
The notions Necessary and WeaklyEssential are familiar from the literature and correspond to what is usually called necessary and essential properties. However, StronglyEssential is new, and according to Zalta, it captures best the intuitive understanding of essential properties. It provides a very simple and clean solution to the problem of excluding the ‘only’ necessary properties from the ‘real’ essential properties. Namely, only those properties count as essential, which an object u exemplifies in all possible worlds in which it is concrete, minus those properties that u exemplifies also in all those possible worlds in which it is not concrete. This move is made possible because of the difference between existence and concreteness in the simplest quantified modal logic. For example, consider the truth that Socrates is essentially human. Socrates (‘s’) exemplifies the property of being human (‘H’) in every world in which he is concrete, so:
WeaklyEssential(H, s).
CEUeTDCollection
If one accepts two additional assumptions:
(6) Socrates is contingent – E!s & E!s.
(7) Being human is concreteness-entailing – x(Hx E!x).
Then one can prove that it is not necessary that Socrates is human since by (6) there is a possible world w1 in which Socrates fails to exemplify being concrete, thus by (7) he fails to exemplify being human in w1:
Necessary(H, s)
Finally, from the definition of StronglyEssential in (5), it follows that indeed it is strongly essential to Socrates that he exemplifies the property of being human:
StronlgyEssential(H, s) (ibid: 681-2).
The account delivers also an intuitively correct result concerning necessary truths transformed into properties of objects. We have already seen that the logical properties, such as being self-identical ([ z z =E z]), are not strongly essential to an object. Socrates exemplifies the property of being self-identical weakly essentially (in every possible world in which he is concrete) and necessarily (in every possible world), therefore, not strongly essentially. Similarly, the other necessary properties that are derived from the necessary truths are excluded. Fine’s example is about Socrates and the mathematical truth that there are infinitely many prime numbers. While it is necessary that there are infinitely many prime numbers if Socrates exists, we would not want to count this truth as a part of Socrates’s essence. Zalta’s account does avoid this, since the property of being such that there are infinitely many prime numbers is exemplified by Socrates in every possible world, thus being necessary and weakly essential, but not strongly essential property of Socrates.
Zalta pays special attention to the counterexample concerning Socrates and the Eiffel Tower (Fine 1994: 5). Fine claims that although it is necessary that Socrates is distinct from the Eiffel Tower, the property of being distinct from the Eiffel Tower is not essential to
CEUeTDCollection
Socrates, for there is nothing in his nature that connects him in any special way to the Tower, which the modal account is not able to convey. Again, Zalta’s account does manage to achieve this. Given the proposed definitions of ‘essential’ and the assumption that Socrates (‘s’) is not identicalE to the Eiffel Tower (‘t’), it can be shown that:
Necessary([ z z E t], s) WeaklyEssential([ z z E t], s)
StronglyEssential([ z z E t], s).
The property of being distinct from the Eiffel Tower is necessary to Socrates and thus weakly essential, therefore, not strongly essential. In this way, Zalta says, ‘we have a natural and well-defined sense in which it is not essential to Socrates that he be distinct from the Eiffel Tower’ (Zalta 2006: 682).
Zalta’s characterization of ‘essential property’ within the simplest quantified modal logic and the theory of abstract objects, does manage to exclude the unwanted properties, thus suggesting that Fine’s criticism was not all encompassing after all. He did succeed in showing that the standard modal account is too simplistic, but not that the difficulty could not be solved by any modal account. Zalta points out that in his proposal, he manages to preserve the close connection between essence and modality, since the standard characterization of essential property is in a way preserved in the definition of StronglyEssential as a conjunct ‘ ( E!u Fu)’. Moreover, the explanation of the difficulty is given in the simplest quantified modal logic, so that no special logic of essence is needed. Most importantly, Zalta’s account seems to undermine Fine’s definition of metaphysical necessity in terms of essence since neither WeaklyEssential nor StronglyEssential implies Necessary. On the contrary, StronglyEssential explicitly excludes necessity. If ‘x exemplifies F necessarily’ then it is not the case that ‘F is strongly essential to x’ (Zalta 2006: 683).
CEUeTDCollection
I agree that Zalta’s definition of the relevant essential property as a property that the object x has in every possible world in which x is concrete and does not have in any possible world in which x is not concrete, neatly gets rid of the trivially essential properties. It does seem to show that the modal characterization of the essential/accidental property distinction can deal with certain problematic cases, but on the other hand, this proposal cannot be taken as a reductive analysis of essence, which was what Fine primarily criticised. After all, besides the necessary existence of objects, the main reason for its success is the fact that the essential property is characterized differently in the case of abstract objects than in the case of ordinary objects. However, this different treatment is justified by the fundamentally different nature of abstract and ordinary objects. Thus, Zalta does seem to invoke the nature of objects in his account at least in this fundamental manner, if not in connection with particular cases.
Concerning Zalta’s claim that being essential does not imply being necessary, I do not think it can be directly applied to Fine’s theory in which the nature of contingent objects is conceived in a radically different way. I will return to this below. Moreover, in Zalta’s account the definition ‘true in all possible worlds’ better characterizes logical necessity, since ordinary objects have only logical properties in all possible worlds.
Let us return to the question of trivially essential properties. We have seen in Chapter 2 that modal essentialists were always aware of the problem concerning the properties that necessarily belong to all objects. They were called trivially essential properties and excluded from the account due to their triviality. That is to say, they belong to all objects merely because they are objects. The recognised exception was the property of being self-identical, which is a unique property belonging to one and only one object. For example, the property of being identical to Socrates belongs only to Socrates and nothing else. However, it is necessarily true that every object is identical to itself. Thus, the property of self-identity, although not universal, is general since it follows logically from the fact that necessarily every
CEUeTDCollection
object is identical to itself and the fact that every object has it merely because it is an object.
This argument for the exclusion of trivially essential properties sounds reasonable and principled; however, Fine showed that the unwanted properties could not be rid of so easy as that. Namely, certain properties can be constructed by combining a trivially essential property with a ‘properly’ essential property, and such properties do not universally belong to every object whatsoever, but we still do not want them to count as essential. How does Zalta’s account deal with such properties?
Zalta mentions the conjunctive property of being human and not identicalE to the Eiffel Tower - [ z Hz & z E t], which could be used in the above example instead of the property of not being identicalE to the Eiffel Tower. This property is strongly essential to Socrates since he exemplifies it in every possible world in which he is concrete, but not in possible worlds in which he is not concrete and hence not human:
Necessarily([ z Hz & z E t], s) WeaklyEssential([ z Hz & z E t], s) StronglyEssential([ z Hz & z E t], s)
Still, it does not seem that this property should be essential to Socrates and that Socrates and the Eiffel Tower should be connected in such a special way.
First, Zalta points out that it is not entirely clear what Fine has in mind when insisting that Socrates’s nature is not connected in any special way to the Eiffel Tower. Why would anyone think that Socrates is in a special way connected with the Eiffel Tower only because being human and not identicalE to the Eiffel Tower is strongly essential to him? Given the simplest quantified modal logic, it is necessary that the Eiffel Tower exists, so every proposition whatsoever implies the existence of the Eiffel Tower. Thus, it is not problematic if Socrates’s nature implies the existence of the Eiffel Tower. It would have been problematic
CEUeTDCollection
if it had implied that the Eiffel Tower is concrete; however, this is not the case (Zalta 2006:
683-4).
As I understand Fine, his complaint that Socrates’s nature is not connected in any special way with the Eiffel Tower is not as much about whether it can be implied from it that the Tower exists or is concrete, but about whether the Eiffel Tower is in any way a constitutive part of Socrates’s nature. The intuition here is that it is not; therefore, the property of not being identicalE to the Eiffel Tower, which specifically mentions it, should not be counted as an essential property of Socrates. Likewise, the property of being human and not identicalE to the Eiffel Tower should not be his essential property either. Fine’s main point is that modal essentialists cannot exclude it without evoking Socrates’s nature, which would make the account circular. Therefore, the question is whether Zalta can exclude the latter property from Socrates’ essential properties without evoking Socrates’s nature, as he managed to do in the case of the property of being distinctE from the Eiffel Tower.
Zalta does have a proposal to this effect: ‘One could place a constraint on the principles governing that notion [strongly essentially] so as to exclude any property which necessarily implies a property that Socrates has in every possible world’ (Zalta 2006: 684).
Fine did consider the possibility of the exclusion of the properties that were at least in part based on some necessary truth due to their irrelevance, but rejected it since not all such properties deserved exclusion. For example, it seems right to count the property of being such that there are sets as an essential property of the null set (Fine 1994: 7). However, all such cases involve abstract objects, so it would appear that Fine’s objection does not work here, where only the essential properties of ordinary objects are discussed.
To sum up, Zalta’s characterization of ‘essential property’ for ordinary objects successfully deals with Fine’s counterexamples within the quantified modal logic, thus proving that the modal characterization is not in principle incapable of capturing the concept
CEUeTDCollection
of essence and essential property. However, the characterization cannot be taken as an analysis that completely dispenses with the need to invoke the natures of objects, since the proposal provides different characterizations of the essential property for ordinary objects and abstract objects. In this respect, Fine’s objection directed at the standard modal account still stands. Moreover, some features of the proposal are controversial, especially the necessary existence of all objects and the notion of the contingently nonconcrete objects. I will return to this after the outline of the characterization of the ‘essential property’ in the case of abstract objects.