Why so named.
The propositions A and O, likewise E and I, are called contradictory propositions because they oppose each other in both quantity and quality. They are mutually opposed to each other or absolutely contradictory.
Relation stated.
If one is true the other must be false.
Illustrations.
(1) A and O compared.
If A is true, as “All metals are elements,” then, O is false, as “Some metals are not elements.” Or, if O is true, as “Some metals are not compounds,” then A is false, as “All metals are compounds.”
(2) E and I compared.
If E is true, as “No birds are quadrupeds,” then I is false, as “Some birds are quadrupeds.” Or, if I is true, as “Some birds are bipeds,” then E is false, as “No birds are bipeds.”
The chief value of the square of opposition springs from the contradictory propositions. The square shows conclusively that any universal affirmative assertion (an A) may best be contradicted by proving a particular negative (an O). For example: To satisfactorily refute the statement that, in this section, all birds migrate to the south in winter, it would be sufficient to prove that the English sparrow and starling do not migrate to the south. The square likewise makes evident that any universal negative (an E) may be conclusively denied by establishing the truth of a particular affirmative (an I). To illustrate: The easiest way to prove the falsity of “No trusts are honest” is to present facts showing that at least trusts A and B are honest.