Coherent, well-organized text familiarizes readers with complete theory of logical inference and its applications to math and the empirical sciences. Part I deals with formal principles of inference and definition. Part II explores elementary intuitive set theory, with separate chapters on sets, relations, and functions. Last section introduces numerous examples of axiomatically formulated theories.
First-Order Logic by Raymond M. Smullyan This self-contained study is both an introduction to quantification theory and an exposition of new results and techniques in "analytic" or "cut free" methods. The focus is on the tableau point of view. Includes 144 illustrations.
Topoi: The Categorial Analysis of Logic by Robert Goldblatt A classic exposition of a branch of mathematical logic that uses category theory, this text is suitable for advanced undergraduates and graduate students and accessible to both philosophically and mathematically oriented readers.
Set Theory and the Continuum Hypothesis by Paul J. Cohen This exploration of a notorious mathematical problem is the work of the man who discovered the solution. The award-winning author employs intuitive explanations and detailed proofs in this self-contained treatment. 1966 edition. Copyright renewed 1994.
The Philosophy of Mathematics: An Introductory Essay by Stephan Körner A distinguished philosopher surveys the mathematical views and influence of Plato, Aristotle, Leibniz, and Kant. He also examines the relationship between mathematical theories, empirical data, and philosophical presuppositions. 1968 edition.
Satan, Cantor and Infinity: Mind-Boggling Puzzles by Raymond M. Smullyan A renowned mathematician tells stories of knights and knaves in an entertaining look at the logical precepts behind infinity, probability, time, and change. Requires a strong background in mathematics. Complete solutions.
