The world’s centre of gravity is changing, from the North Atlantic to Eastern Asia. As world centres of knowledge have correlated historically with world centres of power, this ongoing geopolitical change is likely to bring changes also to the global map of cognition. Knowledge and power are intrinsically related, knowledge is power, it is based on power, and it produces instruments of power. Moreover, the vistas of social scientists and scholars are always circumscribed by the power relations of the social world they are studying. A way of looking into this is to analyse the concepts and the narratives they use and produce. What features do they highlight, and what do they hide? Cognitive change is driven by two kinds of change, change (i.e. new discovery) of evidence, and change of power. On a macro scale, the major forces of power change bearing upon cognitive change have been social mobilizations, for example, of classes, women, and ethnic groups, the rise and decline of states, and, third, economic or ecological crises disrupting the functioning of existing powers. Indigenization and de-Westernization are different programmes. The former is synonymous with nativization and rooting in the particular culture of a population, whereas the latter may be, and often is, an emancipation from Western cultural domination in the name of another universalistic culture. De-Westernization is inherently confrontational, whereas indigenization may range from supplementary to isolationist. Academic indigenization and de-Westernization have in their cognitive challenges similarities with contemporary critical identity movements, such as feminism and ethnic movements. The cognitive challenges mounted by both types of currents proceed across four levels of cognitive depths, claiming canon inclusion of certain thinkers and role models, questioning and rejection of prevailing social narratives, practising new forms of knowledge production, and fourth epistemological or meta-sociological reflections on the old and the new knowledge paradigms. Indigenization should be treated as a limited supplementary project, whereas de-Westernization is likely to advance. It should be an opening of global horizons, not a closure. Pluralism of critique, challenge, and search for other, better ways are decisive for the development of knowledge.