Anyone seeking a readable and relatively brief guide to logic can do no better than this classic introduction. A treat for both the intellect and the imagination, it profiles the development of logic from ancient to modern times and compellingly examines the nature of logic and its philosophical implications. No prior knowledge of logic is necessary; readers need only an acquaintance with high school mathematics. The author emphasizes understanding, rather than technique, and focuses on such topics as the historical reasons for the formation of Aristotelian logic, the rise of mathematical logic after more than 2,000 years of traditional logic, the nature of the formal axiomatic method and the reasons for its use, and the main results of metatheory and their philosophic import. The treatment of the Gödel metatheorems is especially detailed and clear, and answers to the problems appear at the end.
Table of Contents1. Historical background of mathematical logic.
2. Period of transition.
3. Mathematical logic.
4. The metatheory of mathematical logic.
5. Philosophical implications of mathematical logic.
Answers to Problems.
Most Helpful Customer Reviews
Though published in 1971 (2nd ed.), it is still a fine book. It was the text for my Logic course (Information and Computer Science, Ga. Tech). In his preface he addresses the deficiencies of other introductions to logic--omitting historical considerations, not giving what comes after elementary logic, "saying little or nothing about new philosophical problems created by mathematical logic," and not fleshing out the quality of the "openness of logic." He then goes on to remedy those omissions throughout the text. Indexes include a page for Symbols and a 16-page Subject index. The bibliography is well-annotated. Well worth the effort, as it surveys the thought of the greats: Aristotle, Plato, Euclid, Kant, Cantor, Fermat, Hilbert, Russell, Godel, Post, Church, and Turing.