This chapter systematically expounds Vasil'ev's logic of concepts, that is, a logic in which the law of excluded middle does not hold. Sigwart, especially with his concept of the forms of judgment and his critique of particular judgement, exercised a considerable influence on Vasiliev's development of such a logic. Taking up Sigwart's analysis, Vasil'ev gives a strong interpretation of the particular judgment as "Only some (not all) S are P,' while the form "Some, and maybe all, S are P' would correspond to the Aristotelian indefinite proposition. According to Vasil'ev, the strong particular affirmative judgment presupposes the particular negative judgment "Some (the remaining) S are not P,' and vice versa. These constitute one sole judgment, the accidental one. By means of an analysis of the square of opposition, Vasil'ev shows that for the judgments about concepts, which he distinguishes from the judgments about facts, there are three kinds of universal judgments (affirmative, negative, and universal) among which only the relation of contrariety holds, and therefore the law of the excluded fourth holds, not that of excluded middle, as is shown in the triangle of oppositions. The chapter closes with a historical excursus on the principle of excluded middle followed by a debate on particular propositions between Louis Couturat and Salomon Ginzberg, who discuss ideas which show very strong affinities to Vasil'ev's on strong particular judgment.