The aim of this article is to investigate possibilities for conceptions of critical thinking beyond the established educational framework that emphasizes skills. Distancing ourselves from the older rationalist framework, we explain that what we think wrong with the skills perspective is, amongst other things, its absolutization of performativity and outcomes. In reviewing the relevant discourse, we accept that it is possible for the skills paradigm to be change-friendly and context-sensitive but we argue that it is oblivious to other, non-purposive kinds of rationality that are indispensable to critical thought. Our suggestion is that there is an aporetic element in critical thought that is missing from contemporary educational positions. We consider some other efforts to redeem the surplus of criticality that performativity fails to take into account and conclude that the aporetic element that we highlight accommodates better than other theories do the significance of thematizing the taken-for-granted instead of focusing on problem solving.