Handbook of the History of Logic: - Fordham University Faculty

The Assimilation of Aristotelian and Arabic Logic up to the Later Thirteenth Century 317
Categorical propositions are furthermore either affirmative or negative.
Given this we are now in a position to outline the basic relationship between
these propositions. This is done by stating the traditional square of opposition,
which include the four basic relations; contrary, subcontrary, contradiction and
subalternation.
Figure 1. The Square of Opposition
William also presents a hexagon of opposition.
Figure 2. The Hexagon of Opposition
Having presented the fundamentals all textbooks introduce the doctrine of the
matter of propositions. This is a theory that has Ancient sources, but was very
typical for thirteenth century logic, as noted several times already, and assumes
a close relation between logic and metaphysics. The three kinds of matter are