Moral judgements have been a crucial subject-matter of a discussion in the domain of normativity. Many thinkers argue moral judgments are necessarily action-guiding, which prescribe what one ought to do and what ought to be the case. The moral statement “killing is wrong” is prescriptive and locates in the purview of first-order ethical questions. Moral realists widely accept that moral judgments represent propositions, therefore they are subject to truth and false conditions. Thus, moral conclusions can be derived logically from valid premises. How to derive the conclusion “killing is wrong”? How to justify the statement? What does “wrong” mean in this context? This kind of philosophical issue has been labeled as the second-order questions, which is in the purview of metaethics. This article is devoted to the subject of normativity and the nature of moral judgments advocated by metaethicists David Copp and Ralph Wedgwood. The purpose of this article is to outline the current debate on the nature of normative moral judgments. In conclusion, I shall agree with both Copp and Wedgwoodon two points. One, normative moral judgment can be subject to cognition. Two, there are true and false beliefs about particular moral facts which constitute the significant part of the reality we live in.