Overview

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.

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9780198744382

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Reviews

Throughout the book the exposition is clear; the arguments cogent; the formalism as transparent as can be. Proofs are relegated to appendices. This is a rewarding book. It deserves study in any course in philosophical or mathematical logic, and a place in every logician's library. * Louis F Goble, zbmath * A veritable tour de force. * Lloyd Humberstone, Australasian Journal of Philosophy * In their clear and combative style, they introduce the relevant notions and offer rebuttals to arguments that would oppose their own positions ... Oliver and Smiley's book is full of careful and precise developments, as well as witty arguments... provides a good survey of plural logic and the most important issues connected to it. * David A. Nicolas, Notre Dame Philosophical Reviews *

`In their clear and combative style, they introduce the relevant notions and offer rebuttals to arguments that would oppose their own positions. . . Oliver and Smiley's book is full of careful and precise developments, as well as witty arguments. . . provides a good survey of plural logic and the most important issues connected to it.' David A. Nicolas, Notre Dame Philosophical Reviews `A veritable tour de force.' Lloyd Humberstone, Australasian Journal of Philosophy `Throughout the book the exposition is clear; the arguments cogent; the formalism as transparent as can be. Proofs are relegated to appendices. This is a rewarding book. It deserves study in any course in philosophical or mathematical logic, and a place in every logician's library.' Louis F Goble, zbmath

In this second edition the authors refine their fight against singularism, and confirm their Cantor-inspired idea of collection, which goes hand in hand with their vindication of empty terms. The main developments with respect to the first edition, on the one hand, incorporate the authors' recent work on the topic, and, on the other hand, serve to make more explicit what 'the enemy' is ... In sum, the lack of existential assumptions in the authors' system of plural logic, and the genuinely plural character of their notion of plurality (at any level), are emphasized in this second edition, expanded in both the technical and the philosophical aspects. * Paloma Perez-Ilzarbe, MathSciNet * Throughout the book the exposition is clear; the arguments cogent; the formalism as transparent as can be. Proofs are relegated to appendices. This is a rewarding book. It deserves study in any course in philosophical or mathematical logic, and a place in every logician's library. * Louis F Goble, zbmath * A veritable tour de force. * Lloyd Humberstone, Australasian Journal of Philosophy * In their clear and combative style, they introduce the relevant notions and offer rebuttals to arguments that would oppose their own positions ... Oliver and Smiley's book is full of careful and precise developments, as well as witty arguments... provides a good survey of plural logic and the most important issues connected to it. * David A. Nicolas, Notre Dame Philosophical Reviews *

In their clear and combative style, they introduce the relevant notions and offer rebuttals to arguments that would oppose their own positions... Oliver and Smiley's book is full of careful and precise developments, as well as witty arguments... provides a good survey of plural logic and the most important issues connected to it. David A. Nicolas, Notre Dame Philosophical Reviews A veritable tour de force. Lloyd Humberstone, Australasian Journal of Philosophy Throughout the book the exposition is clear; the arguments cogent; the formalism as transparent as can be. Proofs are relegated to appendices. This is a rewarding book. It deserves study in any course in philosophical or mathematical logic, and a place in every logician's library. Louis F Goble, zbmath

Throughout the book the exposition is clear; the arguments cogent; the formalism as transparent as can be. Proofs are relegated to appendices. This is a rewarding book. It deserves study in any course in philosophical or mathematical logic, and a place in every logician's library. * Louis F Goble, zbmath * A veritable tour de force. * Lloyd Humberstone, Australasian Journal of Philosophy * In their clear and combative style, they introduce the relevant notions and offer rebuttals to arguments that would oppose their own positions. . . Oliver and Smiley's book is full of careful and precise developments, as well as witty arguments. . . provides a good survey of plural logic and the most important issues connected to it. * David A. Nicolas, Notre Dame Philosophical Reviews *

Author Information

Alex Oliver read philosophy at Cambridge and Yale. After a Research Fellowship at Gonville and Caius College, Cambridge, he joined the Faculty of Philosophy where he is now a Professor. He was awarded a Leverhulme Major Research Fellowship and the Mind Association's Senior Research Fellowship for work in logic. Timothy Smiley studied logic and philosophy at the University of Fribourg in Switzerland in 1948, before reading mathematics at Cambridge. After service in the RAF and the Air Ministry he was called to the Bar at Gray's Inn, but opted to take up a Research Fellowship at Clare College, Cambridge. He became Senior Tutor of his College and was a University Lecturer in Philosophy before being elected as Knightbridge Professor in 1980.

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