Introduction to Logic

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Courier Corporation, 1999 - Mathematics - 312 pages
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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
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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...

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About the author (1999)

Maria Carla Galavotti is professor of philosophy of science in the department of philosophy at the University of Bologna.
Roberto Scazzieri is professor of economic analysis in the department of economics at the University of Bologna.
Patrick Suppes is Lucie Stern professor emeritus of philosophy at Stanford University.

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