Plural Logic

Hardcover | July 6, 2013

byAlex Oliver, Timothy Smiley

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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; inother 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 distinctionbetween 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 unexpectedrichness of their subject. Mathematicians and linguists, as well as logicians and philosophers, will find surprises in this book.

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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 ...

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. He also has a strong in...

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Format:HardcoverDimensions:304 pages, 9.21 × 6.14 × 0.98 inPublished:July 6, 2013Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0199570426

ISBN - 13:9780199570423

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Table of Contents

1. The project2. History3. Changing the subject4. Predicative analyses5. Terms - singular and plural6. The indeterminacy of plural denotation7. Some basic ideas of plural logic8. Plural descriptions9. Multivalued functions10. Lists11. Singular logic12. Mid-plural logic13. Full plural logic14. Cantorian set theoryPostscript: unfinished businessPrincipal symbolsGlossaryReferencesIndex