Montague grammar

Montague grammar is an approach to natural language semantics, named after American logician Richard Montague. The Montague grammar is based on formal logic, especially higher order predicate logic and lambda calculus, and makes use of the notions of intensional logic, via Kripke models. Montague pioneered this approach in the 1960s and early 1970s.

Montague's thesis was that natural languages (like English) and formal languages (like programming languages) can be treated in the same way:

There is in my opinion no important theoretical difference between natural languages and the artificial languages of logicians; indeed, I consider it possible to comprehend the syntax and semantics of both kinds of language within a single natural and mathematically precise theory. On this point I differ from a number of philosophers, but agree, I believe, with Chomsky and his associates. (Universal Grammar 1970)

Montague published what soon became known as Montague grammar^[1] in three papers:

• 1970: "Universal grammar" (= UG)^[2]
• 1970: "English as a Formal Language" (= EFL)^[3]
• 1973: "The Proper Treatment of Quantification in Ordinary English" (= PTQ)^[4]

In a 2004 paper,^[5] Chris Barker linked Montague's treatment of quantification to the notion of continuation in programming language semantics.

In popular culture

In David Foster Wallace's novel Infinite Jest, the protagonist Hal Incandenza has written an essay entitled Montague Grammar and the Semantics of Physical Modality. Montague grammar is also referenced explicitly and implicitly several times throughout the book.

See also

• Categorial grammar
• Continuation-passing style
• Kripke semantics
• Situation semantics

References

1. The linguist Barbara Partee credibly claims to have invented the term in 1971 “for the system spelled out in Montague's“ UG, EFL and “especially in PTQ”. See her essay "Reflections of a Formal Semanticist as of Feb 2005", p. 14, footnote 36.
2. "Universal grammar". Theoria 36 (1970), 373–398. (reprinted in Thomason, 1974)
3. "English as a Formal Language". In: Bruno Visentini (ed.): Linguaggi nella società e nella tecnica. Mailand 1970, 189–223. (reprinted in Thomason, 1974)
4. "The Proper Treatment of Quantification in Ordinary English". In: Jaakko Hintikka, Julius Moravcsik, Patrick Suppes (eds.): Approaches to Natural Language. Dordrecht 1973, 221–242. (reprinted in Thomason, 1974)
5. See Continuations in Natural Language, Chris Barker, extended abstract for Fourth ACM-SIGPLAN Continuation Workshop ’04 Venice, Italy

Further reading

• Richmond Thomason (ed.): Formal Philosophy. Selected Papers by Richard Montague. New Haven, 1974, ISBN 0-300-02412-6
• Paul Portner, Barbara H. Partee (eds.): Formal Semantics: The Essential Readings, Blackwell, 2002. ISBN 0-631-21542-5
• D. R. Dowty, R.E. Wall and S. Peters: Introduction to Montague Semantics. Kluwer Academic Publishers, 1981, ISBN 90-277-1142-9
• Emmon Bach: Informal Lectures on Formal Semantics. SUNY Press, 1989, ISBN 0-88706-771-9
• B. H. Partee, A.G.B. ter Meulen and R.E. Wall: Mathematical Methods in Linguistics. Kluwer Academic Publishers, 1990, ISBN 90-277-2245-5
• B. H. Partee with Herman Hendriks: Montague Grammar. In: Handbook of Logic and Language, eds. J.F.A.K. van Benthem and A. G. B. ter Meulen Elsevier/MIT Press, 1997, pp. 5–92. ISBN 0-262-22053-9
• Reinhard Muskens Type-logical Semantics to appear in the Routledge Encyclopedia of Philosophy Online (contains an annotated bibliography).

External links

• A Free Montague Parser in a non-deterministic extension of Common Lisp.
• Montague Grammar in historical context. / The theory and the substance of Montague grammar. Central principles. / Further developments and controversies. by Barbara H. Partee.