Vergauwen, A Metalogical Theory of Reference, 2.3.2 Principles of a Montague Grammar, 2.3.2.1 Introduction

by Corry Shores
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Roger Vergauwen

A Metalogical Theory of Reference: Realism and Essentialism in Semantics

Chapter 2: Reference and Theory of Reference

2.3.2 Principles of a Montague Grammar

2.3.2.1 Introduction: an ambitious program

The advances in logical semantics proved relevant to studies on natural languages. Chomsky for example showed how a language's grammar involves 'rewrite rules' that generate sentences from basic grammatical categories. These rules "explicitly represent the internal structure of the sentence." (22b) In terms of describing semantics, generative grammar was too vague. As a result, generative semantics broke-off to remedy the problem. It uses elementary predicate logic to link semantic elements to the deep grammatical structure. However this effort never produced an adequate theory explaining the relation between syntax and semantics.

Chomsky's approach sought-out our innate linguistic capacities. Montague's approach however was not concerned with such psychological issues. He argued that there is no fundamental difference between natural language and the formal languages of logic. So in fact there is a mathematically precise way to describe the relation between syntax and semantics. This is his notion of a "universal grammar." It seeks a uniform treatment for both natural and artificial formal languages. And he makes use of Tarski's concept of truth-conditional semantics. We use models to establish these conditions. To do so, we make use of a semantic metalanguage expressed through an intensional logic. (Vergauwen will return to this notion in the fourth chapter.)

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Vergauwen, Roger. A Metalogical Theory of Reference: Realism and Essentialism in Semantics. London: University Press of America, 1993.