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Concept
Affirming the consequent
Summary
In propositional logic, 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 (e.g., "if the lamp were broken, then the room would be dark"), and invalidly inferring its converse ("the room is dark, so the lamp must be broken"), even though that statement may not be true. This arises when the consequent ("the room would be dark") has other possible antecedents (for example, "the lamp is in working order, but is switched off" or "there is no lamp in the room").
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 called modus tollens and 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 fallacy can be summarized formally as or, alternatively, .
The root cause of such a logical 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" (an abbreviated form of ).
Of the possible forms of "mixed hypothetical syllogisms," two are valid and two are invalid. Affirming the antecedent (modus ponens) and denying the consequent (modus tollens) are valid.
Official source
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