A new approach to semantics – Part I

Abstract

This is the first in a series of articles outlining a new approach to Semantics. The novelty in the approach is that the concept of an interpretation of a logical system is taken as the central concept of Semantics. I hope to show that by means of this approach a satisfactory definition can be given for such controversial concepts as analyticity, and at the same time the approach leads to a unified foundation for formalized Semantics.As the possibility of such definitions has been questioned in recent years, it is an important task to try to give precise definitions. Clearly, this is the task of those philosophers who believe that concepts like analyticity should play a fundamental role in Semantics. On the other hand, the philosophers who have criticized these concepts will now be able to tell just exactly why these definitions are unacceptable to them — instead of being forced to talk in generalities. It seems to me that no further progress is possible until we have precise definitions available for discussion.The fundamental semantic concepts fall into two classes: those, like truth, for which Tarski has offered definitions; and those additional ones, like analytic truth, for which we have Carnap's proposed definitions.