This short article tries first of all to convey the relevance of a philosophy such as the one developed by Castoriadis in a non-systematic and somehow idiosyncratic way and yet deeply coherent in its conclusive sense. It is a patrimony of ideas and theses that have still to be explored, used and elaborated from a perspective that privileges a critical view about the whole of our practice and being. However, Castoriadis’ a-systematic system should itself be critically tested. How much the promise of autonomy and truth it is embodying is truly realized and followed in the spires of its argument? There are at least six weak points in Castoriadis’ “system” that the article intends to present and cursorily discuss.