London Ed submits this for our evaluation:
While apparently conceding that empty proper names have an 'inferential role', rightly underscores the need for me to demonstrate that its meaning is just this role, i.e. to demonstrate that the 'inferential semantics' is a sufficient as well as a necessary explanation of (empty) proper names.
Here are some arguments to elucidate this inferential role, and to show that it is sufficient to explain everything we need to know about empty proper names (indeed, all proper names, but leave that aside for now).
Argument 1. Proper names are neither descriptive nor object-dependent.
Consider the meaning of the following two sentences:
There is a hobbit called 'Frodo'. Frodo has large feet.
I have argued that at least part of the semantics of the proper name 'Frodo' is to join the predicate 'hobbit' in the first sentence to the predicate 'has large feet' in the second. It allows us to infer 'some hobbit has large feet'. And by repeated use of this inference in successive propositions in a narrative, it allows us to connect an increasingly complex description to each character in the narrative. It tells us which character we are talking 'about' by telling us which description to increase. Does it have any further function than this? Is it descriptive? Does it mean something like "hobbit called 'Frodo'"? No, for consider
There is a hobbit called 'Frodo'. There is another hobbit called 'Frodo'.
Clearly if there can be two characters in a narrative with the same name (as sometimes there are), the indefinite description 'called N' is not sufficient to individuate the character. Or consider
There is a hobbit called 'Frodo'. Frodo might not have been called 'Frodo'
This implies 'some hobbit called Frodo might not have been called Frodo', which is not inconsistent, so long as 'some hobbit' is read with wide scope. I won't argue this at length here, but it is easy to show that all the arguments which Kripke levels at the description theory of names can be reused or reinterpreted in the case of empty names. But if an empty proper name is non-descriptive and if there is no object that it corresponds to (either real or intentional), the simplest explanation is that its meaning is its inferential properties.
BV Comment 1. I take it that your view is that no indefinite or definite description supplies the meaning (sense) of any empty name. You rely on Kripke-type arguments. But distinguish:
a. Reference is not routed through sense, but direct
b. Names lack sense entirely.
It might be that while the reference of a name is not routed through an associated sense, the name nevertheless has a sense. Your view, however, rules that out. And doesn't Kripke speak of a sense that "fixes the reference" of a name without being part of the mechanism by which reference is achieved? But let's not get sidetracked into Kripke exegesis!
If I understand you, you want to maintain that names and other singular referring devices such as indexicals and demonstratives are purely syntactical devices. I honestly don't see how that could be true. I gave the example earlier of the first-person singular pronoun. Assume that when Frodo says 'I am hungry' he refers directly to Frodo and not via a special reference-mediating I-sense. Still, any use of 'I' has as part of its meaning that a producer of such a linguistic token is a person or a (potentially) self-conscious being, a being that can speak or think.
In this connection, David Kaplan speaks of character as opposed to content. "The character of an expression is set by linguistic conventions and, in turn, determines the content of the expression in every context." (Themes from Kaplan, p. 505) The character of the pure indexical 'I' is given by the rule:
'I' refers to the speaker or writer. (505)
My criticism, then, is that if the semantics of singular referring devices reduces to the inferential roles these words play, then there is no accounting for Kaplanian content since that does not vary with context or inferential role.
Leaving aside idexicals and demonstratives, all or most names seem to have associated with them a semantic content which cannot be reduced to the purely syntactical. Consider the song Carmelita about an apparently purely fictional character named 'Carmelita.' That name carries the sense 'female.' And the same goes for the wicked Felina in Marty Robbins' El Paso. There are male names, female names, and unisex names. If Carl is married to Carla, then you know the marriage is not same-sex.
Argument 2. Referential insulation
Consider the first sentence above: "There is a hobbit called 'Frodo'". This is indefinite, i.e. it does not tell us which hobbit is called 'Frodo'. Specifically, even if hobbits are mentioned in some earlier part of the narrative, this sentence on its own does not generate any further inferences about hobbits. It is a 'referential insulator', it does not 'refer backwards' to any previous sentence.The second sentence "Frodo has large feet", by contrast, does refer back. But only to the first sentence. Any third sentence can refer back to this one, and a fourth sentence to the third, and we can construct a whole referential chain, each of which refers back to the previous link. But the chain stops at the first sentence, the insulating sentence. This suggests that the second definite sentence, or back-referring sentence, has meaning only insofar as it refers back. But its back-reference is exhausted by its inferential properties. Ergo etc.
BV Comment 2. Suppose I grant the the meaning of 'Frodo' in the second sentence is exhausted by its back reference to 'Frodo' in the first sentence. This back reference is entirely intralinguistic: it is a word-word relation, not a word-world relation. So far, so good. Consider this quantified sentence:
(Ex) (x is a hobbit called 'Frodo' & x has large feet).
'Frodo' in the second sentence -- 'Frodo has large feet' -- plays the role of the second bound variable in the above quantified sentence, and that role is purely syntactical. The second sentence is synonomous with 'He has large feet' in the context in question.
So perhaps what you are up to is this: You want to construe names as pronouns used anaphorically as opposed to demonstratively. You are of course aware of the ambiguity of a sentence like 'Feser inscribed his book.' That could mean that Feser inscribed Feser's book, in which case 'his' is being used anaphorically, or it could mean that Feser inscribed some other person's book, in which case 'his' is being used demonstratively. Suppose I say 'Feser inscribed his book' while pointing to Peter. Then 'his' refers to an extralingusitc item, Peter. On the first disambiguation, however, 'his' is syntactically bound to 'Feser' and the reference is an intralinguistic back reference.
Here is the problem. 'Frodo' in the first sentence cannot be construed as a pronoun used anaphorically. You cannot introduce 'Frodo' without packing some meaning into it. And that is exactly what you do when you say that Frodo is a hobbit. Surely you don't think that 'hobbit' is a purely syntactical device. We agree of course that 'hobbit' has a null extension, but it must have some intension, and that intension cannot be reduced to syntax. Hence 'Frodo' when first introduced has to have some meaning that is irreducible to syntax or inferential role.
Even if back reference is exhausted by inferential properties, and the meaning of a back-referring term reduces to its syntactic role, surely the meaning of a name -- even if it is empty -- cannot on its first introduction be reduced to its syntactic role.
In short, your "ergo, etc." is a non sequitur.
Argument 3. Definition not object-dependent.
The definition of the name 'Frodo' occurs in the first sentence ("There is a hobbit called 'Frodo'"). This tells us that any subsequent usage of 'Frodo' refers back to this sentence. But it is a general existential proposition. On the assumption that general existential propositions aren't object-dependent, it follows that we can define a proper name without requiring an object. Given that we can define its meaning without having an object, it follows that its meaning is not object-dependent.
BV Comment 3: This argument seems OK in relation to empty names. Do you mean it to apply to non-empty names as well?
Argument 4. Pronouns are not object-dependent.
There is a hobbit called 'Frodo'. He has large feet.
Clearly the pronoun 'he' refers back to the first sentence, not to any object. But the two sentences together do not signify any more than the two 'Frodo' sentences above. But if the two 'Frodo' sentences have the same meaning as two object-independent sentences, it follows that the two 'Frodo' sentences are object-independent also.
BV Comment 4. To be true, your thesis has to be modified: Pronouns used anaphorically are not object-dependent.
Suppose you don't know that prosciutto is called 'prosciutto.' But you want some anyway and you know what it looks like. You belly up to the deli counter, point to the delectable item, and say 'I want some of this!' Surely the meaning of the demonstrative pronoun 'this' in this context is object-dependent.
But the same goes for the pure indexical 'I.' The indexical reference is achieved without a demonstration -- there is no need to point to oneself when saying 'I' -- but 'I' is secure against reference failure. One cannot token 'I' without referring to something. So 'I' used indexically -- not as a Roman numeral say -- is object-dependent for its meaning.