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This book aims to be the natural point of entry to what will be a new subject for most readers. Technicalities have been kept to a minimum, and anyone who is familiar with the classical predicate calculus should be able to follow it. The book tackles the logic of plural terms (‘Whitehead and Russell’, ‘the men who wrote Principia Mathematica’, ‘Henry VIII’s wives’, ‘the real numbers’, ‘√−1’, ‘they’); plural predicates (‘surrounded the fort’, ‘are prime’, ‘are consistent’, ‘imply’); and plural quantification (‘some things’, ‘any things’). Current logic is singularist: it only allows terms to stand for at most one thing. By contrast, the foundational thesis of this book is that a particular term may legitimately stand for several things at once, in other words, there is such a thing as genuinely plural denotation. Plural logic is logic based on plural denotation. The book begins by making the case for taking plural phenomena seriously, and argues, by eliminating rival singularist strategies, that the only viable response is to adopt a plural logic. The subsequent development of the conceptual ground includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists. A formal system of plural logic is then presented in three stages, before being applied to Cantorian set theory as an illustration.

This book tackles the logic of plural terms (‘Whitehead and Russell’, ‘the men who wrote Principia Mathematica’, ‘Henry VIII's wives’, ‘the real numbers’, ‘√—1’, ‘they’); plural predicates (‘surrounded the fort’, ‘are prime’, ‘are consistent’, ‘imply’); and plural quantification (‘some things’, ‘any things’). Current logic is singularist: it only allows terms to stand for at most one thing. By contrast, the foundational thesis of this book is that a particular term may legitimately stand for several things at once, in other words, there is such a thing as genuinely plural denotation. Plural logic is logic based on plural denotation. The book begins by making the case for taking plural phenomena seriously, and argues, by eliminating rival singularist strategies, that the only viable response is to adopt a plural logic. The subsequent development of the conceptual ground includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists. A formal system of plural logic is then presented in three stages, before being applied to Cantorian set theory as an illustration. A system of higher-level plural logic is then outlined. It bears a striking similarlty to the set theory.