Rigid Designators

A rigid designator designates the same object in all possible worlds in which that object exists and never designates anything else. This technical concept in the philosophy of language has critical consequences felt throughout philosophy. In their fullest generality, the consequences are metaphysical and epistemological. Whether a statement's designators are rigid or non-rigid may determine whether it is necessarily true, necessarily false, or contingent. This metaphysical status is sometimes out of accord with what one would expect given a statement's apparent epistemological status as a posteriori or a priori. Statements affected include central ones under investigation in philosophical subdisciplines from the philosophy of science to mind to ethics and aesthetics. Hence, much of the discussion in various subdisciplines of philosophy is explicitly or implicitly framed around the distinction between rigid and non-rigid designators.

[size=30]1. A Basic Characterization of Rigid Designation, its Interest, and the Breadth of its Application

1.1 Names, Ordinary Descriptions, and Identity Statements

Philosophical work performed by rigidity is discussed in §3 below, after a more thorough characterization of the notion of rigidity is provided. However, a modicum of understanding about that work is needed for any understanding of what is interesting about rigid designators. Hence, before moving on to refinements in characterizing the notion of rigidity, consider a famous application made by Saul Kripke, who coined the word ‘rigid designator’. Kripke is not the first philosopher to discuss the idea behind the term he coined,[1] but his illuminating discussions have made the importance of rigidity widely appreciated.
Kripke (1980;1971) famously argues that because a rigid designator designates the same object in all possible worlds, an identity statement in which both designators are rigid must be necessarily true if it is true at all, even if the statement is not a priori. His classic example is the identity statement ‘Hesperus is identical with Phosphorus’, which is true, but which was discovered a posteriori to be true. (Let us understand a “statement” to be a sentence under an interpretation; and, following Kripke’s notation in 1971 and elsewhere, let us shorten ‘Hesperus is identical with Phosphorus’ to ‘Hesperus = Phosphorus’ even though Kripke does not do that in 1980.) ‘Hesperus’ is a name that was given to a heavenly body seen in the evening, and ‘Phosphorus’ is a name that was, unknown to the first users of the name, given to that same heavenly body seen in the morning. The heavenly body is Venus.
One might initially suppose that since the statement ‘Hesperus = Phosphorus’ was only discovered empirically to be true, it must be contingently true. But, says Kripke, it is necessarily true. The only respect in which it might have turned out false is not metaphysical but epistemic: thus, one could as well say of a geometrical theorem before it is proven that it might or might not turn out to be true or that it might or might not be provable without the parallels postulate. But if it is true and is provable without the parallels postulate, that is a matter of metaphysical necessity. In the same way, if the statement ‘Hesperus = Phosphorus’ is true, that is a matter of metaphysical necessity.
‘Hesperus = Phosphorus’ is necessarily true if true at all because ‘Hesperus’ and ‘Phosphorus’ are proper names for the same object. Like other names, Kripke maintains, they are rigid: each designates just the object it actually designates in all possible worlds in which that object exists, and it designates nothing else in any possible world. The object that ‘Hesperus’ and ‘Phosphorus’ name in all possible worlds is Venus. Since ‘Hesperus’ and ‘Phosphorus’ both name Venus in all possible worlds, and since Venus = Venus in all possible worlds, ‘Hesperus = Phosphorus’ is true in all possible worlds.
A description like ‘the brightest non-lunar object in the evening sky’ is, on the other hand, notrigid. That explains why the identity statement
[/size]

اقتباس :: (H) ‘Hesperus = the brightest non-lunar object in the evening sky’

[size]
is true but not necessarily true. While Hesperus is in fact the brightest object in the evening sky apart from the moon, Hesperus might have been dimmer: had, say, Hesperus been obscured by cosmic dust, Mars might have been the object designated by ‘the brightest non-lunar object in the evening sky’ rather than Hesperus. In that case, the above identity statement (H) would have been false. So the reason that (H) could have been false is that ‘the brightest non-lunar object in the evening sky’ does not designate Hesperus rigidly. It designates Hesperus in this world, which explains why (H) is true, but this description designates Mars in some other worlds, which explains why (H) could have been false: (H) would have been false had some other such world been actual.

1.2 Standard Clarifications from Kripke

Some potential misunderstandings are well known.
First, a rigid designator is used in a certain way in the actual world. Given that meaning, it designates the same object with respect to all possible worlds, regardless of how this term is used, or not used, in those other possible worlds: for although we identify objects in other worlds by our own names, natives of some of these worlds use other names (Kripke 1980, p. 77). A few philosophers resist this clarification. They find the idea of differentiating between the reference of terms in our world with respect to other worlds, on the one hand, and the reference of terms as used in other worlds, on the other hand, fatally confused (for critical discussion, see Fitch 2004, pp. 103–4). But such objections are not popular.
Second, although the statement (H) is not necessarily true, it is nevertheless Kripke's view and the standard view that the object that is in fact the brightest in the evening sky, Venus (Hesperus),is necessarily identical to Hesperus.
Third and finally, ‘Hesperus’ is rigid because it picks out Hesperus in all worlds that containHesperus. In worlds not containing Hesperus, the designator fails to name anything other than Hesperus. There is more than one account of a rigid designator that conforms to that requirement. On one such account, a rigid designator designates its designatum in every possible world containing the designatum and in other possible worlds the designator fails to designate. In places, Kripke suggests that this is his idea:
[/size]

اقتباس :: When I use the notion of a rigid designator, I do not imply that the object referred to necessarily exists. All I mean is that in any possible world where the object in question doesexist, in any situation where the object would exist, we use the designator in question to designate that object. In a situation where the object does not exist, then we should say that the designator has no referent and that the object in question so designated does not exist (Kripke 1971, p. 146; a disclaimer is reported in Kaplan 1989b, p. 570n.8).

[size]
In other places, Kripke seems to have in mind another account of rigidity: one according to which a rigid designator designates its object in every possible world, whether or not the designatum exists in that world. Hence, he says, “If you say, ‘suppose Hitler had never been born’ then ‘Hitler’ refers here, still rigidly, to something that would not exist in the counterfactual situation described” (Kripke 1980, p. 78).
It may be that no substantive issues ride on which conception of rigidity is adopted (Stanley 1997a, pp. 557, 566ff.; see also Brock 2004, p. 285n.13). On the other hand, some philosophers have held that true statements using a proper name to express that so and so might not have existed are unintelligible unless the relevant name refers to the object in all worlds, period. That might provide a substantive reason for favoring the latter type of rigidity, obstinate rigidity, as Salmon calls it (1981, p. 34). Obstinate rigidity has sometimes been favored on grounds like these (see, e.g., Besson 2009; Gómez-Torrente 2006, p. 250; Plantinga 1985, p. 84: particularities of Plantinga's characteristically interesting account are discussed in the supplement on individual essences in the entry on actualism). Kripke's quote above hints that obstinate rigidity might afford this kind of advantage. But Kripke never argues for one position or another. Despite occasional slips in favor of one or another refined version of rigidity, he deliberately sidesteps these “delicate issues” when he gives them his full attention (1980, p. 21, n. 21).
There are stronger and weaker brands of necessity corresponding to the possible notions of rigidity. Kripke argues that a sentence like ‘Hesperus = Phosphorus’ is at least “weakly” necessary (1971, p. 137): true in all those possible worlds in which Hesperus exists and Phosphorus exists. The statement may enjoy a stronger necessity, too, which would render it true in all worlds, period.[2] In this entry, “necessity” is to be understood as weak necessity (at least).

1.3 Rigidity for a Diversity of Grammatical Categories

Rigidity is most straightforwardly applied to proper names of concrete objects. There is general agreement that ‘Hesperus’ and ‘Barack Obama’ refer rigidly. The debate about which expressions in natural languages are rigid designators is typically set up with a background assumption that proper names are singular terms. Though this assumption has been challenged (Fara, 2015), I will nevertheless assume it for presentational purposes in what follows.
Rigidity is also applied commonly to indexicals, like ‘now’ or ‘you’. If, when I use ‘you’ in a context, my utterance means something like the person at the door (Nunberg 1993; Smith 1989 §5), then presumably it is not rigid. You may be at the door, but in another possible world it is another philosopher who comes visiting. On the other hand, if (as Kaplan proposes: 1989a) ‘you’ refers directly to an individual, without amounting to a disguised description meaning the same as a description like ‘the person at the door’, then it would seem to be rigid. So if I say, pleasantly surprised, “You made good time,” we could discuss reasons for this and conditions under which this might not have been the case, but in all of our considerations the same individual, and not anyone else who might have been at my door in good time or not, is the one in question. The individual in question is the one who is in fact identical to you (as any account could put it). After Kaplan, indexicals have typically been treated as rigid; but there seem to be nonrigid uses.
Demonstratives such as ‘that’ raise similar issues as indexicals. So also do noun phrases like ‘that flower you just picked’ (see King 2001, chap 2, for discussion). As Wolter (2009, p. 457) observes, “there is not yet consensus” about which such expressions “allow non-rigid interpretations and which do not.”
The paradigm example of non-rigid designators, since the work of of Kripke, has been standard definite descriptions, such as ‘the brightest non-lunar object in the evening sky’. However, some definite descriptions, such as ‘the successor of 2’, are rigid designators; their rigidity seems to arise in virtue of facts about metaphysical reality, in this case, the necessity of mathematical facts, rather than facts about the semantic properties of expressions. Such definite descriptions are therefore “de facto” rigid designators. The Russellian view that definite descriptions are quantified expressions is also widely held. Since it is natural to think of rigidity but not, in view of Russell, to think of definite descriptions in connection with singularity, the question dawns of how to think about rigidity with categories of expressions other than singular terms. This broad topic, which surfaces in other connections too, has received much discussion in recent years.
Another category of terms whose singular status raises questions is that of natural kind terms like ‘gold’ and ‘water’. Again, these seem widely to be thought singular at least some of the time. They are frequently counted as rigid. Other related and again apparently singular terms that are sometimes counted rigid include ‘redness’ and ‘loudness’. More controversial are singular terms for properties that are more artificial: ‘bachelorhood’, or ‘soda pop’.
Not just singular terms but also general terms, like ‘tiger’, ‘hot’, and ‘red’ are often recognized as rigid (following Kripke's suggestion: 1980, p. 134). These terms raise complications not present for singular terms.
Terms from other grammatical categories, as well, might admit a rigid/non-rigid distinction. Philosophers have attended relatively little to the status of verbs and adverbs, in this connection (but see, e.g., López de Sa 2008). Compare ‘to begin writing’, ‘to commence writing’, and ‘to do what the teacher commanded at time t’ (where the command was, “Begin writing”). Evidently, the necessity of ‘One is about to begin writing if and only if one is about to commence writing’ is not enjoyed by ‘One is about to begin writing if and only if one is about to do what the teacher commanded at time t’. Arguably, the reason for the modal differences has to do with the rigidity or non-rigidity, in some appropriately extended sense, of the contained verbs. Something similar applies to adverbs. Compare ‘She ran quickly’ with ‘She ran in the manner signaled by her coach’ (where the signal means: Run quickly!).[/size]

Rigid Designators

[size=30]1. A Basic Characterization of Rigid Designation, its Interest, and the Breadth of its Application

1.1 Names, Ordinary Descriptions, and Identity Statements

1.2 Standard Clarifications from Kripke

1.3 Rigidity for a Diversity of Grammatical Categories

Rigid Designators :: تعاليق

Rigid Designators