London Ed writes,
It is a well-known and puzzling fact that proper names are ambiguous. According to the US telephone directory, Frodo Baggins is a real person (who lives in Ohio). But according to LOTR, Frodo Baggins is a hobbit. Not a problem. The name ‘Frodo Baggins’ as used in LOTR, clearly has a different meaning from when used to talk about the person in Ohio. So the argument below is invalid:
Frodo Baggins is a hobbit
Frodo Baggins is not a hobbit
Some hobbit is not a hobbit.
This is because both premisses could be true, but the conclusion could not be true. So your claim that the validity of arguments using fictional names has ‘nothing to do with any semantic property’ is incorrect.
Well, ex contradictione quodlibet. Since anything follows from a contradiction, the conclusion of the above syllogism follows from the premises. So the above argument is valid in that it instantiates a valid argument-form, namely:
Obviously, there is no argument of the above form that has true premises and a false conclusion. So every argument of that form is valid or truth-preserving.
You invoke a Moorean fact. But we have to be very clear as to the identity of this fact.
It is a Moorean fact that proper names, taken in abstraction from the circumstances of their thoughtful use, are not, well, proper. They are common, or ambiguous as you say. It is no surprise that some dude in Ohio rejoices under the name 'Frodo Baggins.'
But so taken, a name has no semantic properties: it doesn't mean anything. It is just a physical phenomenon, whether marks on paper or a sequence of sounds, etc. Pronounce the sounds corresponding to 'bill,' 'john, 'dick.' Is 'dick' a name or a common noun, and for what? How many dicks in this room? How many detectives? How many penises? How many disagreeable males, 'pricks'? How many men named 'Dick'? Consider the multiple ambiguity of 'There are more dicks than johns in the room but the same number of bills.'
A name that has meaning (whether or not it refers to anything) is always a name used by a mind (not a voice synthesizing machine) in definite circumstances. For example, if the context is a discussion of LOTR, then my use and yours of 'Frodo' has meaning: it means a character in that work, despite the fact that in reality there is no individual named. And as long as we stay in that context, the name has the same meaning.
And the same holds in the context of argument. In your argument above 'Frodo Baggins' has the same meaning in both premises.
You can't have it both ways: you can't maintain that 'Frodo Baggins' is a meaningless string that could mean anything in any occurrence (a fictional character, a real man, his dog, a rock group, a town, etc.) AND that it figures as a term in an argument.
To sum up. Whether a deductive argument is valid or not depends on its logcal form. If there is a valid form it instantiates, then it is valid. The validity of the form is inherited by the argument having that form. But form abstracts from semantic content. So the specific meaning of a name is irrelevant to the evaluation of the validity of an argument in which the name figures. But of course it is always assumed that names are used in the same sense in all of their occurrences in an argument. So only in this very abstract sense is meaning relevant to the assessment of validity.