A "renaissance of the university" in the European knowledge society is regarded today as a necessity. However, there is an ongoing debate about what that renaissance should look like. The aim of this article is to take a closer look at these debates, and in particular, the disputes related to the public role of the (future) university in the European knowledge society. The aim however is not to assess the validity of the arguments of each of the protagonists but to place the discussion within a broader socio-historical context. From a genealogical point of view, and drawing upon the work of Foucault and Hunter, it is possible to distinguish two kinds of milieu, each embodying their own "intellectual technology" and each leading to a specific conception of the public role of the university: firstly the principled milieu (with the persona of the academic as critical intellectual), and secondly the governmental milieu (with the persona of the state official or governmental expert). From this genealogical point of view, I will argue that the modern (research) university was from the very beginning a hybrid institution due to the claims and scopes of both milieus. Furthermore, I will argue that the current discussions reveal the ongoing influence of both milieus and their respective gazes and approaches.