How do children resolve the problem of indeterminacy when learning a new word? By one account, children adopt a "taxonomic assumption" and expect the word to denote only members of a particular taxonomic category. According to one version of this constraint, young children should represent polysemous words that label multiple kinds--for example, "chicken," which labels an animal and its meat--as separate and unrelated words that each encode a single kind. Our studies provide evidence against this account: we show that four- and five-year-old children spontaneously expect that a word that has labeled one meaning of a familiar polysemous word will also label its other, taxonomically different meaning. Further, we show that children's taxonomic flexibility is importantly constrained--children do not expect a word to label thematically-related meanings (e.g., "chicken" and "egg"), or the unrelated meanings of homophones (e.g., "bat"[animal] and "bat"[baseball]). We argue that although children are initially guided by the taxonomic constraint when pairing word forms with meanings, they nonetheless relate the taxonomically-different meanings of polysemous words within lexical structure. Thus, for even young children, a single word can label multiple kinds.