contrariness

Contrariness is a term used in philosophy, logic, rhetoric, and everyday discourse to describe a tendency to oppose or hold opposite positions. In a formal logical sense, contrariness designates a relation of opposition between two propositions of the same quality (both affirmative or both negative) in which the two cannot be true at the same time, but they can both be false. The classic examples are universal propositions such as “All S are P” and “No S are P.” They cannot both be true, but they can both be false if some S are P and some S are not P.

In the Aristotelian square of opposition, contraries are contrasted with contradictory and subcontrary relations among A, E, I, and O statements. Contraries (A and E) cannot both be true, while subcontraries (I and O) can both be true but cannot both be false. Contrariness, then, is a specific kind of opposition relevant to universal propositions, distinguishing it from direct negation or contradiction.

Beyond formal logic, contrariness also describes a general disposition to disagree or oppose others’ views in argumentation or conversation. In this sense, a contrarian is someone inclined to challenge predominant opinions or conventional wisdom, sometimes for argumentative or heuristic purposes.

See also: square of opposition, contradiction, subcontrary, logical opposition.