Square of Opposition (Logic)

Square of opposition is a good introduction to logic. Understanding square of opposition will improve our logical thinking.

At the four corners of the square are the four types of statements. In clock wise direction, starting from the top left, they are denoted as A, E, O, and I.

Type A: All S are P or Every S is P (Also known as Universal Affirmative)

Type E: No S is P ( Universal Negative)

Type I: Some S are P ( Particular Affirmative)

Type O: Some S are not P ( Particular Negative)

Square of opposition states that statements A and E are contrary. When one statement is true, the other cannot be true. There is also a possibility that both can be false. For example, if some S are P, then both the statements A and E are false. Similarly, if some S are not P, then both the statements A and E are false.

The two pairs of statements (A, O) and (E, I) are contradictory. This is similar to contrary statements in that when one statement is true, the other cannot be true. However, the missing part is that the possibility of both can be false.

The statements I and O are sub contrary. They both cannot be false. For example, if all S are P, then only type O is false. Similarly, if no S are P, then only type I is false.

The two pairs of statements (A, I) and (E, O) are subaltern. When A is true, I is also true. When E is true, O is also true. The logic is when something is true for the whole part, you can definitely say it is true for its sub set.