The paper describes the manuscript of «On sociology» A. Lappo-Danilevsky (1863-1919), in which he criticized the social doctrine of D.S. Mill (1806-1873), as set out in the VI book «Systems of syllogistic logic and inductive». Analysis of «System of Logic», and in particular, criticism of the positivist «logic of the moral sciences» were the basis of the first social science course of Lappo-Danilevsky, which he read in the St. Petersburg University for two years (1899-1900 and 1900-1901).