In propositional logic, affirming the consequent (also known as converse error, fallacy of the converse, or confusion of necessity and sufficiency) is a formal fallacy (or an invalid form of argument) that is committed when, in the context of an indicative conditional statement, it is stated that because the consequent is true, therefore the antecedent is true. It takes on the following form:
- If P, then Q.
- Q.
- Therefore, P.
which may also be phrased as
- (P implies Q)
- (therefore, Q implies P)
For example, it may be true that a broken lamp would cause a room to become dark. It is not true, however, that a dark room implies the presence of a broken lamp. There may be no lamp (or any light source). The lamp may also be off. In other words, the consequent (a dark room) can have other antecedents (no lamp, off-lamp), and so can still be true even if the stated antecedent is not.[1]
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.[2]
A related fallacy is denying the antecedent. Two related valid forms of logical argument include modus tollens (denying the consequent) and modus ponens (affirming the antecedent).[3]
- ^ Rosen, Kenneth H. (2019). Discrete Mathematics and its Applications: Kenneth H. Rosen. McGraw-Hill. ISBN 978-1260091991.
- ^ Lay, Steven (2014). Introduction to Analysis with Proof, 5th edition. Pearson. ISBN 978-0321747471.
- ^ Hurley, Patrick J. (2012). A Concise Introduction to Logic (11th ed.). Boston, Massachusetts: Cengage Learning. p. 362. ISBN 9781111346232. OCLC 711774631.