# Montague, Richard (1930–1971)

# MONTAGUE, RICHARD

*(1930–1971)*

Richard M. Montague, a logician who taught in the Philosophy Department at the University of California at Los Angeles from 1955 until his premature death in 1971, is probably best known for his contributions to linguistic semantics, although he also made important contributions to mathematical logic and philosophy.

Montague was born in 1930. He attended the University of California at Berkeley both as an undergraduate and a graduate student, concentrating not only in mathematics and philosophy, but in Semitic languages. Working with Alfred Tarski, he completed a doctoral dissertation in 1957 entitled "Contributions to the foundations of axiomatic set theory." By that time he had published a large number of papers in various areas of mathematical logic.

Montague's interests in mathematical logic were general and included set theory, proof theory, model theory, and abstract recursion theory. One early theme in his work in mathematical logic concerned the consequences of semantic reflection for axiomatic versions of set theory and other mathematical theories. That work has been widely cited and is still important.

The work for which Montague is best known was carried out late in his life (beginning with the 1968 publication of "Pragmatics") and dealt with the development of logics intended to serve as vehicles for the interpretation of natural language and the formalization of philosophy. From Tarski, Montague inherited the view that semantical theories could and should be formulated with mathematical precision. However, his project of applying Tarski's techniques to natural language seems to derive more naturally from the work of Rudolf Carnap and Alonzo Church.

Both Carnap and Church worked with a framework for logical formalization, which, although it was developed in connection with the language of mathematical theories, was clearly more broadly applicable. Carnap was mainly interested in using formalization as a tool for clarifying philosophy. Church considered what he called the "logistic method"—that is, the method of logical formalization developed in the first half of the twentieth century—to be applicable in a more general linguistic setting.

Carnap and Church both addressed a major obstacle standing in the way of generalizing Tarskian semantic theories to natural language—the problem of intensionality (which had already been raised by Gottlob Frege). Carnap explored how what are now called possible worlds could be used to model intensionality, while Church sought to formalize Frege's theory of sense and denotation. Influences of both can be seen in Montague's logical framework for interpreting natural language. Like Carnap, Montague appealed to possible worlds, and, like Church, he used higher-order logic. Montague's insight that a logic combining possible worlds with higher-order logic provided a flexible and powerful tool for natural language semantics proved to be fundamentally important.

All of Montague's publications concerning "Montague Grammar" are collected together in *Formal Philosophy: Selected Papers of Richard Montague* (1974). These papers develop the logical framework of "intensional logic." This is a higher-order logic involving on a system of types based on three primitive domains: entities (type e), possible worlds, and the two truth values T and F (type t). If σ and τ are types, then <σ,τ> is also a type and corresponds to the set of functions from the domain of σ to the domain of τ. Thus, for instance, <e,t> is the type of functions from entities to truth values. If σ is a type, then <s,σ > is also a type and corresponds to the set of functions from possible worlds to the domain of σ: <s, <e,t>>, then, is the type of intensions of sets of entities. For a book-length, systematic treatment of intensional logic, see Daniel Gallin's *Intensional and Higher-Order Logic* (1975).

A Montague grammar for a fragment of a language consists of a syntactic account of that fragment, which defines a set of syntactic structures showing how complex phrases are decomposed into components, and a semantic component that shows how a semantic value can be assigned to the structure given an assignment of values to the lexical items occurring in the structure. These values belong to the domains of a model of intensional logic. Intensional logic can serve as an intermediary in the mapping of syntactic structures to values, and as a vehicle for formulating postulates about the meanings of lexical items. This mapping conforms to a correspondence between grammatical categories like "Sentence" and "Noun-Phrase" and the types of intensional logic.

To see how the idea might work, consider the sentence "John wants a car." The noun phrase 'a car' has type <<e,t>,t>; it denotes the set of sets containing at least one car. (The insight that noun phrases denote sets of sets goes back to Frege's 1884 work, *The Foundations of Arithmetic*.) The verb 'wants' corresponds to a function that inputs the intension of a Noun-Phrase denotation and returns a function from entities to truth values. Give this function the intension of 'a car' and it returns a function saying of each entity whether that entity wants a car. The type of 'wants' is therefore <<s, <<e,t>,t>>, <e,t>>. Barbara Partee and Herman L. W. Hendriks provide a useful extended survey of Montague's semantic framework and its subsequent influences in their 1996 essay "Montague Grammar."

Montague himself saw intensional logic and his theory of language as a basis of formalizing philosophy, but the most important direct influence of his work was on the development of linguistic semantics, where its impact was enormous. Montague's semantic techniques can be associated with any generative syntactic framework; his syntactic approach has been less influential, outside of subsequent work in the categorical grammar framework. (See Jacobson 1996, for example.)

Although few philosophers would agree that the goal of formalizing philosophy is enabled by Montague's work, foundational questions raised by his approach have preoccupied and shaped subsequent work in analytic metaphysics and philosophy of language. Much of this influence is indirect, occurring through the work of David Lewis, who attended Montague's courses at UCLA and was influenced by his ideas.

Because of Montague's uncompromising emphasis on the technical dimension, his papers are difficult reading. But even now, they repay careful study. The linguistic papers and other philosophically relevant work were compiled in 1974 in *Formal Philosophy: Selected Papers of Richard Montague*. Further biographical information concerning Montague can be found in Anita and Solomon Feferman's biography of Tarski, *Alfred Tarski: Life and Logic* (2004).

** See also ** Artificial and Natural Languages; Carnap, Rudolf; Church, Alonzo; Computability Theory; Frege, Gottlob; Lewis, David; Logic, History of: Modern Logic; Mathematics, Foundations of; Modal Logic; Model Theory; Proof Theory; Semantics, History of; Set Theory; Tarski, Alfred; Type Theory.

## Bibliography

Carnap, Rudolf. *Meaning and Necessity*. 2nd ed. Chicago: University of Chicago Press, 1956. The first edition was published in 1947.

Church, Alonzo. "The Need for Abstract Entities in Semantic Analysis." *Proceedings of the American Academy of Arts and Sciences* 80 (1951): 100–112.

Church, Alonzo. *Introduction to Mathematical Logic*. Vol. 1. Princeton, NJ: University of Princeton Press, 1959.

Church, Alonzo. "Outline of a Revised Formulation of the Logic of Sense and Denotation (Part I)." *Nous*, 7 (1973): 24–33.

Church, Alonzo. "Outline of a Revised Formulation of the Logic of Sense and Denotation (Part II)." *Nous*, 8 (1974): 135–156.

Feferman, Anita Burdman, and Solomon Feferman. *Alfred Tarski: Life and Logic*. Cambridge, U.K.: Cambridge University Press, 2004.

Frege, Gottlob. *The Foundations of Arithmetic*. 2nd ed. Translated by J. L. Austin. Oxford, U.K.: Oxford University Press, 1953. Originally published in 1884.

Furth, Montgomery, C. C. Chang, and Alonzo Church. "Obituary of Richard M. Montague." Unpublished manuscript. Los Angeles: University of California at Los Angeles Department of Philosophy, 1971.

Gallin, Daniel. *Intensional and Higher-Order Logic*. Amsterdam: North-Holland, 1975.

Jacobson, Paulene. "The Syntax/Semantics Interface in Categorical Grammar." In *The Handbook of Contemporary Semantic Theory*, edited by Shalom Lappin, 89–116. Oxford, U.K.: Blackwell Publishers, 1996.

Montague, Richard. *Formal Philosophy: Selected Papers of Richard Montague*. New Haven, CT: Yale University Press, 1974. Edited and with an introduction by Richmond H. Thomason.

Partee, Barbara H., with Herman L. W. Hendriks. "Montague Grammar." In *Handbook of Logic and Language*, edited by Johan van Benthem and Alice ter Meulen, 5–91. Amsterdam, Netherlands: Elsevier Science Publishers, 1996.

*Richmond H. Thomason (2005)*

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