Abstract: Any comprehensive semantics for number words, such as `two', must explain why they can take on such a wide range of related meanings. Extant analyses offer promising explanations of a wide range of these meanings. On the other hand, they face a number of substantial, previously unrecognized theoretical and empirical challenges: they threaten incoherence, they identify numbers with the wrong sorts of entities, and they seemingly cannot explain the full range of meanings number words can take on. I argue that recognizing numbers as kinds affords a new type of polymorphic analysis, one which not only avoids these challenges, but also improves on extant explanations of polysemy, by expanding their empirical coverage.
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