Claims to equality are dualist in nature: those to whom equality are applicable must be affirmed as morally equal, and their social and economic treatments are to be judged in terms of their morally equal status. In a brief survey, the way this dualist character developed in history is given a broad sketch. Then, the implications of moral equality for equality of treatment are brought into the open. The liberal provenance of equality, as well as the transformation of issues of equality into issues of justice, is underlined.