Abstract

The valuation of sentences containing non-denoting singular terms is obviously the fundamental question to be solved in the construction of a semantics for free logic.2 Besides being fundamental, this question is very difficult, for the notion of truth commonly applied in contemporary logic, i.e., the notion of truth as correspondence with reality, does not fit sentences cortaining references to ‘non-existing objects’,3 which, as such, cannot be constituents of reality. For this reason, a free semantics should provide, first of all, for a new conception of truth, or at least for a suitable generalization of the correspondence theory; but the efforts made until now have not achieved results which we can regard as completely satisfactory from a philosophical point of view.

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