Square of Opposition in Logic

• PHILO 1 (LOGIC) discusses the Square of Opposition.

Logical Opposition

• It's the relationship between propositions sharing subject and predicate but differing in quality, quantity, or both.
• This is illustrated in the "Square of Opposition".

Kinds of Opposition

• There are four kinds of logical opposition: Contradictory, Contrary, Sub-contrary, and Subaltern.

Contradictory Propositions

• These have the same subject and predicate but differ in both quantity and quality.
• Example 1: "All men are wise (A)" and "Some men are not wise (O)."
• Example 2: "All men are not wise (E)" and "Some men are wise (I)."
• Rule: If one is true, the other is false, and vice versa.

Contrary Propositions

• These have the same subject, predicate, and universal extension but differ in quality.
• Example: "All men are wise (A)" and "All men are not wise (E)."
• Rule: If one is true, the other is false; if one is false, the other is doubtful.

Sub-contrary Propositions

• These share the same subject, predicate, and particular extension but differ in quality.
• Example: "Some men are wise (I)" and "Some men are not wise (O)."
• Rule: If one sub-contrary is false, the other is true, but if one is true, the other is doubtful.

Subaltern Propositions

• These share the same subject, predicate, and quality but differ in quantity.
• Example 1: "All men are wise (A)" and "Some men are wise (I)."
• Example 2: "No man is wise (E)" and "Some men are not wise (O)."
• The universal proposition is the subalternant, and the particular proposition is the subalternate.

Rules for Subalternation

• If the universal subalternant is true, the particular subalternate is also true.
• If the particular subalternate is false, the universal subalternant is also false.

Truth Table for Contradictory Propositions

• Opposition applies to A and O, as well as E and I.
• If A or E is TRUE, then O or I is FALSE.
• If A or E is FALSE, then O or I is TRUE.

Truth Table for Contrary Propositions

• It applies to A and E (vice-versa).
• If A/E is TRUE, then E/A is FALSE.
• If A/E is FALSE, then E/A is DOUBTFUL.

Truth Table for Sub-contrary Propositions

• This applies to I and O (vice-versa).
• If I/O is FALSE, then O/I is TRUE.
• If I/O is TRUE, then O/I is DOUBTFUL.

Truth Table for Subalternation (Universal to Particular)

• Applies to A-I; I-A / E-O; O-E
• It's universal to particular.
• If A/E is TRUE, then I/O is TRUE.
• If A/E is FALSE, then I/O is DOUBTFUL.

Truth Table for Subalternation (Particular to Universal)

• If I/O is TRUE, then E/A is DOUBTFUL.
• If I/O is FALSE, then E/A is FALSE.