Ebook: Logic as Algebra

This book is based on the notes for a course in logic given by Paul Halmos. This book retains the spirit and purpose of those notes, which was to show that logic can (and perhaps should) be viewed from an algebraic perspective.Propositional logic and monadic predicate calculus-predicate logic with a single quantifier-are the principal topics treated. The connections between logic and algebra are carefully explained. The key notions and the fundamental theorems are elucidated from both a logical and algebraic perspective.The final section gives a unique and illuminating algebraic treatment of the theory of syllogisms-perhaps the oldest branch of logic, and a subject that is neglected in most modern logic texts.The presentation is aimed at a broad audience-mathematics amateurs, students, teachers, philosophers, linguists, computer scientists, engineers, and professional mathematicians. All that is required of the reader is an acquaintance with some of the basic notions encountered in a first course in modern algebra. In particular, no prior knowledge of logic is assumed. The book could serve equally well as a fireside companion and as a course text.