An Introduction to Logic

292 Pages·1993·31.952 MB·English

by  Morris R. Cohen, Ernest Nagel, John Corcoran (ed.)

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Morris V. Cohen
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second edition edited and introduced by
JOHN CORCORAN

An Introduction to
LOGIC
MORRIS R. COHEN
and
ERNEST NAGEL
Second edition
Edited with an Introduction
by JOHN CORCORAN
Hackett Publishing Company
Indianapolis / Cambridge
First edition copyright 1962
by Harcourt, Brace and Company
New material in second edition copyright * 1993
by Hackett Publishing Company, Inc.
All rights reserved
Printed in the United States of America
99 98 97 96 95 94 93(cid:9) 1 2 3 4 5 6 7
Cover design by Robert Flynn
For further information, please address
Hackett Publishing Company, Inc.
P.O. Box 44937
Indianapolis, Indiana 46244-0937
Library of Congress Cataloging in Publication Data
Cohen, Morris Raphael, 1880-1947.
An introduction to logic/Morris R. Cohen and Ernest Nagel.-
2nd ed./edited, with introduction, by John Corcoran.
p.(cid:9) cm.
Includes bibliographical references and indexes.
ISBN 0-87220-145-7 (cloth: alk. paper).
ISBN 0-87220-144-9 (paper: alk. paper)
1. Logic. I. Nagel, Ernest, 1901-1985. II. Corcoran, John, 1937–
III. Title.
BC108.C67 1993(cid:9) 93-6067
160—dc20(cid:9) CIP
The paper used in this publication meets the minimum
requirements of American National Standard for
Information Sciences—Permanence of Paper for Printed
Library Materials, ANSI Z39.48-1984.
A NOTE ON THE HARVEST
EDITION
This edition makes available separately the first part of our
book AN INTRODUCTION TO LOGIC AND SCIENTIFIC
METHOD. It contains only the Preface, except for the concluding
paragraph; the first, or introductory, chapter; and Book I, on Formal
Logic, but not Book II, on Applied Logic and Scientific Method,
of the original text first published in 1934. It does not, therefore,
embody fully the conception of logic or the pedagogic ideas for
presenting the subject that controlled the composition of the com-
plete text, and that are described in the Preface and Chapter I.
But it does cover a part of the subject that can be conveniently
mastered in a one-semester course; and although it gives greater
attention to the traditional analysis of formal arguments than to
the techniques of symbolic or mathematical logic (which has had
an almost explosive development since the first publication of the
full text), it contains sufficient material for making the reader thor-
oughly acquainted with the basic ideas of deductive logic and de-
monstrative reasoning.
1962(cid:9) E. N.

EDITOR'S PREFACE
My earliest reading in logic was the classic introductory treatment
by Morris R. Cohen and Ernest Nagel that is being presented here as
the second edition of Introduction to Logic, abbreviated IL. This
material originally appeared in 1934 as part of a larger book, Intro-
duction to Logic and Scientific Method, ILSM. Introduction to Logic
was separately published first in 1962; this is a new edition of the
1962 book. No other versions of this material have been published.
The orientation to logic crafted by Cohen and Nagel and articu-
lated in IL is something to be cherished. It is pluralistic and open-
ended. It contains a broad base of solid practical material that
contributes to one's competence in thinking critically. It pays suffi-
cient attention to the philosophical problems both of logic per se
and of our knowledge of logic. Logic is not presented as an unas-
sailable fortress but as something that is or could become vulner-
able; logic is not presented as a completed system but as something
that is in the process of being discovered and articulated; logic is not
presented as something inevitable or foreseeable but as a field where
being open to novelty and being alert to surprises are attitudes that
will be rewarded.
The Cohen-Nagel presentation of logic balances forward-looking
attention, both to practical applications as well as to the need for fu-
ture progress, with a backward-looking attention to the historical
development of logic. In fact, it gives the students hope for the
future of logic by giving them a taste of the enormous steps that have
already been taken since Aristotle.
In addition, the Cohen-Nagel presentation balances respect for
the formal, objective, scientific, and somewhat mathematical aspects
of logic with a sensitivity to its informal, humanistic, and philosoph-
ical aspects. When this book was written the schism between the
symbolic-language approach and the natural-language approach had
not become as wide as it is today. Cohen and Nagel made an effort to
discourage rivalry between these approaches and to encourage ap-
preciation of their complementarity. As a result perhaps, in my ca-
vii
VIII(cid:9) EDITOR'S PREFACE
reer as a logician I have felt equally at home with the formal and the
informal aspects of logic and I have been able to profit from achieve-
ments made from the symbolic-language perspective as well as from
the insights of the natural-language approach, whether by linguists,
phenomenologists, or ordinary-language philosophers.
I read IL for the first time in the spring of 1958, the end of my
second year in college, and I have read it many times since. I have
never read it without noticing something new. Over the years I have
used it as the text for introductory logic courses several times. I have
also used other books as the main text, sometimes alone and some-
times using IL as collateral reading. I was disappointed when it
went out of print. I am happy to have a part to play in bringing it
back into print. I intend to use it as the main text in my introductory
logic courses and to use it as collateral reading in other courses as
well.
This book has been used by generations of logic students. It was
enthusiastically received from the first year of its publication. The
following paragraph is from one of the first reviews. [Charles Malik,
Isis 23 (1935) 284-287].
As an elementary introduction to the meaning and function of
logic in civilized activity, this book is quite valuable. It is intended
to introduce its subject to college students, but it may very profit-
ably be read by the general reader. The style is lucid, the problems
treated are, though elementary, very interesting, and the whole
book is suffused with concrete everyday illustrations. . . . No
educated man should find the least difficulty in going through the
whole book.
A few years later the respected mathematicians Edward Kasner and
James Newman cited ILSM with approval several times in their
1940 book Mathematics and the Imagination [Simon and Schuster,
New York]. In their annotated bibliography (op. cit., p. 364) they
characterize ILSM as follows.
An admirable book in every way. A textbook in a class by itself.
Refreshing and lucid chapters on the entire problem of scientific
method and a special chapter on probable inference, well reasoned,
well written.
The 1934 book went through several printings, staying in print
more than twenty-five years. IL stayed in print an additional twenty
EDITOR'S PREFACE(cid:9) lx
years or more. There have been translations into at least three for-
eign languages.
Morris Cohen (1880-1947) and Ernest Nagel (1901-1985) were
well qualified to write an introductory logic book. In 1906 Cohen
received the Ph.D. in Philosophy from Harvard, where he studied
logic with Josiah Royce (1842-1910), the logician and philosopher
of logic. He taught mathematics at the City College of New York
from 1906 to 1912, when he transferred to the Philosophy Depart-
ment. There he taught logic and other subjects until his retirement
in 1938. He was one of the first philosophers to recognize the impor-
tance of Charles S. Peirce (1839-1914), now considered to be one of
the most original logicians of his time. Cohen's contributions to
logic and, more generally, to philosophy were widely appreciated
during his lifetime. In 1929 he was elected to the prestigious presi-
dency of the Eastern Division of the American Philosophical Asso-
ciation. According to the Columbia Encyclopedia (3rd ed., Columbia
University Press, New York, 1963, page 446), Cohen is rated as one
of the most important American philosophers since William James
(1842-1910).
Ernest Nagel graduated in 1923 from City College of New York
where he studied logic with Morris Cohen. In 1930 he received the
Ph.D. in Philosophy from Columbia University. He started teaching
philosophy at Columbia in 1931. His work with Cohen continued
even when studying at Columbia and when teaching. ILSM, which
was published in 1934, was a joint work mostly based on Cohen's
lecture material but with Nagel doing the lion's share of the actual
writing. After completing ILSM Nagel spent some time in Europe
conferring and working with European logicians, including Rudolf
Carnap (1891-1970). He published extensively in logic, history of
logic, and philosophy of logic. From the 1930's onward Nagel's
work has received wide recognition. In the early and middle 1940's
he was coeditor with Alonzo Church of the Journal of Symbolic
Logic. In the late 1940's he served as president of the Association for
Symbolic Logic. In 1954 the Eastern Division of the American Philo-
sophical Association elected him president, according him the same
honor it had bestowed on his teacher twenty-five years earlier.
There are a few aspects of IL which warrant criticism. The book
has certain features that I would not retain were I to write an intro-
ductory logic text. When I find myself disagreeing with IL on a
point relevant to a lesson, I just tell the students what my view is and
why I prefer it; but I also express respect (and occasionally affection)
for Cohen and Nagel, and when I can, I explain to the students what
X(cid:9) EDITOR'S PREFACE
kinds of sensible deliberations may have led Cohen and Nagel to
their view.
In preparing the second edition, I made every effort to preserve all
considered choices made by Cohen and Nagel. Over the years I had
collected a set of orthographical, bibliographical, typographical,
grammatical, punctuational, computational, and "generational"
points that may have detracted from IL's usefulness as a contem-
porary introductory text. I altered the text accordingly, taking spe-
cial care not to interfere with the views or tastes of the authors, even
when I felt that in the fullness of time they would probably prefer
some emendations. What is presented here is as completely faithful
to the philosophy and style of ILSM as I could make it.
The changes involve some sixty-odd pages. Since the page layout
remains the same, it is easy to compare corresponding pages and
corresponding lines to see exactly what has been changed. My aim
was to preserve the historical integrity of IL while making the book
more useful to students. Because ILSM has been referenced so much
in the literature of logic and especially in American philosophy over
the fifty-odd years since its first publication, pagination of the origi-
nal material remains the same as in the 1934 ILSM except for the
front material, the appendix, the exercises, and the indices. Besides
this preface I have added an introduction which supplements, sum-
marizes, and highlights the individual chapters of IL and which in-
terrelates various chapters. For the convenience of scholars, especially
of intellectual historians, I have constructed a bibliography of all
works referred to in IL. In addition I made new and more compre-
hensive indexes of persons and subjects. For the convenience of
teachers and students I have added new exercises to all chapters and
to the appendix. Some new exercises help the students to gain confi-
dence in and to enjoy their mastery of technical terminology. Some
new exercises require a rather deep appreciation of the implications
of the textual material. Some will provide a basis for extended class
discussion. All of the original 1934 exercises are retained at the end
of the text, as was the case in 1962.
My decision to bring IL back into print was based on the fact that
I found it the best book for the kind of introductory logic course that
I give. Once my decision was made, I received a lot of encourage-
ment that I would like to acknowledge. The most uplifting encour-
agement came from highly accomplished people who attributed to
ILSM a measure of credit for their achievements. Herbert Haupt-
man, mathematician, crystallographer, 1985 Nobel Laureate in
Chemistry, studied logic at City College of New York in the middle