True to its name, A Concise Introduction to Logic, by Craig DeLancey, surveys propositional logic and predicate logic and goes on to introduce selected advanced topics, in little over 200 pages. The book provides an integrated presentation of basic syntactic and semantic concepts and methods of logic. Part I starts with the concept of a formal language. The concept of valid inference, truth tables and proofs are introduced immediately after the first two propositional connectives. Connectives and inference rules are introduced in alternation, to develop a complete simple natural deduction system for propositional logic. Part II, adds the apparatus of quantification and proof rules for a complete predicate logic. The text covers the logic of relations, sentences with multiple quantifiers and Russell’s theory of definite descriptions. The presentation of concepts and principles is orderly, clear and thought provoking. Many topics are introduced with examples of philosophical arguments drawn from classic sources, adding depth of knowledge to an introductory course. The first two parts end with systematic overviews. The focus is on formal deductive logic throughout. Informal fallacies and traditional syllogistic logic are not covered. Advanced topics covered in the final part of the text include an axiomatic approach to logic, mathematical induction, a deduction theorem for propositional logic, and brief introductions to set theory, modal logic and number theory.
The reviewer, Adam Kovach, is Associate Professor of Philosophy at Marymount University in Arlington, VA, where he teaches courses in many subjects including logic.