Square of opposition

Square of opposition. The lower case letters (a, e, i, o) are used instead of the upper case letters (A, E, I, O) here in order to be visually distinguished from the surrounding upper case letters S (Subject term) and P (Predicate term). In the Venn diagrams, black areas are empty and red areas are nonempty. White areas may or may not be empty. The faded arrows and faded red areas apply in traditional logic assuming the existence of things stated as S (or things satisfying a statement S in modern logic). In modern logic, this is not assumed so the faded ones do not hold. (There can be no element in the faded red areas in the modern logic.)
Depiction from the 15th century

In term logic (a branch of philosophical logic), the square of opposition is a diagram representing the relations between the four basic categorical propositions. The origin of the square can be traced back to Aristotle's tractate On Interpretation and its distinction between two oppositions: contradiction and contrariety. However, Aristotle did not draw any diagram; this was done several centuries later by Apuleius and Boethius.