The Square of Opposition is a useful tool for representing and understanding the relationships between categorical statements with the same subject and predicate:

The relationships are defined this way:

Contrariety: The statements cannot both be true, but can both be false.

Contradiction: The statements cannot both be true, and cannot both be false.

Subcontrariety: The statements can both be true, but cannot both be false.

Subimplication: If the universal is true, the particular must be true.

Superimplication: If the particular is false, the universal must be false.

Students might be interested to discover that the square of opposition can be created for non-categorical statements as well. Continue reading The Square of Opposition (for logic nerds only!)