A Formal Universal of Natural Language Grammar

This paper proposes that the possible word-orders for any natural language construction composed of n elements, each of which selects for the category headed by the next, are universally limited both across and within languages to a subclass of permutations on the “universal order of command” 1, . . . n, as determined by their selectional restrictions. The permitted subclass is known as the “separable” permutations, and grows in n as the Large Schröder Series {1, 2, 6, 22, 90, 394, 1806, . . . }. This universal is identified as formal because it follows directly from the assumptions of Combinatory Categorial Grammar (CCG)—in particular, from the fact that all CCG syntactic rules are subject to a Combinatory Projection Principle that limits them to binary rules applying to contiguous non-empty categories.

The article presents quantitative empirical evidence in support of this claim from the linguistically attested orders of the four elements Dem(onstrative), Num(erator), A(djective), N(oun) that have been examined in connection with various versions of Greenberg’s putative 20th Universal concerning their order. A universal restriction to separable permutation is also supported by word-order variation in the Germanic verb cluster, and in the Hungarian verb complex, among other constructions.