J. L. Mackie argued that moral thought and discourse involve commitment to an especially robust kind of normativity, which is too weird to exist. Thus, he concluded that moral thought and discourse involve systematic error. Much has been said about this argument in the last four decades or so. Nevertheless, at least one version of Mackie’s argument, specifically the one focusing on the intrinsic weirdness of the relevant kind of normativity, has not been fully unpacked. Thus, more needs to be (...) said about the issue of how to interpret Mackie’s argument. Moreover, I argue that by looking closely at Mackie’s discussion, we can extract two distinct versions of the argument which together present a tougher, and also more precise, challenge for moral realism than extant versions. In this paper I thus revisit Mackie’s discussion with an eye to making progress on an important issue in contemporary metaethics. (shrink)