This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book aims to demonstrate several significant semantic distinctions between the predicate calculus and natural language, distinctions that make the former inadequate for the study of the semantics and logic of the latter. It discusses plural reference and explains what plural reference is, and shows that natural language, in contrast to the predicate calculus, uses plural referring expressions. The book provides the valid inferences of Aristotelian logic – the Square of Opposition, immediate inferences and syllogisms. It presents some logical relations between multiply quantified sentences and some properties of relations. Accordingly, semantic investigations of semantic and logical properties of natural language can be considered independently of their contribution to the critical purpose of this work.