Sense and Reference in Frege’s Logic

175 Pages·1968·6.811 MB·English

by  Christian Thiel (auth.)

SENSE AND REFERENCE IN FREGE'S LOGIC
CHRISTIAN THIEL
SENSE AND REFERENCE
IN FREGE'S LOGIC
SPRINGER-SCIENCE+BUSINESS MEDIA, B.Y.
SINN UND BEDEUTUNG IN DER LOGIK GOTTLOB FREGES
First published by Verlag Anton Hain, Meisenheim am Glan, 1965
Translated Irom the German by T. J. Blakeley
ISBN 978-90-481-8333-3 ISBN 978-94-017-2981-9 (eBook)
DOI 10.1007/978-94-017-2981-9
© 1968 Springer Science+Business Media Dordrecht
Origina11y published by D. Reidel Publishing Company, Dordrecht, Holland in 1968
Softcover reprint ofthe hardcover lst edition 1968
No part of this book may be reproduced in any form, by print, photoprint,
microfilm, or any other means, without permission from the publisher
PREFACE
The present study of sense and reference in the logic of Frege represents
the first fruits of several years of dealing with the work of this great
German logician.
In the preparation of this work, which was presented as a dissertation
to the Faculty of Philosophy of the Friedrich-Alexander University in
Erlangen/Nuremberg, assistance came from many quarters. lowe most to
Professor R. Zocher, who directed this dissertation with understanding
counsel and unflagging interest. I must also thank Professor P. Lorenzen,
whose courses and seminars provided more inspiration than might be
immediately apparent in the book. Professor W. Britzelmayr of Munich
was so kind as to provide copies of important fragments of Frege's
works. These texts are reproduced with the permission of Professor
H. Hermes, Director of the 'Institut fUr mathematische Logik und Grund
lagenforschung' in Munster, where Frege's works and letters are being
prepared for publication.
The preparation of this work was greatly facilitated by a two-year
grant from the Fritz Thyssen Foundation.
CHRISTIAN THIEL
Nuremberg, February 1965
v
TRANSLATOR'S NOTE
In the difficult matter of Fregean terminology we have taken Ignacio
Angelelli's translation of Two Soviet Studies on Frege as the model. Both
Professor Angelelli and Dr. Thiel have been so kind as to read over the
translation before publication.
VI
TABLE OF CONTENTS
Preface v
Translator's Note VI
Abbreviations IX
Introduction 1
PART ONE
I. The Notion ofthe Begriffsschrift 5
II. Number and Concept 22
III. The Hierarchy of Functions 44
IV. Wertverlaufand the Problem of Expansion 58
PART TWO
V. The Article 'On Sense and Reference' 85
VI. Description, Designation, Assertion: Russell, Jones
and Bierich on Frege's Semantics 103
VII. Synonymity and Sentential Context 118
VIII. The Contamination of On tics and Semantics 142
Summary 158
Bibliography 162
Index of Names 171
VII
ABBREVIATIONS
(Numbers refer to the Bibliography)
AMLG Archiv fUr mathematische Logik und Grundlagenforschung.
AP 'Lettera del sig. G. Frege, etc.' = No. 50.
ASB 'Ausftihrungen tiber Sinn und Bedeutung' = No. 60.
BP 'Ober die Begriffsschrift des Herrn Peano, etc.' = No. 49.
BRL 'Booles rechnende Logik, etc.' = No. 38.
Bs. Begriffsschrift, etc. = No. 37.
BuG 'Ober Begriffund Gegenstand' = No. 37.
Def. 'Begrtindung, etc.' = No. 43.
Den. 'On Denoting' = No. 118.
FL Bochenski, I.M., Formale Logik [Formal Logic] = No. 16.
FuB Function und Begriff = No. 42.
Ged. 'Der Gedanke' = No. 57.
Gef. 'Gedankengeftige' = No. 59.
Geom.III 'Ober die Grundlagen der Geometrie l' (1906) = No. 53.
Geom. IV 'Ober die Grundlagen der Geometrie II' (1906) = No. 53.
Geom. V 'Ober die Grundlagen der Geometrie III' (1906) = No. 53.
Gerh. Phil. Die philosophischen Schriften von Gottfried Wilhelm Leibniz, etc. =
No. 93.
Gg. Grundgesetze der Arithmetik, I = No. 45; II = No. 51-
Gl. Grundlagen der Arithmetik = No. 40.
JDMV Jahresberichte der Deutschen Mathematiker-Vereinigung
KB 'Kritische Beleuchtung, etc.' = No.47 .
KRV Kant, I., Kritik der reinen Vernunft = No. 84.
LM 'Uber Logik in der Mathematik' = No. 64.
LU,I Hussed, E., Logische Untersuchungen = No. 75.
MaN Meaning and Necessity = No. 20.
PA Hussed, E., Philosophie der Arithmetik = No. 74.
Pg. Kant, I., Prolegomena = No. 85.
Pro The Principles ofM athematics = No. 116.
RH Review of Hussed = No. 46.
SuB 'Ober Sinn und Bedeutung' = No. 44.
Tr. 'Ober das Tdigheitsgesetz' = No. 41-
Tract. Wittgenstein, L., Tractatus Logico-Philosophicus = No. 144.
Vern. 'Die Verneinung' = No. 58.
WBBs 'Ober die wissenschaftliche Berechtigung, etc.' = No. 39.
WiF 'Was ist eine Funktion?' = No.52.
ZPPK Zeitschrift fur Philo sophie und philosophische Kritik, N. F.
IX
INTRODUCTION
Frege's distinction between the sense and the reference of a linguistic
expression has received unusually great attention in contemporary philos
ophy. This is only partially explained as a result of the 'Frege Renais
sance' (which up to recently had been restricted to the Anglo-Saxon
world). It is more the result of the direct utility of these Fregean concepts,
either as they are or as modified to intension and extension, in the
analysis of many problems of contemporary philosophy.
This does not mean that there is full agreement on the determination
and applicability of this distinction. On the contrary, its importance is
at least in part due to the disputes which have risen around it. Discussions
about what Frege himself actually meant are rendered difficult by the
fact that he was not always too clear and often far too brief. Recent
interest in these questions, in Germany and elsewhere, makes a more
thorough examination in the light of unpublished texts all the more
welcome.
Such an examination is presented in this book. We have been able to
dispense with a complete presentation of Frege's life and works since
there is an already abundant literature. However, technical considerations
made it impossible to narrow the terrain of discussion beyond a certain
point. The matter of sense and reference is not an isolated part of Frege's
system. The theory of function, concept, and object forms a context in
which any other specific problem of Frege's thought has to be studied.
This explains the division of our work into two main parts, each of
which contains four chapters. The first chapter (I), in addition to some
remarks on the motivation for its construction, contains a presentation
of Frege's Begriffsschrift. We deal with the logistic program in Chapter
II, where stress is put not only on Frege's opposition to the views of
Kant, Mill, and Husserl, but also on his contribution to the under
standing of formalism, which is by no means limited to his negative
criticism of formal arithmetic. Frege's notion of the concept and his
theory of the function form the object of Chapter III. which is followed in
1
SENSE AND REFERENCE IN FREGE'S LOGIC
Chapter IV by a thorough description of the problem of the Fregean
'Wertverlauf-names', which is widely discussed today. Both of these
chapters provide ample opportunity for a presentation of the current
interpretations of Frege's ideas.
The treatment of Frege's thought is completed in the second section by
a presentation of his theory of sense and reference. While Chapter V
deals with the content of Frege's article 'Uber Sinn und Bedeutung',
Chapter VI reports on the discussion which is still going on, with empha
sis on the contributions of Russell, Jones, and Bierich. The last two chap
ters introduce essentially new contributions. In the Fregean context,
Chapter VII provides
(1) a reduction of the synonymity of proper names to that of sentences;
(2) a critique of the currently widespread thesis that Frege recognized
sense and reference only to words in sentential structure: this leads to a
limitation of the contextualist thesis and to further clarity on its valid
components;
(3) proof that a recently published Fregean criterion for the synonymity
of sentences is not only not applicable to many of Frege's own examples
but also clearly contradicts other statements of Frege.
Chapter VIII investigates aspects of Fregean 'Platonism' and the
influence thereof on the doctrine of sense and reference. The main
question is whether or not Frege succeeds in constructing a pure seman
tics without leaving a door open to foreign, ontological elements. Our
answer is clear from the title of the chapter.
This work is a contribution to the continuing discussion. Time will tell
if we have helped in bringing the matter closer to final clarity.
2
PART ONE