1970年發表的《普通英語中量化的特定處理》（The Proper Treatment of Quantification in Ordinary English），提出對自然語言所作的精密化、形式化研究的模式，奠定這一理論的基礎。後來在麻省理工學院、得克薩斯大學、斯坦福大學和俄州立大學都建立基地，以麻省理工學院的帕蒂Barbara Partee和巴赫Emmon Bach最有成就。蒙太格把語言學看作數學的分支，主張採用數學中的遞歸定義來描寫並解釋自然語言和人造語言（邏輯語言），並提出用內涵邏輯來描寫語義並使之形式化。它有三個分支：句法學、語義學和語用學。句法部分主要通過一套規則把小單位組合成大單位。語用部分把句法部分翻譯成內涵邏輯表達式，這一表達式最終可以在語義部分通過語義規則對句子作出模型論的解釋。
The American philosopher and logician Richard Montague, though not a professional linguist, exercised a major influence on semantics in the 1970s and 1980s. Montague was one of the first people systematically to explore the possibilities of a completely rigorous formal analysis of both the syntax and the semantics of natural languages along the lines of logic. The model he created, which is commonly referred to as Montague grammar, has set a standard both with respect to empirical coverage as well as degree of formalization, against which analyses and alternative frameworks are still measured.
The term ‘Montague grammar’ is commonly used to refer to the specific proposal Montague made in his seminal paper The Proper Treatment of Quantification in Ordinary English (1970, first published in 1973). Strictly speaking this is misleading, since Montague wrote a whole series of papers on the application of logic in the analysis of natural language, which differ in their set-up and details. However, the common core of the analyses proposed in the various papers is substantial enough to justify the reference ‘Montague grammar’ tout court.
Montague’s work constitutes a decisive break away from the traditional view that natural languages are too vague and too unsystematic to be treated formally, in the same way as the formal languages of logic and mathematics. This position, which in the history of modern philosophy goes back at least to Russell, Frege, and Tarski, was predominant in philosophy and logic well into the 1970s, although there were some noticeable exceptions. One of them was Hans Reichenbach who in 1947 had already devoted a substantial part of his Elements of Symbolic Logic to the logical analysis of natural language constructions.
A rigorously formal theory of the syntax of a language is a prerequisite for any formal semantics of it, and the apparent impossibility of such a theory of the syntax of natural languages was one of the reasons why Tarski, the founding father of model-theoretic semantics in logic, thought that his semantic methods could never be applied to them. From the rapid developments in generative linguistics in the 1960s and early 1970s, men like Montague, Donald Davidson, David Lewis, and others gained confidence that a formal syntactic theory of natural language was no pipedream, and that, therefore, a formal semantics might also prove to be a possibility.
Although the work in generative linguistics thus constituted an important impetus for the development of formal, model-theoretic semantics for natural language, this is not to say that this undertaking met with much enthusiasm in generative linguistic circles. On the contrary, whereas people like Montague and Davidson were of the opinion that not just the syntax but also the semantics of natural languages can be studied in a precise, formal fashion, this view has remained far from common among generative linguists.
Montague’s work itself forms part of a development which includes the work of Davidson, Lewis, Cresswell and many others. Its characteristics, which to a greater or lesser degree distinguish it from the work of others, are, first of all, the generality and rigor with which Montague carried out his analyses; second, his ample use of whatever logical machinery he deemed necessary; and third, the way in which he combined syntax and semantics.
To start with the first characteristic, in his paper Universal Grammar (1969, published 1970), Montague develops a completely general theory of syntax, semantics and pragmatics of both formal and natural languages, which to a great extent is orthogonal to the specific kind of formal apparatus that one may used in carrying out specific analyses. Although pragmatics in Montague’s sense is a limited area, which roughly coincides with the semantics of indexical and context-dependent expressions, such as pronouns, this general theory may properly be called a ‘logical semiotics.’ The various concrete models which Montague worked out in separate papers are among its instances, as are a score of other approaches. The generality and rigor of the Universal Grammar model make Montague’s views on syntax, semantics, pragmatics and their relationships formally explicit and perspicuous, yet also difficult to fathom.
The second characteristic of Montague’s work is that in describing the semantical behavior of expressions and constructions of natural language, Montague is not bothered by any a priori restrictions on the kind of logical tools he allows himself. Thus he makes ample use of Intentional Logic and Type-Theory, without being bothered by the philosophical and methodological problems that according to some surround the use of these tools. This distinguishes Montague for example from his contemporary Davidson, for whom the use of intentional logic constitutes an extravaganza which has to be rejected on philosophical grounds. Subscribiing to Wuine’s qualms about intentional entities, Davidson feels that the semantics of natural language should be described in terms of extensional, first-order logic, and he dismisses other attempts as follows: ‘There is even a danger that the know-nothings and the experts will join forces; the former, hearing mutterings of possible worlds, trans-worlds, anyway;. Although most semanticists have followed Montague in availing themselves of whatever tools they need, this free use of very powerful tools became balanced during the 1980s by an interesting interest in the semantical expressive power of natural language, i.e., in research on the question of which part of the logical apparatus that one uses is actually needed in the description of natural language. In particular in the context of generalized quantifier theory, of which Montague’s analysis of quantified expressions in ‘The Proper Treatment of Quantification in Ordinary English’ forms one of the starting points, this has led to interesting insights in the differences between natural and formal languages.
The third feature which is characteristic of Montague’s work, and the tradition that followed him, is the way in which syntax and semantics are combined. The core of Montague’s views on this matter is captured by the so-called ‘principle of compositionality of meaning’. This principle can be paraphrased roughly as follows: the meanings of its parts. IT is often referred to as ‘Frege’s principle,’ since it bears an obvious resemblance to the principle of compositionality for extensions which forms the heart of Frege’s solution of the problem of multiply-quantified judgments, but whether this ascription is historically correct is a matter of debate. The current interpretation of the status of the compositionality principle is that of a methodological principle, rather than an empirical hypothesis. A compositional account of a certain type of expression involves both a syntactic and a semantic analysis: he former determines what counts, as the parts of the expression, the latter establishes what the corresponding meanings are.
Natural language was only one of the topics Montague worked on. The majority of his work was on problems in set theory and logic. He also wrote some papers on topics in philosophical analysis, which together with his papers on natural language and papers on modal logic are collected in Montague.
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Max W Wheeler, Reader in Linguistics, is a leading expert on the Catalan language, and researches on phonology and on change in inflectional morphology. He is currently preparing a book on the phonology of Catalan for the Oxford University Press's series The Phonology of the World's Languages. He is joint editor of the electronic Journal of Catalan Studies
A category, in the sense relevant here is a class or division in general scheme of classification.
In modern work the work ‘feature’ is used for a set of mutually exclusive properties of words or phrases. A feature NUMBER might be postulated with singular, dual, and plural as its possible ‘values’. A feature paired with a value can be called a ‘feature specification’. (Intuitively, NUMBER is like a question to which ‘singular’, ‘dual’, and ‘plural’ are the different possible answers, and a feature specification is like a question paired with an answer.) The notation F:v will be used in this article to indicate that the feature F has the value v. Thus the feature specification NUMBER:plural would be a grammatical device to indicate that the feature NUMBER has plural as its value, hence that the expression having that feature specification as part of its grammatical representation is a plural noun rather that a singular or dual one. In phonology a different notation for feature specifications is familiar; ‘[+VOICE]’ would be used where the notation in this article uses ‘VOICE:+’ to indicate that VOICE has the positive value ‘+’.