The notion that cognition unreflectively depends on its historical context plays a central role in Hans-Georg Gadamer’s philosophy. This paper deals with the rather frequent objection to Gadamer that a theory of unreflectiveness of the kind proposed by him reduces the very lack of reflection that it asserts. According to this objection, recognizing the limits of reflection shows that they have been overcome. Indeed, Gadamer argues that context-dependence and the presuppositions (Vorurteile) that it involves are largely unreflected. But this very argument seems to rely on a reflective stance. However, a distinction might be made between (i) a general idea of context-dependence and (ii) awareness of the specific forms of this dependence. (i) of course does not require that all contextually induced presuppositions are, or even may become, fully reflected. But Gadamer tends to argue that most contextual influences are unreflected, an argument that seems to suggest that the limits of reflection can indeed be overcome in sense (ii). This argument does not rely on a general idea of context-dependence, but requires a form of reflection which is both specific and comprehensive in order to succeed.