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"A proper name [is] a word that answers the purpose of showing what thing it is that we are talking about" writes John Stuart Mill in A System of Logic (1. ii. 5.), "but not of telling anything about it". The problem of defining proper names, and of explaining their meaning, is one of the most recalcitrant in modern philosophy.
Mill's definition is as good as any, though it is ultimately not helpful. A proper name tells us which thing is in question, without giving us any other information about it. But how does it do this? What exactly is the nature of this information? There are two puzzles in particular:
Many theories have been proposed about proper names, none of them entirely satisfactory.
In traditional logic, proper names had no place at all. There were only two kinds of propositions: existential ("some men are philosophers") and universal ("all men are mortal"). The subjects of both consisted of a common name ("philosopher", "man") and a quantifier ("all", "some"). Proper names do not therefore signify any constitutuent of any propositon. Aquinas argued that this is because "the intellect" grasps a proposition, and the intellect understands by abstracting the "universal content" from sense perception. The "principle of singularity" that makes Socrates this individual, we cannot grasp at all, except indirectly, by "turning towards the sense appearance" (conversio ad phantasmata). See description that picks out an object that satisfies the description. It is commonly held that Frege held such a view (the description being embedded in what he called the sense (Sinn) of the name. Certainly Russell seems to have espoused such a view in his early philosophical career (Sainsbury, R.M., Russell, London 1979).
So, according to the descriptivist theory of meaning, there's a description of the sense of proper names, and that description, like a definition, picks out the bearer of the name. The distinction between the embedded description and the bearer itself is similar to that between the extension and the intension of a general term, or between Connotation and denotation.
The extension of a general term like "dog" is just all the dogs that are out there; the extension is what the word can be used to refer to. The intension of a general term is basically a description of what all dogs have in common; it's what the definition expresses.
The difficulty with the descriptive theory is what the description corresponds to. It must be some essential characteristic of the bearer, otherwise we could use the name to deny the bearer had such a charaacteristic. The objection is associated with Kripke, although philosophers such as Bradley, Locke and Aristotle had already noticed the problem.
The referential theory is that the meaning of a proper name is simply the individual to which, in the context of its use, the name refers.
Another name for the theory is the "Fido"-Fido theory - because the name "Fido" refers to, or denotes, or picks out, well, Fido. So the name "Fido" means the dog Fido. But now wait a minute. Lots of dogs have been named "Fido." Lots of people have been named "Larry." The referential theory talks about proper names as though there's only one thing that any proper name, such as "Fido," can mean. Right? It says: "the meaning of a proper name is the individual," that one item, "to which it refers." But then isn't that wrong, to say that a proper name like "Fido" can mean any one dog in particular?
Not really, because when we use proper names, we usually understand by the total context which individual we're using the proper name to pick out. So when I said that the name "Larry" means me, you all understood, of course, that when I used the name "Larry" it meant one of the gazillions of guys named "Larry." But just to be clear, let's update the statement of the referential theory, so it includes this stuff about context.
It might be the case that the name "Fido" picks out lots of different dogs; but a given use of the name refers to just one of the animals named "Fido."
The causal theory of names combines the referential view, with the idea that the name's referent is fixed by a baptismal act, whereupon the name becomes a rigid designator of the referent. Subsequent uses of the name succeed in referring to the referent by being linked by a Singular term