A Russellian Approach to Truth

Abstract

A primary goal of semantical analysis is to show how the truth value of a sentence is determined by the semantical roles of its constituent expressions. Russell's contribution in this area is generally thought to be his elimination rules for singular terms. If we look at the contextual definitions for sentences including definite descriptions from the point of view of truth, however, we find that Russell stands in a long tradition of philosophers whose intuitions have been to count simple subject-predicate sentences false when the subject term fails to denote. In a formal semantics this calls for the use of partial functions in interpreting terms and, following Russell, leads to a highly plausible logic underlying a theory of truth for sentences of a natural language. This truth definition for a predicate logic, including an existence predicate and provision for the semantic dicto-re distinctions available through Russell's scope operators for terms, was carried out in the author's doctoral dissertation ([3]). In later manuscripts, the logic was characterized without reliance on an existence predicate and was extended to modals. Similar semantical investigations have been carried out by Mates ([2]), and by Schock ([5]). Recently, Burge ([1]) has proposed an axiomatic development of the semantics as characterizing validity in natural languages. None of these provide for dicto-re distinctions. Mates notes that such a provision (along Russellian lines) is the best way of dealing with paradoxes related to (9>7). The provision for wide scope of terms for non-modal contexts is of course carried out in Russell, and in the author's doctoral dissertation it was put into a