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...

In The Logical Structure of the World (1928), Rudolf Carnap analyzes the fundamental elements of experience, the derivation of qualities, the construction of sensory classes, and the construction of the special and temporal orders. In the short essay, Pseudoproblems in Philosophy (1928), Carnap advances the view, which was to become influential in the 1930s, that in many philosophical disputes, both sides of the argument can be discarded as strictly meaningless. This is one of three books that Open Court is making available in paperback reprint in its Open Court Classics series. The other two are Carnap's Logical Syntax of Language and Schlick's Theory of Knowledge.

Rudolf Carnap's entire theory of Language structure "came to me," he reports, "like a vision during a sleepless night in January 1931, when I was ill." This theory appeared in The Logical Syntax of Language (1934). Carnap argued that many philosophical controversies really depend upon whether a particular language form should be used. This leads him to his famous "Principle of tolerance" by which everyone is free to mix and match the rules of his language and therefore his logic in any way he wishes. In this way, philosophical issues become reduced to a discussion of syntactical properties, plus reasons of practical convenience for preferring one form of language to another. In a tour de force of precise reasoning, Carnap also indicated how two model languages could be constructed. This is one of three books which Open Court is making available in paperback reprint in its Open Court Classics series. The other two are Carnap's The Logical Structure of the World and Schlick's General Theory of Knowledge.

As a leading member of the Vienna Circle, Rudolph Carnap's aim was to bring about a "unified science" by applying a method of logical analysis to the empirical data of all the sciences. This work, first published in English in 1934, endeavors to work out a way in which the observation statements required for verification are not private to the observer. The work shows the strong influence of Wittgenstein, Russell, and Frege.

in die symbolische Logik mit besonderer Berucksichtigung ihrer Anwendungen Von Rudolf Carnap Professor der Philosophie University of California, Los Angeles Dritte, unveranderte Auflage Mit 5 T extahhildungen Springer-Verlag Wien GmbH ISBN 978-3-7091-3141-1 ISBN 978-3-7091-3140-4 (eBook) DOI 10. 1007/978-3-7091-3140-4 Alle Rechte vorbehalten Kein Teil dieses Buches darf ohne schriftliche Genehmigung des Springer-Verlages ubersetzt oder in irgendeiner Form vervielfaltigt werden (c) 1954, 1960, and 1968 by Springer-Verlag Wien Softcover reprint of the bardeover 3rd edition 1968 Library of Congress Catalog Card Number 68-29065 Titel Nr. 8136 Fur lna in tiefer Dankbarkeit Vorwort zur ersten Auflage In der Gestalt der symbolischen oder mathematischen Logik oder Logistik hat die Logik seit etwa 100 Jahren eine voellig neue Form an- genommen. Die Verwendung von Symbolen ist zwar das auffallendste Merkmal der neuen Logik, aber nicht das wesentlichste. Wichtiger sind die Exaktheit der Formulierung, die grosse Ausdehnung des Cnlbietes ins- besondere in der Theorie der Relationen und der Begriffe hoeherer Stufen, und die vielfaltige Anwendungsmoeglichkeit der neuen Methoden. In den letzten Jahtzehnten ist daher das Interesse an der symbolischen Logik in weiteren Kreisen wachgeworden, besonders unter Philosophen und Mathematikern, aber auch unter den Fachwissenschaftlern, die an der Analyse der Begriffe ihrer Fachwissenschaften interessiert sind.

Dieses Buch stellt eine neue, von CARNAP entwickelte Theorie der Induktion und Wahrscheinlichkeit dar, die durch die folgenden grund legenden Auffassungen charakterisiert ist. 1. Jedes induktive Schliessen, im weiten Sinne des nichtdeduktiven oder nichtdemonstrativen Schluss folgerns, ist ein Schliessen auf Grund von Wahrscheinlichkeit. 2. Daher ist die induktive Logik als Theorie von den Prinzipien des induktiven Schliessens dasselbe wie Wahrscheinlichkeitslogik. 3. Der Begriff der Wahrscheinlichkeit, der als Grundbegriff der induktiven Logik dienen soll, ist eine logische Relation zwischen zwei Aussagen oder Satzen, nam lich der Grad der Bestatigung einer Hypothese auf der Grundlage gegebe ner Pramissen. 4. Der sogenannte Haufigkeitsbegriff der Wahrschein lichkeit, wie er in statistischen Untersuchungen verwendet wird, ist zwar an und fur sich ein wichtiger wissenschaftlicher Begriff, als Grundbegriff der induktiven Logik jedoch unbrauchbar. 5. Alle Prinzipien und Lehr satze der induktiven Logik sind analytisch. 6. Daher hangt die Gultig keit des induktiven Schliessens nicht von irgendwelchen synthetischen Voraussetzungen ab, wie etwa dem vielumstrittenen Prinzip der Gleich foermigkeit der Welt. Die erste Aufgabe dieses Buches ist die Eroerterung der allgemeinen philosophischen Probleme betreffend die Natur der Wahrscheinlichkeit und des induktiven Schliessens, die uns zu den eben erwahnten Auffassun gen fuhren wird. Das zweite Ziel ist der tatsachliche Aufbau eines Systems der induktiven Logik, einer Theorie, die auf den angefuhrten Prinzipien beruht. Ein besonderes Augenmerk wurde in diesem Buch darauf gelegt, die intuitive philosophische Grundlegung klar von dem technischen Aufbau des Systems der induktiven Logik zu trennen.

Nach der Bedeutungsanalyse ist der zweite in dies em Buch eror- terte Hauptgegenstand die modale Logik, d. h. die Theorie der Modalitaten, wie Notwendigkeit, Zufalligkeit, Moglichkeit, Unmog- lichkeit usw. Verschiedene Systeme der modalen Logik sind von ver- schiedenen Autoren vorgeschlagen worden. Es scheint mir jedoch, daiS es nicht moglich ist, ein befriedigendes System zu konstruieren, bevor die Bedeutungen der Modalitaten geniigend klargestellt sind. Ich glaube ferner, daiS diese Klarstellung am besten dadurch erfolgen kann, daiS jeder der modalen Begriffe mit einem entsprechenden semantischen Begriff (z. B. Notwendigkeit mit L-Wahrheit) in Kor- relation gebracht wird. Es wird sich zeigen, daiS diese Methode auch zu einer Klarung und Ausschaltung gewisser Ratsel fiihrt, auf die Logiker im Zusammenhang mit den Modalitaten gestoiSen sind. 1m Vorwort des zweiten Bandes der "Studies in Semantics" kiindigte ich meine Absicht an, als nachsten Band ein Buch iiber modale Logik zu veroffentlichen, das unter anderem syntaktische und seman- tische Systeme, die Modalitaten mit Quantifizierung kombinieren, enthalten sollte. Das vorliegende Buch ist jedoch noch nicht die voll- standige Erfiillung dieses Versprechens; es enthalt nur Analysen und Erorterungen von Modalitaten, welche die Konstruktion von moda- len Systemen einleiten. Die Systeme selbst werden hier nicht geboten. In einem an anderer Stelle veroffentlichten Artikel (siehe Bibliogra- phie) habe ich einen Kalkiil und ein semantisches System, das Moda- litaten mit Quantifizierung verkniipft, dargelegt und einige der diese Systeme betreffenden Ergebnisse zusammengefaiSt. Eine umfassen- dere Darstellung der schon gefundenen und noch zu findenden Ergebnisse muiS fiir ein anderes Mal zuriickgestellt werden.

"This book is valuable as expounding in full a theory of meaning that has its roots in the work of Frege and has been of the widest influence. . . . The chief virtue of the book is its systematic character. From Frege to Quine most philosophical logicians have restricted themselves by piecemeal and local assaults on the problems involved. The book is marked by a genial tolerance. Carnap sees himself as proposing conventions rather than asserting truths. However he provides plenty of matter for argument."--Anthony Quinton, Hibbert Journal

Seit beinahe einem Jahrhundert sind Mathematiker und Logiker mit Erfolg bemiiht, aus der Logik eine strenge Wissen- schaft zu machen. Dieses Ziel ist in einem gewissen Sinn erreicht worden: man hat gelemt, in der Logistik mit Symbolen und Formeln ii. hnlich denen der Mathematik in strenger Weise zu operieren. Aber ein logisches Buch muB auBer den Formeln auch Zwischentext enthalten, der mit Hilfe der gewohnlichen Wort- sprache iiber die Formeln spricht und ihren Zusammenhang kIar macht. Dieser Zwischentext laBt oft an Klarheit und Exakt- heit manches zu wiinschen ubrig. In den letzten Jahren nun hat sich bei den Logikem verschiedener Richtungen immer mehr die Einsicht entwickelt, daB dieser Zwischentext das Wesentliche an der Logik ist und daB as darauf ankommt, fUr diese Satze uber Satze eine exakte Methode zu entwickeln. Dieses Buch will die systematische Darstellung einer solchen Methode, der "logischen Syntax", geben (nahere Erlauterungen in der Einleitung, 1, 2). In unserem "Wiener Kreis" und in manchen ahnlich gerich- teten Gruppen (in Polen, Frankreich, England, USA. und ver- einzelt sogar in Deutschland) hat sich gegenwartig die Auffassung immer deutlicher herausgebildet, daB die traditionelle meta- physische Philosophie keinen Anspruch auf Wissenschaftlichkeit machen kann. Was an der Arbeit des Philosophen wissenschaft- lich haltbar ist, besteht - soweit es nicht empirische Fragen betrifft, die der Realwissenschaft zuzuweisen sind - in logischer Analyse. Die logische Syntax will nun ein Begriffsgeb8. ude, eine Sprache liefem, mit deren Hilfe die Ergebnisse logischer Analyse exakt formulierbar sind.

Seit beinahe einem Jahrhundert sind Mathematiker und Logiker mit Erfolg bemuht, aus der Logik eine strenge Wissen. schaft zu machen. Dieses Ziel ist in einem gewissen Sinn erreicht worden: man hat gelernt, in der Logistik mit Symbolen und Formeln ahnlich denen der Mathematik in strenger Weise zu operieren. Aber ein logisches Buch muss ausser den Formeln auch Zwischentext enthalten, der mit Hilfe der gewohnlichen Wort. sprache uber die Formeln spricht und ihren Zusammenhang klar macht. Dieser Zwischentext lasst oft an Klarheit und Exakt. heit manches zu wunschen ubrig. In den letzten Jahren nun hat sich bei den Logikern verschiedener Richtungen immer mehr die Einsicht entwickelt, dass dieser Zwischentext das Wesentliche an der Logik ist und dass es darauf ankommt, fur diese Satze uber Satze eine exakte Methode zu entwickeln. Dieses Buch will die systematische Darstellung einer solchen Methode, der "logischen Syntax," geben (nahere Erlauterungen in der Einleitung, 1, 2). In unserem "Wiener Kreis" und in manchen ahnlich gerich. teten Gruppen (in Polen, Frankreich, England, USA. und ver. einzelt sogar in Deutschland) hat sich gegenwartig die Auffassung immer deutlicher herausgebildet, dass die traditionelle meta. physische Philosophie keinen Anspruch auf Wissenschaftlichkeit machen kann. Was an der Arbeit des Philosophen wissenschaft. lich haltbar ist, besteht - soweit es nicht empirische Fragen betrifft, die der Realwissenschaft zuzuweisen sind - in logischer Analyse. Die logische Syntax will nun ein Begriffsgebaude, eine Sprache liefern, mit deren Hilfe die Ergebnisse logischer Analyse exakt formulierbar sind. Philosophie wird durch Wissen."

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...

This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1977.

Rudolf Carnap and W. V. Quine, two of the twentieth century's most important philosophers, corresponded at length--and over a long period of time--on matters personal, professional, and philosophical. Their friendship encompassed issues and disagreements that go to the heart of contemporary philosophic discussions. Carnap (1891-1970) was a founder and leader of the logical positivist school. The younger Quine (1908-) began as his staunch admirer but diverged from him increasingly over questions in the analysis of meaning and the justification of belief. That they remained close, relishing their differences through years of correspondence, shows their stature both as thinkers and as friends. The letters are presented here, in full, for the first time.
The substantial introduction by Richard Creath offers a lively overview of Carnap's and Quine's careers and backgrounds, allowing the nonspecialist to see their writings in historical and intellectual perspective. Creath also provides a judicious analysis of the philosophical divide between them, showing how deep the issues cut into the discipline, and how to a large extent they remain unresolved.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1971.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1971.

This title is part of UC Press's Voices Revived program, which commemorates University of California Press’s mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1977.

Clear, comprehensive, intermediate introduction to logical languages, applications of symbolic logic to physics, mathematics, biology.

The growing concern throughout the world for the logic, the history, and the sociology of science reveals a comprehensive international movement interested in considering the scientific enterprise in its entirety. The purpose of the "International Encyclopedia of Unified Science," as originally conceived by the late Otto Neurath, was to explore in numerous volumes the foundations of various sciences and to aid the integration of scientific knowledge. Circumstances during World War II and the death of Professor Neurath, however, limited the scope of the "Encyclopedia." The Foundations of the Unity of Science constitutes the only completed unit of the proposed multi-volume "Encyclopedia."