Introduction

This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book presents and analyzes in a fashion typical of traditional logic, the logical and linguistic features of intermediate quantifiers. It explores the basic idea for how to approach the task is introduced, with heavy emphasis on the linguistic meanings and ordinary uses of English intermediate quantifier expressions and on the traditional square of opposition. The book provides the task of completely integrating the three basic intermediate quantifiers into traditional logic is carried out in full. It clearly differentiates logical inference from linguistic meaning (and also, propositions from sentence meanings) provides a better understanding of semantic properties of some English quantifiers and some criticisms of James McCawley’s grammatical analyses. The book is simply not a basic work on the syllogism. Rather, the syllogism is used in the investigations reported and, in the end, it is significantly extended.