Introduction to logic

Table of Contents:

I. Principles of Inference and Definition
1. The Sentential Connectives
2. Sentential Theory of Inference
3. Symbolizing Everyday Language
4. General Theory of Inference
5. Further Rules of Inference
6. Postscript on Use and Mention
7. Transition From Formal to Informal Proofs
8. Theory of Definition

II. Elementary Intuitive Set Theory
9. Sets
10. Relations
11. Functions
12. Set-Theoretical Foundations of the Axiomatic Method

This well-organized book was designed to introduce students to a way of thinking that encourages precision and accuracy. As the text for a course in modern logic, it familiarizes readers with a complete theory of logical inference and its specific applications to mathematics and the empirical sciences.
Part I deals with formal principles of inference and definition, including a detailed attempt to relate the formal theory of inference to the standard informal proofs common throughout mathematics. An in-depth exploration of elementary intuitive set theory constitutes Part II, with separate chapters on sets, relations, and functions. The final section deals with the set-theoretical foundations of the axiomatic method and contains, in both the discussion and exercises, numerous examples of axiomatically formulated theories. Topics range from the theory of groups and the algebra of the real numbers to elementary probability theory, classical particle mechanics, and the theory of measurement of sensation intensities.
Ideally suited for undergraduate courses, this text requires no background in mathematics or philosophy.

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