The Israeli demand that Palestinians recognize Israel as the nation-state of the Jewish people and the Palestinian demand that Israelis recognize the Palestinian refugees’ moral right to return express the two peoples’ need to have their respective causes affirmed by the “other side.” Yet, the two causes are irreconcilable as are the core political narratives that give them meaning. The question then arises as to whether an end to the conflict can even be conceptualized, let alone implemented, with the two peoples adhering to their core narratives and expecting affirmation of their respective causes. This paper’s argument is that John Rawls’ later work contains resources that allow for such a conceptualization. An overlapping consensus over a list of common acknowledgments is possible between adherents to the two peoples’ core narratives. In that list, which is proposed in the paper, each of the two peoples can see its cause implicitly affirmed and its need for recognition met, without having to abandon its core narrative or to explicitly grant the demand for recognition made on it by the other side. Thus, the irreconcilability of narratives does not present an insurmountable obstacle to conceptualizing potentially just and stable relations between the two peoples.