Affirming the consequent, sometimes called converse error, fallacy of the converse, or confusion of necessity and sufficiency, is a formal fallacy of taking a true conditional statement and invalidly inferring its converse even though the converse may not be true. This arises when a consequent has more than one other possible antecedents. Converse errors are common in everyday thinking and communication and can result from, among other causes, communication issues, misconceptions about logic, and failure to consider other causes. The opposite statement, denying the consequent, is a valid form of argument.
Affirming the consequent is the action of taking a true statement and invalidly concluding its converse. The name affirming the consequent derives from using the consequent, Q, of, to conclude the antecedent P. This illogic can be summarized formally as or, alternatively,. The root cause of such a logic error is sometimes failure to realize that just because P is a possible condition for Q, P may not be the only condition for Q, i.e. Q may follow from another condition as well. Affirming the consequent can also result from overgeneralizing the experience of many statements having true converses. If P and Q are "equivalent" statements, i.e., it is possible to infer P under the condition Q. For example, the statements "It is August 13, so it is my birthday" and "It is my birthday, so it is August 13" are equivalent and both true consequences of the statement "August 13 is my birthday". Using one statement to conclude the other is not an example of affirming the consequent, but some people may misapply the approach.
Additional examples
Example 1 One way to demonstrate the invalidity of this argument form is with a counterexample with true premises but an obviously false conclusion. For example: OwningFort Knox is not the only way to be rich. Any number of other ways to be rich exist. However, one can affirm with certainty that "if someone is not rich", then "this person does not own Fort Knox". This is the contrapositive of the first statement, and it must be true if and only if the original statement is true. Example 2 Here is another useful, obviously-fallacious example, but one that does not require familiarity with who Bill Gates is and what Fort Knox is: Here, it is immediately intuitive that any number of other antecedents can give rise to the consequent, and that it is preposterous to suppose that having four legs must imply that the animal is a dog and nothing else. This is useful as a teaching example since most people can immediately recognize that the conclusion reached must be wrong, and that the method by which it was reached must therefore be fallacious. Example 3 Arguments of the same form can sometimes seem superficially convincing, as in the following example: Being thrown off the top of the Eiffel Tower is not the onlycause of death, since there exist numerous different causes of death. Affirming the consequent is commonly used in rationalization, and thus appears as a coping mechanism in some people. Example 4 In Catch-22, the chaplain is interrogated for supposedly being "Washington Irving"/"Irving Washington", who has been blocking out large portions of soldiers' letters home. The colonel has found such a letter, but with the Chaplain's name signed. P in this case is 'The chaplain signs his own name', and Q 'The chaplain's name is written'. The chaplain's name may be written, but he did not necessarily write it, as the colonel falsely concludes.''
