Abstract This paper is a discussion of how James Pustejovsky [Pustejovsky, James, 1995. The Generative Lexicon. MIT Press, Cambridge MA; Pustejovsky, James, 1998a. The semantics of lexical underspecification. Folia Linguistica 32 (3), 323–348] deals with the alleged lexical polysemy of words in semantically and structurally related syntactic contexts. Polysemy is at the centre of current semantic research, in both the cognitive and the generative paradigms. In Section 1 I discuss some similarities and differences between both paradigms and draw attention to a number of as yet unsolved problems. In particular I examine a seeming paradox in Pustejovsky’s theory of ‘qualia-structures’ which are postulated for lexical items. On the one hand Pustejovsky’s theory is based on the claim that polysemy is fundamental to meanings and that linguistic expressions change their semantic features (meanings) in context; on the other hand, the theory of ‘qualia-structures’ seems to favour a monosemy approach. I argue that in Pustejovsky’s account syntagmatically observable polysemy (meaning variation) is projected into the ‘qualia-structures’ of words and that this account is to be distinguished from a monosemy approach based on paradigmatic meaning oppositions between lexical items. In Section 2 special attention is paid to the semantics of verbs with causative/intransitive alternation, e.g. break, which have variable valency and occur in complementary argument structures exemplified by clauses like John broke the bottle and The bottle broke. In particular, the claim that propositions with the intransitive construction (‘unaccusative’) are ‘semantically entailed’ in propositions with the transitive one is called into question. I argue that this claim does not bear on the semantic function (linguistic meaning proper) of the verb or argument structure but rather on different events or states of affairs to which speakers can refer using this kind of verbs with variable valency. It is shown that a logical–referential treatment is incompatible with a coherent concept of ‘semantic entailment’. Taken in its linguistic sense, this concept implies that argument structures with fewer arguments (and, as a consequence, a simpler lexical structure) semantically entail more elaborate argument structures, rather than the other way around. Moreover, evidence is presented that ‘semantic entailment’ does not necessarily imply polysemy but should be regarded as an instance of neutralization.