The traditional square of opposition was developed in the fourth century BC from Aristotle’s works and has been in logic texts ever since. The traditional square of opposition is a diagram of logical relationships among the four types of categorical propositions. The traditional square of opposition has categorical propositions that can determine if an argument is valid or invalid. The standard-form categorical propositions having the same subject terms and the same predicate terms may differ from each other in quality, or in quantity, or in both. In any differing of subject and predicate it is traditionally called opposition.

The four types of standard categorical propositions are universal affirmative, universal negative, particular affirmative and, particular negative. The proposition A is universal affirmative “All S are P.” The proposition E is universal negations “No S are P.” The proposition I is particular affirmative “Some S are P.” And last the O

proposition is particular negations “Some S are not P.”

There are four ways in which propositions may be “opposed” as contradictories, contraries, subcontraries, and as subalternators. These four propositions are used in a diagram that is called the square of opposition. Contradictories have two propositions where one is the denial or the negation of the other which means they cannot both be true and cannot both be false. Either of two propositions related in such a way make it is impossible for both to be true or both to be false. Contraries have two propositions that cannot both be true if the truth of one proves the falsity of the other. A proposition related to another in such a way that if the latter is true, the former must be false, but if the latter is false, the former is not necessarily true. Subcontraries have two propositions that have the same subject and the same predicate terms and agree in quality but differ in quantity and are called...