What is "affirming the consequent"

n. (context logic English) A formal fallacy, committed by reasoning in the form:

If P, then Q.

Q.

Therefore, P.

Affirming the consequent, sometimes called converse error, fallacy of the converse or confusion of necessity and sufficiency, is a formal fallacy of inferring the converse from the original statement. The corresponding argument has the general form:

1. If P, then Q.
2. Q.
3. Therefore, P.

An argument of this form is invalid, i.e., the conclusion can be false even when statements 1 and 2 are true. Since P was never asserted as the only sufficient condition for Q, other factors could account for Q (while P was false).

To put it differently, if P implies Q, the only inference that can be made is non-Q implies non-P. (Non-P and non-Q designate the opposite propositions to P and Q.) This is known as logical contraposition. Symbolically:

(P → Q) ↔ (¬Q → ¬P)

The name affirming the consequent derives from the premise Q, which affirms the "then" clause of the conditional premise.