Subcontrariety

Subcontrariety is a logical relationship between two propositions. Specifically, it applies to two particular negative propositions in traditional categorical logic. Two propositions are subcontraries if they cannot both be false, but they can both be true. This means that at least one of them must be true, but it is possible for both to be true simultaneously. In terms of truth values, if one subcontrary proposition is false, the other must be true. However, if one subcontrary proposition is true, the other can be either true or false.

The subcontrary relationship is often illustrated using a square of opposition, a diagram that shows the relationships between the four types of categorical propositions: universal affirmative (A), universal negative (E), particular affirmative (I), and particular negative (O). Subcontraries are typically represented by the two particular propositions, the I and O statements. For example, the propositions "Some S are P" (I) and "Some S are not P" (O) are subcontraries. If "Some S are not P" is false, then it must be the case that all S are P, which would make "Some S are P" true. However, it is possible for both "Some S are P" and "Some S are not P" to be true simultaneously, for instance, in a case where some S are P and other S are not P. The subcontrary relationship is not as commonly discussed as contrariety or contradiction.