Plural Logic by Alex Oliver

Plural Logic

byAlex Oliver, Timothy Smiley

Hardcover | July 6, 2013

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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.

About The Author

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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Details & Specs

Title:Plural LogicFormat:HardcoverDimensions:304 pages, 9.21 × 6.14 × 0.03 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