Introduction to Logic

Courier Corporation, 1999 - Mathematics - 312 pages
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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Contents

 PRINCIPLES OF INFERENCE AND DEFINITION 1 THE SENTENTIAL CONNECTIVES 3 SENTENTIAL THEORY OF INFERENCE 20 SYMBOLIZING EVERYDAY LANGUAGE 43 GENERAL THEORY OF INFERENCE 58 FURTHER RULES OF INFERENCE 101 POSTSCRIPT ON USE AND MENTION 121 TRANSITION FROM FORMAL TO INFORMAL PROOFS 128
 THEORY OF DEFINITION 151 ELEMENTARY INTUITIVE SET THEORY 175 SETS 177 RELATIONS 208 FUNCTIONS 229 SETTHEORETICAL FOUNDATIONS OF THE AXIOMATIC METHOD 246 Copyright

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Page xii - ... which is adequate to deal with all the standard examples of deductive reasoning in mathematics and the empirical sciences. The concept of axioms and the derivation of theorems from axioms is at the heart of all modern mathematics. The purpose of this...