 Chapter 4 begins a series of chapters that develops more specific rules for correctly drawing inferences. The three propositions of a syllogism can be in one of the  four A E I O categories.  This mathematically yields sixty-four arrangements into syllogisms: AAA, AAE, AAI, AAO, AEA, … OOO. Of these, only fifty-four are compatible with the six general rules for syllogisms. When these moods are duly arranged into figures, further rules are required to determine which have true premises and conclusions (III.4). The Logic thus emphasizes soundness over validity—presumably because arguments with false conclusions are “useless” in application. Much of the Logic’s subsequent importance as a work in formal logic is owing to what Kneale and Kneale (1962 [1984: 319]) refer to as the “quasi-mathematical” rigor with which these rules are derived and stated.