Symbolic Logic: An Accessible Introduction to Serious Mathematical Logic, Volume 2

There is a gap between what many students learn in their first course in formal logic, and what they are expected to know for their second. Symbolic Logic: An Accessible Introduction to Serious Mathematical Logic closes that gap—making topics from both courses accessible even to students with little or no technical background. The text divides naturally into two volumes, the first for reasoning in logic, and the second for reasoning about it. The first volume introduces classical symbolic logic as appropriate for beginning students. The second builds to Gödel’s completness and incompleteness results. A distinctive feature of the last part is a complete development of Gödel’s second incompleteness theorem.Building upon Volume 1, this second volume includes parts III and IV of the text. Part III develops basic results in classical metalogic, including the soundness and completeness of the predicate calculus—that premises prove a conclusion if and only if they entail it. Part IV moves to Gödel’s incompleteness theorems: the first that, under certain constraints, no theory is sufficient to prove one of P or not-P for every sentence P of its language; the second that none is sufficient to prove its own consistency.Tony Roy is professor emeritus at California State University San Bernardino. He was a longtime member of the Philosophy Department, including as professor and department chair. His research and publications are in logic and metaphysics. Symbolic Logic is the product of many years, and of having offered somewhere over a hundred course sections covering different parts of its content. Read more