Subcontrary

In the field of logic, subcontrary expresses a specific relationship between two statements; specifically, subcontrary statements are ones that cannot both be false.

A) Some X are animals.
B) Some X are not animals.

If X = 'cats', A is true. If X = 'carrots', B is true. And if X = things in my house, A and B are both true. There is no X for which one of these is not true. These statements are subcontrary.

In classical logic this was one of the four relationships possible between propositions, as observed in the square of opposition. The others are contradictory, contrary, and subalternation.

Brevity Quest 2016

Sub*con"tra*ry (?), a.

1.

Contrary in an inferior degree.

2. Geom.

Having, or being in, a contrary order; -- said of a section of an oblique cone having a circular base made by a plane not parallel to the base, but so inclined to the axis that the section is a circle; applied also to two similar triangles when so placed as to have a common angle at the vertex, the opposite sides not being parallel.

Brande & C.

3. Logic

Denoting the relation of opposition between the particular affirmative and particular negative. Of these both may be true and only one can be false.

© Webster 1913.

Sub*con"tra*ry, n.; pl. Subcontraries (). Logic

A subcontrary proposition; a proposition inferior or contrary in a lower degree.

© Webster 1913.