Abstract
This paper is a development and extension of the semantical theory for natural languages proposed and developed by the senior author under the name of game-theoretical semantics (GTS).1 The topics discussed include the general explanatory strategies for natural-language semantics employed by GTS, the treatment of negation in GTS, and the thesis that the English quantifier-word “any” is always to be considered a universal quantifier. We shall start with no-problems and then consider any-problems, all the while keeping an eye on methodological considerations.
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Notes
See chapter 1 above for a general discussion, where further references to the literature are provided.
This particular rule is oversimplified, as is shown in Jaakko Hintikka and Lauri Carlson, “Conditionals, Generic Quantifiers, and Other Applications of Subgames”, in F. Cuenthner and S. J, Schmidt, editors, Formal Semantics and Pragmatics for Natural Languages, D. Reidel, Dordrecht, 1979, pp. 1–36; and in chapter 3 above.
One suggestion for such rules would be to formulate a rule for each pair and triple of interacting logical operators (quantifiers and connectives) in all their syntactically relevant positions. Sentences in which there is interaction among more than three operators are sentences to which our argument in section 5 applies. So, supposing our argument to be valid, there can be no rules like the N-rules for quadruples, etc., of interacting logical operators. Though probably comparatively rare in discourse, these latter sentences point up a fundamental limitation to purely “syntactical” negation rules.
Jaakko Hintikka, “Quantifiers vs. Quantification Theory”, Linguistic Inquiry 5 (1974), 153–77; also in Dialectica 27 (1973), 329–58. For a technical discussion of branching quantifiers, see J. Walkoe, J.., “Finite Partially Ordered Quantification”, Journal of Symbolic Logic 35 (1970), 535–55.
Jon Barwise, “On Branching Quantifiers in English”, Journal of Philosophical Logic 8 (1979), 56. Proposition 1 is the relevant claim, for which a proof is given on pp. 73–74.
Edward Klima, “Negation in English”, in Jerry A. Fodor and Jerrold J. Katz, editors., The Structure of Language, Prentice-Hall, Englewood Cliffs, N.J., 1964, pp. 246–323.
Klima, “Negation in English”; Charles J. Fillmore, “On the Syntax of Preverbs”, unpublished paper, Ohio State University, 1966; Robert P. Stockwell, Paul Schachter, and Barbara Hall Partee, The Major Syntactic Structures of English, Holt, Rinehart and Winston, New York, 1973, especially chapter 5.
Hintikka and Carlson, “Conditionals, Generic Quantifiers, and Other Applications of Subgames”.
Gödel’s 1959 article is translated into English as “On a Hitherto Unexploited Extension of the Finitary Standpoint”, Journal of Philosophical Logic 9 (1980), 133–42.
See, eg, Jaakko Hintikka, “Quantifiers in Natural Languages: Some Logical Problems”, in Esa Saarinen, editor, Game-Theoretical Semantics, D. Reidel, Dordrecht, 1979, pp. 81–117; and Hintikka, “Rejoinder to Peacocke”, also in Saarinen, pp. 135–51.
See Noam Chomsky, Rules and Representations, Columbia University Press, New York, 1980, pp. 123–27; and see chapter 9 below.
This was first pointed out to us by Ernest LePore in discussion.
This reading of (84) is the natural reading that results if “anyone” is emphatically stressed, as (i): (i) Jim knows whether John can beat anyone. (85) is the natural reading if (84) is given its normal, unmarked intonation.
Geach, for example, in a similar vein, talks about the “popular view that modern formal logic has applications only to rigorous disciplines like algebra, geometry, and mechanics; not to arguments in a vernacular about more homely concerns. The reason offered would be the complex and irregular logical syntax of vernacular languages.” Reference and Generality, Cornell University Press, Ithaca, N.Y., 1962, p. vii.
See Hintikka, “Quantifiers in Natural Language”.
Alice Davison, “Any as Universal or Existential?” in Johan Van der Auwera, editor, The Semantics of Determiners, Croom Helm, London, 1980, pp. 11–40.
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© 1983 D. Reidel Publishing Company, Dordrecht, Holland
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Hintikka, J., Kulas, J. (1983). AnyProblems — No Problems. In: The Game of Language. Synthese Language Library, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9847-2_4
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DOI: https://doi.org/10.1007/978-94-010-9847-2_4
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