| Summary: | Despite a vast literature on the semantics and pragmatics of cardinal numerals, it has gone largely unnoticed that they exhibit a variety of polarity sensitivity, in that they require contextual support to occur felicitously in the scope of sentential negation. We present the results of a corpus analysis and two experiments that demonstrate that negated cardinals are acceptable when the negated value has been asserted or otherwise explicitly mentioned in the preceding discourse context, but unacceptable when such a value is neither mentioned nor inferable from that context. In this, bare cardinals exhibit both similarities to and differences from other types of numerical expressions. We propose an account of our findings based on the notion of convexity of linguistic meanings (Gärdenfors 2004) and discuss the implications for the semantics of numerical expressions more generally.
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