Abstract
Quantifiers are by common consent among the most important ingredients in the logical structure of both formalized and natural languages. As we all know, formalized quantifiers and their generalizations have been studied extensively by logicians. In contrast, relatively little close attention has been paid to the peculiarities of the logical behavior of quantifiers in natural languages, in spite of the fact that quantifiers have figured conspicuously in some of the most important recent methodological controversies in linguistics.1 It is the purpose of this paper to help to change this situation by surveying some of the non-trivial logical phenomena that we find in examining natural-language quantifiers. In doing so, I am largely restricting my attention to the natural-language counterparts of logicians’ existential quantifier and universal quantifier, neglecting such ‘nonstandard’ quantifier words as ‘many’ and ‘most’. I shall cover in the survey a number earlier observations of mine which have already been partly published,2 but I shall also try to concentrate on certain new insights which serve to extend and to consolidate the old results.
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Bibliography
Carlson, Lauri, and Jaakko Hintikka, ‘Conditionals, Generic Quantifiers, and Other Applications of Subgames’ in E. Saarinen (ed.), Game-Theoretical Semantics, |D. Reidel, Dordrecht, 1978.
Davidson, Donald, ‘Truth and Meaning’, Synthese 17 (1967), pp. 304–323.
Davidson, Donald, ‘On Saying That’, Synthese 19 (1968), pp. 130–146.
Davidson, Donald, ‘True to the Facts’, Journal of Philosophy 66 (1969), pp. 748–764.
Davidson, Donald, ‘Semantics for Natural Languages’, in Linguaggi nella società e nelle tecnica, edizioni di Comunità, Milan, 1970, pp. 177–188.
Davidson, Donald, ‘In Defense of Convention T’, in H. Leblanc (ed.), Truth, Syntax, and Modality, North-Holland, Amsterdam, 1973, pp. 76–86.
Fauconnier, Gilles, ‘Do Quantifiers Branch?’, Linguistic Inquiry 6 (1975), pp. 555–567.
Hintikka, Jaakko, ‘Quantifiers vs. Quantification Theory’, Linguistic Inquiry 5 (1974), pp. 153–177.
Hintikka, Jaakko, ‘On the Limitations of Generative Grammar’, in the Proceedings of the Scandinavian Seminar on Philosophy of Language, Filosofiska Förening & Filosofiska Institutionen vid Uppsala Universitet, Uppsala (1975a), vol. 1, pp. 1–92.
Hintikka, Jaakko, ‘A Counterexample to Tarski-type Truth-Definitions as Applied to Natural Languages’, in Asa Kasher (ed.), Language in Focus: Foundations, Methods and Systems Essays in Memory of Yehoshua Bar-Hillel, D. Reidel, Dordrecht (1975b), pp. 107–112.
Hintikka, Jaakko, ‘Impossible Possible Worlds Vindicated’, Journal of Philosophical Logic 4 (1975c), pp. 475–484.
Hintikka, Jaakko, ‘Quantifiers in Logic and Quantifiers in Natural Languages’, in S. Körner (ed.), Philosophy of Logic, Oxford, Basil Blackwell (1976a), pp. 208–232.
Hintikka, Jaakko, ‘The Prospects of Convention T’, Dialectica 30 (1976b), pp. 61–66.
Hintikka, Jaakko, ‘Partially Ordered Quantifiers vs. Partially Ordered Ideas’, Dialectica 30 (1976c), pp. 89–99.
Hintikka, Jaakko The Semantics of Questions and the Questions of Semantics (Acta Philosophica Fennica, vol. 28, no. 4), North-Holland Publishing Company, Amsterdam, 1976d.
Hintikka, Jaakko and Lauri Carlson, ‘Pronouns of Laziness in Game-Theoretical Semantics’, Theoretical Linguistics 4 (1977), 1–29.
Hintikka, Jaakko, and Esa Saarinen, ‘Semantical Games and the Bach-Peters Paradox’, Theoretical Linguistics 2 (1975), pp. 1–20.
Lakoff, George, ‘Repartee, or a Reply to “Negation Conjunction, and Quantifier”’, Foundations of Language 6 (1970), pp. 398–422.
Lakoff, George, ‘Repartee, or a Reply to “Negation Conjunction, and Quantifier”’, Foundations of Language 6 (1970), pp. 398–422.
Partee, Barbara Hall, ‘Negation Conjunction, and Quantifiers: Syntax vs. Semantics’, Foundations of Language 6 (1970), pp. 153–165.
Partee, Barbara Hall, ‘On the Requirement that Transformations Preserve Meaning’, in Charles J. Fillmore and D. Terence Langendoen (eds.), Studies in Linguistic Semantics, Holt, Rinehart and Winston, New York, 1971, pp. 1–21.
Rogers, Hartley, Jr ., ‘Certain Logical Reduction and Decision Problems’, Annals of Mathematics 64 (1956), pp. 264–284.
Stenius, Erik, ‘Comments on Jaakko Hintikka’s Paper’,Dialectica 30 (1976).
Suranyi, Janos, Reduktionstheorie des Entscheidungsproblems im Prädikatenkalkul der ersten Stufe, Verlag der ungarischen Akademie der Wissenschaften, Budapest, 1959.
Thomason, Richmond (ed.), Formal Philosophy: Selected Essays of Richard Montague, Yale University Press, 1974.
Walkoe, W. J., Jr ., ‘Finite Partially-Ordered Quantification’, Journal of Symbolic Logic 35 (1970), pp. 535–555.
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© 1979 D. Reidel Publishing Company, Dordrecht, Holland
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Hintikka, J. (1979). Quantifiers in Natural Languages: Some Logical Problems, I. In: Hintikka, J., Niiniluoto, I., Saarinen, E. (eds) Essays on Mathematical and Philosophical Logic. Synthese Library, vol 122. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-9825-4_16
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DOI: https://doi.org/10.1007/978-94-009-9825-4_16
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