In this paper we look at the relations between knowledge and thinking through the lens of ignorance. In relation to knowledge, ignorance becomes its “constitutive outside,” and as such it may be politically organised in order to delimit the borders of the right to knowledge [the “ignorance economy,” see Roberts and Armitage (Prometheus 26 (4): 335–354, 2008)]. In this light, the notion of a knowledge-based society should be understood as a society structured along the lines of knowledge distribution: the rights of possession of and access to knowledge demand that ignorance is planned and executed as the condition of their establishment. In relation to thinking, ignorance appears differently. According to Rancière, the teacher's ignorance conditions the student's appearance as Anthropos, a being who can be asked: what do you think about it? Hence, we are dealing with the ambiguity of ignorance which seems to be both the criterion of social exclusion, and the condition of emancipation. Following this thread with reference to Heidegger's discourse on thinking, we would like to explore the possibility of comprehending knowledge and education beyond the relations of ownership and demands of productivity. Following Rancière, we may say that thinking—as displacing the notion of ignorance—stands in the position of “politics” and questions the ways knowledge societies are structured as “police orders” along the lines of knowledge possession and exclusion. © 2020, The Author(s).