Here is a little puzzle I call the Stromboli Puzzle. An earlier post on this topic was defective. So I return to the topic. The puzzle brings out some of the issues surrounding existence. Consider the following argument.Bill tables a second objection, which he also rebuts, and then offers his own account of why the argument is valid, which hinges on a distinction between 'first-level' and 'second-level' uses of exists. I won't comment on these because I think Bill's Objection (1) gets things right. I reject his Reply (1) as follows. If 'Stromboli' has no existing referent, has no referent at all, or has only a nonexisting Meinongian referent, then there is no such thing as Stromboli and therefore 'Stromboli is an island volcano' is not true. It may be false or it may be meaningless, but it certainly can't be true. In which case the argument remains truth-preserving: It has not been shown to take us from truth to falsehood. Bill has not demonstrated that it is invalid.
Stromboli exists.This is a sound argument: the premises are true and the reasoning is correct. It looks to be an instance of Existential Generalization. How can it fail to be valid? But how can it be valid given the equivocation on 'exists'? 'Exists' in the conclusion is a second-level predicate while 'exists' in the initial premise is a first-level predicate. Although Equivocation is standardly classified as an informal fallacy, it induces a formal fallacy. An equivocation on a term in a syllogism induces the dreaded quaternio terminorum, which is a formal fallacy. Thus the above argument appears invalid because it falls afoul of the Four Term Fallacy.
Stromboli is an island volcano.
An island volcano exists.
Objection 1. "The argument is valid without the first premise, and as you yourself have pointed out, a valid argument cannot be made invalid by adding a premise. So the argument is valid. What's your problem?"
Reply 1. The argument without the first premise is not valid. For if the singular term in the argument has no existing referent, then the argument is a non sequitur. If 'Stromboli' has no referent at all, or has only a nonexisting Meinongian referent, then Existential Generalization could not be performed, given, as Quine says, that "Existence is what existential quantification expresses."
But this talk of non-existing referents is already verging on the absurd and it would be better to reject Bill's Reply as nonsensical. After all, an invalid argument is unpersuasive, and yet this argument, even without the first premise, is utterly persuasive. Consider the following dialogues:
A: Stromboli exists.
B: This tells me nothing more than that there is something called 'Stromboli'.
A: Well, Stromboli is an island volcano.
B: OK. So there is an island volcano?
A: Yes, an island volcano exists.
B: Good. Glad we understand each other.
A: Stromboli is an island volcano.
B: So an island volcano exists?
B: What? You just told me Stromboli was one!
A: Yes, but Stromboli doesn't exist.
B: I don't follow you.
A: Stromboli is an island volcano.Do these not have the ring of truth? I think they do. And this point of view is beautifully simple. Compare it, for example, with Bill's 'two-level' account. But I clearly need to say more. Bill, and others, are happy to talk about 'empty' names, names with no referent, names with no existing referent, names with Meinongian referents, and so on. So-called 'free' logics (there are at least three kinds) have been invented to accommodate the notion. I need to say something more about what is going on here.
A: And Stromboli exists!
B: Yes, I know, you just told me. It's an island volcano.
Let's distinguish the meaning of a name from its referent, if any. The meaning of a name is what has to be understood about it in order for sentences involving the name to make sense. This is quite independent of any external referent the name may have, as is shown by the fact that fictional sentences are perfectly understandable despite the proper names within them usually lacking real-world referents. Now, in properly formulated discourse a name has to be introduced before it can be used. This is how the name gets its meaning. If, out of the blue, you say to me 'Stromboli exists!' and I have never been introduced to the name 'Stromboli', then what you say has no meaning for me. I have no information to attach to the name 'Stromboli' and your statement doesn't change my epistemic state. Asked to say something about Stromboli, I can tell you nothing. If, on the other hand, you say 'There is an island volcano called Stromboli', the name 'Stromboli' acquires a meaning. If asked about it I can reply 'It's an island volcano, isn't it?' For me, the name now means this island volcano and you can go on to tell me more about it by using the name. What you say may be complete fiction---there may be no island volcanoes at all---but it will be meaningful, nevertheless. Notice that the name is introduced on the back of (literally behind) an existential claim: 'There is an island volcano---and it is called Stromboli', and it is open for this claim to be false. If, out of the blue, you tell me 'Stromboli is an island volcano', and I have never heard of Stromboli, I have to interpret your sentence as a somewhat compressed existential assertion and name introduction. This is the style adopted by dictionaries. A subsequent use of the name, such as 'Stromboli is extinct', which has similar form, does not carry an implicit existential claim, else we would have two entities in play, an island volcano and an extinct thing, rather than one. Instead, the name means the same thing as was introduced earlier under the same name.
All this, of course, is Ed Ockham's theory of relativity of reference which I think is spot on. Where Ed and I differ is that Ed, I think, holds that negative free logic is needed to make inferences from sentences using names understood in this way. I see this as an unnecessary and counter-intuitive complication to a simple and elegant theory. Logical inference operates on the meanings of sentences not on the real-world objects and properties they might be about. We can make inferences within fictional discourse just as easily as we do in discourse about the real world, using classical logic. In Ed's theory all properly introduced names have meanings and there are no names that lack meaning. Hence we have no need to resort to free logics. Ed may say that in classical logic we have no way of expressing negative singular existentials such as 'Vulcan does not exist'. I answer that this amounts to a rejection of the explicit or implicit existential claim on the back of which the name 'Vulcan' was introduced. See also this post.