Interpretation
Karel Lambert wrote in 1967:
"In fact, one may regard free logic... literally as a theory about singular existence, in the sense that it lays down certain minimum conditions for that concept." The question which concerned the rest of his paper was then a description of the theory, and to inquire whether it gives a necessary and sufficient condition for existence statements.
Lambert notes the irony in that Willard Van Orman Quine so vigorously defended a form of logic which only accommodates his famous dictum, "To be is to be the value of a variable," when the logic is supplemented with Russellian assumptions of description theory. He criticizes this approach because it puts too much ideology into a logic which is supposed to be philosophically neutral. Rather, he points out, not only does free logic provide for Quine's criterion—it even proves it! This is done by brute force, though, since he takes as axioms and, which neatly formalizes Quine's dictum. So, Lambert argues, to reject his construction of free logic requires you to reject Quine's philosophy, which requires some argument and also means that whatever logic you develop is always accompanied by the stipulation that you must reject Quine to accept the logic. Likewise, if you reject Quine then you must reject free logic. This amounts to the contribution which free logic makes to ontology.
The point of free logic, though, is to have a formalism which implies no particular ontology, but which merely makes an interpretation of Quine both formally possible and simple. An advantage of this is that formalizing theories of singular existence in free logic brings out their implications for easy analysis. Lambert takes the example of the theory proposed by Wesley C. Salmon and George Nahknikian, which is that to exist is to be self-identical.
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