There’s a familiar distinction between singular terms that are “de facto” rigid and those that are “de jure” rigid. Paradigm example of the former: “the smallest prime”; paradigm example of the latter: “Socrates” (or, variables).
I’m not sure exactly how “de jure” rigidity is typically characterized. I’ve seen it done through slogans such as: what the name contributes to the truth conditions expressed by sentences in which it figures is just the object it stands for. I’ve seen it done like this: a name is de jure rigid if its rigidity is “due to” the semantics of language, and not to metaphysical facts about the world.
Those two definitions seem to come apart: “the actual inventer of the zip” is plausibly de jure rigid in the second, but not the first, sense.
Let’s concentrate on the first sense of de jure rigidity (so a constraint on getting this right is that actualized descriptions won’t count as de jure rigid in this sense). How could we tighten it up? Well, the task is pretty easy if your semantic theory takes the right shape. For example, suppose you have a semantic theory which in the first instance assigns structured propositions to sentences, and then says what truth conditions these propositions (and thus sentences) have. Then you can say precisely what it is for “name to contribute an object” to the truth conditions of sentences in which it figures: it’s for you to shove an object into the structured prop associated with the sentence.
Notice two things:
(1) this is a semantic characterization: you can read off from the semantics of the language whether or not a given term is de jure rigid. (In this sense, it’s like the characterization of “rigidity” as “referring to the same thing wrt every world”).
(2) this is a local characterization: it only works if you’re working within the right semantic framework (the structured-props one). You can’t use it if you’re working e.g. with Davidsonian truth theories, or possible world semantics.
This raises a natural question: how can we capture de jure rigidity in this, that and the next semantic framework? What interests me is what we can do to this end, working with a general semantics in the sense of Lewis (1970). I can’t see any way to read off de jure rigidity from semantic theory.
But if we appeal to metasemantics (i.e. the theory of how semantic facts get fixed) it looks like we have some options. Suppose, for example you’re one of the word-first guys: that is, like early Field, Fodor, Stalnaker et al, you think that the metasemantic story operates first at the level of lexical items (names, predicates), and then we can offer a reduction of the semantic properties of complex expressions (e.g. definite descriptions, sentences) to the semantic properties of their parts. The de jure rigid terms will be those whose semantic properties are fixed in the following way:
(1) term T refers (simpliciter) to an object X.
(2) term T has the as intension that function from worlds to objects, which, at each world w, will pick out the entity that is identical to what T refers to (simpliciter).
So here’s my puzzle: this looks like a characterization that’s turns essentially on the word-first metasemantic theory. Fair do’s, if you like that kind of thing. But I’m more sympathetic to metasemantic theories like Lewis’s, where the semantic properties of language get determined holistically. If you’re an “interpretationist” (and if you haven’t got the semantic characterizations to help you out, because you’re working with a trad possible world semantics), is there any content in the notion of de jure rigidity? More on this to follow.