Hauser, Chomsky, and Fitch (2002) claim that a core property of the human language faculty is recursion and that this property "yields discrete infinity" (2002: 1571) of natural languages. On the other hand, recursion is often motivated by the observation that there are infinitely many sentences that should be generated by a finite number of rules. It should be obvious that one cannot pursue both arguments simultaneously, on pain of circularity. The main aim of this paper is to clarify both conceptually and methodologically the relationship between recursion and infinity in language. We want to argue that discrete infinity is not derived but a modeling choice. Furthermore, many arguments, both for recursion and infinity in language, crucially depend on particular grammar formalisms. Thus, care should be taken to distinguish, on the one hand, whether to derive infinity from recursion or the other way around, and, on the other hand, the role of recursion in language in general from the role of recursion in specific grammar formalisms.