Classical Square of Opposition

The Classical Square of Opposition is a diagram representing the logical relationships between the four types of categorical propositions (A, E, I, O) that share the same subject and predicate terms. It is an indispensable tool for immediately inferring the truth value of one proposition based on another.

The Four Logical Relationships

1. Contradictory (A & O, E & I)

Contradictory propositions differ in both quantity (universal vs. particular) and quality (affirmative vs. negative). They are exact opposites.

• Rule: They cannot both be true, and they cannot both be false. If one is true, the other must be false.
• Example: If 'All S is P' (A) is true, then 'Some S is not P' (O) is definitively false.

2. Contrary (A & E)

Contrary propositions are both universal (A and E), but they differ in quality.

• Rule: They cannot both be true simultaneously, but they can both be false. (If one is true, the other must be false; if one is false, the other is undetermined).
• Example: 'All dogs are brown' (A) and 'No dogs are brown' (E) cannot both be true. But they can both be false (if some dogs are brown and some are white).

3. Subcontrary (I & O)

Subcontrary propositions are both particular (I and O), but differ in quality.

• Rule: They cannot both be false simultaneously, but they can both be true. (If one is false, the other must be true; if one is true, the other is undetermined).
• Example: 'Some flowers are red' (I) and 'Some flowers are not red' (O) can both be true at the same time.

4. Subalternation (A to I, E to O)

Subalternation refers to the relationship between a universal proposition (the superaltern) and its corresponding particular proposition (the subaltern) of the same quality.

• Rule 1 (Downward): Truth flows downward. If the Universal (A/E) is true, the Particular (I/O) is definitively true.
• Rule 2 (Upward): Falsity flows upward. If the Particular (I/O) is false, the Universal (A/E) is definitively false.