ABSTRACT
Language presents paradigmatic regularities, together with the usual syntagmatic ones that syntax is designed to capture. This chapter proposes a way of deriving systematic hierarchies by analyzing linguistic categories through the algebraic structure of numbering systems (hence by way of dimensions, each recursively defined on the previous). The goal is not to equate “vertical” structuring and “horizontal” syntax, but rather to explore the properties of the former in order to predict certain well-known implicational facts. New recalcitrant data are also brought to bear on the issue, as well as a proposal for acquiring lexical categories in present terms which, it is argued, successfully mimics the acquisition sequence by infants.
