Recursive numeral systems optimize the trade-off between lexicon size and average morphosyntactic complexity

Abstract

Human languages vary in terms of which meanings they lexicalize, but there are important constraints on this variation. It has been argued that languages are under the pressure to be simple (e.g., to have a small lexicon size) and to allow for an informative (i.e., precise) communication with their lexical items, and that which meanings get lexicalized may be explained by languages finding a good way to trade off between these two pressures ([12] and much subsequent work). However, in certain semantic domains, it is possible to reach very high levels of informativeness even if very few meanings from that domain are lexicalized. This is due to productive morphosyntax, which may allow for construction of meanings which are not lexicalized. Consider the semantic domain of natural numbers: many languages lexicalize few natural number meanings as monomorphemic expressions, but can precisely convey any natural number meaning using morphosyntactically complex numerals. In such semantic domains, lexicon size is not in direct competition with informativeness. What explains which meanings are lexicalized in such semantic domains? We will propose that in such cases, languages are (near-)optimal solutions to a different kind of trade-off problem: the trade-off between the pressure to lexicalize as few meanings as possible (i.e, to minimize lexicon size) and the pressure to produce as morphosyntactically simple utterances as possible (i.e, to minimize average morphosyntactic complexity of utterances).