There is a research programme in linguistics that is founded on describing language as an emergent phenomenon. This paper clarifies how the core concept of emergence is deployed in this emergentist programme. We show that if one adopts the weak understandings of the concept of language emergence, the emergentist programme is not fundamentally different from the other non-emergentist research programmes in linguistics. On the other hand, if one adopts the stronger understandings of emergence then the programme would have a unique (...) character, but at the cost of some corollaries (philosophical, but not only) which the emergentist linguists would seemingly want to avoid. We show that if the emergentists accept those corollaries, the resulting hypothetical emergentist programme would be totally different from the emergentist programme in its present shape. We conclude that the emergentist programme, as it stands, should be either abandoned or reshaped in both theory and methodology. (shrink)