Abstract

This book is designed for an introductory course in logic on the freshman-sophomore level. The approach to logic through set theory is justified by the fundamental importance of set theory in mathematics, and by the fact that most students entering college are acquainted with set theory. The author begins by explaining the basic notions and laws of set theory, and shows how the four standard types of propositions are translated into the notation of set theory. Propositional logic is introduced and related to set theory by interpreting truth-tables in terms of sets and subsets. A simplified first order functional calculus is developed without quantifiers by using an unconventional notation resembling that of set theory as closely as possible. The nature and techniques of deductive proof are treated at length. Beyond these formal topics there are interesting discussions of the application of logical laws in ordinary language arguments, in probability theory, and in circuit theory. The material is organized in units suitable for fifty minute classes with excellent exercises at the end of each unit. Answers are provided to half the questions in the exercises to allow the student to test himself. The book ends with a brief note on scientific discovery and axiomatics.--T. D. Z.