Abstract The aim of this article is to give an example of how an exercise in post-critical educational research might be conceptualised. The example refers to an inquiry into building a public sphere around education in Poland. First, a post-critical approach in educational research is defined with reference to the two dominant perspectives of social research, namely the (neo)positivistic and the critical paradigm. Next, and following insights of Hannah Arendt and Jacques Rancière, the idea of building is presented in terms of the persistent introduction of a new beginning into a social reality through acting in line with an assumption (an axiom) that, from the point of view of critical knowledge about the current status quo, seems fictional (or impossible). Such a persistent verification of an impossible axiom aims at establishing a sphere of exception from the dominant social order, offering—through the ideas of Alain Badiou and Giorgio Agamben—a non-dialectical logic of social transformation. Finally, in conclusion the article focuses on the phenomenon of condensation as one of the key results of the exemplary research project analysed throughout the text. This points to the kind of knowledge that post-critical research projects are able to bring about.
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