How should we conceive of conflicts that seem intractable? Is there any hope of a resolution? We observe impasses between various groups concerning the Israeli and Palestinian conflict, the Movement for Black Lives and racial conservatives, and Indigenous voices versus settler colonial states. Some aspects of these impasses can surely be explained by an unwillingness by one or more parties to the conflict to yield any ground. Might there also be room for misunderstanding generated by radically different ways of conceiving the world? According to the different worlds thesis, people come to radically different understandings of the world because they inhabit incompatible conceptual realities. In this article, I endeavor to explore possible ways of understanding the thesis and its potential impact on certain normative practices we tend to take for granted.