Abstract: The argumentation of legitimacy of law has gone through the process of several negations. The development of natural science has made natural law become empty metaphysical talk, and positive law begins to look for its legitimacy in social facts. After Hume’s problem was raised, looking for legitimacy of law in social facts was called a“naturalistic fallacy”. Analytical legal positivism then turned legitimacy into validity, looking for legitimacy in the law itself, however, its theoretical foundation was not able to jump out the restriction of Hume’s problem. The purpose of law, as practical rationality, is to guide people’s act, solve legal problems,and realize social justice, so it is not very wise to introduce Hume’s problem, which is purely theoretical, into the practical province of law. After going through this cognitive process of negation of negation, it is crucial to face the law’s nature of practical rationality, understand and treat Hume’s problem with a practical attitude, so as to properly handle the relationship of law and morality or law and social facts.

Key words: Hume’s problem, legitimacy, naturalistic fallacy, practical rationality