Aristotle represented the relations of the four logical propositions by what is termed the square of opposition.Viewed from the standpoint of the square, the relations may be summed up as follows:
1. Contrary Propositions.
Why so named.
As related to each other, A and E are said to be contrary because they seem to express contrariety to the greatest degree.
Relation stated.
If one is true, the other must be false, but both may be false.
Illustrations.
(1) If one is true, the other must be false; e. g., if A is true, as “All metals are elements,” then E is false, as “No metals are elements.” Or, if E is true, as “No birds are quadrupeds,” then A is false, as “All birds are quadrupeds.”
(2) Both may be false. If A is false, as “All men are wise,” then E may be false, as “No men are wise.”