Grammaire Formelle, Grammaire Générative et Grammaire

In this paper I analyze the significance of two theorems of formal grammar theory for generative grammar: Peters and Ritchie's theorem about undecidability of membership for transformationnal languages and Parikh's theorem about existence of inherently ambiguous context-free languages. My analysis supports a general thesis which concerns not only the application of the whole formal grammar theory to generative grammar, but any application of mathematics to grammar. This thesis is the following: one cannot expect that mathematics helps to discover any deep and interesting property of human language but, on the other hand, a mathematical study of the descriptive and notional apparatus of grammars is a compulsory methodological preliminary. In other words mathematical linguistics provides a theory of control for the devices, the concepts and the aims of grammatical theories. This is so because mathematical linguistics, and formal grammar especially, is developed to study linguistics facts already represented. And this representation 1) is far from being neutral or "objective" and 2) forces grammars to be algorithms.Section 5 of the paper is a discussion of the features, bounded to the representation, which are implicitly admitted in the major part of grammatical approaches. Readers who remember the content of Peters and Ritchie's theorem and Parikh's theorem can omit the beginings of sections 3 and 4. Section 2 is a very sketchy overview of contemporary mathematical linguistics.