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A sharp tension exists about the nature of human language between two opposite parties: those who believe that statistical surface distributions, in particular using measures like surprisal, provide a better understanding of language processing, vs. those who believe that discrete hierarchical structures implementing linguistic information such as syntactic ones are a better tool. In this paper, we show that this dichotomy is a false one. Relying on the fact that statistical measures can be defined on the basis of either structural or non-structural models, we provide empirical evidence that only models of surprisal that reflect syntactic structure are able to account for language regularities.