Al-Tanaqud: Contradiction and the Square of Opposition

Four forms, one square: The four proposition forms [A] [E] [I] [O] are not independent — they are logically interconnected. The Square of Opposition maps all four relationships.

Picture the square: Know it, and you can instantly know what follows from any given proposition. Picture a square: top left is [A] (All S is P); top right is [E] (No S is P); bottom left is [I] (Some S is P); bottom right is [O] (Some S is not P).

The four relationships: There are four relationships.

• Al-Tanaqud (contradiction, diagonal): between [A] and [O], and between [E] and [I]. Rule: they cannot both be true and cannot both be false — always one true and one false. If [A] "Every human is mortal" is true, then [O] "Some humans are not mortal" is false. If [E] "No human is a prophet" is false, then [I] "Some humans are prophets" is true. This is the most powerful logical weapon in debate: to destroy [A], prove [O].
• Al-Tadadd (contrariety, top row): between [A] and [E]. Rule: they cannot both be true, but both can be false. "Every human is a scholar" [A] and "No human is a scholar" [E] cannot both be true, but both are false in reality — because some humans are scholars and some are not. Proving one is true forces the other to be false, but proving one is false does not prove the other is true.
• Tadat al-Taht (subcontrariety, bottom row): between [I] and [O]. Rule: they can both be true, but cannot both be false. "Some humans are scholars" [I] and "Some humans are not scholars" [O] are both true. But they cannot both be false — at least one of them must always be true.
• Al-Tadakhul (subalternation, vertical): between [A] and [I], and between [E] and [O]. Rule: truth flows downward — if [A] "Every human is mortal" is true, then [I] "Some humans are mortal" must be true. If [E] "No human is a god" is true, then [O] "Some humans are not gods" must be true. But if [I] is true, [A] may or may not be true (some does not imply all). Universal truth guarantees particular truth; particular truth does not guarantee universal truth.

Example

In Islamic theology — [E] falls: In Islamic theology: "No created thing is divine" [E]. Find one particular thing that is divine [I] — and the [E] falls.

Tanaqud, the logical killer: This is Tanaqud, the logical killer. The Shia refutation of Umayyad claims uses exactly this structure.

Key Terms

• Tanaqud (التناقض) — contradiction
• Tadadd (التضاد) — contrariety
• Tadat al-Taht — subcontrariety
• Tadakhul (التداخل) — subalternation
• Square of Opposition — مربع المعارضة

Quran or Hadith

None quoted on this slide.

Fresh diagram to be drawn: THE key diagram of this session: the Square of Opposition itself — four corners [A] [E] [I] [O], with the four relationships labelled on its diagonals, top, bottom, and sides. Must be drawn fresh in Project Desk colours, interactive if possible (tap a corner to see what follows).