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Not unreasonable: Carving vague dimensions with contraries and contradictions

Language provides multiple ways of conveying the opposite: A person not happy can be unhappy, sad, or perhaps neither, just not happy. Rather than being redundant, we hypothesize that uncertainty about the meaning of negation markers allows listeners to derive fine-grained distinctions among these various alternatives. We formalize this hypothesis in a probabilistic model of gradable adjectives (e.g., happy), and use this to address an outstanding puzzle: how to interpret double negations (e.g., not unhappy). Our model makes surprising additional predictions about a putative difference between morphological antonyms (unhappy) and negated positives (not happy): Listeners should judge unhappy as more sad than not happy only when confronted with alternatives in context; when interpreted in isolation, we predict no difference in understanding. Two behavioral experiments confirm consistent orderings of interpretations that interact with the presentational context in the way predicted. These findings support the hypothesis that listeners represent uncertainty even about the most logical elements of language.