Introduction to Logic

This book was written to serve as a textbook for a first course in modern logic. Coherent and well organized, it familiarizes readers with an exact and complete theory of logical inference and its applications to mathematics and the empirical sciences. The first part 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 the second part, with separate chapters on sets, relations, and functions. The final part introduces numerous examples of axiomatically formulated theories in both the discussion and exercises. 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 book demands no background in mathematics or philosophy.