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Are there any "canonical" (or at least, quite good) papers that attempt to justify the supposition made in the model theory for classical first-order logic that the domain in non-empty?

I know that free logic was developed (at least in part) to avoid this assumption, since "something exists" doesn't seem (to many) to be a logical truth.

Intuitively, I could see the assumption being justified in something like the following manner: you cannot have a logic that quantifies over individuals without there being at least one individual. In this sense, it is just a necessary presupposition, but perhaps not to be regarded as a "logical truth" in the same sense as the law of excluded middle might be.

Is there any literature discussing this issue in the philosophy of logic? In particular, any literature which attempts to defend this assumption?

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In classical first-order logic, the empty domain is just a "single" special case, and it makes sense to exclude it, because this simplifies things. The first time I tried to seriously apply modal logic, this is the place where I got stuck, because handling non-existence and invalidity is quite challenging. But I wonder about classical multi-sorted first order logic, because some domains could be empty, but not all, and hence we are no longer talking about a "single" special case. –  Thomas Klimpel Jul 10 '13 at 17:42

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One reason is to preserve certain intuitive relationships that we would like. All children like icecream implies Some child likes icecream only if the set of children is never empty. The assumption that universal quantification is a strengthening of existential quantification only holds if the domain is not empty. See this blog post for a discussion of this use within mathematics.

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+1 for a nice mathematical justification. I was hoping for more philosophical justifications, but this is helpful nonetheless. –  Dennis Jan 8 '13 at 18:02

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