Blackburn argues against naturalistic moral realism. He argues that there is no conceptual entailment from satisfying a naturalistic predicate to satisfying a moral predicate. But the moral is conceptually supervenient on the natural. However, this conjunction of conceptual supervenience with lack of conceptual entailment is something the non-realist can explain, but the realist cannot. I argue first that Blackburn’s best formulation of his challenge is his first one. Subsequently he reformulates it as a demand for a ‘ban on mixed worlds’. (...) Critics have directed their arguments against this formulation but they are ineffective against Blackburn’s first formulation. My second thesis is, even so formulated the realist can meet the challenge. The bare conceptual supervenience of the moral on the natural can be given a realist explanation by understanding names of moral properties as descriptive names of natural properties. (shrink)