Introduction

This introduction presents an overview of the key concepts discussed in the subsequent chapters of this book. The book presents a fashion typical of traditional logic, the logical and linguistic features of intermediate quantifiers. These quantifiers express logical quantities which fall in between Aristotle's two quantities of categorical propositions— universal and particular. The book shows the basic logic of intermediate quantifiers to consist of the relationships displayable on an Aristotelian-like square of opposition. It explains how the many new inference patterns revealed by advances on intermediate quantifiers motivate hypotheses about semantic features of English quantifier expressions. The book also shows how valid inferences between non-linguistic propositions are explanatorily linked to semantic properties of words, phrases, and sentences typically used to express them. Crucial to the analysis is the distinction between sentence meaning and proposition expressible in a use of a sentence. The book considers syllogism analogues which contain quantifiers that are modifications of straight fractions.