Modus Tollens
Modus tollens is a deductively valid form of inference: given a conditional and the negation of its consequent, infer the negation of the antecedent.
P1) If P, then Q. (P → Q)
P2) Not Q. (¬Q)
∴
C) Not P. (¬P)
Also called denying the consequent.
Example (sound)
1. If Boots is a cat, then Boots is an animal. 2. Boots is not an animal. ∴ 3. Boots is not a cat.
Don’t confuse with:
- Modus Ponens (affirming the antecedent; also valid)
- Denying the antecedent (invalid: P → Q, ¬P, ∴ ¬Q; fallacious)