opposition, square

opposition, square of

Geometrical representation of the traditional logical relations of opposition (contradictories, contraries, subalterns) among the four types of propositions (universal affirmative or A-proposition, universal negative or E, particular affirmative or I, particular negative or O) in the Aristotelian doctrine of the syllogism. At the top left is the A; at the top right is the E; below the A is the I; and below the E is the O. The A and the O, like the E and I, are contradictories (diagonal relations); the A and the E are contraries; and the I is subaltern to (hence implied by) the A, the O subaltern to the E. Whereas contradictories have opposite truth-values (one true, the other false), contraries cannot both be true but can both be false.