Square of opposition

The below relations, contrary, subcontrary, subalternation, and superalternation, do hold based on the traditional logic assumption that things stated as S (or things satisfying a statement S in modern logic) exist. If this assumption is taken out, then these relations do not hold.

Abelard also points out that subcontraries containing subject terms denoting nothing, such as 'a man who is a stone', are both false.

And points to Boethius' translation of Aristotle's work as giving rise to the mistaken notion that the O form has existential import.