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The Logic and Meaning of Plurals. Part I

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Abstract

Contemporary accounts of logic and language cannot give proper treatments of plural constructions of natural languages. They assume that plural constructions are redundant devices used to abbreviate singular constructions. This paper and its sequel, “The logic and meaning of plurals, II”, aim to develop an account of logic and language that acknowledges limitations of singular constructions and recognizes plural constructions as their peers. To do so, the papers present natural accounts of the logic and meaning of plural constructions that result from the view that plural constructions are, by and large, devices for talking about many things (as such). The account of logic presented in the papers surpasses contemporary Fregean accounts in its scope. This extension of the scope of logic results from extending the range of languages that logic can directly relate to. Underlying the view of language that makes room for this is a perspective on reality that locates in the world what plural constructions can relate to. The papers suggest that reflections on plural constructions point to a broader framework for understanding logic, language, and reality that can replace the contemporary Fregean framework as this has replaced its Aristotelian ancestor.

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References

  • Almog, J. et al. (eds.) (1989) Themes from Kaplan, Oxford University Press, Oxford.

    Google Scholar 

  • Bäuerle, R. et al. (eds.) (1983) Meaning, Use, and Interpretation of Language, Walter de Gruyter, Berlin.

    Google Scholar 

  • Benacerraf, P. and Putnam, H. (eds.) (1983) Philosophy of Mathematics, 2nd edn, Cambridge University Press, Cambridge.

    Google Scholar 

  • Bocheński, I. M. (1961) A History of Formal Logic, translated and edited by I. Thomas, University of Notre Dame Press, Notre Dame.

    Google Scholar 

  • Boolos, G. (1975) On second-order logic, Journal of Philosophy 72, 509–537.

    Google Scholar 

  • Boolos, G. (1984) To be is to be a value of a variable (or to be some values of some variables), Journal of Philosophy 81, 430–448.

    Google Scholar 

  • Boolos, G. (1985a) Nominalist Platonism, Philosophical Review 94, 327–344.

    Google Scholar 

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

    Google Scholar 

  • Boolos, G. and Jeffrey, R. (1989) Computability and Logic, 3rd edn, Cambridge University Press, Cambridge.

    Google Scholar 

  • Burge, T. (1977) A theory of aggregates, Noûs 11, 97–117.

    Google Scholar 

  • Church, A. (1956) Introduction to Mathematical Logic, revised and enlarged edn, Princeton University Press, Princeton.

    Google Scholar 

  • Davidson, D. (1967) The logical form of action sentences, in Rescher (ed.) (1967), pp. 105–122.

  • Dummett, M. (1991) Frege: Philosophy of Mathematics, Harvard University Press, Cambridge, MA.

    Google Scholar 

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

    Google Scholar 

  • Frege, G. (1884) Die Grundlagen der Arithmetik, Köbner, Breslau; translated by J. L. Austin as The Foundations of Arithmetic, Basil Blackwell, Oxford, 1980, 2nd revised edn.

    Google Scholar 

  • Frege, G. (1892), Über Begriff und Gegenstand, Vierteljahresschrift für Wissenschaftliche Philosophie 16, 192–205; translated, together with its draft, as “On concept and object” in Frege (1979), pp. 87–117.

    Google Scholar 

  • Frege, G. (1902) Letter to Russell, 28.7.1902, translation of the German original in Frege (1980).

  • Frege, G. (1979) Posthumous Writings, ed. by H. Hermes et al., Basil Blackwell, Oxford.

    Google Scholar 

  • Frege, G. (1980) Philosophical and Mathematical Correspondence, ed. by G. Gabriel et al., Basil Blackwell, Oxford.

    Google Scholar 

  • Gödel, K. (1947) What is Cantor's continuum problem, The American Mathematical Monthly 54, 515–525; revised and expanded version in Benacerraf and Putnam (eds.), 1983, pp. 470–486.

    Google Scholar 

  • Grandy, R. E. (1976) Anadic logic and English, Synthese 32, 395–402.

    Article  Google Scholar 

  • Hazen, A. P. (1993) Against pluralism, Australasian Journal of Philosophy 71, 132–144.

    Article  Google Scholar 

  • Kamp, H. and Reyle, U. (1993) From Discourse to Logic, Kluwer, Dordrecht.

    Google Scholar 

  • Kaplan, D. (1989) Demonstratives, in Almog et al. (1989), pp. 481–563.

  • Kenny, A. (1963) Action, Emotion, and Will, RKP, London.

    Google Scholar 

  • Kleene, S. C. (1967) Mathematical Logic, Wiley, New York.

    Google Scholar 

  • Kneale, W. and Kneale, M. (1962) The Development of Logic, Clarendon Press, Oxford.

    Google Scholar 

  • Leonard, H. S. and Goodman, N. (1940) The calculus of individuals and its uses, Journal of Symbolic Logic 5, 45–55.

    Google Scholar 

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

    Google Scholar 

  • Link, G. (1983) The logical analysis of plurals and mass terms: A lattice-theoretic approach, in Bäuerle et al. (1983), pp. 245–257; reprinted in Link (1998), pp. 11–34.

  • Link, G. (1991) Plural, in von Stechow and Wunderlich (eds.) (1991), pp. 418–440; reprinted in Link (1998), pp. 35–75.

  • Link, G. (1995) Algebraic semantics for natural language: Some philosophy, some applications, International Journal of Human–Computer Studies 43, 765–784; reprinted in Link (1998), pp. 189–211.

    Google Scholar 

  • Link, G. (1998) Algebraic Semantics in Language and Philosophy, CSLI Publications, Stanford.

    Google Scholar 

  • Lønning, J. T. (1996) Plurals and collectivity, in ter Meulen and van Benthem (eds.) (1996), pp. 1009–1053.

  • Massey, G. J. (1976) Tom, Dick, and Harry, and all the king's men, American Philosophical Quarterly 13, 89–107.

    Google Scholar 

  • Mates, B. (1972) Elementary Logic, 2nd edn, Oxford University Press, New York.

    Google Scholar 

  • Mill, J. S. (1884) A System of Logic, People's ed., Longman, Green, & Co, London.

    Google Scholar 

  • Morton, A. (1975) Complex individuals and multigrade relations, Noûs 9, 309–318.

    Google Scholar 

  • Oliver, A. (1994) Frege and Dummett are two, Philosophical Quarterly 44, 74–82.

    Google Scholar 

  • Peano, G. (1889) Arithmetices principia, nova methodo exposita, Bocca, Turin; translated as “The principles of arithmetic, presented by a new method” by van Heijenoort in van Heijenoort (ed.) (1967), pp. 83–97.

    Google Scholar 

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

    Google Scholar 

  • Quine, W. V. (1972) Methods of Logic, 3rd edn, RKP, London.

    Google Scholar 

  • Quine, W. V. (1973) The Roots of Reference, Open Court, La Salle, IL.

    Google Scholar 

  • Quine, W. V. (1991) Immanence and validity, Dialectica 45, 219–230.

    Google Scholar 

  • Rescher, N. (ed.) (1967) The Logic of Decision and Action, University of Pittsburgh Press, Pittsburgh.

    Google Scholar 

  • Resnik, M. D. (1988) Second-order logic still wild, Journal of Philosophy 85, 75–87.

    Google Scholar 

  • Russell, B. (1903) Principles of Mathematics, Cambridge University Press, Cambridge; 2nd edn, George Allen & Unwin, London, 1937.

    Google Scholar 

  • Russell, B. (1908) Mathematical logic as based on the theory of types, American Journal of Mathematics 30, 222–262; reprinted in van Heijenoort (ed.) (1967), pp. 150–182.

    Google Scholar 

  • Russell, B. (1919) Introduction to Mathematical Philosophy, George Allen & Unwin, London.

    Google Scholar 

  • Schein, B. (1993) Plurals and Events, MIT Press, Cambridge, MA.

    Google Scholar 

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

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

    Google Scholar 

  • Tarski, A. (1929) Les fondaments de la géométrie des corps, Księga Pami \c{a} tkowa Pierwszego Polskiego Zjazdu Matematycznego, supplement to Annales de la Société Polonaise de Mathématique 7, 29–33; translated as “Foundations of the geometry of solids” in Tarski (1956), pp. 24–29.

  • Tarski, A. (1956) Logic, Semantics, Metamathematics, Oxford University Press, Oxford; 2nd edn, Hackett Publishing Company, Indiana, 1983.

    Google Scholar 

  • Taylor, B. and Hazen, A. P. (1992) Flexibly structured predication, Logique et Analyse 35, 375–393.

    Google Scholar 

  • ter Meulen, A. and van Benthem, J. (eds.) (1996) Handbook of Logic and Language, Elsevier, New York.

    Google Scholar 

  • Tomberlin, J. E. (ed.) (1994) Philosophical Perspectives, 8: Logic and Language, Ridgeview, Atascadero, CA.

    Google Scholar 

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

    Google Scholar 

  • van Inwagen, P. (1990) Material Beings, Cornell University Press, Ithaca.

    Google Scholar 

  • van Inwagen, P. (1994) Composition as identity, in Tomberlin (ed.) (1994), pp. 207–220.

  • von Stechow, A. and Wunderlich, D. (eds.) (1991) Semantik/Semantics: Ein internationales Handbuch der zeitgenössischen Forschung/An International Handbook of Contemporary Research, de Gruyter, Berlin.

    Google Scholar 

  • Whitehead, A. N. and Russell, B. (1910–3) Principia Mathematica, Vols. I–III, Cambridge University Press, Cambridge; 2nd edn, 1927.

    Google Scholar 

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

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

    Article  Google Scholar 

  • Yi, B.-U. (1999a) Is two a property?, Journal of Philosophy 95, 163–190.

    Google Scholar 

  • Yi, B.-U. (1999b) Is mereology ontologically innocent?, Philosophical Studies 93, 141–160.

    Article  Google Scholar 

  • Yi, B.-U. (LMP II) The logic and meaning of plurals, II, The Journal of Philosophical Logic, forthcoming.

  • Yi, B.-U. (preprint) Is there a plural object?, unpublished manuscript.

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  1. Department of Philosophy, University of Minnesota, 831 Heller Hall, 271-19th Av. S., Minneapolis, MN, 55455

    Byeong-Uk Yi

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Yi, BU. The Logic and Meaning of Plurals. Part I. J Philos Logic 34, 459–506 (2005). https://doi.org/10.1007/s10992-005-0560-9

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