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Plural quantifiers: a modal interpretation

Rafal Urbaniak (UGent)
(2014) SYNTHESE. 191(7). p.1605-1626
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Abstract
One of the standard views on plural quantification is that its use commits one to the existence of abstract objects-sets. On this view claims like 'some logicians admire only each other' involve ineliminable quantification over subsets of a salient domain. The main motivation for this view is that plural quantification has to be given some sort of semantics, and among the two main candidates-substitutional and set-theoretic-only the latter can provide the language of plurals with the desired expressive power (given that the nominalist seems committed to the assumption that there can be at most countably many names). To counter this approach I develop a modal-substitutional semantics of plural quantification (on which plural variables, roughly speaking, range over ways names could be) and argue for its nominalistic acceptability.
Keywords
Nominalism, Boolos, Plural quantification, Higher-order logic, Quantifiers, Tokens, Modality, QUANTIFICATION, ONTOLOGY

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Please use this url to cite or link to this publication:

MLA
Urbaniak, Rafal. “Plural Quantifiers: A Modal Interpretation.” SYNTHESE, vol. 191, no. 7, 2014, pp. 1605–26, doi:10.1007/s11229-013-0354-5.
APA
Urbaniak, R. (2014). Plural quantifiers: a modal interpretation. SYNTHESE, 191(7), 1605–1626. https://doi.org/10.1007/s11229-013-0354-5
Chicago author-date
Urbaniak, Rafal. 2014. “Plural Quantifiers: A Modal Interpretation.” SYNTHESE 191 (7): 1605–26. https://doi.org/10.1007/s11229-013-0354-5.
Chicago author-date (all authors)
Urbaniak, Rafal. 2014. “Plural Quantifiers: A Modal Interpretation.” SYNTHESE 191 (7): 1605–1626. doi:10.1007/s11229-013-0354-5.
Vancouver
1.
Urbaniak R. Plural quantifiers: a modal interpretation. SYNTHESE. 2014;191(7):1605–26.
IEEE
[1]
R. Urbaniak, “Plural quantifiers: a modal interpretation,” SYNTHESE, vol. 191, no. 7, pp. 1605–1626, 2014.
@article{4443770,
  abstract     = {{One of the standard views on plural quantification is that its use commits one to the existence of abstract objects-sets. On this view claims like 'some logicians admire only each other' involve ineliminable quantification over subsets of a salient domain. The main motivation for this view is that plural quantification has to be given some sort of semantics, and among the two main candidates-substitutional and set-theoretic-only the latter can provide the language of plurals with the desired expressive power (given that the nominalist seems committed to the assumption that there can be at most countably many names). To counter this approach I develop a modal-substitutional semantics of plural quantification (on which plural variables, roughly speaking, range over ways names could be) and argue for its nominalistic acceptability.}},
  author       = {{Urbaniak, Rafal}},
  issn         = {{0039-7857}},
  journal      = {{SYNTHESE}},
  keywords     = {{Nominalism,Boolos,Plural quantification,Higher-order logic,Quantifiers,Tokens,Modality,QUANTIFICATION,ONTOLOGY}},
  language     = {{eng}},
  number       = {{7}},
  pages        = {{1605--1626}},
  title        = {{Plural quantifiers: a modal interpretation}},
  url          = {{http://doi.org/10.1007/s11229-013-0354-5}},
  volume       = {{191}},
  year         = {{2014}},
}

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