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Jan, Classical predicate logic demands the domain be non-empty.
"On the LHS, however, we find 'exists' which is not obviously a logical expression. Indeed, I claim that it is not a logical expression like 'some' or 'all' or 'not.' It is a 'content' expression" I see this as begging the question on your part. "Exists" is not a logical expression only if we import some meaning into it. But what the deflationary account says is that the expressions are interchangeable. If we replaced "exists" with "has Predicate #1930 in the Universal Register of Predicates" then no such illicit importation would occur to us, yes? "But now it should be clear that the definition gives us no deflationary account of existence. What it does is presuppose existence by presupposing that the domain of quantification is a domain of existents." Here, however, I agree with you. The purported definition assumes that quantification is over existing things only. In a logic that does not carry such a restriction, the definition fails. Two strategies to save the deflationary account would seem to remain - showing that the relevant logic in this discussion is one where the domain is restricted to existing things, or attempting a deflationary account of something's being in the existing subset of the domain (which would suffice). The second seems much harder than the first on a first glance.
Leo, What's the alternative? That at all worlds where you do not exist, you are not self-identical? (if existence is self-identity, then that seems to follow) Well, at those worlds where you do not exist, what is it that is not self-identical anyway? In a domain with everything but Bill, what is the truth-value of "Bill is self-identical"? "Bill is not self-identical"?
I don't see why the domain of quantification has to be restricted to things that exist. Certainly there are logics that allow you to quantify over more.
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Jul 17, 2012