This thesis argues for a novel conception of political realism as a theory of political legitimacy: the Dual Convergent Conception. The thesis is framed by the thought that one way of theorising about political legitimacy involves working out how reasonable people can achieve a stable political order so that, despite their profound moral differences, they may live together governed by principles they have sufficient moral reason to affirm from within their own point of view. I argue that this ultimately involves making a special sort of argument that takes reasonable disagreement about justice seriously: a Disagreement to Legitimacy argument. This is an argument with two parts. The first part involves finding the best explanation of reasona...