(Necessarily) Finite Lexis

This short work sets out to argue that the set of simple expressions comprising the lexicon of a given individual and the lexis of a given community are not just contingently but necessarily finite at any given moment in time. Where the lexicon is concerned, this is done by adapting a very simple argument presented by Fred Dretske (1965) concerning whether an individual can count to infinity. This is extended to the more challenging case of the lexis of a community by introducing lexicalization as a condition, which facilitates the same sort of argument as presented for the lexicon. Though the lexicon and lexis are often implicitly assumed to be finite, with little need for further argumentation, there does appear to be grounds for the stronger and more interesting claim that they are necessarily finite at any given moment in time.