How are contrary propositions different from contradictory propositions in Aristotle’s logic?
In Aristotle’s logic, the distinction between contrary and contradictory propositions lies in their truth conditions and logical structure regarding the same subject and predicate.12
Contradictory Propositions
Propositions are contradictories if they are opposed in both quantity (universal vs. particular) and quality (affirmative vs. negative). For example, a universal affirmative (A) and a particular negative (O), or a universal negative (E) and a particular affirmative (I), are contradictories. They are defined by the rule that one must be true and the other must be false; they cannot both be true and they cannot both be false.123
Contrary Propositions
Contraries occur between two universal categorical propositions that differ only in quality (one affirmative, one negative). For instance, "Every S is P" and "No S is P" are contraries. Unlike contradictories, these cannot both be true at the same time, but they can both be false.123
In summary, while contradictories represent a complete logical opposition where truth values are mutually exclusive and exhaustive, contraries represent a stronger opposition that excludes the possibility of both being true but allows for the possibility that both are false.12