Human language is unique among the communication systems of the natural world: it is socially learned and, as a consequence of its recursively compositional structure, offers open-ended communicative potential. The structure of this communication system can be explained as a consequence of the evolution of the human biological capacity for language or the cultural evolution of language itself. We argue, supported by a formal model, that an explanatory account that involves some role for cultural evolution has profound implications for our understanding of the biological evolution of the language faculty: under a number of reasonable scenarios, cultural evolution can shield the language faculty from selection, such that strongly constraining language-specific learning biases are unlikely to evolve. We therefore argue that language is best seen as a consequence of cultural evolution in populations with a weak and/or domain-general language faculty.