Abstract: Known as the Encyclopedia of Marxism, Anti-Duhring, on the basis of adhering to the dialectical materialism and historical materialism world outlook and methodology, has completed the criticism and transcendence of the ethical dimension "Hume's Problem". It clarified that ethics and morality were rooted in the social material production method. After discussing what is the capitalist mode of production in the field of facts, it exposed the inherent contradictions of capitalist society and the inevitability of capitalist economic crisis, and then clarified the realization of Communism and human liberation. It successfully bridged the gap between Facts and Values. Such criticism and transcendence had important practical significance in the process of socialist construction and improvement in the new era.