Abstract
Over the past two decades, theoretical linguistics has taken a probabilistic turn. Maximum entropy (ME) has been endorsed as a model of probabilistic phonology because of its classical guarantees for grammatical inference. Yet, little is known about the basic organizing principles of ME phonology beyond circumstantial evidence of ME’s ability to fit specific patterns of empirical frequencies. The study of ME typologies is difficult because they consist of infinitely many grammars that cannot be exhaustively listed and directly inspected. Uniform Probability Inequalities (Anttila and Magri 2018) are a new tool that solves the problem: they characterize cases where one phonological mapping has a probability smaller than another mapping and this probability inequality holds uniformly for every grammar in the typology. In other words, uniform probability inequalities are universals of probabilistic grammars. We present a new generalization about ME uniform probability inequalities and argue that they are phonologically paradoxical and prune the set of ME universals down to almost nothing. This suggests that ME is not a suitable model of phonology.
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