Since their inception in the 1980s, complexity sciences have been described as a revolutionary new domain of research. By describing some of the practices and assumptions of its representatives, the present article shows that this field is an association of subdisciplines laying on existing disciplinary footholds. The general question guiding us here is: On what basis do complexity scientists consider their inquiry methods and results as valuable? To answer it, I describe five "epistemic argumentative regimes," namely the ways in which complexity scientists argue the credibility of their research, and five "ontological views," that is the ways in which they interpret the material and formal causes of their study objects and models. Finally, the article proposes the term of "regime of evidence" to designate the specific combination of one ontological view with one or more epistemic argumentative regimes.