And the “third level” concerns the syllogism, its moods, and the conditions under which it yields a conclusion: it must contain a universal affirmative proposition; no conclusion follows from two negative premises, two particular premises, or a negative minor premise and a particular major premise. Rather, there must be either two affirmative premises, one of which is universal, or a negative minor premise and a particular major premise. It also concerns other rules governing the forms and types of syllogism, established through proof by contradiction—which is reduced to the rule governing the contradictory of a proposition—or through reduction to the proposition’s converse or contrapositive.

They then explained the material content of syllogisms, dividing them into:

“Demonstrative”: those whose premises are certain. They restricted certainties to the categories they mentioned: inward and outward sense perceptions, self-evident truths, mass-transmitted reports, and propositions established by experience. Some also added propositions established by intuition.

“Rhetorical”: those whose premises are widely accepted, whether certain or uncertain.

“Dialectical”: those whose premises are conceded by the opponent, whether certain, widely accepted, or otherwise.

“Poetic”: those whose premises are felt rather than believed, such as those that evoke joy, sorrow, or laughter.

“Fallacious, sophistical”: those whose premises are disguised with semblances of truth.