The ubiquity of order in the first categorial grammars

Among the differences which divide the two trends of formal grammars of the 20th century, those dealing with word order have remained until now hardly analysed. However, the conception of word order in the first categorical grammars (from 1935 to 1959) contrasts strongly with Chomsky's transformational model (1957) and their originality in this respect requires careful examination. Indeed, Ajdukiewicz's syntax (1935), Bar-Hillel's bidirectional grammar(1953) and Lambek's associative syntactic calculus (1958, 1959) agree on handling order by having it intervene at all levels of analysis simultaneously. This paper clarifies the treatment of word order in these three categorical grammars and compares them in order to establish at a conceptual level the significance of their respective contributions to the formalization of order.