Here in Wales there has always been a great shortage of names, and almost everyone has to make do with 'Jones' or 'Williams'. Accordingly, there has arisen the tradition of appending the occupation to the name. This is not unique to Wales, and so there are many surnames that are occupations - 'Smith', 'Baker', 'Cooke', and so on.

So 'Bob the Builder' starts out as a rigid designator - 'Bob', and an appended disambiguating description. Just as there is more than one Nixon, so there is more than one Bob. Such names are rigid, but not definite. But once I have made clear that it is Bob the builder I am referring to and not Bob the sagger-maker's bottom-knocker, then it is the same person I am referring to whatever I am saying: "Bob might have been called 'Sam' and joined the fire service." If he had, of course he would not have been called 'Bob the Builder', but 'Fireman Sam'. But for this to have any meaning, it must be Bob who would have been called Sam, and Bob who would have joined the fire service - to suppose that Fireman Sam was called 'Sam' and joined the fire service is to suppose nothing at all, and simply to have changed the subject of discussion - It's a whole other story.

The rigidity of the name is inherent in the way we speak. In due course, Bob might have a son, who due to the aforementioned name shortage is also called Bob, and as often happens, he might follow his father's profession. And then we would need to further disambiguate Bob the Builder and Bob Builderson, or Bob the Builder Senior and Bob the Builder Junior, or some other scheme; thus there is a flow between names and descriptions...

But there is not the same flow between definiteness and rigidity. There are many builders named, Bob, and there are at least 2 philosophers named Bob on this very thread. But there is only one Bob the Builder, and here he is:



Accept no imitations! #therealbobthebuilder.

One might say that the rigidity of names is a function of their arbitrariness; they are Humpty-Dumpty-an in meaning exactly what the speaker intends:

"I don't know what you mean by 'glory,' " Alice said.
Humpty Dumpty smiled contemptuously. "Of course you don't—till I tell you. I meant 'there's a nice knock-down argument for you!' "
"But 'glory' doesn't mean 'a nice knock-down argument'," Alice objected.
"When I use a word," Humpty Dumpty said, in rather a scornful tone, "it means just what I choose it to mean—neither more nor less."
"The question is," said Alice, "whether you can make words mean so many different things."
"The question is," said Humpty Dumpty, "which is to be master—that's all."

This totalitarian anarchy becomes unworkable applied to the whole language, but limited to names, and signalled by a beginning capital, it seems to work just fine. 'Alice' means the Alice I am talking about and none other, and you don't know which Alice I am talking about until I tell you (It's Alice-through-the-Looking-Glass). In the same way, there are many builder's named 'Bob', but only one Bob-the-Builder.

Names are rigid even if ambiguous, whereas if descriptions are ambiguous, they are not definite.