The Mathematics of Language Universals

The question of language universals is central to cognitive sciences but still controversial. The universalist view holds that all languages are deeply similar and that identifying their universal properties is the subject mat- ter proper of linguistics. The anti-universalist view holds that languages differ in arbitrary ways and whatever languages seem to share is due to accidents of their history. Language universals have so far been studied inductively, by surveying the world’s languages, cataloguing phenomena, and observing systematic gaps. However, deriving language universals in a systematic and principled manner remains a largely unsolved problem. The difficulty is compounded by the fact that many interesting universals are statistical, making their direct induction particularly challenging. Our project will thus lay the foundation of a new indirect approach to language universals, whereby (1) candidate universals are derived formally from (categorical and stochastic) linguistic models through a sophisticated mathematical analysis of their “geometry” and then (2) validated on large databases of the world’s languages. By combining expertise in mathematical linguistics (French team) with expertise in theoretical and large-scale typological linguistics (Stanford team), the project promises to break new ground on the central question of the place of language in human cognition.