Some formal considerations on the generation of hierarchically structured expressions

In this note we define a machine that generates nests. The basic relations commonly attributed to linguistic expressions in configurational syntactic models as well as the device of chains postulated in current transformational grammar to represent distance relations can be naturally derived from the assumption that the combinatorial syntactic procedure is a nesting machine. Accordingly, the core of the transformational generative syntactic theory of language can be solidly constructed on the basis of nests, in the same terms as the general theory of order, an important methodological step that provides a rigorization of Chomsky’s minimalist intuition that the simplest way to generate hierarchically organized linguistic expressions is by postulating a combinatorial operation called Merge, which can be internal or external. Importantly, there is reason to think that nests are a useful representative tool in other domains besides language where either some recursive algorithm or evolutionary process is at work, which suggests the unifying force of the mathematical abstraction this note is based on.