Viebahn (2018) has recently argued that several tests for ambiguity, such as the conjunction-reduction test, are not reliable as tests for polysemy, but only as tests for homonymy. I look at the more fine-grained distinction between regular and irregular polysemy and I argue for a more nuanced conclusion: the tests under discussion provide systematic evidence for homonymy and irregular polysemy but need to be used with more care to test for regular polysemy. I put this conclusion at work in the context of the debate over the alleged referential-attributive ambiguity of the definite article. In reply to various criticisms, defenders of the ambiguity view argue that this is a case of polysemy. But opponents object that the dual use of the definite article fails tests for ambiguity. The debate seems to have come to stalemate, unless the relevance of the tests is determined for cases of alleged polysemy. I conclude that the balance of considerations incline towards rejecting the ambiguity thesis.