My comments are in blue.
1. Another claim which is nearly Moorean. I claim that the following argument is valid:
Frodo is a hobbit
Frodo has large feet
Some hobbit has large feet
I am not saying that the premisses are true. Clearly if there are no such things as hobbits, the first sentence has to be false. But it [the argument] is valid. The premisses can't be true and the conclusion false. If there were such a thing as Frodo, and if he was a hobbit, and if he had large feet, it has to be the cases that some hobbit (him) has large feet. So the argument is valid.
[. . .]
2. Assuming the argument above is valid, what fact makes it valid? I claim that it is a purely semantic property of the proper name 'Frodo'. I.e. it is in virtue of the meaning of 'Frodo' that the premisses cannot be true with the conclusion false. By 'purely semantic', I mean a feature of the term that it continues to possess even though it has no extension, i.e. there is nothing it refers to or denotes.
Stylistic comment: I would strike “continues to possess” and substitute “possesses.” After all it can't be your view that purely fictional names go from having extensions to not having them.
Substantive comment: What you say in #1 above seems correct. But now you take a turn that is reasonably resisted. You want to know what makes the Frodo argument valid. I say it is valid because it has a valid form:
a is F
a is G
Some F is G.
It is this form that makes it impossible for an argument having this form to have true premises and a false conclusion. It has nothing to do with any semantic property of a substituend of the arbitrary individual constant, 'a.' Whether the subject matter of an argument is fiction or fact makes no difference to its validity or to the explanation of its validity. Logic abstracts from content; hence it treats 'Frodo,' 'Noah,' 'Churchhill' and 'Obama' the same, as substituends of an arbitrary individual constant.
It is not clear what you are claiming. Are you saying that there is a semantic property that only (purely) fictional names have? And what is this semantic property? Does 'Noah' have it as well?
Here is one guess at what you might mean. Purely fictional names, as such, do not and cannot have existing referents. Otherwise they wouldn't be purely fictional. Given, as you believe, that (a) the only referents are existing referents, and that (b) there are no modes of existence/being, you seem to be saying that purely fictional names, qua purely fictional names, do not and cannot have referents, full stop. Now if every sentence in which such a name figures is false (as you seem to believe), then there is no argument featuring purely fictional names that has true premises and a false conclusion. Therefore every such argument is by default valid (given the technical definition of validity that we both accept).
Is that what you mean?
If yes, then perhaps the semantic property you are talking about is the propery of necessarily not having a referent. Call this property 'P.' Now is P an intrinsic property of a name like 'Frodo' or is it a relational property? But surely there is no intrinsic property of a name that makes it a purely fictional name, and thus a name necessarily extensionless. What makes a name purely fictional is primarily the intention of the author, and secondarily the intentions of the readers (listeners, etc) who are complicit with the author in the fictional enterprise.
This is not Moorean. Someone could claim that the argument is valid because 'Frodo', if meaningful, refers to a non-existing thing, and because it refers to the same non-existing thing in both premisses. Some arguments against:
Comment: Why do you ignore the simplest and most obvious explanation of validity, the one I gave above?
(i) The Razor: why posit non-existing things in order to explain a matter of logic, when a semantic explanation would suffice? E.g. we don't need weird entities to explain the validity of 'every bachelor is unmarried, some people are bachelors, some people are unmarried'.
Comment: One problem is that I don't understand what you mean by a semantic explanation of validity. I grant you that the Frodo argument is valid: anyone who argues in accordance with the pattern embodied in that argument argues correctly. But I don't see that this has anything to do with whether the terms in the argument have non-null extensions. A Meinongian will say that 'Frodo is a hobbit' is true. But I am prepared to grant you that the sentence is false. But it doesn't matter since we know from Logic 101 that a valid argument can have false premises and a false conclusion.
(ii) "Frodo is a hobbit, he has large feet, some hobbit has large feet" is also valid. Do we need strange entities to explain the validity of arguments containing pronouns?
(iii) "Frodo is a hobbit who has large feet, some hobbit has large feet" is also valid. Do we need strange entities to explain the validity of arguments containing the word 'who'?
(iv) "Frodo is a hobbit with large feet, some hobbit has large feet" is also valid. Do we need strange entities to explain this? (My hunch is that the Meinongian will give up on this point. The onus is then on him to explain the difference between this one and any of the previous ones).
Comment: The validity of each of the variant arguments can be explained in the manner I indicated.
3. Now for the radical claim: the inferential property above is both necessary and sufficient to explain fictional individuation. Necessary is obvious. If we don't accept the validity, we could suppose that each token of the term 'Frodo' referred to a different character, and thus no two sentences in LOTR was ever about the same character. Clearly no one could understand the story if that were so. Sufficient is not so obvious, I will not defend that here.
Comment: Now you have really lost me. First of all, what is the inferential property? Presumably you mean that empty names have a property that explains the validity of (all? Some?) of the arguments in which they figure. What property is that? The property of being necessarily extensionless? Then why don't you say that?
And what is fictional individuation? You don't think that Frodo is a genuine individual. If he were, he would be a nonexistent individual and you reject such individuals. So there is no individual, Frodo. But if there is no individual, then there is no question of individuation in either the epistemological or the ontological sense of this term. Presumably, you mean by 'individuate' pick out, single out, identify in a way that supports cross-referencing? You need to explain this.
If this is what you mean, then on your view there is no Frodo to pick out or single out in thought. On your nominalism, all there is is the name. And you can't eke by with that alone. When I think about Frodo, I am not thinking about 'Frodo.' In fact, I can think about Frodo even if I have temporarily forgotten what his name is. Suppose I am thinking about the corpulent side-kick of Don Quixote, but have forgotten his name. I am thinking about Sancho Panza despite my not remembering that his name is 'Sancho Panza.'
Any adequate theory has to distinguish among: empty names, tokenings thereof, and tokenings thereof with understanding. If a voice synthesizer makes the sound associated with 'Frodo,' then the name is tokened, but nothing semantic is going on.
4. The really really radical claim: the semantic feature that explains individuation in fiction also explains individuation 'in reality'. So radical I won't try to defend it here. The defence would be roughly on the lines of: the same phenomenon cannot have two different causes. Same effect = same cause, which is a well accepted principle of scientific explanation. Obviously this would require defending that the effect is the same: I won't go into that here. The main pillars of the theory are (1) and (2) above. Inferences involving fictional names are valid, even though the premisses are never true. And the explanation of their validity does not involve Meinongian objects.
Comment: Once again, you haven't told us what individuation is. That word is a piece of philosophical jargon, not of ordinary language. No sentence containing it could count as Moorean. So you have to explain the term. And you have to meet my objection that there cannot be individuation in either the epistemological/semantic or ontological sense if there is no individual. How do you avoid embracing this inconsistent triad:
There are no fictional individuals.
Questions about individuation makes sense only if there are individuals.
Fictional names individuate.
I should think that your “really really radical claim” is hopeless. There is a huge difference between a genuine individual such as Obama and Frodo. You won't be able to paper over this difference especially since you reject Meinongian individuals and Plantingian haecceity properties.