Over the course of human history there appears to have been a global shift in moral values towards a broadly ‘liberal’ orientation. Huemer argues that this shift better accords with a realist than an antirealist metaethics: it is best explained by the discovery of mind-independent truths through intuition. In this article I argue, contra Huemer, that the historical data are better explained assuming the truth of moral antirealism. Realism does not fit the data as well as Huemer suggests, whereas antirealists (...) have underappreciated resources to explain the relevant historical dynamics. These resources include an appeal to socialization, to technological and economical convergences, to lessons learned from history, to changes induced by consistency reasoning and to the social function of moral norms in overcoming some of the cooperation problems that globalizing societies face. I point out that the realist’s explanans has multiple shortcomings, that the antirealist’s explanans has several explanatory virtues, and conclude that the latter provides a superior account of the historical shift towards liberal values. (shrink)