Mastering how to convey meanings using language is perhaps the main challenge facing any language learner. However, satisfactory accounts of how this is achieved, and even of what it is for a linguistic item to have meaning, are hard to come by. Nick Chater was one of the pioneers involved in the early development of one of the most successful methodologies within the cognitive science of language for discovering meaning: distributional semantics. In this article, we review this approach and discuss its successes and shortcomings in capturing semantic phenomena. In particular, we discuss what we dub the "distributional paradox:" how can models that do not implement essential dimensions of human semantic processing, such as sensorimotor grounding, capture so many meaning-related phenomena? We conclude by providing a preliminary answer, arguing that distributional models capture the statistical scaffolding of human language acquisition that allows for communication, which, in line with Nick Chater's more recent ideas, has been shaped by the features of human cognition on the timescale of cultural evolution.
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