and statements of negation. Thus, presenting a likeness in the form of a syllogism must involve a general statement, a universal proposition. This is the likeness established in the mind against which particular instances are measured to determine their status. Without its universality, such inference would be impossible, since the instance whose status is sought might fall outside its scope.

Hence it is said: no syllogism can be formed from two particular propositions; rather, one of them must be universal. Nor can a syllogism be formed from two negative propositions; rather, one of them must be affirmative. Otherwise, neither of the two negations is included within the other. A statement of general application is therefore indispensable.

The total number of combinations used to construct these likenesses is sixteen. The first proposition is either particular or universal, and either affirmative or negative. These are four possibilities; multiplying them by four gives sixteen. Combinations of two particular propositions are excluded, whether both are affirmative, both negative, or one negative and the other affirmative. These account for six of the sixteen. Combinations of two negative propositions are also excluded, whether both are particular, both universal, or one of each. However, the combination of two particular negative propositions has already been included in the first exclusion, leaving two further combinations to be excluded from the sixteen.

Also excluded is the combination of a universal negative minor premise with a particular affirmative major premise. For when the major premise is particular, the negation need not intersect with it. Affirmation is different: two particular affirmations intersect. Likewise, a particular affirmation and a universal negation intersect, because what is affirmed falls within the scope of the general negation.