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.
Stromboli is an island volcano.
An island volcano 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.
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."
Objection 2: "The first premise is redundant because we presuppose that the domain of quantification is a domain of existents."
Reply 2: Well, then, if that is what you presuppose, then you can state your presupposition by writing, 'Stromboli exists.' Either the argument without the first premise is an enthymeme or it is invalid. If it is an enthymeme, then we need the first premise to make it valid. If it is invalid, then it is invalid.
Therefore, we are stuck with the problem of explaining how the original argument is valid, which it surely is.
My answer is that the original argument is an enthymeme an unstated premise of which links the first- and second-level uses of 'exist(s)' and thus presupposes the admissibility of the first-level uses. Thus we get:
A first-level concept F exists (is instantiated) iff it is instantiated by an individual that exists in the first-level way.
Stromboli is an individual that exists in the first-level way.
Stromboli is an island volcano.
The concept island volcano exists (is instantiated).
And island volcano exists.
Now what does this rigmarole show? It shows that Frege and Russell were wrong. It shows that unless we admit as logically kosher first-level uses of 'exist(s)' and cognates, a simple and obviously valid argument like the the one with which we started cannot be made sense of.
'Exists(s)' is an admissible predicate of individuals, and existence belongs to individuals: it cannot be reduced to, or eliminated in favor of, instantiation. This has important consequences for metaphysics.
For more on the topic of existence see my "Existence: Two Dogmas of Analysis," in Neo-Aristotelian Perspectives in Metaphysics, Routledge 2014, forthcoming.