Peter Alexander 
Introduction to Logic [PDF ebook] 
The Criticism of Arguments

Originally published in 1969. This book is for undergraduates whether specializing in philosophy or not. It assumes no previous knowledge of logic but aims to show how logical notions arise from, or are abstracted from, everyday discourse, whether technical or non-technical. It sets out a knowledge of principles and, while not historical, gives an account of the reasons for which modern systems have emerged from the traditional syllogistic logic, demonstrating how certain central ideas have developed. The text explains the connections between everyday reasoning and formal logic and works up to a brief sketch of systems of propositional calculus and predicate-calculus, using both the axiomatic method and the method of natural deduction. It provides a self-contained introduction but for those who intend to study the subject further it contains many suggestions and a sound basis for more advanced study.