The following is a selection of texts from the recent philosophical debate about plural forms in natural language. The texts involve discussion of whether plural forms can be legitimately interpreted as non-first-order resources, discussion of their ontological commitments and discussion of their possible applications within the philosophy of logic and mathematics. Many of the texts have been influenced by the work of GeorgeBoolos.
Subcategories:
-
David Armstrong, Universals and scientific realism, (Cambridge: Cambridge University Press: 1978)
- Hanoch Ben-Yami, Logic \& Natural Language: On Plural Reference and Its Semantic and Logical Significance, (Aldershot: Ashgate: 2004)
- Alan Berger, "A Formal Semantics for Plural Quantification. Intersentential Binding and Anaphoric Pronouns as Rigid Designators", Noûs 36 (2002), pp. 50-74
- Max Black, "The elusiveness of sets", Review of Metaphysics 24 (1970), pp. 614--636
- George Boolos, "1879?", in ClarkHaleReadingPutnam, pp. 31-48 (1994)
- George Boolos, Logic, Logic, and Logic, (Cambridge, MA: Harvard University Press: 1998)
- George Boolos, "Nominalist Platonism", Philosophical Review 94 (1985), pp. 327--344
- George Boolos, "On second-order logic", Journal of Philosophy 72 (1975), pp. 509--527
- George Boolos, "Reading the Begriffsschrift", Mind 94 (1985), pp. 331--334
- George Boolos, "To Be is to Be the Value of a Variable (or to Be Some Values of Some Variables)", Journal of Philosophy 81 (1984), pp. 430--450
- John P. Burgess, "E Pluribus Unum: Plural Logic and Set Theory", Philosophia Mathematica 12 (2004), pp. 193--221
- John P. Burgess and Gideon Rosen, A subject with no object. Strategies for nominalistic interpretation of mathematics, (Oxford: Oxford University Press: 1997)
- Lauri Carlson, "Plural Quantifiers and Informational Independence", Acta Philosophica Fennica 35 (1982), pp. 163-174
- Roy T Cook, "Aristotelian logic, axioms, and abstraction", Philosophia Mathematica 11(3) (2003), pp. 195-202
- Michael Dummett, Frege: Philosophy of Mathematics, (London: Duckworth: 1991)
- Yuri Gurevich and Saharon Shelah, "Interpreting Second-Order Logic in the Monadic Theory of Order", Journal of Symbolic Logic 48 (1983), pp. 816-828
- A. P. Hazen, "Against Pluralism", Australasian Journal of Philosophy 71 (1993), pp. 132-144
- A. P. Hazen, "Relations in Lewis's Framework Without Atoms", Analysis 57 (1997), pp. 243-248
- A. P. Hazen, "Relations in Monadic Third-Order Logic", Journal of Philosophical Logic 26 (1997), pp. 619-628
- Geoffrey Hellman, "Real Analysis without Classes", Philosophia Mathematica 2 (1994), pp. 228-250
- James Higginbotham, "On higher-order logic and natural language", in SmileyPhilosophicalLogic, pp. 1--27
- J. Higginbotham and B. Schein, "Plurals", in NelsXIXProceedings, pp. (1989)
- David Kaplan, "Generalized Plurality Quantification ", Journal of Symbolic Logic 31 (1966), pp. 154-155
- David Kaplan, "Rescher's Plural Quantification", Journal of Symbolic Logic 31 (1966), pp. 153-154
- Fred Landman, Events and Plurality: The Jerusalem Lectures, (Dordrecht, Holland: Kluwer: 2000)
- Ran Lanzet and Hanoch Ben-Yami, "Logical Inquiries into a New Formal System with Plural Reference", in HendricksFOLRevisited, pp. 173--224 (2004)
- John P. Burgess and Alan P. Hazen and David Lewis, "Appendix on Pairing", in LewisPartsOfClasses, pp. 121-149 (1991)
- David Lewis, "Mathematics is Megethology", Philosophia Mathematica 1 (1993), pp. 3-23
- David Lewis, Parts of Classes, (Oxford: Basil Blackwell: 1991)
- Godehard Link, Algebraic Semantics in Language and Philosophy, (Stanford: CSLI: 1997)
- Øystein Linnebo and David Nicolas, "Superplurals in English", Analysis 68 (2008), pp. 186-197
- Øystein Linnebo, "Plural Quantification" (2004), http://plato.stanford.edu/entries/plural-quant/
- Øystein Linnebo, "Plural Quantification Exposed", Noûs 37 (2003), pp. 71-92
- Gerald J. Massey, "Tom, Dick and Harry, and All the King's Men", American Philosophical Quarterly 13 (1976), pp. 89-107
- Vann McGee, "Everything", in SherBetweenLogicAndIntuition, pp. (2000)
- Vann McGee, "How We Learn Mathematical Language", Philosophical Review 106 (1997), pp. 35-68
- Vann McGee and Agustin Rayo, "A puzzle about de rebus belief", Analysis 60 (2000), pp. 297-299
- Adam Morton, "Complex Individuals and Multigrade Relations", Noûs 9 (1975), pp. 309-18
- David Nicolas, "Mass nouns and plural logic", Linguistics and Philosophy (forthcoming) (2008), pp.
- Alex Oliver and Timothy Smiley, "Multigrade Predicates", Mind 113 (2004), pp. 609--681
- Alex Oliver and Timothy Smiley, "Strategies for a Logic of Plurals", Philosophical Quarterly 51 (2001), pp. 289-306
- Charles Parsons, "The structuralist view of mathematical objects", Synthese 84 (1990), pp. 303--347
- Stephen Pollard, "Plural Quantification and the Iterative Conception of Set", Philosophy Research Archives 11 (1986), pp. 579-87
- W. V. Quine, "On what there is", Review of Metaphysics 2 (1964), pp. 21-38
- W. V. Quine, Philosophy of logic, (Oxford: Oxford University Press: 1970)
- Agustín Rayo, "Beyond Plurals", in RayoUzquianoAbsoluteGenerality, pp. 220--254 (?) (2006)
- Agustin Rayo and Gabriel Uzquiano, "Toward a theory of second-order consequence", Notre Dame Journal of Formal Logic 40 (1999), pp. 315-325
- Agustin Rayo, "Word and Objects", Noûs 36 (2002), pp. 436-464
- Agustin Rayo and Stephen Yablo, "Nominalism Through De-Nominalization", Noûs 35 (2001), pp. 74-92
- Nicholas Rescher, "Plurality Quantification and Quasi-Categorical Propositions", Journal of Symbolic Logic 27 (1962), pp. 373-374
- Nicholas Rescher, Topics in Philosophical Logic, (New York: Humanities Press: 1968)
- Michael Resnik, "Second-Order Logic Still Wild", Journal of Philosophy 85 (1988), pp. 75--87
- Lothar Ridder, Mereologie, (Frankfurt/Main: Kostermann: 2002)
-
Marcus Rossberg, Second-Order Logic: Ontological and Epistemological Problems, PhD thesis, University of St Andrews, (2006)
- Bertrand Russell, The principles of mathematics, (London: Allen and Unwin: 1982)
- Barry Schein, Plurals and Events, (Cambridge, MA: MIT Press: 1993)
- Stewart Shapiro, Foundations without foundationalism: a case for second-order logic, (Oxford: Oxford University Press: 1991)
- Richard Sharvy, "A More General Theory of Definite Descriptions", Philosophical Review 89 (1980), pp. 607-624
- Peter Simons, "Higher-order quantification and ontological commitment", Dialectica 51 (1997), pp. 255-271
- Peter M. Simons, "Number and Manifolds", in SmithPartsMoments, pp. 160--198 (1982)
- Peter Simons, Parts: A study in ontology, (Oxford: Oxford University Press: 1987)
- Peter M. Simons, "Plural Reference and Set Theory", in SmithPartsMoments, pp. 199--256 (1982)
- Eric Stenius, "Sets", Synthese 27 (1974), pp. 161-88
- Gabriel Uzquiano, "Plural Quantification and Classes", Philosophia Mathematica 3 (2003), pp. 67-81
- Timothy Williamson, "Everything", Philosophical Perspectives 17 (2003), pp. 415--465
- Byeong-Uk Yi, "Is Two a Property?", Journal of Philosophy 96 (1999), pp. 163-190
- Byeong-Uk Yi, Understanding the Many, (London: Routledge: 2002)
Number of topics: 67
Bibliography entries relating to this topic in BibTeX format:
@Book{ArmstrongUniversalsAndScientificRealism,
author = {David Armstrong},
title = {Universals and scientific realism},
booktitle = {Universals and scientific realism},
year = {1978},
publisher = {Cambridge University Press},
address = {Cambridge},
}
@Book{BenYamiLogicAndNaturalLanguage,
author = {Hanoch Ben-Yami},
title = {Logic \& Natural Language: On Plural Reference and Its Semantic and Logical Significance},
booktitle = {Logic \& Natural Language: On Plural Reference and Its Semantic and Logical Significance},
year = {2004},
publisher = {Ashgate},
address = {Aldershot},
}
@Article{BergerFormalSemanticsForPluralQuantification,
author = {Alan Berger},
title = {A Formal Semantics for Plural Quantification. Intersentential Binding and Anaphoric Pronouns as Rigid Designators},
journal = {Noûs},
year = {2002},
volume = {36},
number = {1},
pages = {50--74},
}
@Article{BlackElusivenessOfSets,
author = {Max Black},
title = {The elusiveness of sets},
journal = {Review of Metaphysics},
year = {1970},
volume = {24},
pages = {614--636},
}
@InCollection{BoolosEighteenSeventyNine,
author = {George Boolos},
title = {1879?},
crossref = {ClarkHaleReadingPutnam},
year = {1994},
pages = {31--48},
}
@Book{BoolosLogicLogicLogic,
author = {George Boolos},
title = {Logic, Logic, and Logic},
booktitle = {Logic, Logic, and Logic},
year = {1998},
publisher = {Harvard University Press},
address = {Cambridge, MA},
}
@Article{BoolosNominalistPlatonism,
author = {George Boolos},
title = {Nominalist Platonism},
journal = {Philosophical Review},
year = {1985},
volume = {94},
pages = {327--344},
}
@Article{BoolosOnSecond,
author = {George Boolos},
title = {On second-order logic},
journal = {Journal of Philosophy},
year = {1975},
volume = {72},
pages = {509--527},
}
@Article{BoolosReadingTheBegriffsschrift,
author = {George Boolos},
title = {Reading the Begriffsschrift},
journal = {Mind},
year = {1985},
volume = {94},
pages = {331--334},
}
@Article{BoolosToBeIsTheValue,
author = {George Boolos},
title = {To Be is to Be the Value of a Variable (or to Be Some Values of Some Variables)},
journal = {Journal of Philosophy},
year = {1984},
volume = {81},
pages = {430--450},
}
@Article{BurgessEPluribusUnum,
author = {John P. Burgess},
title = {E Pluribus Unum: Plural Logic and Set Theory},
journal = {Philosophia Mathematica},
year = {2004},
volume = {12},
pages = {193--221},
}
@Book{BurgessRosenSubjectWithNoObject,
author = {John P. Burgess and Gideon Rosen},
title = {A subject with no object. Strategies for nominalistic interpretation of mathematics},
booktitle = {A subject with no object. Strategies for nominalistic interpretation of mathematics},
year = {1997},
publisher = {Oxford University Press},
address = {Oxford},
}
@Article{CarlsonPluralQuantifiers,
author = {Lauri Carlson},
title = {Plural Quantifiers and Informational Independence},
journal = {Acta Philosophica Fennica},
year = {1982},
volume = {35},
pages = {163--174},
}
@Article{CookAristotelianLogic,
author = {Roy T Cook},
title = {Aristotelian logic, axioms, and abstraction},
journal = {Philosophia Mathematica},
year = {2003},
volume = {11(3)},
pages = {195--202},
}
@Book{DummettFregePhilosophyOfMathematics,
author = {Michael Dummett},
title = {Frege: Philosophy of Mathematics},
booktitle = {Frege: Philosophy of Mathematics},
year = {1991},
publisher = {Duckworth},
address = {London},
}
@Article{GurevichShelahInterpretingSecondOrderLogic,
author = {Yuri Gurevich and Saharon Shelah},
title = {Interpreting Second-Order Logic in the Monadic Theory of Order},
journal = {Journal of Symbolic Logic},
year = {1983},
volume = {48},
number = {3},
pages = {816--828},
}
@Article{HazenAgainstPluralism,
author = {A. P. Hazen},
title = {Against Pluralism},
journal = {Australasian Journal of Philosophy},
year = {1993},
volume = {71},
pages = {132--144},
}
@Article{HazenRelationsLewisFramework,
author = {A. P. Hazen},
title = {Relations in Lewis's Framework Without Atoms},
journal = {Analysis},
year = {1997},
volume = {57},
pages = {243--248},
}
@Article{HazenRelationsMonadicThirdOrder,
author = {A. P. Hazen},
title = {Relations in Monadic Third-Order Logic},
journal = {Journal of Philosophical Logic},
year = {1997},
volume = {26},
pages = {619--628},
}
@Article{HellmanRealAnalysisWithoutClasses,
author = {Geoffrey Hellman},
title = {Real Analysis without Classes},
journal = {Philosophia Mathematica},
year = {1994},
volume = {2},
pages = {228--250},
}
@InCollection{HigginbothamOnHigher,
author = {James Higginbotham},
title = {On higher-order logic and natural language},
crossref = {SmileyPhilosophicalLogic},
pages = {1--27},
}
@InCollection{HigginbothamScheinPlurals,
author = {J. Higginbotham and B. Schein},
title = {Plurals},
crossref = {NelsXIXProceedings},
year = {1989},
COMPLAINT={This item has no Pagerange field. Edit it in TWiki and add one.},
}
@Article{KaplanGeneralizedPluralityQuantification,
author = {David Kaplan},
title = {Generalized Plurality Quantification },
journal = {Journal of Symbolic Logic},
year = {1966},
volume = {31},
pages = {154--155},
}
@Article{KaplanReschersPluralityQuantification,
author = {David Kaplan},
title = {Rescher's Plural Quantification},
journal = {Journal of Symbolic Logic},
year = {1966},
volume = {31},
pages = {153--154},
}
@Book{LandmanEventsAndPlurality,
author = {Fred Landman},
title = {Events and Plurality: The Jerusalem Lectures},
booktitle = {Events and Plurality: The Jerusalem Lectures},
year = {2000},
publisher = {Kluwer},
address = {Dordrecht, Holland},
}
@InCollection{LanzetBenYamiNewSystemWithPluralReference,
author = {Ran Lanzet and Hanoch Ben-Yami},
title = {Logical Inquiries into a New Formal System with Plural Reference},
crossref = {HendricksFOLRevisited},
year = {2004},
pages = {173--224},
}
@InCollection{LewisBurgessHazen,
author = {John P. Burgess and Alan P. Hazen and David Lewis},
title = {Appendix on Pairing},
crossref = {LewisPartsOfClasses},
year = {1991},
pages = {121--149},
}
@Article{LewisMegethology,
author = {David Lewis},
title = {Mathematics is Megethology},
journal = {Philosophia Mathematica},
year = {1993},
volume = {1},
pages = {3--23},
}
@Book{LewisPartsOfClasses,
author = {David Lewis},
title = {Parts of Classes},
booktitle = {Parts of Classes},
year = {1991},
publisher = {Basil Blackwell},
address = {Oxford},
}
@Book{LinkAlgebraicSemanticsInLanguage,
author = {Godehard Link},
title = {Algebraic Semantics in Language and Philosophy},
booktitle = {Algebraic Semantics in Language and Philosophy},
year = {1997},
publisher = {CSLI},
address = {Stanford},
}
@Article{LinneboNicolasSuperpluralsInEnglish,
author = {Øystein Linnebo and David Nicolas},
title = {Superplurals in English},
journal = {Analysis},
year = {2008},
volume = {68},
pages = {186--197},
}
@Article{LinneboPluralQuantificationExposed,
author = {Øystein Linnebo},
title = {Plural Quantification Exposed},
journal = {Noûs},
year = {2003},
volume = {37},
pages = {71--92},
}
@Article{MasseyTomDickHarry,
author = {Gerald J. Massey},
title = {Tom, Dick and Harry, and All the King's Men},
journal = {American Philosophical Quarterly},
year = {1976},
volume = {13},
pages = {89--107},
}
@InCollection{McGeeEverything,
author = {Vann McGee},
title = {Everything},
crossref = {SherBetweenLogicAndIntuition},
year = {2000},
COMPLAINT={This item has no Pagerange field. Edit it in TWiki and add one.},
}
@Article{McGeeHowWeLearn,
author = {Vann McGee},
title = {How We Learn Mathematical Language},
journal = {Philosophical Review},
year = {1997},
volume = {106},
pages = {35--68},
}
@Article{McGeeRayoAPuzzleAboutDeRebusBelief,
author = {Vann McGee and Agustin Rayo},
title = {A puzzle about de rebus belief},
journal = {Analysis},
year = {2000},
volume = {60},
number = {4},
pages = {297--299},
}
@Article{MortonComplexIndividuals,
author = {Adam Morton},
title = {Complex Individuals and Multigrade Relations},
journal = {Noûs},
year = {1975},
volume = {9},
pages = {309--18},
}
@Article{NicolasMassNounsAndPlural,
author = {David Nicolas},
title = {Mass nouns and plural logic},
journal = {Linguistics and Philosophy},
year = {2008},
volume = {(forthcoming)},
COMPLAINT={This item has no Pagerange field. Edit it in TWiki and add one.},
}
@Article{OliverSmileyMultigradePredicates,
author = {Alex Oliver and Timothy Smiley},
title = {Multigrade Predicates},
journal = {Mind},
year = {2004},
volume = {113},
pages = {609--681},
}
@Article{OliverSmileyStrategiesLogicPlurals,
author = {Alex Oliver and Timothy Smiley},
title = {Strategies for a Logic of Plurals},
journal = {Philosophical Quarterly},
year = {2001},
volume = {51},
pages = {289--306},
}
@Article{ParsonsStructuralistViewOfMathematicalObjects,
author = {Charles Parsons},
title = {The structuralist view of mathematical objects},
journal = {Synthese},
year = {1990},
volume = {84},
pages = {303--347},
}
@Article{PollardPluralQuantification,
author = {Stephen Pollard},
title = {Plural Quantification and the Iterative Conception of Set},
journal = {Philosophy Research Archives},
year = {1986},
volume = {11},
pages = {579--87},
}
@Article{QuineOnWhatThereIs,
author = {W. V. Quine},
title = {On what there is},
journal = {Review of Metaphysics},
year = {1964},
volume = {2},
pages = {21--38},
}
@Book{QuinePhilosophyOfLogic,
author = {W. V. Quine},
title = {Philosophy of logic},
booktitle = {Philosophy of logic},
year = {1970},
publisher = {Oxford University Press},
address = {Oxford},
}
@InCollection{RayoBeyondPlurals,
author = {Agustín Rayo},
title = {Beyond Plurals},
crossref = {RayoUzquianoAbsoluteGenerality},
year = {2006},
pages = {220--254 (?)},
}
@Article{RayoUzquianoSecondOrderConsequence,
author = {Agustin Rayo and Gabriel Uzquiano},
title = {Toward a theory of second-order consequence},
journal = {Notre Dame Journal of Formal Logic},
year = {1999},
volume = {40},
pages = {315--325},
}
@Article{RayoWordAndObjects,
author = {Agustin Rayo},
title = {Word and Objects},
journal = {Noûs},
year = {2002},
volume = {36},
pages = {436--464},
}
@Article{RayoYabloNominalismThroughDeNominalization,
author = {Agustin Rayo and Stephen Yablo},
title = {Nominalism Through De-Nominalization},
journal = {Noûs},
year = {2001},
volume = {35},
number = {1},
pages = {74--92},
}
@Article{RescherPluralityQuantification,
author = {Nicholas Rescher},
title = {Plurality Quantification and Quasi-Categorical Propositions},
journal = {Journal of Symbolic Logic},
year = {1962},
volume = {27},
pages = {373--374},
}
@Book{RescherTopicsPhilosophicalLogic,
author = {Nicholas Rescher},
title = {Topics in Philosophical Logic},
booktitle = {Topics in Philosophical Logic},
year = {1968},
publisher = {Humanities Press},
address = {New York},
}
@Article{ResnikSecond,
author = {Michael Resnik},
title = {Second-Order Logic Still Wild},
journal = {Journal of Philosophy},
year = {1988},
volume = {85},
pages = {75--87},
}
@Book{RidderMereologie,
author = {Lothar Ridder},
title = {Mereologie},
booktitle = {Mereologie},
year = {2002},
publisher = {Kostermann},
address = {Frankfurt/Main},
}
@Book{RussellPrinciplesOfMathematics,
author = {Bertrand Russell},
title = {The principles of mathematics},
booktitle = {The principles of mathematics},
year = {1982},
publisher = {Allen and Unwin},
address = {London},
}
@Book{ScheinPluralsEvents,
author = {Barry Schein},
title = {Plurals and Events},
booktitle = {Plurals and Events},
year = {1993},
publisher = {MIT Press},
address = {Cambridge, MA},
}
@Book{ShapiroFoundationsWithoutFoundationalism,
author = {Stewart Shapiro},
title = {Foundations without foundationalism: a case for second-order logic},
booktitle = {Foundations without foundationalism: a case for second-order logic},
year = {1991},
publisher = {Oxford University Press},
address = {Oxford},
}
@Article{SharvyMoreGeneralTheoryDefiniteDescriptions,
author = {Richard Sharvy},
title = {A More General Theory of Definite Descriptions},
journal = {Philosophical Review},
year = {1980},
volume = {89},
pages = {607--624},
}
@Article{SimonsHigherOrderLogicAndOntologicalCommitment,
author = {Peter Simons},
title = {Higher-order quantification and ontological commitment},
journal = {Dialectica},
year = {1997},
volume = {51},
pages = {255--271},
}
@InCollection{SimonsNumberAndManifolds,
author = {Peter M. Simons},
title = {Number and Manifolds},
crossref = {SmithPartsMoments},
year = {1982},
pages = {160--198},
}
@Book{SimonsParts,
author = {Peter Simons},
title = {Parts: A study in ontology},
booktitle = {Parts: A study in ontology},
year = {1987},
publisher = {Oxford University Press},
address = {Oxford},
}
@InCollection{SimonsPluralReference,
author = {Peter M. Simons},
title = {Plural Reference and Set Theory},
crossref = {SmithPartsMoments},
year = {1982},
pages = {199--256},
}
@Article{SteniusSets,
author = {Eric Stenius},
title = {Sets},
journal = {Synthese},
year = {1974},
volume = {27},
pages = {161--88},
}
@Article{UzquianoPluralQuantificationClasses,
author = {Gabriel Uzquiano},
title = {Plural Quantification and Classes},
journal = {Philosophia Mathematica},
year = {2003},
volume = {3},
pages = {67--81},
}
@Article{WilliamsonEverything,
author = {Timothy Williamson},
title = {Everything},
journal = {Philosophical Perspectives},
year = {2003},
volume = {17},
pages = {415--465},
}
@Article{YiIsTwoProperty,
author = {Byeong-Uk Yi},
title = {Is Two a Property?},
journal = {Journal of Philosophy},
year = {1999},
volume = {96},
pages = {163--190},
}
@Book{YiUnderstandingMany,
author = {Byeong-Uk Yi},
title = {Understanding the Many},
booktitle = {Understanding the Many},
year = {2002},
publisher = {Routledge},
address = {London},
}
Number of topics: 67
-- AgustinRayo - 04 May 2003
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Revision r1.7 - 17 May 2005 - 22:53 - MarcusRossberg
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Copyright © 1999-2003 by the contributing authors.
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