The rigidity of proper names might seem to be a contingent fact about natural language: it might seem that a language in which names are not rigid designators should be possible. Indeed, the literature usually presents the claim that proper names are rigid as empirical, derived not from theory but from observation. Stanley, for instance, explicitly writes that the thesis that names are rigid is ‘an empirical claim about natural language’ (1997, p. 566). The question then arises: why are the proper names of our natural languages rigid? This question, which is never raised by Kripke, deserves some attention.

By contrast to Kripke, I will attempt in this chapter to derive rigidity, or something close to it, from more basic facts about our use of names. It will turn out that rigidity is a necessary property of names.

Attempts to derive rigidity from some more basic facts about language exist in the literature. Kaplan, for instance, has asked:

This idea, that the reference of a name is independent of what is said in the rest of the sentence in which it occurs (the principle of the independence of reference, or PIR), can be clarified and demonstrated as follows. Suppose someone intends to say that Aristotle might have been a physician instead of a philosopher. She starts saying that, but is interrupted after having said only ‘Aristotle might have been’. Although failing to say anything about Aristotle, she did refer to him. The reference of ‘Aristotle’ is determined independently of what she intended to say about him. Similarly, if we did not hear clearly what a speaker has said, yet did hear him say ‘Aristotle’, we may know to whom he referred: the referent is determined independently of those parts we failed to hear. Reference is even independent of the fact that we talk about what is merely possible and not actual, or vice versa: if one was interrupted after having said only ‘Aristotle …’, or ‘Aristotle, as you all know …’, then one has referred to Aristotle, while what one said does not determine whether the situation one intended to describe was actual or merely possible.

That is why I gave above incomplete sentences as examples: the reader knew who is mentioned in those partial sentences, although they specified no situation – actual, possible or impossible. This shows that the reference of a name occurring in any of those sentences is independent of the way the sentence containing it might be completed.

Here is a chess picture of the logic of discourse. We first take some chess pieces: this is reference by means of proper names, and in this way the identity of the particulars we talk about is determined. We then arrange these pieces on the board: this is the description of a situation, either actual or merely possible, which is specified by the rest of the sentence. The identity of the chess pieces we pick is independent of the way we later arrange them.

Why is the reference of names independent of what is said in the rest of the sentence containing them? The reason is that, first, unlike definite descriptions and demonstrative phrases, names have no descriptive content, which could relate them to other things mentioned in the sentence. Second, unlike pronouns and definite descriptions, names are not used as anaphors and therefore they cannot have their reference depend on the reference of other phrases in the sentence in the way the reference of anaphors does. And I don’t see any other way – with one possible exception soon to be discussed – in which the reference of a phrase might be dependent on other words or phrases in the same sentence. Of course, it cannot be ruled out that I have failed to notice some special construction which does generate such dependence. Yet this would not refute the principle but only show that it does not apply to all possible uses of names; and it is also likely that in such constructions names indeed would not be rigid.

The fact that names are different in these aspects from definite descriptions, demonstrative phrases, and pronouns is of course not contingent: we consider as names those singular terms that are not pronouns nor have their reference determined by the meaning of words that compose them in the way that the reference of definite descriptions and demonstrative phrases is. Consequently, the PIR is not a contingent fact about names.³

Phrases that share some features both with names and with definite descriptions do exist, in the form of definite descriptions that have grown capital letters: ‘The United Nations’, ‘Central European University’, and so on. Apart from some special cases, the description here has to apply to the thing named, although it does not participate in determining the reference of the phrase. It seems that this standardized use of the capitalized description also prevents it from relating to other parts of the sentence in a way that might influence its reference. So it seems the PIR does hold even for this limiting case of names.

Notice that I have not claimed that the PIR applies only to names: other terms and phrases may have their reference depend on other words and phrases in the sentence, but it need not be so. This is indeed the case with many uses of pronouns, definite descriptions and demonstrative phrases. I shall return to this below.

Before proceeding with additional points, let us consider two objections that might be raised to the PIR. First, as I have maintained that the reference of a name is independent of what is said in the rest of the sentence containing it, its reference should be determinable independently of what is said by the rest of that sentence. But suppose someone says, ‘Zeno invented the Arrow Paradox’: the audience might know that he is talking about Zeno of Elea and not Zeno the Stoic precisely by relying on other parts of the utterance; in this case, by relying on the fact that the Arrow was mentioned, a paradox invented by Zeno of Elea. Accordingly, contrary to what the PIR claims, a name’s reference might be determined by what is said in the rest of the sentence containing it.

This objection, however, confuses a semantic point with an epistemic one; and although it correctly describes the epistemic point, it does not apply to the semantic one, in which we are interested here. The audience indeed may come to know to whom a speaker referred with a name or expression by reliance on the meaning of other parts of the sentence uttered; this is the epistemic point. However, it should be possible to determine the reference of the name independently of this procedure; this is the semantic aspect of the independence of reference. After all, it is possible that the speaker made a mistake and ascribed the invention of the paradox to Zeno the Stoic. To ascertain whether he is right (Elea) or mistaken (the Stoic), it should be possible to determine to which Zeno he referred without reliance on what he said of him. And this is the idea expressed by the semantic principle of the independence of reference.

The second objection to the principle runs as follows. Suppose I introduce a name for a person, saying, for instance, ‘Let this baby be John Smith’. The reference of ‘John Smith’ is determined, in this case, by what is said in the part of the sentence preceding it, in apparent disagreement with the PIR. However, when such a sentence is used in a naming event, the name is only mentioned in the utterance; the naming speech act, if successful, makes a future use of the name possible. The form of the sentence should not mislead us into thinking that the name is used to refer in the specific utterance concerned: the sentence could be substituted in that context by ‘I name this baby “John Smith”’, where the mentioning is explicit. Yet even if one does not accept this response to the apparent counterexample, then we have here an exception to the PIR only in the special case in which a name is introduced into language with a specific reference.

Turning back to rigidity, if the PIR is accepted, then names can be shown to be rigid in the following sense. According to the principle, the reference of a name is determined independently of what is said in the rest of the sentence containing it. Consequently, if what is said by the rest of the sentence makes it necessary to consider a variety of possibilities in order to determine its truth-value, the reference of the name that the sentence contains is determined independently of these possibilities and is therefore the same for all. The name is therefore rigid.

In one place in NN, while critically discussing the alleged problem of transworld identity, Kripke comes close to explaining rigidity in a way similar to the way developed here. He writes:

Yet we should also note some differences. I have attempted to derive rigidity from a more general principle of the reference of names. Nothing of this sort is found in Kripke’s work, which argues ‘intuitively’ for the rigidity of proper names (NN, 49) by means of examples alone.

Another difference between what Kripke says in the quoted passage and the approach developed here is that only according to the former do ‘we begin with the objects, which we have, and can identify, in the actual world’. On the view developed here we may ‘begin’ with objects that do not really exist, objects which we do not have in the actual world. We shall see some examples of this below, where I shall also note some further related differences.

Lastly, in the quoted passage Kripke is trying to explain rigidity, but I shall eventually suggest the PIR as an improvement on the rigidity claim. So far, the PIR has been used to support and derive the rigidity of proper names. However, I shall now turn to difficulties in the accepted conception of rigidity. These difficulties might lead us to consider the PIR as expressing more accurately than the concept of rigidity the facts about names that the latter was meant to capture.

Let us consider the following sentence:

On the other hand, according to the rigidity claim, the question of the designation of ‘Isaac’ in (1) is still unsettled. The question is the following. When we use a name to talk about a possible situation in which the person that the name designates when used to tal...