Sentential Logic

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: