Subcontraries

Subcontraries are a pair of categorical propositions of the particular forms: Some S are P (I) and Some S are not P (O). They belong to the traditional square of opposition, which relates four kinds of categorical propositions: All S are P (A), No S are P (E), Some S are P (I), and Some S are not P (O).

The defining feature of subcontraries is that they cannot both be false and they can both be true. In the classical reading, I and O carry existential import, meaning there must be some subject S in the domain. Under this reading, at least one of the subcontraries is true, and both can be true if there are some S that are P and some S that are not P. In modern predicate logic, existential import is not assumed, so both I and O can be false when the subject class S is empty.

Example: Some dogs are brown. Some dogs are not brown. These statements illustrate a subcontrary pair: it is possible for both to be true (there are brown dogs and non-brown dogs), and it is possible for one to be true and the other false, or for both to be false if there are no dogs at all.

Relation to other forms: Subcontraries are distinct from contraries (A vs E), which cannot both be true, and from contradictories (A vs O and E vs I), which cannot both be true or both be false. Subcontraries specifically concern the I and O forms and their capacity to share a truth value under different assumptions about existence.