Affirming the consequent

Affirming the consequent is a formal logical fallacy that results from confusing the concepts of "necessary" and "sufficient." The fallacy takes the following logical form:

• If P, then Q.
• Q.
• Therefore, P.

The following is an example:

• If Jack is meeting an important client today, he will wear his blue suit.
• Jack is wearing his blue suit.
• Therefore, Jack is meeting an important client today.

Affirming the consequent is fallacious because the initial premise does not rule out situations in which Q could be true even without P. In other words, in formal logic, as in general speech, "if" does not mean "only if" or "if and only if." In the example given above, even if the first premise is invariably true, Jack could decide to wear his blue suit on other days. Compare the following argument, which, while superficially similar, is valid:

• If Jack is meeting an important client today, and not otherwise, he will wear his blue suit.
• Jack is wearing his blue suit.
• Therefore, Jack is meeting an important client today.

Denying the antecedent is a variant that takes the following form:

• If P, then Q.
• Not P.
• Therefore, not Q.

Denying the antecedent is fallacious for the same reason given above.

The fallacy is often used to support false belief systems, as the following example shows:

• If the Qur'an is true, Mecca must be a real place.
• Mecca is a real place.
• Therefore, the Qur'an is true.

This reasoning is fallacious because nothing stops even an avowed fiction author from using a real place as a setting.