The concept of cosmopolitics developed by Isabelle Stengers and Bruno Latour keeps open the question of who and what might compose the common world. In this way, cosmopolitics offers a way to avoid the pitfalls of reasonable politics, a politics that, defining in advance that the differences at stake in a disagreement are between perspectives on a single reality, makes it possible to sideline some concerns by deeming them unrealistic and, therefore, unreasonable or irrelevant. Figuring the common world as its possible result, rather than as a starting point, cosmopolitics disrupts the quick recourse to ruling out concerns on the basis of their ostensible lack of reality. And yet, questions remain as to who and what can participate in the composition of the common world. Exploring these questions through ethnographical materials on a conflict around caribou in Labrador, I argue that a cosmopolitics oriented to the common world has important limitations and that another orientation might be possible as well.