Singular Terms, Existence and Truth: Some Remarks on a First Order Logic of Existence

Abstract

I. It is true that there is a considerable variety of ways in which a semantics can be built for a first order logic of existence and denotationless singular terms. But it is also true that several such ways serve for several purposes in logical analysis, not all the same. The aim of this report is to show that if negations of singular existence sentences are to be explicated in a first order logic of existence, then one should be guided in semantics by reasonable principles, to wit (1) an atomic sentence is true only if every singular term in it denotes a member of the universe and (2) bound variables in terms or formulas range only over the given universe. In what follows we argue that some logics that have been fitted to a semantics without (1) or (2) encounter intuitive difficulties. On the other hand, under the guidance of (1) and (2) it is possible to offer an intuitively satisfactory general logical treatment of existence and denotationless singular terms.