What is rigid designator?

Saul Kripke, answered from the texts and cited to the page.

Saul Kripke answers

A rigid designator is a term that designates the same object in all possible worlds.¹ That is the core of it, but the notion is easily misread, so let me say what it does not mean. When I say a designator is rigid, I do not mean that the word could not have been used differently — of course language might have been otherwise. I mean something about how we use the expression in our language when we describe counterfactual situations.²

Take the phrase "the inventor of bifocals." When we talk about some other possible world, we use that phrase to refer to whoever in that world would have invented bifocals — not to the person whom people in that world might have called by that phrase. That is what makes it non-rigid: under some circumstances one man would have been the inventor of bifocals, under other circumstances another man would have.³

A rigid designator, by contrast, always picks out the same object, whichever counterfactual situation we are describing. The contrast with definite descriptions is the heart of the matter. Suppose we say that "Aristotle" means "the greatest man who studied with Plato." Then in some possible world where a different man studied with Plato and was the greatest such student, that man would be Aristotle — which is not what we mean at all.⁴

If instead we use the description merely to fix the reference — to pick out which man we intend — then Aristotle is Aristotle in every world where he exists, and we can coherently say "suppose Aristotle had never gone into philosophy at all" without meaning anything about whoever happened to study with Plato.⁵ The Frege-Russell view, as I read it, makes proper names non-rigid by treating them as equivalent to definite descriptions.

If "Moses" means "the man who led the Israelites out of Egypt," then in a counterfactual situation where some other man did the leading, "Moses" would refer to him — not to Moses himself.⁶ That consequence seems to me plainly wrong. When we use "Moses" we refer rigidly to a particular man, and we refer to that man even when talking about counterfactual situations in which he did none of the things we associate with him.⁷

One further clarification: rigidity does not require that the designated object exist in every possible world.⁸ If you say "suppose Hitler had never been born," the name "Hitler" still refers rigidly to that man — to something that would not exist in the counterfactual situation being described.⁹ The rigidity is about the reference, not about a guarantee of existence across worlds.

Sources

1. What do I mean by 'rigid designator'? I mean a term that designates the same object in all possible worlds.

   1. Identity and Necessity, p. 9

2. When I say that a designator is rigid, and designates the same thing in all possible worlds, I mean that, as used in our language, it stands for that thing, when we talk about counterfactual situations.

   Naming and Necessity, pp. 85–86

3. So, in this sense, the expression 'the inventor of bifocals' is nonrigid: Under certain circumstances one man would have been the inventor of bifocals; under other circumstances, another man would have.

   1. Identity and Necessity, p. 9

4. If we used that as a definition, the name 'Aristotle' is to mean 'the greatest man who studied with Plato'. Then of course in some other possible world that man might not have studied with Plato and some other man would have been Aristotle.

   Naming and Necessity, p. 65

5. If, on the other hand, we merely use the description to fix the referent then that man will be the referent of 'Aristotle' in all possible worlds. The only use of the description will have been to pick out to which man we mean to refer.

   Naming and Necessity, p. 65

6. If that is what the name 'Moses' means, and if we wished to talk about a situation in which some other man had led the Israelites out of Egypt, then in using the name 'Moses' in counterfactual situations, we would be using it to refer to the man who in those situations would have led the Israelites out of Egypt, and this would not be Moses himself.

   Reference and Existence, p. 12

7. when we use the name 'Moses' it always means or refers to man, the particular man, who—I suppose they are right about the rest—in fact led the Israelites out of Egypt... We use the name 'Moses' rigidly to refer to a certain man, and we use it to refer to that man even when talking about counterfactual situations in which the man didn't lead the Israelites out of Egypt.

   Reference and Existence, p. 12

8. in talking about the notion of a rigid designator, I do not mean to imply that the object referred to has to exist in all possible worlds, that is, that it has to necessarily exist.

   1. Identity and Necessity, pp. 9–10

9. 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.

   Naming and Necessity, pp. 85–86