Plural logic

s:1218:"Alex Oliver and Timothy Smiley provide a natural point of entry to what for most readers will be a new subject. Plural logic deals with plural terms, plural predicates, and plural quantification. Current logic is singularist: its terms 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. Theauthors argue that plural phenomena need to be taken seriously and that the only viable response is to adopt a plural logic, a logic based on plural denotation. They expound a framework of ideas thatincludes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists. A formal system of plural logic is presented in three stages, before being applied to Cantorian set theory as an illustration. The authors' approach is an attractive blend of no-nonsense argumentative directness and open minded liberalism, and they convey the exciting and unexpected richness of their subject. Mathematicians and linguists, as well aslogicians and philosophers, will find surprises in this book.";