The attribution of essential and accidental properties to things has been connected with de re necessity and possibility as opposed to de dicto necessity and possibility. De re/de dicto distinction was introduced in medieval logic, although it was already implicit in Greek logic.
Roughly, the modal expressions ‘possibly’ and ‘necessarily’ are used de dicto in case they modify an entire non-modal sentence or proposition (dictum) and are used de re in case they attribute a modal characteristic to a particular item(s) or feature(s) (Lat. res = a thing) mentioned in the non-modal sentence. For example, a sentence ‘A seated man can walk’
under de dicto reading (‘It is possible that a seated man walk’) means ‘It is possible that-a-seated-man-walk (that is, while seated)’. That which is asserted in a non-modal sentence (that-a-seated-man-walk) is considered as the subject about which the mode is predicated and since a man who sits does not walk, the sentence under de dicto reading is false. Under de re reading, it is about the object simpliciter, namely the subject of the sentence, and the modal
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adverb qualifies the copula. Accordingly, the sentence means ‘A seated man has the power or ability to walk’.36 In other words, a man, who is described as sitting, has as a man the ability to walk, and this is true.
The next thing to consider is what the best formalization of de re modal claims, such as ‘Jerry is necessarily a mouse’ is. Now, it seems natural to hold that the predicate ‘is necessarily a mouse’ attributes a necessary property to our Jerry and ‘necessarily’ could be formally presented as a predicate modifier: ‘Jerry is necessarily-a-mouse’. David Wiggins defends such predicate-modifier account of essentialist claims (Wiggins 1976 and 2001). He points out that essentialist claims in English are expressed by a de re use of ‘must’, for example, ‘Socrates must be a man’. According to him, de re/de dicto distinction is explicated in terms of the scope of ‘necessarily’. In case of de re, ‘necessarily’ governs a predicate (marked with ‘Nec’) and in case of de dicto, ‘necessarily’ governs a complete sentence (marked as ‘ ’). In the formalization of de re uses Wiggins uses an abstraction operator and
‘Nec’: [Nec[( x)(Man x)]], <Socrates>, which reads as ‘Anything that is Socrates must be a man’.37One should note that in this way the explanation of necessity runs in the language of properties and having of properties – ‘Socrates has a property of being necessarily a man’
(1976: 293 and 2001: 113).
Maybe even more plausible and closer to traditional understanding is the copula-modifier account, which is a slight variant of the predicational approach. It was proposed by McGinn, who thought that Wiggins’s proposal did not quite capture the original sentence
‘Socrates is necessarily a man’ (McGinn 2000). According to Wiggins’s proposal, Socrates has a property of being necessarily a man, but this leaves the way in which Socrates is said to have this modal property still open. However, original sentence looks like this question is
36 See, for example, Gallois 1998 and Ashworth 1998.
37 x(Man x) is the abstract for the property that any x has just if x is a man and we express the claim that Socrates falls in the extension of this property as: x(Man x), <Socrates>. Then we add Nec to the abstract – Nec[( x)(Man x)], so that it is clear that it governs a predicate (forming with it a complex predicate), leaving the subject term <Socrates> outside of the scope of the modality (Wiggins 2001: 113).
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already settled: Socrates has the property predicated of him in the mode of necessity. This understanding is captured in the copula-modifier theory, where ‘necessarily’ modifies the copula ‘is’, and not the predicate ‘is a man’: ‘Socrates is-necessarily a man’. Accordingly, Socrates has a non-modal property being a man, which he possesses in the mode of necessity.
Here, modal expressions are understood as ‘copula modifiers’ that specify whether an objects instantiates a property in the necessary or the contingent mode. The theory is a linguistic counterpart of the ontological theory according to which modality is a matter of the strength of the instantiation relation. Further, McGinn plausibly supports his theory with linguistic evidence: ‘[W]e say “Socrates must be a man”, “Aristotle could be a farmer”, “Plato happens to be a philosopher”. But there are no parallel constructions for “red”, “large” etc. When we convert “is” to “must” we incorporate the modality right into the copula grammatically, and this is the natural way to express modal claims outside of stilted philosophical usage.’ (ibid:
75-78).
Although the predicational approach accords better with the modal attribution – an object has this or that modal property, or an object has this or that property in a certain modal mode – today the sentential approach to the formalization of de re modal claims is customary.
It enables us to express essentialist claims in more familiar first-order predicate calculus with added sentential modal operator, ‘ ’, where the essentialist claims are formalized as quantification into modal formulae. Moreover, they are evaluated within the possible worlds semantics.
I cannot go into technical details here so let me present only the core idea of the possible worlds semantics. The de dicto modality is basically interpreted as quantification over possible worlds: necessity as a universal quantification over worlds and possibility as an existential quantification over possible worlds. Accordingly, a proposition is necessary or necessarily true iff true in every possible world; and a proposition is possible or possibly true
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iff true in some possible world. De re modal statements are about what is possible or necessary for particular objects, consequently, for the interpretation of de re modality, we need to add to the domain of possible worlds also the domain of individuals as a quantification domain.38 Now, as propositions are true or false in possible worlds, objects exist or fail to exist in possible worlds. Accordingly, ‘An object x has necessarily a property F’ is true iff x has F in every world (in which it exists), and ‘An object x has possibly a property F’ is true iff x has F in some world (in which it exists).
Thus equipped, we can proceed with the formal representation of de re statements in quantified modal logic. Take for example the following two formulae: x x and x x. The first says that the proposition (dictum) that something (not necessarily the same thing in each world) is is true in every possible world, and the second says that there is a thing (res) and concerning this thing (de re), it – the very same thing – is in every possible world. The main idea behind the distinction is that de dicto formulae do not depend on just how we match up an individual in one world with an individual in another as de re do (Cresswell & Hughes 1996: 250-51). From the syntactic point of view, the de dicto formulae are those in which no variable occurs free within the scope of a modal operator ‘ ’ ( x x) and the rest are de re ( x x). This criterion, however, does not classify simple statements of the form Fa, where a stands for a genuine proper name, as de re as we would like, but as de dicto instead, since qualifies a closed sentence Fa. The reason why we would want it to be de re is a semantic one. Genuine proper names are supposed to be rigid designators, i.e., designating the same individual in all possible worlds. Consequently, individual constants are required to be rigid designators and the truth-conditions for Fa require, in turn, the identification of an
38 There are two possibilities of treating the domain of quantification. One, the simplest option, is to assume a single domain of quantification that contains all possible objects (the fixed-domain or possibilist approach). The other is to assume that the domain of quantification changes from world to world and contains only objects that actually exist in a given world (the world-relative or actualist approach). Both approaches have its advantages and disadvantages, although most of logicians prefer the world-relative approach (Kripke 1963, Fine 1978).
Recently, it has been suggested that the fixed-domain approach can be reconciled with actualism (Linsky and Zalta 1994 and 1996).
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individual across possible worlds. In this case, we get an amended criterion for the de re/de dicto distinction: a formula is de dicto if no free variable or constant occurs within the scope of a modal operator ‘ ’ (Fine 1978:143).