How many meanings does a word have and how do speakers agree in them in all possible discourse situations? This question addresses the problem of coping with the distinction between lexical vagueness and polysemy and with the creation of new meanings. The complexity of this objective becomes most obvious in lexicography and computational linguistics. The author deals with this question as a problem of reference, of how speakers refer consistently to their environment by means of mental models. Criteria for the representation of this cognitive phenomenon are drawn from a discussion of the philosophy of language and mind as well as cognitive psychology and experimental psycholinguistics. The selected method is set up within the framework of cognitive linguistics along with an elaboration of a theory of mental categorization. Theory and method join in a unification-based formalism to represent how polysemy develops metonymically within discourse domains and metaphorically across discourse domains. By resolving the count-mass metonymy with a fragment of grammatical default rules in a German-English machine translation system the unification-based representation is validated.