Affirming the consequent

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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→Q (P implies Q) ∴Q→P (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), or the lamp might be functional but switched 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. Converse errors are common in everyday thinking and communication and can result...

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