One influential positive argument for moral realism is the Explanatory Indispensability Argument. A crucial premise of this argument is the explanatory relevance of moral properties. On this premise, moral properties, such as wrongness, rightness, courage, and cowardice, are explanatorily indispensable to some empirical phenomena. Although there has been a lively debate on this premise, one crucial challenge to this thesis, what I call the Scientific Standard Challenge, has not been properly discussed. After explaining this challenge and a related concern, I (...) argue that in response to this central challenge, the proponents of the argument should take what I call the localist turn to defend the explanatory indispensability of moral properties. The localist turn encourages the defenders of moral explanations to be more sensitive to the nature of each moral explanation. For instance, some moral explanations are explanations of social matters, so the standards they need to meet are provided by relevant branches of the social sciences. On the other hand, some other moral explanations are about our psychology, so the theoretical standards those explanations need to meet should come from psychology. I illustrate how this localist project can be conducted in the case of the moral explanation that appeals to injustice. I argue that the field of comparative politics provides the theoretical standards moral explanations of institutional change need to meet. I shall then illustrate how a sophisticated moral explanation can meet those theoretical standards and how this moral explanation can be strong evidence of injustice’s explanatory indispensability. (shrink)