Modus Ponens
Modus ponens is a deductively valid form of inference: given a conditional and its antecedent, infer the consequent.
P1) If P, then Q. (P → Q)
P2) P.
∴
C) Q.
Also called affirming the antecedent. The “if” part of the conditional is the antecedent; the “then” part is the consequent.
Example (sound)
1. If Boots is a cat, then Boots is an animal. 2. Boots is a cat. ∴ 3. Boots is an animal.
Example (unsound, false premise)
1. If Greg is human, then Greg has gills. (false) 2. Greg is human. ∴ 3. Greg has gills.Form is still valid; argument is unsound because P1 is false.
Don’t confuse with:
- Modus Tollens (denying the consequent; also valid)
- Affirming the Consequent (invalid)