Several scholars have claimed or implied that the Paris Agreement imposes a collective obligation on states to keep global warming below 2°C, but what is a collective obligation from a legal point of view? The literature that asserts the existence of a collective obligation fails to address this question. In this article I argue two points. Firstly, while a legally binding collective obligation for states is not a theoretical impossibility, the Paris Agreement has not demonstrably created such an obligation; therefore, the collective obligation that appears in the treaty constitutes at most an objective of the Agreement, albeit a crucial one. Secondly, while state observance of the Agreement's apparent collective obligation (but, in fact, paramount objective) is necessary for the success of the treaty, the Agreement does not provide for a process to resolve the global mitigation burden into state-level ambition commitments to ensure that the paramount objective is met. While this is a significant failing of the Agreement, the provisions in the 2018 Paris Rulebook on the global stocktake are sufficiently loose to allow for this mechanism to play a role in the ‘individuation’ of the mitigation burden.