In term 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.
Depiction from the 15th century
Relations are ways in which several entities stand to each other. They usually connect distinct entities but some associate an entity with itself. The adicity of a relation is the number of entities it connects. The direction of a relation is the order in which the elements are related to each other. The converse of a relation carries the same information and has the opposite direction, like the contrast between "two is less than five" and "five is greater than two". Both relations and properties express features in reality with a key difference being that relations apply to several entities while properties belong to a single entity.
G. E. Moore introduced the distinction between internal and external relations.
F. H. Bradley formulated a regress argument to defend the claim that relations do not exist.
The nature of relations was reconceptualized following various academic developments in the 19th century, such as the formulation of the logic of relations by Augustus De Morgan.
Gottfried Wilhelm Leibniz held that relations do not have fundamental reality and described the world instead as a collection of unconnected monads.
