Graduate-level historical study is ideal for students intending to specialize in the topic, as well as those who only need a general treatment. Part I discusses traditional and symbolic logic. Part II explores the foundations of mathematics, emphasizing Hilbert's metamathematics. Part III focuses on the philosophy of mathematics.
Introduction to Logic by Patrick Suppes Part I of this coherent, well-organized text deals with formal principles of inference and definition. Part II explores elementary intuitive set theory, with separate chapters on sets, relations, and functions. Ideal for undergraduates.
On Formally Undecidable Propositions of Principia Mathematica and Related Systems by Kurt Gödel First English translation of revolutionary paper (1931) that established that even in elementary parts of arithmetic, there are propositions which cannot be proved or disproved within the system. Introduction by R. B. Braithwaite.
Natural Deduction: A Proof-Theoretical Study by Dag Prawitz The author of this study formulated the theories behind intuitionistic type theory and modern proof-theoretic semantics. He explains the principles of his proof-theoretical system, and he illustrates its applications to natural deduction. 1965 edition.
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.
Logic for Mathematicians by J. Barkley Rosser Examination of essential topics and theorems assumes no background in logic. "Undoubtedly a major addition to the literature of mathematical logic." — Bulletin of the American Mathematical Society. 1978 edition.
