Introduction to Semantics and Formalization of Logic [antikvár]

PREFACE TO THE ONE-VOLUME EDITION The two volumes of my Studies in Semantics, both of which deal with semantical concepts and their relations to syntactical concepts, are here combined in one book. Except for minor corrections the text of both volumes is unchanged; the original pagination has been preserved, in order to facilitate references. Both bibliographies have been brought up to date. In the original preface to volume II, I indicated my intention of writing another volume in this series, which was to deal with the logic of modalities. My book Meaning and Necessity (1947) may be regarded as a partial fulfillment of the promise. It does not give the actual construction of systems of modal logic, but it lays the groundwork for this task through philosophical discussions and semantical analyses of modalities with the help of the semantical concepts of extension and intension. Since then I have studied various more comprehensive modal systems with variables of all finite levels; but these investigations are not yet finished. Rudolf Carnap University of California at Los Angeles July 1958 PREFACE The purpose of this book In recent years many philosophers and scientists interested in the logical analysis of science have become aware that we need, in addition to a purely formal analysis of language, an analysis of the signifying function of language — in other words, a theory of meaning and interpretation. It is the purpose of this book to furnish a theory of this kind, called semantics. It will be seen that this theory, if sufficiently developed, contains not only a theory of designation, i.e. the relation between expressions and their meaning, but also a theory of truth and a theory of logical deduction. Semantical concepts are often used, not only in science but in everyday life. When, for example, a person says that a certain word is used by him in a different sense than by somebody else, or that a certain assertion is true or that it is false, that a particular statement is analytic, i.e. true for purely logical reasons, that another statement follows from the first, or is compatible with it or contradicts it, — then in all these cases he applies semantical concepts. Thus some of the problems of semantics deal with familiar concepts and are by no means new. The task of a systematic construction of semantics is to find adequate, exact definitions for the customary semantical concepts and for new concepts related to them, and to supply a theory based on these definitions. The development of semantics Semantical concepts, especially the concept of truth, have been discussed by philosophers since ancient times. But a systematic development with the help of the exact instru-