An Introduction to Logic

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Hackett Publishing, 1993 - Philosophy - 232 pages
7 Reviews
A revised reprint of the Harcourt, Brace and Company edition of 1962. Written for independent study and suitable for an introductory course in logic, this classic text combines a sound presentation of logic with effective pedagogy and illustrates the role of logic in many areas of humanistic and scientific thought. Cohen and Nagel's elegant integration of the history of philosophy, natural science, and mathematics helps earn this work its distinguished reputation.
  

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4.0 out of 5 stars A UNIQUE INTRODUCTION TO LOGIC, November 6, 2009
By Ole Anders (Coquina Beach, FL USA)
This review is from:Corcoran's edition of the Cohen-Nagel classic An Introduction
to Logic (Paperback)
This is the only introductory logic book that discusses the 1931 Gödel axiom system. It is also the only introductory logic book that discusses the distinction between argument forms and argument schemes (patterns). There are many other important topics treated here and nowhere else in introductory texts.
 

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A particularly good and comprehensive intro that focuses upon the relations between formal logic, critical thinking, and scientific methodology. Cohen and Nagel are part of the pragmatist tradition that views logic as the "theory of inquiry" (Dewey's phrase). This approach traces its roots back to Aristotle, but has contemporary adherents of such stature as Jaakko Hintikka.
The approach focuses upon formal logic as a tool for organizing information in the ongoing process of inquiry. Deduction does not so much reveal new data as order our ideas and evidence in such a manner that we are able to ask more effective questions.
The purely mathematical issues are still arguably too centered around the syllogism, but such weaknesses are readily compensated with other texts (Patrick Suppes' classic from the '50's "Introduction to Logic" for example). But even here, the authors' introduction and handling of quantifiers takes things beyond the Greek and Medieval limits.
One of the additional aspects of this book that I especially appreciate is the chapter on measurement. From the above mentioned pragmatist perspective, measurement is most assuredly a "logical" issue, since it is deeply invested in issues of inquiry, and the formal properties of measurement are themselves inherently logical/mathematical in character. (On this last, see Krantz, Suppes, Tversky's "Foundations of Measurement", volumes I -- III.)
 

Contents

THE SUBJECT MATTER OF LOGIC
3
Partial Evidence or Probable Inference
13
The Use and Application of Logic
21
The Traditional Analysis of Propositions 30
28
Compound Simple and General Propositions
44
THE RELATIONS BETWEEN PROPOSITIONS
52
The Traditional Square of Opposition
65
THE CATEGORICAL SYLLOGISM
76
The Calculus of Propositions
126
The Function of Axioms
129
Structural Identity or Isomorphism
137
The Independence and Consistency of Axioms
143
PROBABLE INFERENCE
151
The Mathematics or Calculus of Probability
158
Interpretations of Probability
164
SOME PROBLEMS OF LOGIC
173

The Reduction of Syllogisms
87
The Sorites
94
The Alternative Syllogism
100
GENERALIZED OR MATHEMATICAL LOGIC
110
Their Function and Value
117
The Laws of Thought
181
AppendixExamples of Demonstration
189
Exercises
200
Bibliography of Works Cited
221
Copyright

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About the author (1993)

Morris Raphael Cohen, who taught philosophy at the City College of New York and who began life as the son of Russian-Jewish immigrants, was one of the foremost Jewish intellectuals in America during the first half of the twentieth century. He expounded a philosophy of rationalism and realism in step with contemporary science and relevant to the social issues of his times and, through his books and teaching, had a widespread influence. His book, Reason and Nature (1931), offered a clear exposition and critique of the central concepts in science and sought to demonstrate that the scientific method required rational elements (mathematics and formal logic) no less than experimental procedures that appealed to sense experience.

Born in Czechoslovakia, Ernest Nagel emigrated to the United States and became a naturalized American citizen. In 1923 he graduated from the City College of New York, where he had studied under Morris Cohen, with whom he later collaborated to coauthor the highly successful textbook, An Introduction to Logic and Scientific Method (1934). Pursuing graduate studies at Columbia University, he received his Ph.D. in 1930. After a year of teaching at the City College of New York, he joined the faculty of Columbia University, where in 1955 he was named John Dewey Professor of Philosophy. In 1966 he joined the faculty of Rockefeller University. Nagel was one of the leaders in the movement of logical empiricism, conjoining Viennese positivism with indigenous American naturalism and pragmatism. In 1936 he published in the Journal of Philosophy the article "Impressions and Appraisals of Analytic Philosophy," one of the earliest sympathetic accounts of the works of Ludwig Wittgenstein, Moritz Schlick, and Rudolf Carnap intended for an American audience. Nagel was esteemed for his lucid exposition of the most recondite matters in logic, mathematics, and natural science, published in essays and book reviews for professional journals, scientific periodicals, and literary reviews. Two of his books, now out of print, consisted of collections of his articles, Sovereign Reason and Other Studies in the Philosophy of Science (1954) and Logic Without Metaphysics and Other Essays in the Philosophy of Science (1957). He also wrote a monograph, Principles of the Theory of Probability (1939) which appeared in the International Encyclopedia of Unified Science. In his major book-length work, The Structure of Science, Nagel directed his attention to the logic of scientific explanations.

John Corcoran has worked as an entertainment reporter, critic & feature reporter in TV stations in Washington, DC, Boston & Los Angeles, earning Emmys in each market. He has been a radio talk show host, after-dinner speaker, freelance writer, columnist & author. He wants you to know he is not Johnnie Cochran the lawyer, or John Cochran the network newscaster.

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