Creation myths of generative grammar, and the mathematics underlying Syntactic Structures∗

SS) inaugurated a fifty-year period during which the great majority of theoretical syntactic inves-tigation done in the USA, and even worldwide, concentrated on a single underlying view of how syntax should be scientifically regarded. In the years after 1957, it was standard to take a sentence to be a sequence of words associated with some kind of description of its structure; to ‘consider a language to be a set (finite or infinite) of sentences, each finite in length and constructed out of a finite set of elements’; and to take a grammar to be ‘a device that generates all of the grammatical sequences... and none of the ungrammatical ones ’ (SS: 13). Generating a sentence meant pro-viding the possibility of constructing it by means of a procedure defined by the grammar, just as the arithmetical procedure ‘take an integer and multiply it by itself ’ can be said to generate the set of perfect squares. Structural descriptions of sentences were taken to be derivational histories — sequences of steps through which a sentence could be derived.1 The impact of SS on American linguistics has often been compared to a scientific revolution in the sense of Kuhn. The proposals in the book convinced many linguists in the 1950s and early 1960s to turn their intellectual lives around and take up a new conception of their subject. Lasnik (2000) builds a graduate course in syntax on the content of SS together with some much mor