Affirming the consequent

Affirming the consequent is a logical fallacy in the form of a hypothetical proposition. Propositionally speaking, Affirming the consequent is the logical equivalent of assuming the converse of a statement to be true. The fallacy of affirming the consequent occurs when a hypothetical proposition comprising an antecedent and a consequent asserts that the truthfulness of the consequent implies the truthfulness of the antecedent. This is fallacious because it assumes a bidirectionality when it does not necessarily exist.

This fallacy has the following argument form:
 * If P, then Q.
 * Q.
 * Therefore, P.

This logical error is called the fallacy of affirming the consequent because it is mistakenly concluded from the second premise that the affirmation of the consequent entails the truthfulness of the antecedent. One way to demonstrate the invalidity is to use a counterexample. Here is an argument that is obviously incorrect:


 * If P.G. Wodehouse wrote the Bible (P), then P.G. Wodehouse is a good writer (Q).
 * P.G. Wodehouse is a good writer (Q).
 * Therefore, P.G. Wodehouse wrote the Bible (P).

The previous argument was obviously incorrect, but the next argument may be more deceiving:


 * If someone is human (P), then she is mortal (Q).
 * Anna is mortal (Q).
 * Therefore Anna is human (P).

But in fact Anna can be a cat; very much a mortal, but not a human one.

However, be aware that a similar argument form is valid in which the first premise asserts "if and only if" rather than "if". Similarly, the converse of a statement can be validly assumed to be true so long as the "if and only if" phrase is attached.