The distinction between de re (‘of the thing’) and de dicto (‘of the statement’) claims of necessity is central to the doctrine of essentialism—the view that individuals hold some (or all) of their properties necessarily. In this essay I will examine three different ways in which this distinction may be symbolised in formal logic and assess the pros and cons of each before reaching a verdict as to which is to be preferred, and upon what grounds.

To illustrate the difference between these two types of claim, consider the following proposition:

(1)    Socrates is necessarily human.

which admits of two possible readings:

(1a)    It is necessarily the case that that Socrates is human.

(1b)    Socrates holds the property of being human necessarily.

As Plantinga (1978: 28) points out, the de dicto reading, (1a), may be understood as assigning necessity to the proposition

(1′)    Socrates is human.

i.e. (1a) is true iff (1′) obtains in all possible worlds (cf. Kripke 1963). However, on the de re reading, (1b), the necessity relates to the way in which the property of ‘being human’ is held by an individual (Socrates), rather than to the truth of (1′), as per the de dicto reading (Plantinga, op. cit.). Assuming that the name Socrates ‘rigidly designates’ (Kripke 1980: 48) a particular individual, viz., the historical Socrates, then the two readings appear to exhibit something resembling a scope distinction concerning the concept of necessity (Sainsbury 1991: 240). This is relevant to essentialism since the readings differ in their existential commitments, and so the way in which they are formally symbolised will affect the outcome of arguments that contain one or more essentialist premisses. Conversely, if we cannot capture the formal difference between (1a) and (1b), then either our modal logic is ambiguous, or else the distinction between de re and de dicto readings is illusory, neither of which appears tenable.

The simplest symbolisation of (1) is

(2)    ⃞Fa

where F is the predicate ‘____ is human’, a is Socrates, and ⃞ is the modal operator for necessity. Under the standard modal semantics (Kripke op. cit.), this states that in all possible worlds, the proposition Fa, or (1′), is true. In order for this to be the case then either (i) Socrates must exist in all possible worlds and be human in each of them, or (ii) we must be able to say of Socrates that is human with respect to worlds in which he does not exist. The former interpretation makes Socrates a necessary being, since in order for (2) to be true, he must exist in every possible world. This is incompatible with the highly plausible claim that Socrates might conceivably not have existed, and so is contingent. On this interpretation, anything that possesses one or more essential properties must itself exist necessarily. Furthermore, if existence can be construed as a property (cf. Frege 1884: 103) that is essential to all actual things, then this commits us to the highly counterintuitive and metaphysically contentious claim that every actual being must necessarily have existed, as represented by the Barcan Formula (Menzel 2007a: 2.1).

The second interpretation of (2) requires the use of positive free logic in which the usual constraints upon names (i.e. that they must refer) are relaxed, enabling true or false statements to be made about non-actual entities. Just as statements about fictional entities are true or false with respect to ‘fictional worlds’ (Walton 1978: 311)—e.g. Sherlock Holmes is a detective who smokes a pipe, solves crimes, etc.—statements about contingent entities may be evaluated with regard to the possible world in which they are uttered, or their ‘context of utterance’ (Williamson 1998: 270). In the case of Socrates, the relevant context of utterance is the actual world, which fixes the sense of the proposition. The ‘context of evaluation’ (ibid.), on the other hand, will vary according to the possible world under consideration. On this view, only worlds in which Socrates exists and is not human would render the statement false, since in worlds where there is no Socrates, this name is understood in accordance with its original context of utterance, in which Socrates is human. Hence we can say that (1′) is true even in worlds where Socrates does not exist. However, such an approach seems somewhat ad hoc, and the possibility of allowing such ‘empty names’ adds complexity to classical logic.

In order to avoid this unwanted baggage, we might instead make Fa contingent upon the existence of Socrates in a given world, i.e.

(3)    ⃞(E!a ⊃ Fa)

where E! is the existence predicate (cf. Plantinga 1978: 56). This does not entail that Socrates exists necessarily, as per the first interpretation of (2), but still requires the use of empty names since in order for the conditional

(3′)    E!a ⊃ Fa

to be true in all possible worlds, its antecedent and consequent must both assume a truth value (typically false) with respect to worlds in which the name a does not refer. Thus (3) requires the use of negative free logic.

One potential objection to this formulation is that it symbolises the apparently simple modal proposition, (1), as a conditional. Although this may seem surprising and unintuitive, such anomalies are by no means unprecedented,1 and it does not constitute a knock-down argument against this approach. More problematic is an argument by Williamson (2002: 233–4) purporting to show that in order for (3) to hold, (3) must itself be a necessary existent, i.e.

(3″)    ⃞T[φ(a)] ⊃ ⃞E![φ(a)]

where T[] is the truth predicate and φ(a) is any statement involving a, including (3) [Efird 2006: 5]. This in turn requires that a necessarily exists, thus yielding a similar problem as per the first interpretation of (2), with the added difficulty that any statement of an individual’s essential properties must itself exist necessarily, which is dubious given that language is a contingent phenomena.2

The third and final option for symbolising de re necessity employs Prior’s (1957) modal logic, Q, which was devised as a logic of contingent entities that would modal logic of the ‘myth that whatever exists exists necessarily’ (Prior op. cit. 48). In Q, de re necessity would be symbolised as

(4)    ¬♢¬Fa

where ♢ is the modal operator for possibility, whilst de dicto necessity would be symbolised as per (2). This has the advantage of retaining most of classical logic as it avoids the need for empty names. However, Q’s modal operators differ from the conventional possible world semantics in that they are not duals, i.e. Q denies that ⃞φ ≡ ¬♢¬φ and ♢φ ≡ ¬⃞¬φ. Consequently, (4) is true iff there are no possible worlds in which Socrates both exists and is not human, since unlike the ⃞ operator, ♢ does not have existential import for worlds in which Socrates does not exist.

Prior’s modal logic, however, is not without its drawbacks. With the exception of the sort of essentialist claims illustrated above, Q does not permit any necessary truths about contingent entities. This has the peculiar consequence that even apparently tautologies such as

(5)    Pa & ¬Pa

are only contingently (rather than necessarily) true in cases where a denotes a contingent entity, since (5) can only be stated in worlds where a exists, and so is not true in every possible world (Menzel 2007b). Williamson (op. cit.) considers this a result of Prior confusing context of utterance with context of evaluation, but this peculiarity hardly seems worse than Williamson’s own acceptance of the necessity of existence, or the positive free logician’s view that statements may obtain in worlds where the names that they contain fail to refer.

In conclusion, each of the three ways in which the essentialist claim that an individual possesses certain necessary properties de re can be symbolised comes with its own costs and advantages. ⃞Fa entails necessary existence and, along with ⃞(E!a ⊃ Fa), requires the use of free logic, whilst ¬♢¬Fa retains classical logic but rejects the duality of the modal operators. The question as to which of these is correct thus turns upon one’s acceptance of their metaphysical implications, rather than mere notational convenience. Prior’s approach has the considerable advantage that it is able to explain the necessity of existence represented by the Barcan Formula in terms of a property that all existent things hold necessarily (i.e. de re), as opposed to it being necessary that they had to exist (de dicto) [cf. Wiggins 1976]. The resulting symbolisation also accords with Plantinga’s characterisation of de re necessity as representing the thought that ‘the object in question could not conceivably have lacked the property in question’ (Plantinga 1969: 236; original italics). Thus, despite its idiosyncrasies, Q offers perhaps the best method of symbolising essentialist claims of de re necessity without committing oneself to the implausible thesis that such individuals are necessary beings.

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1 Russell (1905), for example, symbolises definite descriptions as complex conjunctions.

2 The attempt to symbolise de dicto necessity as ⃞T[φ(a)] exhibits the same difficult, although this can perhaps be avoided by replacing (3″) with the conditional E![φ(a)] ⊃ T[φ(a)].

References

Efird, David 2006: ‘Necessary Existence and the Semantics of Quantified Modal Logic’ (forthcoming).

Frege, Gottlob 1884: The Foundations of Arithmetic. In The Frege Reader, M. Beaney (ed.), pp. 84–129.

Kripke, Saul 1963: ‘Semantical Considerations on Modal Logic’. In Reference and Modality, L. Linsky (ed.), pp. 63–72.

————    1980: Naming and Necessity. Oxford: Blackwell.

Menzel, Christopher 2007a: ‘Actualism’. The Stanford Encyclopedia of Philosophy, Spring 2007 Edition. E. N. Zalta (ed.). <http://plato.stanford.edu/archives/spr2007/entries/actualism/>.

————    2007b: ‘Prior’s Modal Logic’ (supplement). The Stanford Encyclopedia of Philosophy, Spring 2007 Edition. E. N. Zalta (ed.). <http://plato.stanford.edu/archives/spr2007/entries/actualism/Prior.html/>.

Plantinga, Alvin 1969: ‘De Re et De Dicto’. Noûs, 3(3), pp. 235–58.

————    1978: The Nature of Necessity. Oxford: Oxford University Press.

Prior, A. N. 1957: Time and Modality. Oxford: Clarendon Press.

Russell, Bertrand 1905: ‘On Denoting’. In The Philosophy of Language, 3rd Edition, A. Martinich (ed.), pp 200–7.

Sainsbury, Mark 1991: Logical Forms. Oxford: Blackwell.

Walton, Kendall L. 1978: ‘Fearing Fictions’. In Aesthetics and the Philosophy of Art, P. Lamarque and S. H. Olsen (eds.), pp. 307–19.

Wiggins, David 1976: ‘The De Re Must’. In Truth and Meaning, G. Evans and J. McDowell (eds.), pp. 285–312.

Williamson, Timothy 1998: ‘Bare Possibilia’. Erkenntnis, 48. pp. 257–73.

————    2002. Necessary Existents. In Logic, Thought and Language. A. O’Hear (ed.). Cambridge: Cambridge University Press.