Journal of Philosophical Logic

, Volume 35, Issue 3, pp 239–288 | Cite as

The Logic and Meaning of Plurals. Part II

Article

Abstract

In this sequel to “The logic and meaning of plurals. Part I”, I continue to present an account of logic and language that acknowledges limitations of singular constructions of natural languages and recognizes plural constructions as their peers. To this end, I present a non-reductive account of plural constructions that results from the conception of plurals as devices for talking about the many. In this paper, I give an informal semantics of plurals, formulate a formal characterization of truth for the regimented languages that results from augmenting elementary languages with refinements of basic plural constructions of natural languages, and account for the logic of plural constructions by characterizing the logic of those regimented languages.

Key Words

class irreducibility of plurals logic model theory natural language non-axiomatizability of logic plural regimentation of plurals second-order logic semantics set singular the many the one 

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References1

  1. Boolos, G. (1984) To be is to be a value of a variable (or to be some values of some variables), J. Philos. 81, 430–448.CrossRefGoogle Scholar
  2. Boolos, G. (1985a) Nominalist Platonism, Philos. Rev. 94, 327–344.CrossRefGoogle Scholar
  3. Boolos, G. (1985b) Reading the Begriffsschrift, Mind 94, 331–344.CrossRefGoogle Scholar
  4. Enderton, H. (1972) A Mathematical Introduction to Logic, Academic Press, New York.Google Scholar
  5. Frege, G. (1884) Die Grundlagen der Arithmetik (Breslau: Köbner); translated by J. L. Austin as The Foundations of Arithmetic (Oxford: Basil Blackwell, 1980), 2nd revised ed.Google Scholar
  6. Garner, B. A. (1998) A Dictionary of Modern American Usage, Oxford University Press, New York.Google Scholar
  7. Kim, J. (1998) Philosophy of Mind, Westview Press, Boulder.Google Scholar
  8. Lewis, D. (1991) Parts of Classes, Basil Blackwell, Oxford.Google Scholar
  9. Quine, W. V. (1970) Philosophy of Logic, Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
  10. Rayo, A. and Uzquiano, G. (1999) Toward a theory of second-order consequence, Notre Dame J. Form. Log. 40, 315–325.CrossRefGoogle Scholar
  11. Russell, B. (1902) Letter to Frege, in van Heijenoort (1967) pp. 124–125.Google Scholar
  12. Simons, P. M. (1982) Numbers and manifolds, in Smith (ed.), pp. 160–198.Google Scholar
  13. Smith, B. (ed.) (1982) Parts and Moments: Studies in Logic and Formal Ontology, Philosophia Verlag, München.Google Scholar
  14. van Heijenoort, J. (1967) From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931, Harvard University Press, Cambridge, MA.Google Scholar
  15. Yi, B.-U. (1995) Understanding the Many, Ph. D. Dissertation, UCLA; revised version with a new preface (New York & London: Routledge, 2002).Google Scholar
  16. Yi, B.-U. (1998) Numbers and relations, Erkenntnis 49, 93–113.CrossRefGoogle Scholar
  17. Yi, B.-U. (1999) Is two a property?, J. Philos. 95, 163–190.CrossRefGoogle Scholar
  18. Yi, B.-U. (LMP I) The logic and meaning of plurals. Part I, The Journal of Philosophical Logic 35, 459–506.Google Scholar
  19. Yi, B.-U. (preprint) Is logic axiomatizable?, unpublished manuscript.Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.University of MinnesotaDepartment of PhilosophyMinneapolisUSA

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