In the lecture we propose a mechanism for resolving the disagreement of the epistemic peers in the condition of their deep disagreement, caused, on the one hand, by the cognitive diversity of the agents, which constitutes the prerequisite for argumentation, and the commitment model of obtaining rational knowledge, which, unlike the BDI model, makes it dependent from refuting the objections in the dialog. For the parties to overcome the disagreement in the dialog in favor of the birth of truth means to construct the truth as a joint design project and to create agreement about it on the basis of a design-constructionist procedure, taking into account the difference between the significative phenomena of representation and assessment of arguments, or differences in the assessments of arguments by the author and the addressee. The mechanism is tested on the example of the relevant reasoning by G. Agamben about the impact of the pandemic on the university social life.