An Introduction to Logic
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.
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.)
THE SUBJECT MATTER OF LOGIC
Partial Evidence or Probable Inference
The Use and Application of Logic
The Traditional Analysis of Propositions 30
Compound Simple and General Propositions
THE RELATIONS BETWEEN PROPOSITIONS
The Traditional Square of Opposition
THE CATEGORICAL SYLLOGISM
The Calculus of Propositions
The Function of Axioms
Structural Identity or Isomorphism
The Independence and Consistency of Axioms
The Mathematics or Calculus of Probability
Interpretations of Probability
SOME PROBLEMS OF LOGIC
The Reduction of Syllogisms
The Alternative Syllogism
GENERALIZED OR MATHEMATICAL LOGIC
Their Function and Value
The Laws of Thought
AppendixExamples of Demonstration
Bibliography of Works Cited