Page 366 - Encyclopedia of Philosophy of Language

Formal Semantics
necessity (see Davies 1978). One apparent advantage of the 'weak necessity' option is that it permits a very direct formulation of typical essentialist claims. The claim that Socrates is necessarily human, for example, is the claim that it is not possible that Socrates should exist without being human. One disadvantage is that the 'weak necessity' option provides no way of expressing claims of necessary existence.
Given the actualist interpretation of the quantifiers, and the interpretation of 'D' as expressing strong necessity, the converse Barcan formula at (14) above also fails. Intuitively, the reason is as follows. It may be that, for every world w, all the objects that exist at w have a certain property P at w, but that some object that exists at a world w' fails to exist at another world w" and furthermore lacks property P at w".
See also: Formal Semantics; Necessity; Possible Worlds.
Bibliography
Aqvist L 1984 Deontic logic. In: Gabbay D, Guenthner F 1984
Boolos G 1979 The Unprovability of Consistency. Cambridge University Press, Cambridge
Boolos G, Jeffrey R 1989 Computability and Logic, 3rd edn. Cambridge University Press, Cambridge
Bull R, Segerberg K 1984 Basic modal logic. In: Gabbay D, Guenthner F 1984
Chellas B F 1980 Modal Logic An Introduction. Cambridge University Press, Cambridge
Davies M K 1978 Weak necessity and truth theories. Journal of Philosophical Logic T. 415-39
Fine K 1978 Model theory for modal logic. Part I: The
de re/de dicto distinction. Journal of Philosophical Logic
7:125-56
Forbes G 1985 The Metaphysics of Modality. Oxford Uni-
versity Press, Oxford
Forbes G 1988 Languages of Possibility An Essay in Philo-
sophical Logic. Basil Blackwell, Oxford
Gabbay D, Guenthner F 1984 Handbook of Philosophical
Logic, vol. 2. Extensions of Classical Logic. Reidel, Dor-
drecht
Hughes G E, Cresswell M J 1968 An Introduction to Modal
Logic. Methuen, London
Hughes G E, Cresswell M J 1984 A Companion to Modal
Logic. Methuen, London
Kripke S A 1963 Semantic considerations on modal logic.
Acta Philosphica Fennica 16: 83-94
Kripke S A 1980 Naming and Necessity. Basil Blackwell,
Oxford
Lemmon E J, Scott D S 1977 The 'Lemmon Notes' An Intro-
duction to Modal Logic. Basil Blackwell, Oxford
Lewis C I 1912 Implication and the algebra of logic. Mind
21: 522-31
Lewis C I, Langford C H 1932 Symbolic Logic. Century,
New York. 2nd edn., 1959, Dover, New York
Marcus R B 1962 Interpreting quantification. Inquiry 5:252-
59
Montague R 1963 Syntactical treatments of modality. Acta
Philosophica Fennica 16: 153-67
Plantinga A 1974 The Nature of Necessity. Oxford University
Press, Oxford
Quine W V O 1960 Word and Object. MIT Press, Cambridge,
MA
Quine W V O 1976 Three grades of modal involvement. In:
The Ways of Paradox and Other Essays. Harvard Uni-
versity Press, Cambridge, MA
Smiley T J 1963 The logical basis of ethics. Acta Philosophica
Fennica 16: 237-46
Montague grammar is a model for grammar that deals with the syntax and semantics of natural language. The emphasis lies on phenomena that are interesting from a semantic point of view (see Sect. 2). A salient aspect of Montague grammar is its methodology, which is characterized by the principle of com- positionality of meaning (Sect. 3). This methodology has as a consequence that there is a systematic relation between syntax and semantics: though distinct, they are forced to remain in step with each other. Mon- tague grammar constituted a fundamentally new approach to the semantics of natural language because of this systematic relation and the application of methods from mathematical logic (Sect. 1). Semantics
is, in Montague grammar, model-theoretic semantics (Sect. 4). Meanings are formalized as intensions (Sect. 5), and represented using intensional logic (Sect. 6). An impression of Montague's most influential article (Montague 1973) is given in Sects. 6 and 7. An over- view of the subsequent developments is given in Sect. 8.
1. Historical Background
Montague grammar emerged around 1970, and con- stituted a fundamentally new approach to the sem- antics of natural language. In order to understand the importance of this approach, it is useful to consider the situation in that period of some neighboring disci-
344
Montague Grammar T. M. V. Janssen