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Alex Oliver and Timothy Smiley provide a new account of plural logic. They argue that there is such a thing as genuinely plural denotation in logic, and expound a framework of ideas that includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists.
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Alex Oliver and Timothy Smiley provide a new account of plural logic. They argue that there is such a thing as genuinely plural denotation in logic, and expound a framework of ideas that includes the distinction between distributive and collective predicates, the theory of plural descriptions, multivalued functions, and lists.
Produktdetails
- Produktdetails
- Verlag: Oxford University Press, USA
- Revised, Enlarg
- Seitenzahl: 352
- Erscheinungstermin: 27. Dezember 2016
- Englisch
- Abmessung: 233mm x 156mm x 25mm
- Gewicht: 603g
- ISBN-13: 9780198744382
- ISBN-10: 0198744382
- Artikelnr.: 47866593
- Verlag: Oxford University Press, USA
- Revised, Enlarg
- Seitenzahl: 352
- Erscheinungstermin: 27. Dezember 2016
- Englisch
- Abmessung: 233mm x 156mm x 25mm
- Gewicht: 603g
- ISBN-13: 9780198744382
- ISBN-10: 0198744382
- Artikelnr.: 47866593
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.
* 1: The project1.1 Plural phenomena1.2 Plurals in mathematics and
logic
* 2: 1.3 Strategies for a logic of plurals1.4 Manoeuvres of a
consertative logician: a case study1.5 Plan of the bookHistory2.1
Distributive and collective predication2.2 Mill2.3 Frege2.4
Lesniewski2.5 Russell2.6 Russell to Boolos
* 3: Changing the subject3.1 Changing the subject to sets3.2
Uniformity3.3 Against the naive version of changing the subject3.4
Changing the subject and the predicate3.5 The pain of paradox3.6
Changing the subject is simply not on3.7 Changing the subject in
practiceAppendix. Events to the rescue?
* 4: Predicative analyses4.1 Russell's theory of plural descriptions4.2
Other predicative analyses4.3 The equivocity objection4.4 Boolos's
'reciprocal illumination'4.5 Boolos's second-order representation of
plurals4.6 Boolos and equivocity4.7 Rumfitt's purified Boolosian
schemeAppendix. Dummett and Frege on plurals
* 5: Terms--singular and plural5.1 Terms5.2 Varieties of singular
term5.3 Varieties of plural term5.4 The Russellian idea of singular
term5.5 Nested terms5.6 Empty terms5.7 Predication
* 6: The indeterminacy of plural denotation6.1 Two accounts of
denotation6.2 Plural descriptions: some elementary facts6.3 Which
account is correct?6.4 Dissenting voices I6.5 Free relatives and why
-- questions6.6 Dissenting voices II6.7 Indeterminacy
* 7: Some basic ideas of plural logic7.1 Variables and
quantification7.2 Inclusion and identity7.3 Zilch7.4 Distributive
predicates7.5 Collective predicatesAppendix 1. Ex nihilo nihil
fitAppendix 2. Das Nichts selbst nichtet
* 8: Plural descriptions8.1 A theory of descriptions8.2 Formalizing the
theory, definability, and ineliminability8.3 Exercises for the
reader8.4 SuperpluralsAppendix. Sharvy's theory of descriptions
* 9: Multivalued functions9.1 Varieties of function9.2 Mathematicians
and logicians9.3 Functions and relations9.4 The ambiguity
objection9.5 Proposals for eliminating them
* 10: Lists10.1 Lists as terms10.2 Term-forming 'and'10.3 Lists as
strings10.4 Places and positions10.5 Terms vs strings in the
literatureAnalyses assessedAppendix.In defence of multigrade
predicates
* 11: Singular logic11.1 Topic neutrality11.2 Syntax11.3 Axioms11.4
Metatheorems11.5 SemanticsAppendix. Soundness and completeness proofs
* 12: Mid-plural logic12.1 Ideas12.2 Syntax12.3 Axioms12.4
Metatheorems12.5 Semantics12.6 Relation of mid-plural logic to
singular logic12.7 The algebra of pluralsAppendix. Soundness and
completeness proofs
* 13: Full plural logic13.1 Syntax13.2 Semantics13.3 Expressive
power13.4 Partial axiomatization13.5 Comprehension13.6 Choice
* 1415: Cantorian set theory14.1 Plurals and sets14.2 Cantor's
collections14.3 The empty set14.4 Singletons14.5 Ur-elements14.6 A
superstructure, not a foundation14.7 Iterative Cantorian set
theory14.8 Developing the theoryAppendix. Development of the
theoryHigher-level plural logic15.1 Pseudo-singular terms15.2
Higher-level plural logic: some basic ideas15.3 Description15.4
Levels15.5 Partial axiomatization15.6 Does set theory rest on a
mistake?
* Postscript: unfinished business1 Second-order plural logic2 Partial
functions3 Other topics
* Principal symbols
* Glossary
* References
* Index
logic
* 2: 1.3 Strategies for a logic of plurals1.4 Manoeuvres of a
consertative logician: a case study1.5 Plan of the bookHistory2.1
Distributive and collective predication2.2 Mill2.3 Frege2.4
Lesniewski2.5 Russell2.6 Russell to Boolos
* 3: Changing the subject3.1 Changing the subject to sets3.2
Uniformity3.3 Against the naive version of changing the subject3.4
Changing the subject and the predicate3.5 The pain of paradox3.6
Changing the subject is simply not on3.7 Changing the subject in
practiceAppendix. Events to the rescue?
* 4: Predicative analyses4.1 Russell's theory of plural descriptions4.2
Other predicative analyses4.3 The equivocity objection4.4 Boolos's
'reciprocal illumination'4.5 Boolos's second-order representation of
plurals4.6 Boolos and equivocity4.7 Rumfitt's purified Boolosian
schemeAppendix. Dummett and Frege on plurals
* 5: Terms--singular and plural5.1 Terms5.2 Varieties of singular
term5.3 Varieties of plural term5.4 The Russellian idea of singular
term5.5 Nested terms5.6 Empty terms5.7 Predication
* 6: The indeterminacy of plural denotation6.1 Two accounts of
denotation6.2 Plural descriptions: some elementary facts6.3 Which
account is correct?6.4 Dissenting voices I6.5 Free relatives and why
-- questions6.6 Dissenting voices II6.7 Indeterminacy
* 7: Some basic ideas of plural logic7.1 Variables and
quantification7.2 Inclusion and identity7.3 Zilch7.4 Distributive
predicates7.5 Collective predicatesAppendix 1. Ex nihilo nihil
fitAppendix 2. Das Nichts selbst nichtet
* 8: Plural descriptions8.1 A theory of descriptions8.2 Formalizing the
theory, definability, and ineliminability8.3 Exercises for the
reader8.4 SuperpluralsAppendix. Sharvy's theory of descriptions
* 9: Multivalued functions9.1 Varieties of function9.2 Mathematicians
and logicians9.3 Functions and relations9.4 The ambiguity
objection9.5 Proposals for eliminating them
* 10: Lists10.1 Lists as terms10.2 Term-forming 'and'10.3 Lists as
strings10.4 Places and positions10.5 Terms vs strings in the
literatureAnalyses assessedAppendix.In defence of multigrade
predicates
* 11: Singular logic11.1 Topic neutrality11.2 Syntax11.3 Axioms11.4
Metatheorems11.5 SemanticsAppendix. Soundness and completeness proofs
* 12: Mid-plural logic12.1 Ideas12.2 Syntax12.3 Axioms12.4
Metatheorems12.5 Semantics12.6 Relation of mid-plural logic to
singular logic12.7 The algebra of pluralsAppendix. Soundness and
completeness proofs
* 13: Full plural logic13.1 Syntax13.2 Semantics13.3 Expressive
power13.4 Partial axiomatization13.5 Comprehension13.6 Choice
* 1415: Cantorian set theory14.1 Plurals and sets14.2 Cantor's
collections14.3 The empty set14.4 Singletons14.5 Ur-elements14.6 A
superstructure, not a foundation14.7 Iterative Cantorian set
theory14.8 Developing the theoryAppendix. Development of the
theoryHigher-level plural logic15.1 Pseudo-singular terms15.2
Higher-level plural logic: some basic ideas15.3 Description15.4
Levels15.5 Partial axiomatization15.6 Does set theory rest on a
mistake?
* Postscript: unfinished business1 Second-order plural logic2 Partial
functions3 Other topics
* Principal symbols
* Glossary
* References
* Index
* 1: The project1.1 Plural phenomena1.2 Plurals in mathematics and
logic
* 2: 1.3 Strategies for a logic of plurals1.4 Manoeuvres of a
consertative logician: a case study1.5 Plan of the bookHistory2.1
Distributive and collective predication2.2 Mill2.3 Frege2.4
Lesniewski2.5 Russell2.6 Russell to Boolos
* 3: Changing the subject3.1 Changing the subject to sets3.2
Uniformity3.3 Against the naive version of changing the subject3.4
Changing the subject and the predicate3.5 The pain of paradox3.6
Changing the subject is simply not on3.7 Changing the subject in
practiceAppendix. Events to the rescue?
* 4: Predicative analyses4.1 Russell's theory of plural descriptions4.2
Other predicative analyses4.3 The equivocity objection4.4 Boolos's
'reciprocal illumination'4.5 Boolos's second-order representation of
plurals4.6 Boolos and equivocity4.7 Rumfitt's purified Boolosian
schemeAppendix. Dummett and Frege on plurals
* 5: Terms--singular and plural5.1 Terms5.2 Varieties of singular
term5.3 Varieties of plural term5.4 The Russellian idea of singular
term5.5 Nested terms5.6 Empty terms5.7 Predication
* 6: The indeterminacy of plural denotation6.1 Two accounts of
denotation6.2 Plural descriptions: some elementary facts6.3 Which
account is correct?6.4 Dissenting voices I6.5 Free relatives and why
-- questions6.6 Dissenting voices II6.7 Indeterminacy
* 7: Some basic ideas of plural logic7.1 Variables and
quantification7.2 Inclusion and identity7.3 Zilch7.4 Distributive
predicates7.5 Collective predicatesAppendix 1. Ex nihilo nihil
fitAppendix 2. Das Nichts selbst nichtet
* 8: Plural descriptions8.1 A theory of descriptions8.2 Formalizing the
theory, definability, and ineliminability8.3 Exercises for the
reader8.4 SuperpluralsAppendix. Sharvy's theory of descriptions
* 9: Multivalued functions9.1 Varieties of function9.2 Mathematicians
and logicians9.3 Functions and relations9.4 The ambiguity
objection9.5 Proposals for eliminating them
* 10: Lists10.1 Lists as terms10.2 Term-forming 'and'10.3 Lists as
strings10.4 Places and positions10.5 Terms vs strings in the
literatureAnalyses assessedAppendix.In defence of multigrade
predicates
* 11: Singular logic11.1 Topic neutrality11.2 Syntax11.3 Axioms11.4
Metatheorems11.5 SemanticsAppendix. Soundness and completeness proofs
* 12: Mid-plural logic12.1 Ideas12.2 Syntax12.3 Axioms12.4
Metatheorems12.5 Semantics12.6 Relation of mid-plural logic to
singular logic12.7 The algebra of pluralsAppendix. Soundness and
completeness proofs
* 13: Full plural logic13.1 Syntax13.2 Semantics13.3 Expressive
power13.4 Partial axiomatization13.5 Comprehension13.6 Choice
* 1415: Cantorian set theory14.1 Plurals and sets14.2 Cantor's
collections14.3 The empty set14.4 Singletons14.5 Ur-elements14.6 A
superstructure, not a foundation14.7 Iterative Cantorian set
theory14.8 Developing the theoryAppendix. Development of the
theoryHigher-level plural logic15.1 Pseudo-singular terms15.2
Higher-level plural logic: some basic ideas15.3 Description15.4
Levels15.5 Partial axiomatization15.6 Does set theory rest on a
mistake?
* Postscript: unfinished business1 Second-order plural logic2 Partial
functions3 Other topics
* Principal symbols
* Glossary
* References
* Index
logic
* 2: 1.3 Strategies for a logic of plurals1.4 Manoeuvres of a
consertative logician: a case study1.5 Plan of the bookHistory2.1
Distributive and collective predication2.2 Mill2.3 Frege2.4
Lesniewski2.5 Russell2.6 Russell to Boolos
* 3: Changing the subject3.1 Changing the subject to sets3.2
Uniformity3.3 Against the naive version of changing the subject3.4
Changing the subject and the predicate3.5 The pain of paradox3.6
Changing the subject is simply not on3.7 Changing the subject in
practiceAppendix. Events to the rescue?
* 4: Predicative analyses4.1 Russell's theory of plural descriptions4.2
Other predicative analyses4.3 The equivocity objection4.4 Boolos's
'reciprocal illumination'4.5 Boolos's second-order representation of
plurals4.6 Boolos and equivocity4.7 Rumfitt's purified Boolosian
schemeAppendix. Dummett and Frege on plurals
* 5: Terms--singular and plural5.1 Terms5.2 Varieties of singular
term5.3 Varieties of plural term5.4 The Russellian idea of singular
term5.5 Nested terms5.6 Empty terms5.7 Predication
* 6: The indeterminacy of plural denotation6.1 Two accounts of
denotation6.2 Plural descriptions: some elementary facts6.3 Which
account is correct?6.4 Dissenting voices I6.5 Free relatives and why
-- questions6.6 Dissenting voices II6.7 Indeterminacy
* 7: Some basic ideas of plural logic7.1 Variables and
quantification7.2 Inclusion and identity7.3 Zilch7.4 Distributive
predicates7.5 Collective predicatesAppendix 1. Ex nihilo nihil
fitAppendix 2. Das Nichts selbst nichtet
* 8: Plural descriptions8.1 A theory of descriptions8.2 Formalizing the
theory, definability, and ineliminability8.3 Exercises for the
reader8.4 SuperpluralsAppendix. Sharvy's theory of descriptions
* 9: Multivalued functions9.1 Varieties of function9.2 Mathematicians
and logicians9.3 Functions and relations9.4 The ambiguity
objection9.5 Proposals for eliminating them
* 10: Lists10.1 Lists as terms10.2 Term-forming 'and'10.3 Lists as
strings10.4 Places and positions10.5 Terms vs strings in the
literatureAnalyses assessedAppendix.In defence of multigrade
predicates
* 11: Singular logic11.1 Topic neutrality11.2 Syntax11.3 Axioms11.4
Metatheorems11.5 SemanticsAppendix. Soundness and completeness proofs
* 12: Mid-plural logic12.1 Ideas12.2 Syntax12.3 Axioms12.4
Metatheorems12.5 Semantics12.6 Relation of mid-plural logic to
singular logic12.7 The algebra of pluralsAppendix. Soundness and
completeness proofs
* 13: Full plural logic13.1 Syntax13.2 Semantics13.3 Expressive
power13.4 Partial axiomatization13.5 Comprehension13.6 Choice
* 1415: Cantorian set theory14.1 Plurals and sets14.2 Cantor's
collections14.3 The empty set14.4 Singletons14.5 Ur-elements14.6 A
superstructure, not a foundation14.7 Iterative Cantorian set
theory14.8 Developing the theoryAppendix. Development of the
theoryHigher-level plural logic15.1 Pseudo-singular terms15.2
Higher-level plural logic: some basic ideas15.3 Description15.4
Levels15.5 Partial axiomatization15.6 Does set theory rest on a
mistake?
* Postscript: unfinished business1 Second-order plural logic2 Partial
functions3 Other topics
* Principal symbols
* Glossary
* References
* Index