Abstract
The grammatical and semantical theories of the late Richard Montague present us with a most interesting treatment, perhaps the most interesting existing treatment, of certain aspects of the syntax and semantics of natural languages.1 These theories are not satisfactory in their present form, however, not even if we restrict our attention to those linguistic phenomena that Montague himself primarily wanted to cover, together with certain closely related phenomena. The most central of these seems to be the variety of ways in which quantification is represented in natural languages. This concern is highlighted by the title of Montague’s last published paper, The Proper Treatment of Quantification in Ordinary English’. In my own paper, I shall concentrate on the nature of natural-language quantifiers for the same reasons as Montague. In view of the importance of the problem of treating natural-language quantifiers, it is in order to point out and to discuss a number of shortcomings of Montague semantics in this department. It is of course the very precision and force of Montague’s treatment that lends a special interest to these shortcomings. Just because Montague was so successful in carrying out certain general strategic ideas in the formal theory of language, the shortcomings of his treatment point to general morals in the theory and methodology of linguistics and of the logical analysis of natural language.
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Notes
See the following papers by Montague: ‘Pragmatics’, in Contemporary Philosophy: A Survey (ed. by Raymond Klibansky), La Nuova Italia Editrice, Florence, 1968, pp. 102–122
‘On the Nature of Certain Philosophical Entities’, The Monist 53 (1969), 159–194
‘English as a Formal Language’, in Linguaggi nella societa e nella tecnica (ed. by Bruno Visentini et al), Milan, 1970, pp. 189–22
‘Universal Grammar’, Theoria 36 (1970), 373–398
‘Pragmatics and Intensional Logic’, in Semantics of Natural Language (ed. by Donald Davidson and Gilbert Harman), D. Reidel, Dordrecht, 1972, pp. 142–168
‘The Proper Treatment of Quantification in Ordinary English’, in Approaches to Natural Language (ed. by Jaakko Hintikka, Julius M. E. Moravcsik, and Patrick Suppes), D. Reidel, Dordrecht and Boston, 1973, pp. 221–242.
Cf. also Richard Montague’s shorter papers and notes on related topics, including ‘Comments on Moravcsik’s Paper’ in Approaches to Natural Language, pp. 289–294
(together with Donald Kalish) ‘That’, Philosophical Studies 10 (1959), 54–61
‘Logical Necessity, Physical Necessity, Ethics, and Quantifiers’, Inquiry 4 (1960), 259–269. The development of Montague’s views on the foundations of logic and linguistics was not without sharp turns, however. At one point he rejected altogether intensional logic as a viable tool of logical, philosophical, and grammatical analysis. This rejection was not recorded in print, however.
(Cf. nevertheless his paper,‘Syntactical Treatments of Modality’, Acta Philosophica Fennica 16 (1963), 153–167.)
Cf., e.g., ‘Pragmatics and Intentional Logic’ on the specification of intensions.
Cf., e.g., ‘English as a Formal Language’, pp. 202–203.
Cf., e.g., PTQ, pp. 233–234 and passim.
See my paper, ‘Carnap’s Semantics in Retrospect’, Synthese 25 (1972–73), 372–397.
See Chapter 5, entitled ‘Denoting’, in The Principles of Mathematics, Allen and Un win, London, 1903, pp. 53–65. Peter Geach finds further anticipations in the medieval literature; see Logic Matters, Blackwell, Oxford, 1972, pp. 6, 8.
Cf., e.g., ‘English as a Formal Language’, p. 193, and PTQ, p. 231.
Cf. ‘On the Nature of Certain Philosophical Entities’.
Knowledge and Belief, Cornell University Press, Ithaca, N.Y. 1962, Ch. 6; ‘The Modes of Modality’, reprinted in my Models for Modalities, D. Reidel, Dordrecht, 1969, Ch. 5.
This important distinction has not yet received the systematic modern treatment it amply deserves. See nevertheless my Models for Modalities, pp. 120–121.
See PTQ, p. 230.
This was in fact allowed in Montague’s earlier formulations. Cf., e.g., ‘Pragmatics and Intensional Logic’, p. 146.
Other reasons were given (however sketchily) for this kind of treatment in my paper ‘The Semantics of Modal Notions and the Indeterminacy of Ontology’, in Semantics of Natural Language (ed. by Donald Davidson and Gilbert Harman), D. Reidel, Dordrecht and Boston, 1972, pp. 398–414.
This is the starting-point of Peter Geach’s problem of ‘intentional identity’, cf. Logic Matters, Blackwell Oxford, 1972, Ch. 4.4.
Cf. my ‘On the Logic of Perception’ in Models for Modalities (note 11).
Cf. my ‘Existential Presuppositions and Uniqueness Presuppositions’ (note 17).
See ‘On the Logic of Perception’ (note 20).
Cf. ‘Existential Presuppositions and Uniqueness Presuppositions’ (note 17).
In ‘English as a Formal Language’, p. 217, Montague mentions that “English has... certain... devices for reducing ambiguity.” He lists several, including the peculiar behavior of ‘any’. Unfortunately.neither Montague’s diagnosis of the reasons for the peculiar behavior of ‘any’ (it is alleged to have the maximal scope) nor the cure he prescribes (changing the syntactical rules for other quantifiers) are correct, it seems to me.
Notice that this problem is not solved by the procedure Montague advocates in ‘English as a Formal Language’, p. 217 (see the preceding footnote).
See George Lakoif, ‘On Generative Semantics’, in Semantics: An Interdisciplinary Reader (ed. by Danny D. Steinberg and Leon A. Jakobovits), Cambridge University Press, Cambridge, 1971, pp. 232–296, especially pp. 240–246. Notice that their effects on the scopes of quantifiers can always be gathered from the surface structure, however.
Cf. Edward S. Klima, ‘Negation in English’, in The Structure of Language (ed. by Jerry A. Fodor and Jerrold J. Katz), Prentice-Hall, Englewood Cliffs, N.J., 1964, pp. 246–323. especially pp. 276–280.
I am in the process of trying to develop one, based on what I call the game-theoretical semantics for natural-language quantifiers. Cf. ‘Quantifiers vs. Quantification Theory’, Linguistic Inquiry (forthcoming).
Klima’s theory (note 28) correctly predicts that ‘any’ has existential force in (16). It fails for other reasons, however, and hence does not offer an acceptable way out here. Montague was right, it seemed to me, in holding that ‘any’ has only the force of a universal quantifier, Klima notwithstanding.
See, e.g., Noam Chomsky, ‘Deep Structure, Surface Structure, and Semantic Interpretation’, in Semantics (note 26), pp. 183–216, especially pp. 187–188.
See note 29.
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Hintikka, J., Hintikka, M.B. (1989). On the Proper Treatment of Quantifiers in Montague Semantics. In: The Logic of Epistemology and the Epistemology of Logic. Synthese Library, vol 200. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-2647-9_7
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