Abstract
In earlier papers, I have sketched an approach to logical and linguistic semantics that embodies some of the same ideas on which Wittgenstein’s notion of language game is based.1 One of these ideas is that in order to appreciate the semantics of a word (or any other primitive expression of a language) we should study its function in the rule-governed human activities that serve to connect the language (or the fragment of a language) with the world. What Wittgenstein called “language games” can typically be considered such linking activities. In the languages (or parts of languages) that I will study in this chapter, certain activities of this kind are construed as games in the strict sense of the mathematical theory of games. They are called “semantical games”, and the semantics based on them is called game-theoretical semantics. Its basic ideas are explained most easily by reference to formal but interpreted first-order languages. Such a language, say L, can be assumed to have a finite number of primitive predicates that are interpreted on some given fixed domain D.
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Notes
See chapter 1 above. For earlier work see the papers collected in Esa Saarinen, editor, Game-Theoretical Semantics, D. Reidel, Dordrecht, 1979. Chapter 2 above provides a philosophical motivation for game-theoretical semantics along Kantian lines. For further references see section I of the bibliography at the end of this volume.
See section II (ix) of the bibliography.
See chapter 3 above and Jaakko Hintikka and Lauri Carlson, “Conditionals, Generic Quantifiers, and Other Applications of Subgames”, in Saarinen, Game-Theoretical Semantics, pp. 179–214.
See chapter 3 above and also section II (v) of the bibliography for Godel’s paper, and for the literature generated by it.
See sections II (iii)–(iv) of the bibliography.
See sections II (i)–(ii) of the bibliography.
Jaakko Hintikka, “‘ls’, Semantical Games, and Semantical Relativity”, Journal of Philosophical Logic 8 (1979), 433–68 (reprinted as the preceding chapter).
The term “syncategorematic” is sometimes used for this purpose. Both etymology and medieval usage make it more natural to speak instead of “transcategorematic” terms.
Cf. Ockham (Michael J. Loux, translator and editor, Ockham’s Theory of Terms, University of Notre Dame Press, Notre Dame, Indiana, 1974, pp. 8–9); J. L. Ackrill, Aristotle’s Categories and De Interpretatione, Clarendon Press, Oxford., 1963, p. 79; Theodor Gomperz, Greek Thinkers, vol. 4 (tr. by G. G. Berry), Murray, London, 1912, p. 39; and Charles Kahn, “Questions and Categories”, in Henry Hiz, editor, Questions, D. Reidel, Dordrecht, 1978, pp. 227–78 (passim).
See Adolf Trendelenburg, Geschichte der Kategorienlehre, Bethge, Berlin, 1846; Emile Benveniste, “Catégories de pensée et catégories de langue”, in Problémes de Linguistique générale, Gallimard, Paris, 1966, pp. 63–74; and Charles Kahn, “Questions and Categories”.
See, for example, Hermann Bonitz, Uber die Kategorien des Aristoteles, Staatsdruckere, Vienna, 1853.
See, for example, O. Apelt, Beiträge zur Geschichte der griechischen Philosophie, Leipzig, 1891.
Aristotle, Categoriae, 1 b 25–2 a 10.
See, for example, Heinrich Maier, Die Syllogistik des Aristoteles, vols. 1–2, Tubingen, 1896–1900; and W. D. Ross, Aristotle’s Metaphysics, vols. 1–2, Clarendon Press, Oxford, 1924.
Aristotle sometimes uses the term “genus” in another, narrower, sense, as a mere correlate to the term “species”. In this sense, categories of course are not genera. However, this sense is not relevant to our present problems. See Posterior Analytics II, 19, 100 b 1–2.
Since I am not sure that I have understood Bresnan’s view fully, the responsibility for the following discussion is nevertheless mine and not hers.
David M. Perlmutter, “On the Article in English”, in M. Bierwisch and K. E. Heidolph, editors, Progress in Linguistics, Mouton, The Hague, 1970, pp. 233–48.
For a sample of such attempts, see F. J. Pelletier, editor, Mass Terms: Some Philosophical Problems, D. Reidel, Dordrecht, 1979.
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© 1983 D. Reidel Publishing Company, Dordrecht, Holland
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Hintikka, J. (1983). Semantical Games and Aristotelian Categories. In: The Game of Language. Synthese Language Library, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9847-2_8
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