Chomsky Meets Lambek
In this paper I will examine the relationship between Chomsky’s Minimalist Program and Lambek’s Categorial Grammar. The two formalisms appear to have nothing in common—their ontologies are different, the degree of formalization of the framework is much higher in Lambek’s Calculus than in Chomsky’s Minimalist Program, the representation of the relationships among the units and the way problems are handled vary sharply between them. Even the concept of what a grammar is is radically disparate.
Nevertheless, the evolution of strategies in Chomskyan Generative Grammar has similarities with the evolution of aspects that are central to Categorial Grammar, and central to Lambek’s framework. For instance, the Merge operation in Chomsky’s Minimalist Program can be understood as an unformalized version of Categorial Grammar’s Functional Application. More recently, Chomsky has proposed substituting “doublings” for movement, which coincides with the spirit of Extensions in Lambek’s Calculus. More generally, by dropping different levels of representation and the transformations that operated among them, Chomsky has proposed a “flat” conception of grammar that is more similar to the one proposed by Lambek’s followers in Categorial Grammars.
On the other hand, some of Chomsky’s Minimalist proposals could provide interesting new directions for Categorial Grammarians. One area would be to find a set of metagrammatical universals. For instance, we might consider the very general operations that exist among the strings that are needed in order to perform the operators for building up Types to be Formal Universals: e.g., Concatenation Operators, as defined in Lambek Calculus, or Discontinuous Operators, first proposed by Moortgat (1988), and developed in Solias (1992), Morrill and Solias (1993), Morrill (1995), and Solias (1998), among others.