Handbook of Logic and Languageby Johan F.A.K. van Benthem, Alice ter Meulen
The logical study of language is becoming more interdisciplinary, playing a role in fields such as computer science, artificial intelligence, cognitive science and game theory. This new edition, written by the leading experts in the field, presents an overview of the latest developments at the interface of logic and linguistics as well as a historical perspective.
The logical study of language is becoming more interdisciplinary, playing a role in fields such as computer science, artificial intelligence, cognitive science and game theory. This new edition, written by the leading experts in the field, presents an overview of the latest developments at the interface of logic and linguistics as well as a historical perspective. It is divided into three parts covering Frameworks, General Topics and Descriptive Themes.
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Handbook of Logic and Language
By Johan van Benthem Alice ter Meulen
ELSEVIERCopyright © 2011 Elsevier B.V.
All right reserved.
Chapter OneMontague Grammar
Barbara H. Partee, with Herman L.W. Hendriks
"Montague grammar" is a term that was first applied soon after the untimely death of Richard Montague (September 20, 1930 – March 7, 1971) to an approach to the syntax and semantics of natural languages based on Montague's last three papers (Montague, 1970b,c, 1973). The term may be taken in a narrower or a broader sense, since continuing research has led to a variety of work that can be considered to involve either "developments of" or "departures from" Montague's original theory and practice. In its narrower sense, "Montague grammar", or "MG", means Montague's theory and those extensions and applications of it which remain consistent with most of the principles of that theory. But the boundaries are vague and if taken somewhat more broadly, as the present author (who I believe coined the term) is inclined to do, the term extends to a family of principles and practices which still constitute a large part of the common basis for the field of formal semantics.
The term has never been restricted to Montague's work alone and it should not be, given that Montague was not single-handedly responsible for all of the ideas that were articulated in his papers; others such as David Lewis, Terry Parsons and Max Cresswell were contemporary contributors to more or less the same enterprise, as will be noted below. But Montague's work was particularly influential, in part because of the fact that the three papers just cited give a remarkably clear, concise, and complete statement of a powerful general theory, a good indication of a range of alternative more particular theories and formal tools and three different "fragments" of English that illustrate both the general theory and some of the choices that are available within it.
The plan of this article is to highlight the historical development of Montague grammar as both narrowly and broadly construed, with particular attention to the key ideas that led Montague's work to have such a great impact on subsequent developments. Section 1.2 outlines the historical context of Montague's work, describing earlier traditions in semantics in logic and philosophy that laid some of the foundations for Montague's work and the contrasting traditions in linguistics, against which Montague's work represented a fundamental and controversial change. Section 1.3 provides a selective overview of the basic principles and methodology of Montague grammar as laid out in "Universal Grammar" (Montague, 1970c) and some of the highlights of Montague's best-known and most influential paper, "The Proper Treatment of Quantification in Ordinary English" ("PTQ"; Montague, 1973), with brief remarks about Montague's two other fragments (Montague, 1970b,c). In the final section of the paper we discuss the influence of Montague's work and Montague grammar on subsequent developments and theoretical innovations in linguistics and philosophy, illustrate the evolution from "Montague grammar" to a more heterogeneous but interrelated family of theoretical approaches by tracing progress in several key problem areas and venture an assessment of some of the main achievements and controversies that make up Montague's legacy.
1.2 Montague Grammar in Historical Context
It is important to look at the historical context in which Montague grammar developed, since the history of Montague grammar is also the history of the emergence of a new interdisciplinary field, formal semantics. One might reasonably speak of the Montagovian revolution in semantics as a landmark in the development of linguistics comparable to the Chomskyan revolution in generative grammar. The potential for fruitful interaction among linguists, philosophers and logicians had already existed for some time before Montague's work and some cross-fertilization had already taken place, but not until Montague made his foundational contributions was there a satisfactory systematic and comprehensive framework that could support the explosion of fruitful research on natural language semantics and the syntax-semantics interface that has occurred since the publication of his seminal papers.
1.2.1 Earlier Traditions in Semantics
Contemporary formal semantics has roots in several disciplines, most importantly logic, philosophy, and linguistics. The central figure in its recent history was Richard Montague, a logician and philosopher whose seminal works in this area date from the late 1960s and the beginning of the 1970s. But Montague's work did not occur in a vacuum, and the development of "Montague grammar" and of formal semantics more generally, has involved contributions from many sources before, during and after Montague's work, sometimes in separate historical strands and sometimes in the form of fruitful interdisciplinary collaboration among linguists, philosophers, logicians, and others, the fruits of which are evident in many of the other chapters in this Handbook.
At the time of Montague's work, semantics had been a lively and controversial field of research for centuries and radically different approaches to it could be found across various disciplines. One source of deep differences was (and still is) the selection of the object of study: there are at least as many different kinds of "central questions" as there are ways in which issues involving meaning may be relevant to a given discipline. Desiderata for a theory of meaning come out quite differently if one focuses on language and thought, or on language and communication, on language and truth, or on language "structure" per se. Here we will restrict our attention to the different traditions that fed into Montague grammar, principally logic, "formal philosophy", and generative grammar. The psychologism prevalent in much of linguistics and fundamental to the Chomskyan research program, contrasts with the anti-psychologism explicitly argued by Frege (1892) and prevalent in the traditions of philosophical logic and model theory from which Montague's work arose. This is bound to lead not only to differences in the nature of the questions being asked (although both are concerned with structure and the relation between form and meaning) but also to serious differences about the terms in which answers might be framed.
A more accidental but no less profound source of differences is the research methodology prevalent in the field within which one approaches questions of semantics. Thus Katz and J.A. Fodor (1963) in the early years of generative linguistics concentrated first on "semantic features", using methodology influenced by phonology to study questions of meaning and structure. Where the logician Quine would say: "Logic chases truth up the tree of grammar" (1970, p. 35), Katz and Fodor were equally seeking a compositional account of how the meanings of sentences were determined from the meanings of the smallest parts and the syntactic derivation of the whole from those parts, but they conceived of semantic projection rules chasing "features", not truth, up the tree of grammar, analyzing meanings as representable in terms of complexes of features rather than in terms of truth conditions. This was the practice David Lewis was deploring on the first page of his 1970 paper "General Semantics":
But we can know the Markerese translation of an English sentence without knowing the first thing about the meaning of the English sentence: namely, the conditions under which it would be true. Semantics with no treatment of truth conditions is not semantics. Translation into Markerese is at best a substitute for real semantics, relying either on our tacit competence (at some future date) as speakers of Markerese or on our ability to do real semantics at least for the one language Markerese.
I believe linguists did presuppose tacit competence in Markerese and moreover took it to represent a hypothesis about a universal and innate representation, what Jerry (J.A.) Fodor later dubbed the Language of Thought (e.g., Fodor, 1975), and therefore not in need of further interpretation (see Jackendoff, 1996, for a contemporary defense of a similar view). The problems that resulted and still result, however, from making up names for operators like "CAUSE" or features like "AGENT" without addressing the formidable problems of defining what they might mean, are evident whenever one looks at disputes that involve the "same" operators as conceived by different linguists or in the analysis of different languages or even different constructions in the same language.
To a philosopher like Vermazen (1967) or Lewis (1970), the language of "markerese" looked empty. To the generative linguist, the concern with truth seemed puzzling: the concern was with mental representation, because semantics was part of the language faculty, the explication of which was the linguist's central concern. The interpretation of (the innate) semantic primitives would be in terms of concepts and the study of details of such interpretation might relate to semantics in something like the way phonetics relates to phonology, involving an interface at which linguistic and non-linguistic (but still psychological) factors might intermingle. "Actual" truth was taken to be irrelevant to semantics and the richer conception behind the notion of truth conditions and entailment relations did not come to be widely appreciated within linguistics for some time. Linguists in the 1960s and early 1970s sought accounts of synonymy, antonymy, anomaly and ambiguity, structural notions that concerned such things as how many meanings a given sentence had and which meanings were shared by which sentences. These were kinds of questions which largely concerned sameness and difference of meaning and ways in which meanings are structured and therefore might be fruitfully addressed in terms of representations. Linguistic studies of lexical meaning were sometimes concerned with paraphrase and metonymy, but this did not generalize to any systematic attention to inference or entailment. The increasing influence of truth-conditional semantics on linguistics therefore led to a concomitant gradual shift in the nature of the questions linguists might ask about meanings and not only to a change in the arsenal of tools available for digging out answers.
The truth-conditional tradition in semantics has its source in the work of those logicians and philosophers of language who viewed semantics as the study of the relation between language on the one hand and whatever language is about on the other, some domain of interpretation which might be the real world or a part of it, or a hypothesized model of it, or some constructed model in the case of an artificial language. Such philosophers and logicians, at least since Frege, have tended strongly to view semantics non-psychologistically, making a distinction between language and our knowledge of it and generally taking such notions as reference, truth conditions and entailment relations as principal data a semantic description has to get right to reach even minimal standards of adequacy.
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