Problems require solutions. But what is defined as a problem, and how are answers and solutions found? In view of the climate catastrophe, the unjust distribution of wealth, and the demand for liveable housing and urban spaces for all, purely technical solutions are often promoted, while existing power relations are ignored.In contrast, we propose nonsolution as a politicised approach to the problem of finding solutions. We adopt the term nonsolution, and the conceptual outlook it represents, from the writings of sociologist, historian, and urban theorist Siegfried Kracauer in order to open up spaces for critical thinking along the lines of radical democracy: solutions are not avoided; rather, an active nonsolution is pursued. The "non" signifies the rejection of closed identities, the affirmation of conflict and opposition, and the integration of architecture into political alliances.With regard to housing and urban development under the pressure of capitalisation and exclusion, we combine planning practice with political theory to develop a critique of architectural practice.