Category mistakes are sentences such as ‘Colourless green ideas sleep furiously’ or ‘The theory of relativity is eating breakfast’. Such sentences are highly anomalous, and this has led a large number of linguists and philosophers to conclude that they are meaningless (call this ‘the meaninglessness view’). In this paper I argue that the meaninglessness view is incorrect and category mistakes are meaningful. I provide four arguments against the meaninglessness view: in Sect. 2, an argument concerning compositionality with respect to category (...) mistakes; in Sect. 3 an argument concerning synonymy facts of category mistakes; in Sect. 4 concerning embeddings of category mistakes in propositional attitude ascriptions; and in Sect. 5 concerning the uses of category mistakes in metaphors. Having presented these arguments, in Sect. 6 I briefly discuss some of the positive motivations for accepting the meaninglessness view and argue that they are unconvincing. I conclude that the meaninglessness view ought to be rejected. (shrink)