Affirming the Consequent
Affirming the consequent is a deductively invalid form: from a conditional and its consequent, illegitimately concluding the antecedent.
P1) If P, then Q. (P → Q)
P2) Q.
∴
C) P. ✗ INVALID
Counter-example (showing invalidity)
1. If Snoopy is a cat, then Snoopy is an animal. (true) 2. Snoopy is an animal. (true) ∴ 3. Snoopy is a cat. (false: he's a dog)
Homer's bear-patrol argument
1. If the Bear Patrol is working, there won't be any bears around. 2. There aren't any bears around. ∴ 3. The Bear Patrol is working.Lisa’s tiger rock counter-example exposes the fallacy.
Value as ampliative reasoning
Affirming the consequent maps onto the structure of hypothesis testing:
1. If hypothesis H is correct, we'll observe O. 2. We observe O. ∴ 3. H is correct.Deductively invalid, but observation O still raises credence in H. This is how science actually works (see Ampliative Argument, Inference to the Best Explanation). The mistake is treating the inference as deductive when it’s really ampliative.
Don’t confuse with:
- Modus Ponens (valid: P → Q, P ∴ Q)
- Modus Tollens (valid: P → Q, ¬Q ∴ ¬P)
- Denying the antecedent (also invalid: P → Q, ¬P ∴ ¬Q)