Plural logic
著者
書誌事項
Plural logic
Oxford University Press, c2013
- : hbk
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注記
Includes bibliographical references and index
内容説明・目次
内容説明
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 roots 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.
目次
- 1. The project
- 2. History
- 3. Changing the subject
- 4. Predicative analyses
- 5. Terms-singular and plural
- 6. The indeterminacy of plural denotation
- 7. Some basic ideas of plural logic
- 8. Plural descriptions
- 9. Multivalued functions
- 10. Lists
- 11. Singular logic
- 12. Mid-plural logic
- 13. Full plural logic
- 14. Cantorian set theory
- Postscript: unfinished business
- Principal symbols
- Glossary
- References
- Index
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