Abstract Taking Boaventura de Sousa Santos' argument that there is no global social justice without global cognitive justice as its starting point, this article suggests that there is no global climate justice without global cognitive justice (implying both ontological justice and epistemological justice). If we take "the ontological turn" in anthropology and other disciplines and its focus on indigenous ontologies seriously, however, we seem to end up in a situation that is difficult to maneuver in relation to conventional understandings of climate justice. When discussing climate change in relation to multiple ontologies, there are two risks: 1) reproducing what I call "the coloniality of reality", arguing that indigenous ontologies are actually nothing but a cultural (mis-) representation of the world; 2) reproducing a conservative relativism that leads to nothing but the maintenance of status quo and that bears a resemblance to climate change denial. A thorough ethnographic understanding of what I would call "the moral meteorology" of the Andes and a broadened understanding of climate change, however, make it possible to navigate between the Scylla of coloniality and the Charybdis of relativism and to articulate a radical critique of fossil-fueled capitalism from a relational ontology, demanding climate justice while denouncing coloniality, and discussing the political ontology of climate change without ignoring its political ecology - and vice versa. Key words: Coloniality; climate justice; cognitive justice; political ontology; political ecology; Aymara