This paper inquires into the extent to which humans are specially constituted relative to other animals by their language. First a principled concept of evolutionary specialness is operationalized. Then it is agreed that humans satisfy the criteria for this sort of specialness in consequence of the kind of cultural evolution in which they have participated. However, it is argued that although certain representational capacities limited to highly social and intelligent animals are necessary for such cultural evolution, the representational capacities in themselves are not special. Instead, the special property of humans that leads them to explosive niche-construction is the propensity to stabilize coordination through socially controlled self-narration. This propensity indeed depends on special aspects of human language, though syntactical structure is not necessarily among them.