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Abstract.  The central argument of this article turns on the dual-nature thesis. This thesis sets out the claim that law necessarily comprises both a real or factual dimension and an ideal or critical dimension. The dual-nature thesis is incompatible with both exclusive legal positivism and inclusive legal positivism. It is also incompatible with variants of non-positivism according to which legal validity is lost in all cases of moral defect or demerit (exclusive legal non-positivism) or, alternatively, is affected in no way at all by moral defects or demerits (super-inclusive legal non-positivism). The dual nature of law is expressed, on the one hand, by the Radbruch formula, which says that extreme injustice is not law, and, on the other, by the correctness argument, which says that law's claim to correctness necessarily includes a claim to moral correctness. Thus, what the law is depends not only on social facts, but also on what the law ought to be.