I argue that the question �what is complexity science?� presents an opportunity to think critically about complexity science, and to ask the question tells us something about what work still needs to be done in understanding complex social dynamics. The paper is a performance of complexity science, putting complexity science to the ultimate test asking, how can complexity science help us answer the question �what is complexity science�? Making a distinction between the study of complex social orders and complex social orderings, I argue there continues to be a problem of establishing the grounds upon which complexity science can be seen to offer an adequate account of social dynamics, in particular because of a continued tendency towards determinism and reductionism. I suggest that the concept of emergence needs to be re-thought, and, drawing upon Luhmann, that a key role for complexity science is to ask, how is ignorance dealt with?