The traditional emphasis of linguistic theory on Humboldt’s “infinite use of finite means” has to be based on a characterization of the “finite means,” i.e. the lexicon. What does a language user store in the lexicon, and in what form?
We explore this question in the context of the Parallel Architecture (Jackendoff 2002), which strictly separates phonological, syntactic, and semantic/conceptual structures, and links them by means of interface links. A word consists of a piece of each of these structures, plus interface links between them. In these terms, rules of grammar can be stated as declarative templates or schemas – piece of linguistic structure containing variables. Hence the “rules of grammar” are contained in the lexicon, and “knowledge of language” is represented in a uniform format. As in other constraint-based frameworks, novel utterances are built by instantiating the variables of schemas by the operation of Unification.
Within this outlook, morphology emerges as the grammar of word-sized pieces of structure and their constituents, comprising morphosyntax and its interfaces to word phonology, lexical semantics, and phrasal syntax. Canonical morphology features a straightforward mapping among these components; irregular morphology is predominantly a matter of noncanonical mapping between constituents of morphosyntax and phonology.
An important aspect of morphology is that many, perhaps most of its patterns are not productive. In Relational Morphology, nonproductive patterns can be described in terms of schemas that are formally parallel to those for productive patterns. However, they do not encode affordances for building new structures online; rather, they motivate relations among items stored in the lexicon, which can be formalized as relational links.
Crucially, this relational function is not confined to nonproductive patterns. Productive schemas too can functional relationally within the lexicon; they can be thought of as schemas that have “gone viral.” In other words, the principles used to build novel structures online are simply a subset of the schemas in the lexicon. We conclude that the focus in linguistic theory on the “infinite use of finite means” has deflected attention from a more basic issue: the form of the lexicon and the relationships within it.
This raises the question of how lexical relations are to be expressed. We show that the well-known mechanism of inheritance should be explicated, not in terms of minimizing the number of symbols in the lexicon, but in terms of increased redundancy. We propose a generalization of inheritance to include lexical relations that are nondirectional and symmetrical, and we develop a notation for relational links that pinpoints the regions of commonality between pairs of words, between words and schemas, and between pairs of schemas.
We conclude that linguistic theory should be concerned with relations among lexical items, from productive to marginal, at least as much as with the online construction of novel forms. We further conclude that the lexicon is richly textured, in a fashion that invites comparison with other domains of human knowledge.
https://ase.tufts.edu/cogstud/jackendoff/papers/Jackendoff&Audring_forthcoming_OHMT.pdf (Ray Jackendoff and Jenny Audring)