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The Logic and Meaning of Plurals. Part II

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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.

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Notes

  1. Only works directly referred to in this paper are listed below. See Yi (LMP I) for a more comprehensive list of works germane to the subject matter of this paper.

References

Only works directly referred to in this paper are listed below. See Yi (LMP I) for a more comprehensive list of works germane to the subject matter of this paper.

  • 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.

    Article  Google Scholar 

  • Boolos, G. (1985a) Nominalist Platonism, Philos. Rev. 94, 327–344.

    Article  Google Scholar 

  • Boolos, G. (1985b) Reading the Begriffsschrift, Mind 94, 331–344.

    Article  Google Scholar 

  • Enderton, H. (1972) A Mathematical Introduction to Logic, Academic Press, New York.

    Google Scholar 

  • 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.

  • Garner, B. A. (1998) A Dictionary of Modern American Usage, Oxford University Press, New York.

    Google Scholar 

  • Kim, J. (1998) Philosophy of Mind, Westview Press, Boulder.

    Google Scholar 

  • Lewis, D. (1991) Parts of Classes, Basil Blackwell, Oxford.

    Google Scholar 

  • Quine, W. V. (1970) Philosophy of Logic, Prentice-Hall, Englewood Cliffs, NJ.

    Google Scholar 

  • Rayo, A. and Uzquiano, G. (1999) Toward a theory of second-order consequence, Notre Dame J. Form. Log. 40, 315–325.

    Article  Google Scholar 

  • Russell, B. (1902) Letter to Frege, in van Heijenoort (1967) pp. 124–125.

  • Simons, P. M. (1982) Numbers and manifolds, in Smith (ed.), pp. 160–198.

  • Smith, B. (ed.) (1982) Parts and Moments: Studies in Logic and Formal Ontology, Philosophia Verlag, München.

    Google Scholar 

  • van Heijenoort, J. (1967) From Frege to Gödel: A Source Book in Mathematical Logic, 1879-1931, Harvard University Press, Cambridge, MA.

    Google Scholar 

  • Yi, B.-U. (1995) Understanding the Many, Ph. D. Dissertation, UCLA; revised version with a new preface (New York & London: Routledge, 2002).

  • Yi, B.-U. (1998) Numbers and relations, Erkenntnis 49, 93–113.

    Article  Google Scholar 

  • Yi, B.-U. (1999) Is two a property?, J. Philos. 95, 163–190.

    Article  Google Scholar 

  • Yi, B.-U. (LMP I) The logic and meaning of plurals. Part I, The Journal of Philosophical Logic 35, 459–506.

  • Yi, B.-U. (preprint) Is logic axiomatizable?, unpublished manuscript.

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Correspondence to Byeong-uk Yi.

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Yi, Bu. The Logic and Meaning of Plurals. Part II. J Philos Logic 35, 239–288 (2006). https://doi.org/10.1007/s10992-005-9015-6

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