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, often it is purely technical solutions that are promoted, meaning existing power relations are ignored. In contrast, we propose nonsolution, a politicised approach to the problem of finding a solution. We pick up the word nonsolution, and the conceptual outlook it stands for, from the writings of sociologist, historian and urban theorist Siegfried Kracauer, to open up spaces for thinking critically along the lines of radical democracy: solutions are not avoided, but rather an active nonsolution is pursued. The non marks the rejection of closed identities, the affirmation of conflict and opposition, and the entering of architecture into political alliances. With regard to housing and urban development against the pressure of capitalisation and exclusion, we combine planning activity with political theory to form a critique of architectural practice.