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 ('Whitehead and Russell', 'Henry VIII's wives', 'the real numbers', 'the square root of -1', 'they'), plural predicates ('surrounded the fort', 'are prime', 'are consistent', 'imply'), and plural quantification ('some things', 'any things'). 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. The authors 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 that includes 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. Technicalities have been kept to a minimum, and anyone who is familiar with the classical predicate calculus should be able to follow it. 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 as logicians and philosophers, will find surprises in this book. This second edition includes a greatly expanded treatment of the paradigm empty term zilch, a much strengthened treatment of Cantorian set theory, and a new chapter on higher-level plural logic.

About the Series: The aim of this series is to bring together important recent writings in major areas of philosophical inquiry, selected from a variety of sources, mostly periodicals, which may not be conveniently available to the university student or the general reader. The editors of each volume contribute an introductory essay on the items chosen and on the questions with which they deal. A selective bibliography is appended as a guide to further reading. About this volume: When we say a certain rose is red, we seem to be attributing a property, redness, to it. But are there really such properties? If so, what are they like, how do we know about them, and how are they related to the objects which have them and the linguistic devices which we use to talk about them? This collection presents these ancient problems in a modern light. In particular, it makes accessible for the first time the most important contributions to the contemporary controversy about the nature of properties. Those new to the subject will find the clearly-written introduction, by two experts in the field, an invaluable guide to the intricacies of this debate. The volume illustrates very well the aims and methods of modern metaphysics and shows how a thorough understanding of the metaphysics of properties is crucial to most of analytic philosophy.

Timothy Smiley has made ground-breaking contributions to modal logic, free logic, multiple-conclusion logic, and plural logic. He has illuminated Aristotle's syllogistic, the ideas of logical form and consequence, and the distinction between assertion and rejection, and has worked to debunk the theory of descriptions. This volume brings together new articles by an international roster of leading logicians and philosophers in order to honour Smiley's work. Their essays will be of significant interest to those working across the logical spectrum-in philosophy of language, philosophical and mathematical logic, and philosophy of mathematics.

Timothy Smiley has made ground-breaking contributions to modal logic, free logic, multiple-conclusion logic, and plural logic. He has illuminated Aristotlea (TM)s syllogistic, the ideas of logical form and consequence, and the distinction between assertion and rejection, and has worked to debunk the theory of descriptions. This volume brings together new articles by an international roster of leading logicians and philosophers in order to honour Smileya (TM)s work. Their essays will be of significant interest to those working across the logical spectruma "in philosophy of language, philosophical and mathematical logic, and philosophy of mathematics.