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PLURAL QUANTIFICATION LOGIC: A CRITICAL APPRAISAL

Published online by Cambridge University Press:  01 March 2009

HANOCH BEN-YAMI
HANOCH BEN-YAMI*
Affiliation:
Philosophy Department, Central European University
*
*PHILOSOPHY DEPARTMENT CENTRAL EUROPEAN UNIVERSITY 1051 BUDAPEST, HUNGARY, E-mail:[email protected]
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Abstract

I first show that most authors who developed Plural Quantification Logic (PQL) argued it could capture various features of natural language better than can other logic systems. I then show that it fails to do so: it radically departs from natural language in two of its essential features; namely, in distinguishing plural from singular quantification and in its use of an ‘is-one-of’ relation. Next, I sketch a different approach that is more adequate than PQL for capturing plural aspects of natural language semantics and logic. I conclude with a criticism of the claim that PQL should replace natural language for specific philosophical or scientific purposes.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 2 , Issue 1 , March 2009 , pp. 208 - 232
Copyright
Copyright © Association for Symbolic Logic 2009

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References

BIBLIOGRAPHY

Armstrong, D. M. (1978). Nominalism and Realism: Universals and Scientific Realism, Vol. I. Cambridge, UK: Cambridge University Press.Google Scholar
Barker, C. (1998). Partitives, double-genitives, and anti-uniqueness. Natural Language & Linguistic Theory, 16, 679–717.CrossRefGoogle Scholar
Ben-Yami, H. (2004). Logic & Natural Language: On Plural Reference and Its Semantic and Logical Significance. Aldershot, England: Ashgate. Revised and updating version available from: http://web.ceu.hu/phil/benyami/L&NL-Rvsd/L&NL-Rvsd.html.Google Scholar
Ben-Yami, H. (2006). A critique of Frege on common nouns. Ratio (new series), 19, 148–155.Google Scholar
Black, M. (1971). The elusiveness of sets. The Review of Metaphysics, 24, 614–636.Google Scholar
Boolos, G. (1984). To be is to be a value of a variable (or To be some values of some variables). Reprinted in his (1998), Logic, Logic, and Logic. Cambridge, MA: Harvard University Press, pp. 54–72.CrossRefGoogle Scholar
Boolos, G. (1985). Nominalist Platonism. Reprinted in his (1998), Logic, Logic, and Logic. Cambridge, MA: Harvard University Press, pp. 73–87.CrossRefGoogle Scholar
Burgess, J. P., & Rosen, G. (1997). A Subject With No Object: Strategies for Nominalistic Interpretation of Mathematics. Oxford, UK: Oxford University Press.Google Scholar
Evans, G. (1977). Pronouns, quantifiers, and relative clauses (I). Reprinted in his (1985), Collected Papers. Oxford, UK: Oxford University Press, pp. 76–152.CrossRefGoogle Scholar
Frege, G. (1879). Begriffsschrift: Eine der Arithmetischen nachgebildete Formelsprache des reinen Denkens. Halle A/S: Verlag von Louis Nebert.Google Scholar
Geach, P. T. (1962). Reference and Generality: An Examination of Some Medieval and Modern Theories. Emended edition 1968, Ithaca: Cornell University Press.Google Scholar
Grice, H. P. (1967). Logic and conversation. Reprinted in his (1989), Studies in the Way of Words. Cambridge, MA: Harvard University Press, pp. 1–143.Google Scholar
van Inwagen, P. (1990). Material Beings. Ithaca: Cornell University Press.Google Scholar
Jackendoff, R. (1977). X-bar Syntax: A Study of Phrase Structure. Cambridge, MA: MIT Press.Google Scholar
Keenan, E., & Stavi, Y. (1986). A semantic characterization of natural language determiners. Linguistics and Philosophy, 9, 253–326.CrossRefGoogle Scholar
Ladusaw, B. (1982). Semantic constraints on the English partitive construction. Proceedings of WCCFL, 1, 231–242.Google Scholar
Lanzet, R. (2006). An Alternative Logical Calculus: Based on an Analysis of Quantification as Involving Plural Reference, thesis submitted atTel-Aviv University, Tel-Aviv. Available from: http://www.ceu.hu/phil/benyami/Lanzet-AlternativeCalculus.pdf.Google Scholar
Lanzet, R., & Ben-Yami, H. (2004). Logical inquiries into a new formal system with plural reference. In Hendricks, V. F., Neuhaus, F., Pedersen, S. A., Scheffler, U, & Wansing, H., editors. First-Order Logic Revisited. Berlin: Logos Verlag, pp. 173–223.Google Scholar
Lewis, D. (1991). Parts of Classes. Oxford, UK: Blackwell.Google Scholar
Linnebo, Ø. (2003). Plural quantification exposed. Noûs, 37, 71–92.CrossRefGoogle Scholar
Linnebo, Ø. (2004). Plural quantification. In Zalta, E. N., editor. The Stanford Encyclopedia of Philosophy (Winter 2004 Edition). Available from: http://plato.stanford.edu/archives/win2004/entries/plural-quant/.Google Scholar
Matthewson, L. (2001). Quantification and the nature of crosslinguistic variation. Natural Language Semantics, 9, 145–189.CrossRefGoogle Scholar
McKay, T. J. (2006). Plural Predication. Oxford, UK: Clarendon Press.CrossRefGoogle Scholar
Oliver, A., & Smiley, T. (2006). A modest logic of plurals. Journal of Philosophical Logic, 35, 317–348.CrossRefGoogle Scholar
Quine, W. V. (1953). Mr. Strawson on logical theory. Reprinted in his (1976), The Ways of Paradox and Other Essays, second edition. Cambridge, MA: Harvard University Press, pp. 139–157.Google Scholar
Quine, W. V. (1960). Word and Object. Cambridge, MA: The MIT Press.Google Scholar
Quine, W. V. (1992). Pursuit of Truth. Cambridge, MA: Harvard University Press.Google Scholar
Rayo, A. (2002). Word and objects. Noûs, 36, 436–464.CrossRefGoogle Scholar
Rayo, A. (2007). Plurals. Philosophical Compass, 2, published in Online Early Articles.CrossRefGoogle Scholar
Russell, B. (1957). Mr. Strawson on referring. Mind, 66, 385–389.CrossRefGoogle Scholar
Sauerland, U., & Yatsushiro, K. (2004). A silent noun in partitives. In Moulton, K., & Wolf, M., editors. Proceedings of NELS 34. Amherst, MA: GLSA, University of Massachusetts, pp. 101–112.Google Scholar
Schein, B. (2006). Plurals. In Lepore, E., & Smith, B. C., editors. The Oxford Handbook of Philosophy of Language. Oxford, UK: Oxford University Press, pp. 716–767.Google Scholar
Selkirk, L. (1977). Some remarks on noun phrase structure. In Culicover, P., Wasow, T., & Akmajian, A., editors. Studies in Formal Syntax. New York: Academic Press, pp. 285–316.Google Scholar
Strawson, P. F. (1950). On referring. Reprinted in his (1971), Logico-Linguistic Papers, London: Methuen, pp. 1–27.Google Scholar
Strawson, P. F. (1952). Introduction to Logical Theory. London: Methuen.Google Scholar
Szabolcsi, A. (2001). The syntax of scope. In Baltin, M., & Collins, C., editors. The Handbook of Contemporary Syntactic Theory. Oxford, UK: Blackwell, pp. 607–633.CrossRefGoogle Scholar
Vendler, Z. (1962). Each and every, any and all. Mind, 71, 145–160.CrossRefGoogle Scholar
Yi, B. (1999). Is two a property? The Journal of Philosophy, 96, 163–190.CrossRefGoogle Scholar
Yi, B. (2005–2006). The logic and meaning of plurals. Journal of Philosophical Logic, 34, 459–506 and 35, 239–288.CrossRefGoogle Scholar