MEANING AND NECESSITY A Study in Semantics and Modal Logic By
RUDCJLF C RNAP Professor of Philosophy in the University of Chicago
THE UNIVERSITY OF CHICAGO PRESS CHICAGO ILLINOIS THE UNIVERSITY OF
CHICAGO PRESS, CHICAGO 37 Cambridge University Press, London, N. W.
1, England W. J. Gage Co., Limited, Toronto 2B, Canada Copyright
1947 by the University of Chicago. All rights reserved. Published
1947. Second Impression 1948. Composed and printed by THE
UNIVERSITY OF CHICAGO PRESS, Chicago, Illinois, U. S. A. PREFACE
The main purpose of this book is the development of a new method
for the semantical analysis of meaning, that is, a new method for
analyzing and describing the meanings of linguistic expressions.
This method, called the method of extension and intension, is
developed by modifying and ex tending certain customary concepts,
especially those of class and property. The method will be
contrasted with various other semantical methods used in
traditional philosophy or by contemporary authors. These other
methods have one characteristic k corfflHbi Wrhey all regard an
expression in a language as a name of a concrete or abstract
entity. In contradistinc tion, the method here proposed takes an
expression, not as naming any thing, but as possessing an intension
and an extension. This book may be regarded as a third volume of
the series which I have called Studies in Semantics, two volumes of
which were published ear lier. However, the present book does not
presuppose the knowledge of its predecessors but is independent.
The semantical terms used in the present volume are fully explained
in the text. The present method for defining the L-terms for
example, L-true, meaning logically true, analytic differs from the
methods discussed in the earlier Introduction to Semantics. I now
think that the method used in this volume is more satisfactory for
lan guages of a relatively simple structure. After meaning
analysis, the second main topic discussed in this book is modal
logic, that is, the theory of modalities, such as necessity, contin
gency, possibility, impossibility, etc. Various systems of modal
logic have been proposed by various authors. It seems to me,
however, that it is not possible to construct a satisfactory system
before the meanings of the modalities are sufficiently clarified. I
further believe that this clarification can best be achieved by
correlating each of the modal concepts with a cor responding
semantical concept for example, necessity with L-truth. It will be
seen that this method also leads to a clarification and elimination
of certain puzzles which logicians have encountered in connection
with modalities. In the Preface to the second volume of Studies in
Semantics, I announced my intention to publish, as the next volume,
a book on modal logic containing, among other things, syntactical
and semantical systems which combine modalities with
quantification. The present book, however, is not as yet the
complete fulfilment of that promise it contains vi PREFACE only
analyses and discussions of modalities, preliminary to the construc
tion of modal systems The systems themselves are not given here. In
an article published elsewhere see Bibliography, I have stated a
calculus and a semantical system combining modalities with
quantification, and have summarized some of the results concerning
these systems. A more comprehensive exhibition of results already
foundand those yet to be found must be left for another time. The
investigations of modal logic which led to the methods developed in
this book were made in 1942, and the first version of this book was
writ ten in 1943, during a leave of absence granted by the
University of Chi cago and financed by the Rockefeller Foundation.
To each of these insti tutions I wish to express my gratitude for
their help. Professors Alonzo Church and W. V. Quine reaorhe first
version and discussed it with me in an extensive correspondence...
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