Abstract
In earlier publications, I have outlined a largely novel approach2 to the semantics of certain formal languages and the semantics of certain fragments of natural languages.3 In this approach, the truth of a sentence S is defined as the existence of a winning strategy for one of the two players, called Myself, in a certain two-person game G(S) associated with S.4 Intuitively, G(S) may be thought of as an attempt on the part of Myself to verify S against the schemes of an actively resistant opponent who is called Nature. On the basis of this idea, most of the game rules can be anticipated. For instance, I win if the game ends with a true primitive sentence, and Nature wins if it ends with a false one. For quantifier phrases like “any Y who Z” and “every Y who Z”, the game rules can also be anticipated. As special cases we have the following rules:
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Notes
The research reported here was supported by a Fellowship from the John Simon Guggenheim Memorial Foundation for 1979–80 and by The Florida State University. I have greatly profited from comments by Steven Weisler on an earlier draft of this chapter and also from the comments of two anonymous referees for Linguistics and Philosophy. Most of the putative counterexamples in section 2 that can be turned into evidence for my theory were suggested to me by Lauri Carlson, whose help has been important in other ways as well. Donald Provence first brought examples like (58) to my attention. All these contributions and others that I may have forgotten are gratefully acknowledged.
But not completely novel. Over and above the partial anticipations that belong to logicians’ folklore and that will be mentioned below, Risto Hilpinen has unearthed a neat anticipation of the main idea of game-theoretical semantics in C. S. Peirce. See Hilpinen, “On C. S. Peirce’s Theory of Propositions: Peirce as a Precursor of Game-Theoretical Semantics”, The Monist, 65 (1982), 182–88.
Most of my earlier papers in this direction are reprinted in Esa Saarinen, editor, Game-Theoretical Semantics, D. Reidel, Dordrecht, 1979. Cf. also my monograph, The Semantics of Questions and the Questions of Semantics (Acta Philosophica Fennica, vol. 28, n. 4), North-Holland, Amsterdam, 1976; and see the other chapters of this book for more recent developments.
The notions mentioned here are explained more fully elsewhere. To find such explanations, please consult the index of Saarinen, Game-Theoretical Semantics. See also chapter 1 above, and the index to this book.
See, eg, Edward S. 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; or Robert P. Stockwell, Paul Schachter, and Barbara Hall Partee, The Major Syntactic Structures of English, Holt, Rinehart and Winston, New York, 1973, especially ch. 5.
Cf. Charles Kahn, “Questions and Categories”, in Henry Hiz, editor, Questions, D. Reidel, Dordrecht, 1978, pp. 227–78; also, see chapter 8 above.
Jaakko Hintikka and Lauri Carlson, “Pronouns of Laziness in Game-Theoretical Semantics”, Theoretical Linguistics 4 (1977), 1–29.
Charles J. Fillmore, “The Position of Embedding Transformations in a Grammar”, Word 19 (1963), 208–31; and cf., eg, Noam Chomsky, “Conditions on Transformations”, in Stephen R. Anderson and Paul Kiparsky, editors, A Festschrift for Morris Halle, Holt, Rinehart and Winston, New York, 1973, pp. 232–86, reprinted in Essays on Form and Interpretation, North-Holland, Amsterdam, 1977, pp. 80–160.
Turning putative counterexamples into support for my theory not only enhances its credibility by increasing the number of its confirming instances. One does not have to be a Popperian to believe that being able to withstand serious challenges, eg, in the form of prima facie counterexamples, is a good index of the veracity of a theory. After all, it is seen even from Bayes’s notorious formula that a priori unlikely evidence supports a theory more strongly than a priori likely evidence, ceteris paribus.
The possibility of this generalization was first pointed out to me by Lauri Carlson.
For the notion of informational independence and its connection with branching quantifiers, see Saarinen, Game-Theoretical Semantics, especially Jaakko Hintikka, “Quantifiers vs. Quantification Theory”, pp. 49–79.
See my book The Semantics of Questions, especially chapters 2–3.
The rule (G. and) in its simplest form is formulated in the papers included in Saarinen, Game-Theoretical Semantics. A special case of (G. and) says that when the game has reached a sentence of the form X and Y, where X and Y are clauses. Nature chooses one of the conjuncts X and Y, whereupon the game is continued with respect to it. Pronouns or other anaphoric expressions in the chosen conjunct are to be replaced by their head if this head is in the other conjunct. Normally, this head has to be a proper name. (The problem of extending (G. and) to uses of “and” to connect terms (NPs) will not be discussed here.) Giving, as 1 shall do, (G. and) priority over (G. any), is of course a significant change in (O. any).
The methodological precepts proposed in the first chapter of my book Models for Modalities, D. Reidel, Dordrecht, 1969, still seem to me to be pertinent.
This consequence is spelled out most explicitly in my paper, “Quantifiers in Natural Languages: Some Logical Problems”, in Saarinen, Game-Theoretical Semantics, pp. 81–117, especially pp. 104ff. It is to be noted that the arguments I give there for the conclusion that the set of all grammatical (acceptable) sentences of English is not recursively enumerable rest on certain assumptions that are, according to my own lights, not beyond doubt. However, as we shall see, Chomsky is not challenging these admittedly problematic premises.
Noam Chomsky, Syntactic Structures, Mouton, The Hague, 1957, p. 13.
Ibid., p.17.
Noam Chomsky, Essays on Form and Interpretation, North-Holland, Amsterdam, 1977, p. 202.
Published as Rules and Representations, Columbia University Press, N.Y., 1980. See here pp. 123–27.
The question of the acceptability of (63) should not be confused with the question of the acceptability of such closely related sentences as (i) You must not pick any apple that is red. (ii) You may pick any apple. I have offered an explanation for their grammaticality in Saarinen, Game-Theoretical Semantics, pp. 142–45.
See chapter 7 above.
It is very interesting to see, as we have just seen, that Chomsky himself is trying to deal with the recalcitrant phenomena by means of a rule that depends on a mapping to semantical representations. An unwary reader of, say, Syntactic Structures would have expected him to try to show how the syntactical derivation of the unacceptable strings is impossible. I find this aspect of Chomsky’s new proposal commendable. However, an attempt to give a syntactical account of the phenomena that the any-thesis serves to explain soon leads to grave difficulties. The main semantical peculiarity of “any” is that it interacts with its environment, even beyond the clause it occurs in. An attempt to account for such phenomena syntactically is bound to lead to a conflict with the cyclic principle, which uin effect rules out interaction with such external elements in the application process of syntactical rules.
See Chomsky, Essays on Form and Interpretation, pp. 72–73; and see 57–58.
Indeed, one can hardly avoid here the conjecture that the requisite restrictions do not depend on the transformational situation as much as on the perceptual distance of the output sentence from some underlying pattern of a “normal sentence”.
See my book The Semantics of Questions, especially chapters 8 and 11.
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© 1983 D. Reidel Publishing Company, Dordrecht, Holland
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Hintikka, J. (1983). On The Any-Thesis and the Methodology of Linguistics. In: The Game of Language. Synthese Language Library, vol 22. Springer, Dordrecht. https://doi.org/10.1007/978-94-010-9847-2_9
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